Number, structure, and mathematical theology in Dieterich Buxtehude's Basso Ostinato psalm Settings

PDF

Download

Open document

Flip pages

Summarize

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

NUMBER, STRUCTURE, AND MATHEMATICAL THEOLOGY

IN DIETERICH BUXTEHUDE’S BASSO OSTINATO PSALM SETTINGS

by

Malachai Komanoff Bandy

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(HISTORICAL MUSICOLOGY)

August 2022

Copyright 2022 Malachai Komanoff Bandy

ii
ACKNOWLEDGEMENTS

Michael Maier wrote seven alchemical treatises in 1617 “with a hot quill”; I clacked away on a
similarly scorching keyboard to assemble this dissertation, which could not have materialized
without the unwavering help and encouragement of many beloved friends and colleagues. I thank
the faculty of the USC Musicology and Early Music departments for making USC Thornton my
intellectual home, so rich a place for performance-practice and symbolism studies. In particular, I
thank my principal advisor, Adam Knight Gilbert—inimitable “informator” of my work and
musicianship in multitudinous capacities. I likewise thank Rotem Gilbert and the all-seeing and
all-knowing Bruce Brown, who along with Dietrich Bartel generously offered wise counsel and
trenchant comments as members of my dissertation committee; also Joanna Demers, who
supported this research with an independent study during my coursework and by serving on my
qualifying committee. I am grateful for the support of the USC Graduate School, including an
Oakley Endowed Fellowship (2020-2021) and a Provost Fellowship (2015-2020).
I was fortunate to present some of this research at conferences organized by the American
Musicological Society (2020), the Society for Christian Scholarship in Music (2019, 2020), the
Society for Seventeenth-Century Music (2019), and the AMS Pacific Southwest Chapter and
Northern California Chapter (2018, 2019); I thank members for their feedback and votes of
confidence in my work. Members of the Internationale Dieterich Buxtehude Gesellschaft,
especially Kerala Snyder, welcomed me in Lübeck in 2018 and provided comments on an early
version of my analysis of Herr, wenn ich nur Dich hab’ (BuxWV 38). The Books, Text, and
Images working group of the USC Levan Institute of the Humanities provided companionship
during long hours of lockdown writing and created virtual venues for presenting work in

iii
progress. My Pomona College students in MUS 121 (spring 2020-2022) inspired me with their
insights and enthusiasm. During my own undergraduate years, David Ferris, Greg Barnett, and
Peter Loewen at Rice University fostered my interest in music history and research.
Finally, I offer heartfelt thanks to Adam Bregman for innumerable discussions about this
project in its formative stages, as well as for crucial engraving assistance; Lisa Pon for friendship
and interdisciplinary art-history counsel; my mother, Ruth Underwood, for her encouragement of
my lifelong musical and mathematical pursuits; and most of all, Eva Lymenstull, for her
steadying hand and unceasing assurance—including cheerfully tolerating years of one-sided
conversations about numbers. I could not have finished this without such loving support.

iv

TABLE OF CONTENTS

Acknowledgements ......................................................................................................................... ii

List of Figures ................................................................................................................................ vi

List of Musical Examples .............................................................................................................. ix

Abstract .......................................................................................................................................... xi

Preface .......................................................................................................................................... xiv

Introduction ......................................................................................................................................1

Chapter 1: Numerology and Mysticism in J. S. Bach and Buxtehude Studies ...............................6
1.1 - Numerological Analyses of J. S. Bach’s Works ..............................................9
1.2 - Numerological Analyses of Buxtehude’s Organ Works ...............................15
1.3 - Pietism and Rosicrucianism in Bach and Buxtehude Studies .......................21

Chapter 2: Seventeenth-Century Alchemy, Rosicrucianism, and Theological Mathematics .......35
2.1 - Seventeenth-Century Alchemy, Christianity, and Numerology ....................35
2.2 - Numbers and Geometry in Rosicrucian Allegory .........................................56
2.3 - Rosicrucian Numerical Theology in Seventeenth-Century Mathematics .....77

Chapter 3: Contextualizing the Hamburg School of Contrapuntists ............................................91
3.1 - Buxtehude’s Hamburg Circle: Weckmann, Bernhard, and Reincken ...........91
3.2 - Johann Theile: Learned Counterpoint, Canon, and Alchemy .......................95
3.3 - A New Reading of Johannes Voorhout’s Musical Party ............................105
3.4 - Andreas Werckmeister ................................................................................114

Chapter 4: Analyzing the Basso Ostinato Psalm Settings: Introduction, Methodology,
and Examples from Laudate pueri Dominum (BuxWV 69) ......................................142
4.1 - Buxtehude’s Vocal Music ...........................................................................142
4.2 - Counting Methodology and Buxtehude’s Organ Tablature ........................145
4.3 - Figurate Numbers and Alchemical Geometry: A Primer ............................149
4.4 - Pythagorean-Ratio Examples: Laudate pueri Dominum (BuxWV 69) .......158

Chapter 5: Herr, wenn ich nur Dich hab’ (BuxWV 38) .............................................................165
5.1 - A Mysterious Rosicrucian Manuscript in Hamburg ....................................172
5.2 - “Theil” vs. “Heil”: A Poem .........................................................................176
5.3 - “Squaring the Circle” ...................................................................................179

Chapter 6: Quemadmodum desiderat cervus (BuxWV 92) ........................................................186
6.1 - Hexagrams and Aqua vitae ..........................................................................197
6.2 - Trinity in Unity and Unity in Trinity ...........................................................206
v

Chapter 7: Beyond the Psalms: Further Numerical Applications within Buxtehude’s Works ...209
7.1 - Ostinato Basses as Musical-Numerical Rhetoric ........................................209
7.2 - Example: Sicut Moses exaltavit serpentem in deserto (BuxWV 97) ...........214
7.3 - Conclusion ...................................................................................................243

Bibliography ................................................................................................................................249

Appendix: Editions of Select Ostinato Psalm Settings, based on Organ Tablature
and Performance Parts in the Düben Collection ........................................................279
Herr, wenn ich nur Dich hab’ (BuxWV 38) ........................................................279
Quemadmodum desiderat cervus (BuxWV 92) ...................................................283

vi
LIST OF FIGURES

1.1. Anton II Wierix, title page from Cor Iesu amanti sacrvm (ca. 1585/6) ............................26

1.2. Daniel Cramer, Emblem VIII from Emblemata Sacra (1624) ..........................................28

2.1. Heinrich Khunrath, ‘Lab-Oratorium,’ Amphitheatrum sapientiae aeternae (1609) ..........45

2.2. Abraham von Franckenberg, table from Raphael oder Artzt-Engel (1676)
and transcription .................................................................................................................48

2.3. Robert Fludd, divine monochord and man as microcosm, Utriusque cosmi...
historia I and II (1619) ......................................................................................................50

2.4. Simon Studion, “wheel of the heavens” from Naometria (1604) ......................................70

2.5. Triangular and quadrilateral numbers, as constructed from the given generating
functions, with points labeled by counting number (taken from Schneider,
“Between Rosicrucians and Cabbala,” 315) ......................................................................80

3.1. Johann Theile’s “Harmonischer Baum” from the Musikalisches Kunstbuch (left)
and Athanasius Kircher’s “Arbor Philosophica” from Ars magna sciendi,
1669 (right) ........................................................................................................................97

3.2. Theile’s twenty-four patrons for his 1673 Stile antico masses (left) vs. Studion’s
“wheel of the heavens” from Naometria, 1604 (right) ....................................................101

3.3. Johannes Voorhout, Musical Party, 1674, Hamburg, Museum für Hamburgische
Geschichte ........................................................................................................................106

3.4. Buxtehude’s poem in Werckmeister’s Harmonologia musica (1702) ............................120

4.1. The first seven triangular (triangle) figurate numbers .....................................................150

4.2. Correspondences between the lines of the Tetraktys and the formation of a three-
dimensional tetrad (modern graphic by Malin Fitger, 2020) ...........................................151

4.3. The first five quadrilateral (square) figurate numbers .....................................................152
4.4. [Johannes Remmelin], figurate numbers from Mysterium Arithmeticum, 1615
(taken from Schneider, “Between Rosicrucians and Cabbala,” 317) ..............................153

4.5. The first four “star” (stellar) figurate numbers ................................................................154

vii
4.6. Johann Christian Lange, Mystical geometrical figures from Theologia Christiana
in Numeris (1702) ............................................................................................................155

4.7. Michael Maier, Emblem XIV, “This is the Dragon that eats its own tail
(the Ouroboros),” from Atalanta fugiens (1617) .............................................................157

4.8. Heinrich Nollius, the REBIS (sacred androgyne) holding a compass and straight
edge and standing on a geometrical representation of the numbers one, three,
and four, from Theoria Philosophiae Hermetica (1617) .................................................157

5.1. Triangle, square, and star “figurate” numbers .................................................................169

5.2. Hexagram as a union of opposing triangles .....................................................................170

5.3. Thirty-seven and seventy-three as two “star” numbers contained in a single
star, in two ways: thirty-seven as inner hexagon (left) and as inner star (right) ..............171
5.4. Hexagram details from Kircher, Arithmologia, 1665 (left) and Robert Fludd,
Utriusque cosmi, 1619 (right) ..........................................................................................172

5.5. Anonymous, excerpt from the “Einfältig ABC-Büchlein Der Rosenkreuzer,”
Rosicrucian manuscript in the Staats- und Universitätsbibliothek Hamburg,
ca. 1700 (above), with detail from this same text below; textual similarity
to Herr, wenn ich nur Dich hab’ is marked at the top .....................................................174

5.6. Dieterich Buxtehude, Laudatory poem for Johann Theile, printed in Theile’s
St. Matthew Passion (1673) .............................................................................................177

5.7. Michael Maier, Emblem XXI, “Make of the Man and Woman a Circle,”
from Atalanta fugiens (1617) ...........................................................................................180

5.8. Herr, wenn ich nur Dich hab’: note-totals, factorization structure, and
juxtaposed circular and square properties ........................................................................184

6.1. Jacques de Senlecque, title-page engraving, Basil Valentine’s Révelation
des mystères des teintures essentielles des sept métaux (1646/1668) ..............................198

6.2. Senlecque, “Aqua vitae” flask and hexagram detail from Valentine
engraving (1646/1668) .....................................................................................................202

6.3. Salomon Trismosin, Stag decoration on plate VIII from Splendor Solis (1582) .............205

6.4. Stag from Sir George Ripley’s “Emblematicall Scrowle” (n.d.) .....................................205

6.5. Stag and unicorn, figure III from The Book of Lambspring (1556/1678) ........................206

viii
6.6. Arthur Dee, Title-page hexagram with chiastic “Trinity in Unity” inscription,
Arcana arcanorum (n.d.) .................................................................................................207

7.1. Dieterich Buxtehude, Sicut Moses exaltavit serpentem in deserto (BuxWV 97):
Map of keys and meter .....................................................................................................216

7.2. Sicut Moses: Map of keys, meter, and section lengths by number of measures ..............218

7.3. Michelangelo, Sistine Chapel serpent detail (1508) ........................................................219

7.4. Julius Goltzius, Crucifixion engraving after Maarten de Vos (ca. 1580) ........................222

7.5. Comparison of detail from Crucifixion by Goltzius, ca. 1580 (left) and printer’s
mark from The Chemical Wedding, 1616 (right) .............................................................223

7.6. Johannes Mylius, Exaltatio emblem from Philosophia reformata (1622) ......................225

7.7. Michael Maier, Emblem L, “The Dragon kills the woman, and she kills it,
and together they bathe in the blood,” from Atalanta fugiens (1617) .............................233

7.8. After Flamel, “a Rod and Serpents swallowing it up,” illustration 1 based
on Flamel’s Exposition, taken from William Salmon’s edition of the Hieroglyphicall
Figures, in Bibliothèque des philosophes chimiques (1672) ...........................................234

7.9. After Flamel, “a Cross where a Serpent was crucified,” illustration 2 based
on Flamel’s Exposition, taken from William Salmon’s edition of the Hieroglyphicall
Figures, in Bibliothèque des philosophes chimiques (1672) ...........................................235

7.10. After Flamel, “Deserts, or Wildernesses...a number of Serpents, which ran
up and down here and there,” illustration 3 based on Flamel’s Exposition, taken
from William Salmon’s edition of the Hieroglyphicall Figures, in Bibliothèque des
philosophes chimiques (1672) ..........................................................................................236

7.11. Sicut Moses: Map of keys, meter, section lengths, and embedded figurate numbers ......239

ix
LIST OF MUSICAL EXAMPLES

4.1. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38),
opening in organ tablature from the Düben Collection ...................................................147

4.2. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), m. 70 .....................148

4.3. Buxtehude, Laudate pueri Dominum (BuxWV 69), first page, showing
complete ostinato .............................................................................................................161

4.4. Buxtehude, Laudate pueri Dominum, mm. 71-75 ...........................................................163

4.5. Buxtehude, Laudate pueri Dominum, mm. 76-78 ...........................................................163

4.6. Buxtehude, Laudate pueri Dominum, mm. 47-50 ...........................................................164

5.1. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), ostinato bass ..........165

5.2. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 6-8 (left) and mm. 21-22 (right) .........166

5.3. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 12-20 ...................................................168

5.4. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 53-56 ...................................................168

5.5. Buxtehude, Herr, wenn ich nur Dich hab’, ostinato bass as 4-3-2-1 (four beats, three
measures, two notes and two groups of three-note scales, unity in circular path) ...........182

6.1. Dieterich Buxtehude, Quemadmodum desiderat cervus (BuxWV 92), ostinato bass .....189

6.2. Buxtehude, Quemadmodum desiderat cervus, mm. 22-23 (top) and
mm. 109-14 (bottom) .......................................................................................................190

6.3. Buxtehude, Quemadmodum desiderat cervus, mm. 15-25 ..............................................191

6.4. Buxtehude, Quemadmodum desiderat cervus, mm. 22-24 (left)
and mm. 30-31 (right) ......................................................................................................192

6.5. Buxtehude, Quemadmodum desiderat cervus, mm. 58-68 ..............................................193

6.6. Buxtehude, Quemadmodum desiderat cervus, mm. 69-75 ..............................................194

6.7. Buxtehude, Quemadmodum desiderat cervus, mm. 94-96 ..............................................195

x
7.1. Dieterich Buxtehude, Sicut Moses exaltavit serpentem in deserto (BuxWV 97),
opening Adagio ................................................................................................................216

7.2. Buxtehude, Sicut Moses, Allegro fugal motive ................................................................217

7.3. Buxtehude, Sicut Moses, mm. 141-50, canonic imitation ................................................238

7.4. Buxtehude, Sicut Moses, mm. 197-206, quasi-fauxbourdon ...........................................238

7.5. Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), ostinato bass (top);
Sicut Moses, mm. 52-54, ostinato bass (bottom) .............................................................240

7.6. Buxtehude, Sicut Moses, mm. 51-63, internal ostinato quotation from
Herr, wenn ich nur Dich hab’ (BuxWV 38) ....................................................................242

xi
ABSTRACT

Despite his reputation as Germany’s preeminent organist-composer of the late seventeenth
century, Dieterich Buxtehude (ca. 1637-1707) remains a surprisingly elusive character in the
Western musical canon. Few contemporary documents detailing his life survive, only a few of
his works can be firmly dated, he published almost nothing relative to his known output—and
most manuscripts in his hand were lost by 1750. Consequently, modern scholarship tends to
emphasize better-documented peripheral aspects such as his known influence on J. S. Bach. Most
historians also assume Buxtehude’s purely Lutheran identification based on his high-profile job
as organist, music director, and Werkmeister (accountant) at the most prestigious Lutheran
church in Lübeck, a major center of Hanseatic power. Emerging details about Buxtehude’s life,
however, complicate exclusively Lutheran impressions of his religious and intellectual
proclivities. Most recently, Olga Gero traced the previously unidentified text of Buxtehude’s
sacred concerto Fallax mundus to a Flemish Jesuit emblem book. This adds to a growing list of
works, including a Pange lingua and a Salve desiderium incorporating Marian texts, appearing
strangely un-Lutheran for a composer of his employment and social prominence.
This project offers a new perspective regarding Buxtehude’s mystical-musical interests,
by illuminating elements of number symbolism, alchemy, and occult philosophy within his basso
ostinato psalm settings: Herr, wenn ich nur Dich hab’ (BuxWV 38), Quemadmodum desiderat
cervus (BuxWV 92), and Laudate pueri Dominum (BuxWV 69). Across these pieces,
coordination between textual meaning and measure number, note number, and large- and small-
scale congruence between them points to a numerically conscious premeditation. This also
manifests in geometrical design: major sectional proportions repeatedly align with the

xii
Pythagorean ratios 1:2 and 3:4, while “figurate” numbers—especially triangle, square, and the
palindromic “star” numbers thirty-seven and seventy-three—form the foundation for
Buxtehude’s bass-line patterns and textual division points. These features offer insight into
Buxtehude’s compositional process, whose mathematical intricacy surpasses our current
understanding and pedagogy of seventeenth-century music. His most elaborate mathematical
schemes also accompany texts thematically resonant with seventeenth-century alchemical
precepts. This corroborates and deepens questions about known occult fascinations within
Buxtehude’s milieu: as David Yearsley has shown, Buxtehude’s close friends practiced
counterpoint for philosophical reasons outside of musical composition. Despite post-
Enlightenment personal legacies stripped of esoteric elements, their treatises intertwine
functional music-theory discourse with alchemical innuendo and compositional puzzles
demanding a “gnosis” of counterpoint as potent, transformative magic.
Several studies from the 1980s and early 2000s by Piet Kee and Carol Jarman examine
the numerical proportions of individual Buxtehude organ works. However rigorous, concrete
meaning of mathematical occurrences remains ambiguous in the absence of associated texts.
Relying on a combination of textual and numerical content, my analyses reveal in Buxtehude’s
vocal works recurring numerical tropes widely associated with the union of heaven and earth in
seventeenth-century alchemy and Rosicrucianism. As the apex of musical-geometrical
symbolism, his setting of Psalm 73 “solves,” through compositional dimensions, the infamous
impossibility of “Squaring the Circle,” alchemical symbol for divine unification. Ultimately,
cognizance of Buxtehude’s musical engagement with number begins to close significant gaps in
our current understanding of his thought, Christian identity, and compositional progeny.
Recognizing esoteric aspects of Buxtehude’s work as conceptually foundational refocuses his

xiii
image within exoteric historiography and expands our vocabulary surrounding seventeenth-
century German compositional practice.

xiv
PREFACE

There exists much misunderstanding…about the function of number in early
music. At the mention of the word “numerology” many people have frightful
visions of complicated calculations which spoil one’s pleasure in the music and
hinder one’s approach to it.
1

– Piet Kee, “Astronomy in Buxtehude’s Passacaglia” (1984)

Walking back to my seat after giving my first conference paper about numbers in Buxtehude’s
vocal music—a paper grounded in careful research, presented with appropriate caution to
generally positive reception—I overheard a distinguished professor from a local university say to
a colleague (in full voice), “Thank God we won’t have to listen to another paper about numbers.
How pointless.” It got me thinking: it is no secret that numerology
2
is deeply divisive within
musicology, yet virtually no literature exists about the disciplines’ interactions, aside from
singular critiques of equally singular studies. Meaning, formal scholarly critiques of
numerological musicology, as an unacknowledged subgenre of sorts, are often just as
individualized, idiosyncratic, and unrepeatable as the numerical findings they aim to debunk. As
in conference discussion, just a small proverbial “step back” often reveals arguments more about
personal skepticism or “belief” in numerology at large than about the actual music and
numbers—or especially historical contexts different from ours—at hand.

1
Piet Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato
Works.” The Diapason 75 (1984), reprinted in Organists’ Review (August 2007): 27.
2
This is a loaded term with different connotations and definitions across disciplines. For the
rest of this project, I define “numerology” as the study of a composition’s quantifiable numerical
attributes, not as general investigation into numbers’ abstract qualities or mystical meanings.
This definition that I propose reflects recent musicology’s treatment of the term, despite the
irony that the literal definition of “numerology”—the actual study of numbers—now falls under
the category of number theory in mathematics.

xv
Surely no single party deserves blame. Without the stability of an existing body of
recognized literature, every numerological argument effectively begins from scratch, scholars
cannot coherently build on one another’s work, and foundational questions crucial to mutual
understanding between factions rarely get articulated. In numerical analyses, how much evidence
is enough? How much is too much? What kind of evidence is most convincing? How many
interconnected numerical phenomena occur by chance? To what extent does a composer’s
intention matter (and if so, do we need a “letter home”
3
from that composer)? How historical can
modern numerical analysis really be, and should we care? Do computing tools alone denote
credibility? Can people actually hear compositional numbers…and if not, why write about them?
The list goes on.
One dissertation cannot alone solve all musicological-numerology feuds, particularly
when so little of the discourse takes place in publications.
4
I have no grandiose aspirations to this
end. But I think it is important to bring up this issue of “belief” that does not seem to so widely
plague other musicological subfields, as a call for more clearly divided observation from
interpretation, and calculation from speculation, in present and future numerological musicology
in general.
5
I would like to clarify my intentions and interpretive boundaries in this project, to all
readers, whether or not claiming “belief” in numerology or number symbolism—its very
existence, specific application to music, or methodological worth. The numerical information I

3
To borrow Adam Gilbert’s term, referring to a letter affirming the impossible-to-affirm.
(For instance, “Dear Diary, I organized a composition entirely around numbers today...”)
4
At least relative to what seems to take place in informal conversation at conferences, and/or
during Q-and-A sessions.
5
This will perhaps resonate with others who face criticism that one realizes, upon closer
scrutiny and usually in retrospect, is not necessarily aimed at the actual work in question, or the
soundness of its particular method. As for any topic that intersects with symbolism, the illusion
that “belief” in numerology or “belief” in symbolism is necessary for appreciating all possible
methodologies creates an inherently inhospitable intellectual climate.

xvi
present does not concern belief; it is factual information upon which to form ideas, as I have and
present here, that might change our conception of Buxtehude’s compositional process.
Throughout any sections intentionally opening doors for further speculation about Buxtehude’s
circle of friends or their intellectual interests, I hope to have made this clear.
Much of the biographical and contextual information contained in this dissertation
specifically concerns a relationship between theory (theoria) and practice (practica), and more
than most methodologies, numerology naturally balances itself on a fine line between them.
While my analyses sound theoretical, in the sense that I examine constructional elements of
Buxtehude’s music for written (rather than sounding) consumption, I believe this information to
be useful in practical performance as well. I, myself, stumbled upon this topic as a performer: in
a rehearsal in 2010, I noticed the sudden interruption by the doxology in measure 77 of
Buxtehude’s Laudate pueri Dominum (BuxWV 69). A few years later in a recording project, I
noticed a similar moment in the sixth Membra Jesu Nostri (BuxWV 75) cantata, in which the
bass voice (possibly speaking “as” Jesus for the only point in the cycle), provides a similar
interruption—in a fleeting basso ostinato context no less—on measure 99. My only non-
performance early discovery like these came in graduate school, during the score-identification
portion of my 2017 comprehensive exams: a similar “Alleluia” elision/interruption moment on
measure 55 of Herr, wenn ich nur Dich hab’ (BuxWV 38) both helped me correctly identify the
piece as Buxtehude’s and prompted the beginning stages of this project.
Thus, while much of this dissertation is theoretical, in the sense that there are numbers
and some calculations involved, I believe that Buxtehude’s numerical underpinnings should in
fact inform performance. Numerical analyses of this repertoire can quickly illuminate helpful
things such as large-scale parallelism between sections of text and, like the measure-number

xvii
breadcrumbs that led me to this topic, moments of numerical interest that often reliably indicate
those of greatest textual and rhetorical interest. In this sense, and to Piet Kee’s point quoted
earlier, I hope that the non-numerical context I present supports this kind of practical reading, in
providing evidence that Buxtehude really did have intellectual reasons to conceive his pieces this
way.
In this spirit, I hope that Buxtehude enthusiasts and performers might take away from this
project more than an agreement or disagreement in my theory that Buxtehude was interested in
Rosicrucianism or anything else, and especially more than a “belief” in musical numerology. I
hope to impart a reverence-through-understanding that, in playing and studying these pieces
from the Hamburg school of Buxtehude and his friends, we in the twenty-first century participate
in something just a bit larger than previously thought. Ultimately, all historical performance or
musicology is about a desire to commune with the past. I hope that any new numerical-
constructional insight I can offer into Buxtehude’s music brings us all closer to 1670s Lübeck,
and in doing so lends a different kind of agency to Buxtehude’s and his friends’ music in our
modern eyes and ears. In providing a platform for their ideas about a Pythagorean and
Neoplatonic cosmos and music’s Ficinian and Paracelsian healing powers as sonic alchemy, we
confirm the contrapuntal “brothers’” long-held belief in the power of their musical Harmonia to
reconcile the seemingly unreconcilable: whether or not joining heaven and earth, as they
theorized, we realize a small part of its transcending of time and space, by linking their time with
ours through a deeper appreciation of their craft.

1
INTRODUCTION

Johannes Voorhout’s 1674 painting Musical Party, now in Hamburg, contains the only known
image of composer Dieterich Buxtehude (ca. 1637-1707), the subject of this dissertation, there
depicted music-making among composer friends individually named in Voorhout’s inscription.
1

Buxtehude was misidentified within the scene for centuries after his death, until 2006, when
process-of-elimination archival discoveries revealed him to be the viol player. Within an
otherwise scant biography, Buxtehude’s legendary reputation as an organist might seem to
preclude stringed instruments as likely attributes. Yet this image offers a clue lurking in plain
sight for 300 years, as he fingers his initials, “D” and “B”(-flat), on the fretboard.
2
This puzzle
serves as analog to a reconsideration of Buxtehude’s intellectual influences and compositional
practice; Voorhout’s fretboard detail, transposed from canvas to score, encapsulates the latent
conspicuousness of the ciphers this project explores within seventeenth-century German musical
thought and expression. Merging biographical information about Buxtehude’s circle of friends
with a close examination of evident Hermetic
3
influences in their works produced during

1
The inscription is on the sheet music on the center-right figure’s knee. See chapter 3 for an
image of the painting and for more information about the inscription and the music, as central
components in a discussion of the painting’s identification issues and historiography.
2
It is unclear how widely known this detail was, or for how long, before appearing in the
second edition of Kerala Snyder’s monograph (2007). In a footnote, Snyder mentions learning
about it through conversations and emails with Dorothea Schröder and Friedemann Hellwig in
2006. Published theories about Buxtehude as the viol player (without this fretboard detail) go
back to 1987. See Kerala J. Snyder, Dieterich Buxtehude: Organist in Lübeck, 2nd ed.
(Rochester, NY: University of Rochester Press, 2007), 503.
3
Referring to Hermes Trismegistus, or the “Thrice-Greatest Hermes,” the Hellenistic
combination of the Greek god Hermes with the Egyptian god Thoth. While likely not a real
person, he has been credited with tens of thousands of writings throughout history, concerning
alchemy, astronomy, philosophy, and more. For more contextual information, also with an
emphasis on the alchemical connections to Hermes that this dissertation later explores, see
2
Buxtehude’s lifetime, I aim to untangle webs of interrelated music, image, text, and numerology
in Buxtehude’s three basso ostinato psalm settings, which constitute half of his six extant basso
ostinato vocal works.
This dissertation centers on Buxtehude’s music, but my analytical approach is largely
interdisciplinary in tracing evidence in Buxtehude’s craft to intellectual traditions with extra-
musical roots. Thus, this study begins with a review of the main literature surrounding the
intersecting topics of numerology, mysticism, (Christianized) alchemy, Rosicrucianism, before
presenting relevant biographical details about Buxtehude’s circle of friends. Chapter 1
contextualizes Buxtehude and J. S. Bach in modern scholarship, reviews numerical analyses of
Bach’s and Buxtehude’s music, and reopens the debate about Buxtehude’s possible involvement
with the German Pietist movement, to introduce my theory that numerical features of
Buxtehude’s music point to Rosicrucian more than Pietist influence. Chapter 2 then highlights
points of intersection between alchemy, music, and Christian theology, via number, analyzes the
original Rosicrucian manifestos from a numerological perspective, and ends with examples of
Rosicrucian numerology’s influence on and appearances in “mainstream” seventeenth-century
mathematics. Finally, chapter 3 connects these concepts to Buxtehude’s intellectual world, in an
attempt to reconstruct Buxtehude-contemporary thought about number, alchemy, and
compositional technique. This builds upon David Yearsley’s work on musical canon (also called
“fugue” or “fuga”) as a topical analog to seventeenth-century alchemical practice, particularly
the precept that “multiplicity springs from unity.”
4
This chapter thus introduces and situates

Richard Smoley, “From Lead to Gold: Hermes and Alchemy,” Rosicrucian Digest 1 (2011): 12–
20.
4
To the untrained eye, a canon looks like an incomplete, single-line melody; but encased in
this single compositional “seed,” a clever musician finds complex multi-voice polyphony,
restored by determining the intended starting points, ending points, and relative durations of new
3
important members of Buxtehude’s social circle within this esoteric contrapuntal tradition, with
discussions and examples of evident occult philosophy within their works and friendship.
Featured characters include Johann Theile, Johann Adam Reincken, Christoph Bernhard, and
Andreas Werckmeister, and the chapter concludes with a discussion of the identification issues in
Johannes Voorhout’s painting Musical Party, in which at least Reincken and Buxtehude appear
in what I argue is a specifically Rosicrucian context.
The remaining four chapters present numerological analyses of Buxtehude’s three basso
ostinato psalm settings, plus a through-composed vocal work thematically and numerically
related to these three works of entirely ostinato design. Chapter 4 introduces Buxtehude’s
œuvre—and issues of sources, texts, notation, function, and musical forms—in order to
contextualize his vocal ostinato works within his compositional output. It also details my specific
numerical-analytical methods and presents an overview of the few mathematical operations to
which I subject numbers in my analyses. To demonstrate various elements of my methodology, I
draw examples from Buxtehude’s Laudate pueri Dominum (BuxWV 69). Numerically, this piece
serves as an excellent model of figural-number grounds and instrumental statements’ dictating
large-scale structural proportion, while its unusually long and complicated ground supports the
idea that Buxtehude constructs his ground basses for inaudible reasons. In this section, I also
briefly discuss Buxtehude’s use of viol consort texture in his compositions, since BuxWV 69 is
one of only two pieces for this scoring among his surviving works.

voices all singing this same material. The best-engineered canons sometimes even yield
“perpetual” counterpoint, in which an infinite number of voices can enter with the same material
at various intervals and theoretically never end. The combination of these precise
characteristics—“eternal” counterpoint in a multiplicity of voices and inversions, all born of one
unassuming musical “seed”— effortlessly aligned canonic counterpoint with alchemical pursuit
of eternal enlightenment, via the Philosophers’ Stone, in seventeenth-century music theory.

4
Chapter 5 presents a numerical analysis of Buxtehude’s Herr, wenn ich nur Dich hab’
(BuxWV 38). This work contains the richest and most intricate evidence of systemic numerical
composition within Buxtehude’s œuvre. Its numerical sophistication makes it an excellent case
study against which to measure other numerically engaged works, particularly in issues of
proportion (for instance, the ground-bass pattern as compositional microcosm and macrocosm)
and repeated appearances of triangle, square, and star “figural” numbers. Geometrical evidence
from Rosicrucian manuscripts and alchemical treatises about enlightenment and divine
unification aligns with Buxtehude’s compositional-numerical choices, in which Buxtehude
ultimately uses number and text to mathematically “Square the Circle” in music.
Building upon the evidence presented in chapters 4 and 5, chapter 6 treats Buxtehude’s
setting of Psalm 42, Quemadmodum desiderat cervus (BuxWV 92). This work shares many
numerical features with Herr, wenn ich nur Dich hab’, especially a structural foundation
centered on the palindromic numbers thirty-seven and seventy-three, with additional linguistic-
numerical puns and Pythagorean-ratio awareness on large and small scales. “Star” numbers
feature prominently within the work’s structural core, which suggests that Buxtehude knew that
the alchemical symbol for aqua vitae—which features prominently in the text—is the same
hexagram as these “star” numbers. An engraving of alchemist Basil Valentine in the treatise
Revelation des mysteres des tinctures essentiales des sept metaux (Paris, 1668) combines these
features, equating hexagrams, aqua vitae, the number seven, and musical Harmonia with
alchemical transformation and enlightenment.
Chapter 7 further discusses the overall meanings of the different numerical “figures”
present in Buxtehude’s basso ostinato psalm settings, while considering ways in which
Buxtehude uses these numbers relative to his other compositional tools with which they
5
intermingle. It further suggests new ways of thinking about ground basses as symbols for eternity
specifically related to number and suggests future directions for numerological research of
seventeenth-century music both within and beyond Buxtehude’s œuvre. To demonstrate the
potential usefulness of numerical modes of analysis across his œuvre, this chapter also presents
an analysis of Sicut Moses exaltavit serpentem in deserto (BuxWV 97). In this work,
intersections between Rosicrucian-favored numbers sixty-four, eighty-one, and thirty-seven and
seventy-three govern the work’s larger structure and textual division points, while its text is
largely comprised of alchemy-related imagery. Most strikingly, an extended appearance of the
ground bass pattern of Herr, wenn ich nur dich hab’, at a textually appropriate moment, suggests
that Buxtehude uses ground basses—and their numerical underpinnings—rhetorically, in other
works, to communicate themes of divine unification and transformation.

Style Notes

1. This dissertation contains many numbers. Throughout, I will follow the convention of
spelling out numbers under 100 (“thirty-seven”), unless specifically in the context of
mathematical operations (“3 x 7”; “product of 3 and 7”), measure numbers (“measure
23”), or chapter references (“chapter 2”).

2. Many terms involving alchemy and Rosicrucianism, or related to Esotericism in general,
contain multiple commonly used spellings. For some such terms, I will use common
variations to distinguish between different branches of practice (and I will note these in
footnotes, at the first use). For example, I use “kabbalah” only to refer to ancient Jewish
mysticism in actual Jewish practice, while “cabala” refers to any Christianized version of
this practice after the sixteenth century.

3. Further style notes relating just to my musical analyses can be found in chapter 4.

4. Authors of alchemical texts often capitalize the names of metals and elements, to
differentiate the “common” substance from its more precious “activated” or
“philosophical” type. In modern prose, as in the case of “Mercury,” this makes it difficult
to distinguish between the physical substance and any god or planet that shares its name.
While the reader might find the names of certain elements capitalized in excerpted
quotations or source titles, in my own prose I capitalize the names of gods and planets,
while keeping the names of elements (“philosophical” or not) lowercase.
6
CHAPTER 1
Numerology and Mysticism in J. S. Bach and Buxtehude Studies

As biographical subjects go, Dieterich Buxtehude (ca. 1637-1707) was not so kind to historians:
relative to his legendary reputation as organist, music director, and Werkmeister (accountant) at
Lübeck’s prestigious Marienkirche (St. Mary’s Church), he left far fewer surviving publications,
documents, and scores in his hand than historians know existed.
1
Despite these obstacles, Kerala
Snyder has across her career crafted a rich enough image of seventeenth-century North German
musical life to bridge any knowledge gaps about Buxtehude himself, piecing together available
archival material concerning Lübeck, St. Mary’s workings, Buxtehude’s close friends and
colleagues, and paper trails of his Abendmusik activities. Since its first publication in 1987, two
years before the reunification of Germany, Snyder’s monograph Dieterich Buxtehude: Organist
in Lübeck has remained the most comprehensive study of Buxtehude’s life and works.
2
Snyder
divides the book into four sections, each containing (respectively) information about
Buxtehude’s social and musical environment, an overview of his compositions and publishing
habits, specialized studies of his various works, and appendices. These 100-page appendices
could easily stand on their own as a separate volume, as they contain a complete Buxtehude
catalog, a list and transcriptions of his poetry and accounting records, his works’ principal
sources, selected texts, inventories, and a chart of every chorale melody he set.

1
Kerala J. Snyder, Dieterich Buxtehude: Organist in Lübeck, 2nd ed. (Rochester, NY:
University of Rochester Press, 2007), 316–20.
2
Snyder, Dieterich Buxtehude, xi–xiii. Snyder’s preface to the second edition repositions her
work relative to newer scholarship; it is clear from reading those scholars’ work that everyone
treats Snyder as Buxtehude studies’ foundational source.
7
The 2007 edition of Snyder’s biography, released for the tercentenary of Buxtehude’s
death, reflects revisions interesting not only factually, but also as evidence of Buxtehude
scholarship’s changing face over the twenty years between publications. The most striking
example is the updated identification of Buxtehude as the viol player, not the centered male
listener, in Johannes Voorhout’s 1674 painting Musical Party (Musizierende Gesellschaft in
German, formerly Häusliche Musikszene), the only known image of Buxtehude.
3
In terms of
physical sources, many archival materials sequestered for safety in a salt mine in Bernburg after
the 1942 bombings of Lübeck were earlier presumed lost. After the German reunification, some
of these returned to Lübeck, including the accounting records that Buxtehude kept as
Werkmeister for St. Mary’s.
4
Another important addition is information about the discovery of
J. S. Bach’s personal copy of Buxtehude’s Nun freut euch lieben Christen gmein (BuxWV 210),
which he apparently made as a teenager.
5
His copy is in organ tablature, suggesting that the
original likely was as well.
6
More strictly biographically, one finds new choice morsels, such as
correspondence confirming that the Buxtehude family was bilingual, which tells us that
Buxtehude began acquiring languages—of which he would ultimately amass at least seven—
before adulthood.
7
Of similar interest, new information about Buxtehude’s organs at St. Mary’s

3
Snyder, Dieterich Buxtehude, 109–13.
4
Snyder, Dieterich Buxtehude, xi. For the first edition, Snyder only had access to these
records through 1685. Unfortunately, printed copies of Buxtehude’s church music known to have
once been part of the Lübeck archives are still missing.
5
Snyder, Dieterich Buxtehude, 105–6.
6
As I explicate in chapter 4, seventeenth-century organ tablature allows for much more
streamlined note-counting within both individual parts and over entire systems than does staff
notation. I argue that this feature might account for Buxtehude’s apparent preference for this
system later than some other composers in North Germany, aside from tablature’s paper-saving
advantages.
7
This particular artifact was uncovered in a rat’s nest during restoration of Buxtehude's
father’s church in Helsingør (St. Olai). Snyder, Dieterich Buxtehude, 11.
8
in Lübeck reveals that the large organ likely remained tuned in some form of meantone for the
duration of Buxtehude's tenure.
8
The final chapter concerns Buxtehude's work and influence
outside of Lübeck, particularly in Hamburg and Stockholm. Much of this information directly
applies to the present study, particularly regarding Buxtehude’s intellectual circle of contrapuntal
and musical-rhetorical innovators, including Johann Theile, Christoph Bernhard, and Johann
Adam Reincken in Hamburg.
9
Also from outside Lübeck, we know that Buxtehude’s friend
Gustav Düben
10
sent scribes from Stockholm to copy various manuscripts of Buxtehude’s—
Buxtehude signed several of their ink copies in pencil, suggesting his approval of their
correctness,
11
and we have Düben to thank for preserving the largest single collection of
Buxtehude’s extant works and one of the few in his hand: Membra Jesu Nostri.
Part II of Snyder’s monograph, which deals extensively with Buxtehude's compositions,
contains a compact section on Buxtehude’s works of learned counterpoint, including several
solutions to puzzle-canons that Snyder was the first in the twentieth century to solve.
12
Michael
Dodds and David Yearsley have contributed equally important work on this topic, with all three
scholars approaching from slightly different angles: Snyder from a big-picture catalog
perspective, Dodds with special interest in intersections between codified music theory and

8
Snyder, Dieterich Buxtehude, 79–88.
9
See chapter 2.
10
For an examination of their friendship, including possible times their paths might have
crossed, see Snyder, Dieterich Buxtehude, 121.
11
Informal interview with archivist Arndt Schnoor, Bibliothek der Hansestadt Lübeck,
September 2018.
12
Snyder, Dieterich Buxtehude, 218–22.
9
improvisational practice (especially as related to Werckmeister),
13
and Yearsley about the
meanings of Bach-era counterpoint as rhetoric and topic.
14

1.1 – Numerological Analyses of J. S. Bach’s Works
In a wide range of scholarship and concert programming, as well as our larger formation and
propagation of the Western canon, Buxtehude often finds his place somewhere connected to, but
also in the shadow of, J. S. Bach. This is somewhat ironic, considering the brevity of their
chronological overlap: Buxtehude was at the height of his career and twenty-two years from
death at the time of Bach’s birth in 1685, and two years from death during their only in-person
contact, in 1705. The combination of Buxtehude’s sparse biography and Bach’s modern
reputation as cultural benchmark of contrapuntal mastery often invites inadvertent distortion in
telling and retelling the story of Bach’s trip on foot to visit Lübeck in 1705. In print, one most
often finds the story of their meeting employed as a tool to elevate Buxtehude’s image by
association than to emphasize or more pointedly explore whatever prowess attracted the young
Bach in the first place.
15
Even in scholarship, Buxtehude is sometimes conspicuously absent

13
Michael R. Dodds, “Columbus’s Egg: Andreas Werckmeister’s Teachings on Contrapuntal
Improvisation in Harmonologia musica (1702),” Journal of Seventeenth-Century Music 12, no. 1
(2006). https://sscm-jscm.org/v12no1.html. Dodds works through Werckmeister’s technique of
inventing double augmentation canons by means of parallel thirds. A solution to one of
Buxtehude’s canons requires this technique. For critique and contextualization of this method vs.
other contemporary practices, see David Yearsley, “Ideologies of Learned Counterpoint in the
Northern German Baroque” (PhD diss., Stanford University, 1995), 78.
14
“Ideologies of Learned Counterpoint in the Northern German Baroque.” PhD diss.,
Stanford University, 1995. Yearsley has also done the most significant work on Johann Theile,
who serves as the most concrete connection between Buxtehude and esoteric interests. See
chapter 3.
15
Nearly every Buxtehude program note does this. For a recent example, see the California
Bach Society’s North German Masters program from 2017
(https://www.calbach.org/blog/2017/2/7/program-notes-north-german-masters).
10
from works bearing his name: Geoffrey Webber’s Northern German Church Music in the Age of
Buxtehude, for example, uses Buxtehude as a point of departure but delves more into the lives
and works of other Baltic musicians with whom he associated.
16
This finds a poignant analog in
Lübeck’s Marienkirche: a plaque marking the area where Buxtehude’s grave lay before its
destruction in the 1942 bombings hangs next to a more prominent twentieth-century relief
sculpture of Bach, with the date “1705” in large letters commemorating his visit.
I do not mean to suggest that this is a problem to overcome. Rather, I highlight this
cultural impulse—a reliance on Bach to help us tell Buxtehude’s story—as one that this
dissertation consciously takes up, even while fully steeped in Buxtehude’s music and existing
scholarship. For lack of answers to questions about Buxtehude’s intellectual environment and
interests, I too look to Buxtehude’s social contacts for concrete details in which to ground my
central argument and methodology. For issues involving alchemy and counterpoint, this means
turning to sources by and about Buxtehude’s friends Johann Theile and Johann Adam
Reincken,
17
and for Pythagoreanism in music theory to Andreas Werckmeister’s published
treatises.
18
But for examples of both modern number-symbolism scholarship of seventeenth-
century music and insights into esoteric contrapuntal techniques, via the work of Ruth Tatlow
and David Yearsley, respectively—all roads lead back to Bach.

16
Geoffrey Webber, Northern German Church Music in the Age of Buxtehude, (Oxford:
Clarendon Press, 1996).
17
See especially chapters 1 and 2 of David Gaynor Yearsley, “Ideologies of Learned
Counterpoint in the Northern German Baroque” (PhD diss., Stanford University, 1995).
18
Especially in excellent translation by Dietrich Bartel. See Andreas Werckmeister, Andreas
Werckmeister’s Musicalische Paradoxal-Discourse: A Well-Tempered Universe, trans. Dietrich
Bartel, Contextual Bach Studies (Lanham: Lexington Books, 2017). For equally excellent
secondary research on Werckmeister, see Bartel’s introduction to his translation just listed, but
also Dietrich Bartel, “Andreas Werckmeister’s Final Tuning: The Path to Equal Temperament,”
Early Music 43 (2015): 503–12.
11
In existing studies of seventeenth-century number symbolism, Bach reigns supreme, both
in quantity of available studies and range of methodologies and calculations authors use within
them. Some analyses involve external apparatus such as number alphabets, magic squares, and
paragrams, while others rely primarily on note and measure counting, either as observable with
the naked eye or manipulated through advanced statistical calculation. In most cases, authors
tend to read numerical consistencies as encoding either theological or biographical details (i.e.,
biblical messages or Bach’s name or important dates) into his music. While work on number
symbolism in Bach is at least informally recognized among musicologists as its own subfield of
musicology, the majority of its modern proponents, especially on the Internet, originate from
outside of formal musicology. Many amateur forums exist, for example, precisely to unravel
Bach’s mathematical encoding; these are typically started and run by and for math or puzzle
enthusiasts, often also with intersecting theological interests, seeking to prove Bach’s
mathematically certifiable genius, or in some cases, his prophetic gifts as God’s musical
messenger on earth.
19

In formal studies, Ruth Tatlow’s skeptical Bach and the Riddle of the Number Alphabet,
based on her dissertation, provides the most scholarly perspective to date on the popular
twentieth-century mythology that Bach routinely and pervasively used alphabet systems in his
works. She centers her study on the writings of theologian and musicologist Friedrich Smend
(1893-1980), who in 1947 first published his theory of Bach’s cabalistic
20
use of the natural-
order number alphabet (A=1, B=2, to Z=24) as a vehicle for biblical subtext. From a

19
There are many with this kind of theological angle, but this is one of the most popular:
https://www.bach-cantatas.com/Topics/Numbers.htm.
20
Spelling note: from here on, I will only use “kabbalah” to refer to ancient Jewish
mysticism in actual Jewish practice, and “cabala” to refer to any Christianized version of this
practice after the sixteenth century.
12
methodological perspective, Tatlow’s work, logically founded on disproof rather than proof,
provides a sound model of number-symbolism investigation. Whether or not one agrees with
Tatlow’s methodology, reviews from the time of its publication make it clear that Bach number-
symbolism, as a musicological subfield, had quite a lot to prove: as John Butt states in one such
review, “A miracle has come to pass: a book concerning Bach and number symbolism which is
sensible, perceptive, and scholarly.”
21

Tatlow’s approach, which one could call “meta-musicological,” involves examining
Smend’s root causes for his belief in Bach’s use of number alphabets. From his writings, Tatlow
discovers that his predisposition to believe in number symbolism forms a necessary part of his
concept of Bach’s genius (“But Bach, like other great minds, enjoyed the setting and solving of
puzzles”).
22
Number alphabets were certainly used in Lutheran Germany—Tatlow outlines over
fifty different varieties—but those most common in serious seventeenth-century Christian circles
were the Latin trigonal and the Greek and Hebrew milesian forms,
23
with Smend’s natural-order
alphabet more prevalent by Bach’s time only in non-religious contexts.
24

Arguably the most important aspect of Bach and the Riddle of the Number Alphabet to
number-symbolism studies is Tatlow’s historiographical work in tracing nineteenth- and
twentieth-century constructions of Bach’s genius as “unique” relative to the assumption that he,

21
John Butt, “Review of Bach and the Riddle of the Number Alphabet,” Music & Letters 73,
no. 1 (February 1992): 105, https://doi.org/10.1093/ml/73.1.105.
22
Ruth Tatlow, Bach and the Riddle of the Number Alphabet (Cambridge: Cambridge
University Press, 1991), 8.
23
Tatlow, 130–32. The Latin trigonal alphabet is based on triangular numbers, such that
A=1, B=3, C=6...Z=276. Hebrew milesian ascends (in various increments) from Alep=1 to
Taw=400, and Greek milesian from Alpha=1 to Omega=800.
24
Smend also confuses elements of cabala and the purely literary poetical paragram. While
Bach may have used paragram to stimulate invention, as did contemporary intellectuals in other
fields, any use of musical codes based on his own name bears little relation to true cabala
speculativa. See Tatlow, Bach and the Riddle of the Number Alphabet, 37.
13
more than other people, enjoyed puzzles, mathematical codes, and paragrams. If many more
composers than Bach used number alphabets, paragrams, or riddles as part of their regular
compositional processes, then study of them yields purely historical information, without any
grandiose testimony to Bach’s specialness within the canon. As Butt puts it, if Bach’s only
contemporary to use number alphabets turned out to be Kuhnau, “it is unlikely that so much
paper would already have been wasted on the subject.”
25

After the success of Bach and the Riddle of the Number Alphabet,
26
Tatlow’s numerical
investigations took a fascinating turn: despite her skeptical approach to the subject, in examining
other methodologies, checking data, and comparing these to passages from eighteenth-century
treatises mentioning the importance of maintaining good proportion in musical composition, she
began to notice certain undeniable numerical patterns in Bach’s manuscript and publication
habits. With the release of her most recent book, which outlines these phenomena, Bach’s
Numbers: Compositional Proportion and Significance, she entered a challenging space in which
her work remained too rigid for the Bach mathematical enthusiast, but too number-focused, yet
un-statistical in the modern computational sense, for the blanket skeptic.
27
It represents, however,
the best historically and mathematically supported methodology and evidence on the subject of

25
Butt, “Review of Bach and the Riddle of the Number Alphabet,” 107.
26
The only highly negative evaluation I am aware of comes from Bach number-enthusiast
David Rumsey, who accuses Tatlow of skewing the truth in order to intentionally obscure Bach’s
genius. See David Rumsey, “Bach and Numerology: ‘Dry Mathematical Stuff’?” Literature &
Aesthetics 7 (1997): 143–65.
27
While not many unilaterally negative critiques of Bach’s Numbers appear in print, the ones
that do demonstrate the field’s unusual divisiveness, even when implemented and presented so
carefully. More intricacies in these disagreements exist to untangle than makes sense to discuss
here; it suffices to say that in many such reviews, the common appearance of phrases suggesting
overwhelm, such as “barrage of numbers,” perhaps bespeaks a basic misunderstanding of
Tatlow’s evidence. For example, see Pieter Bakker, Postmodern Numbers: Ruth Tatlow on
Proportions in the Written Music of J. S. Bach, trans. Pleuke Boyce (Schraard: Kunst en
Wetenschap, 2015), http://www.huygens-fokker.org/docs/Tatlow.pdf.
14
Bach’s conscious use of numbers—not number alphabets—since Herbert Anton Kellner’s
articles on the tunings of Bach’s keyboard instruments.
28
Tatlow bases what she calls her
“historically informed analytical technique” on theoretical and theological concepts drawn from
contemporary literature, eventually centering her methodology on Bach-era aesthetic ideals of
pleasing proportions.
29
After establishing from her reading the term “Proportional Parallelism” to
describe various musical techniques composers might use to make their works proportionally
attractive (to eighteenth-century standards), Tatlow presents evidence of Bach’s active use of its
basic precepts. Similar to David Yearsley’s work on (textual) rhetorical aspects of seventeenth-
century counterpoint’s meaning and uses,
30
Tatlow’s literary analyses add considerable
connotational dimension to common terms like “harmony,”
31
“proportion,”
32
and “unity.”
33

In comparing working and finalized copies of manuscripts and publications, Tatlow
demonstrates that Bach kept regular score of his numbers of measures, in a level of detail far
surpassing a practical need to mind performance lengths. Bach seems to have developed and
perfected his compositions by adjusting the number of bars as he worked on them, even from the
earliest planning stages.
34
Some of Tatlow’s further supporting discoveries include the fact that

28
Herbert Anton Kellner, “Was Bach a Mathematician?” English Harpsichord Magazine 2,
no. 2 (1978): 32-36.
29
Tatlow explains her reasoning for using historical sources to inform her methodology, and
outlines some of the unique challenges therein, in her philosophical article “When the Theorists
are Silent: Mattheson, Bach and the Development of Historically Informed Analytical
Techniques,” In What Kind of Theory Is Music Theory, ed. P. Broman, Stockholm Studies in
Musicology 1 (Stockholm: Stockholm University, 2007), 203–16.
30
For instance, David Gaynor Yearsley, “Alchemy and Counterpoint in an Age of Reason,”
Journal of the American Musicological Society 51, no. 2 (1998): 201–43.
31
Ruth Tatlow, Bach’s Numbers: Compositional Proportion and Significance (Cambridge:
Cambridge University Press, 2015), 93.
32
Tatlow, Bach’s Numbers, 108.
33
Tatlow, Bach’s Numbers, 75.
34
Tatlow, Bach’s Numbers, 102–29.
15
that measure totals in Bach’s published works are almost always a multiple of 10, frequently 100
and sometimes 1000; they also tend to contain multiple layers of proportional parallelism, on
different scales.
35
Despite her number-alphabet skepticism in Bach and the Riddle of the Number
Alphabet, she also concludes that Bach had a special interest in the numbers 213, 123, and 312,
as iterations of the letters BAC/H in the natural order and milesian number alphabets.
36
Tatlow’s
work is convincing, not only in its historical grounding and methodological scruples, but also
consistency: all of the “collections and multi-movement works that Bach published or left in fair
copy” exhibit the aforementioned characteristics.
37

1.2 – Numerological Analyses of Buxtehude’s Organ Works
While this dissertation is the first study to approach Buxtehude’s vocal music with related
mathematical and occult-philosophical interest, as in Bach scholarship, several studies from the
1980s and early 2000s examine the numerical proportions of individual organ works by
Buxtehude. Unlike Tatlow’s work on J. S. Bach, none reveals evidence of truly systemic
proportion, and proposed meanings behind compositional numbers remain abstract in the
absence of sung text, which could mark numerical occurrences or provide a thematic foundation
for numerological research beyond the composition. Likewise, because these scholars typically
only analyze one piece that exhibits certain special characteristics, their methodology often
proves too individualized to apply to multiple works.

35
For Tatlow’s summary of her findings, see Ruth Tatlow, Bach’s Numbers: Compositional
Proportion and Significance (Cambridge: Cambridge University Press, 2015), 33–35.
36
Tatlow, Bach’s Numbers, 12. This is the kind of assertion Tatlow initially tried to disprove
in Bach and the Riddle of the Number Alphabet, but it “appears so frequently throughout
[Bach’s] published works that [she] decided to include it as one of the three characteristics of
[his] proportional parallelism.”
37
Tatlow, Bach’s Numbers, 367.
16
The first and only dissertation handling Buxtehude and number symbolism is keyboardist
Stephen Ackert’s DMA thesis from 1979,
38
which only discusses organ works and predates by
twenty-five years Kerala Snyder’s greatest strides in piecing together Buxtehude’s biographical
information.

The second half of Ackert’s thesis contains an exhaustive catalog of compositional
numbers (i.e., subject lengths, number of entries, measure totals) in Buxtehude’s organ pieces,
arranged by individual work, in chart form.
39
This chart provides a sense of compositional
consistencies among the works he measures, but it does not sort his data into hierarchies (i.e., of
numbers appearing most frequently or potentially foundational to compositional planning), and
he is therefore understandably reluctant to interpret the numerical consistencies he maps:

…those organ works which have survived show Buxtehude to have been much
interested in the potential of numbers in organizing musical structures, but little
involved in the practice of number symbolism. In this he can be seen as
representing the trend among intellectuals of his time away from mystical and
symbolically oriented thought and toward the Age of Reason.
40

With the benefit of reading forty more years of scholarship since he submitted this thesis, one
might conclude that Ackert’s conception of Buxtehude’s proto-Enlightenment numerical
inclinations resembles older attitudes toward this repertoire.
41
In terms of historiography,

38
Stephen Francis Ackert, “Numerical Structures in the Organ Works of Dietrich
Buxtehude” (DMA diss., University of Wisconsin - Madison, 1979).
39
Ackert, “Numerical Structures,” 24–50.
40
Ackert, “Numerical Structures,” 16.
41
One problematic element in Ackert’s study comes in his discussion of number alphabets:
he misspells—and therefore mathematically miscalculates—Buxtehude’s first name, but then
later demonstrates that numerical value’s import to some of the pieces he analyzes. Buxtehude
used several spellings of his name, but “Dieter” is not one of them. Its natural-order value is 59,
a number that Ackert then finds repeatedly, as a “BACH”-like calling card. I mention this
because Kerala Snyder specifically cited this issue (in conversation) as a counterexample to any
numerical Buxtehude study, in the early stages of this project. See Ackert, “Numerical
Structures,” 10.
17
however, his work reflects a tendency that persists to this day, in framing his study’s larger
numerical purpose wholly in relation to Bach scholarship:

Although the numerical structures... are interesting in themselves, their
musicological significance lies in the historical proximity of Buxtehude’s music
with that of Johann Sebastian Bach, who carried numerology as a symbolic
vehicle to great heights. The intricate and symbolically profound use of numerical
structures in Bach’s [music]…has attracted much attention on the part of
musicologists. It is important to note that, whereas Bach’s use of such structures
towered above that of any other Baroque composer, he was not the only composer
of that period to explore this aspect of music.
42

Without building directly on Ackert’s work, independent scholar Carol Jarman published
two studies in the 2000s on Buxtehude’s numbers: allegorical analyses of the organ Ciaconas in
C minor (BuxWV 159) and E minor (BuxWV 160), in which she claims that the former is based
on the Nicene Creed and the latter on the Rosary.
43
According to Jarman’s analysis, each of the
E-minor Ciacona’s “full” eight-measure statements of the bass depicts a different Rosary scene.
44

She arrives at this entirely from numerical calculations and believes that several “partial”
statements of the bass are expressly designed to bring the total measures to 125, or 5
3
(5 x 3 is
15, one for each Mystery). Her central argument about the C-minor Ciacona hinges on similar
calculations, but her noting of cameo appearances of several related chorale melodies—including

42
Ackert, “Numerical Structures,” 56.
43
Carol Jarman, “Buxtehude’s Ciacona in C Minor and the Nicene Creed,” The Musical
Times 146 (2005): 58–69.
44
Carol Jarman, “Butehude’s E minor Ciacona and the Rosary,” The Organist (The Royal
College of Organists), (1994). This summary is taken from Jarman’s own summary in the
introduction to her article about the C-minor Ciacona.
18
“Wir glauben all an einen Gott,” the Lutheran rendering of the Creed—provides strong support
from non-numerical sources.
45

Organist Piet Kee’s numerological study of Buxtehude’s D-minor organ Passacaglia
provides some of the most compelling numerical evidence of all, but connections between
numerical elements and their interpretation are not always clear. In his 1984 article,
46
Kee argues
that the Passacaglia is a numerical rendering of the lunar cycle, in its co-mingling of the
compositional numbers four, seven, and particularly twenty-eight (interpreted as weeks, days,
month).
47
This piece’s sole source, the “Andreas-Bach-Buch,” which contains many other
contemporary ostinato works, also provides an enticing clue: the variations and measures in
Buxtehude’s Passacaglia and Pachelbel’s D-minor Ciacona have been numbered.
48
One cannot
necessarily prove why an eighteenth-century person was counting these, but it remains
provocative.
To introduce his larger argument, Kee mentions a connection between “figurate”
numbers
49
and ground iterations in basso ostinato works of the North German school.
50
But in no
publication does he mention the number of notes in a ground (rather than only ground iterations)

45
Jarman, “Buxtehude’s Ciacona,” 60. The appearance of recognizable, texted music in an
instrumental work allows for more thematically focused numerical understanding and
interpretation.
46
Reprinted in 2007.
47
Piet Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato
Works,” The Diapason 75 (1984), reprinted in Organists’ Review (August 2007): 27–33.
48
Kee, “Astronomy,” 29–30.
49
Also called “figural” or “figured” numbers. See chapter 2 for a discussion of these
numbers in Rosicrucian mathematical theology. See chapter 4 for an explanation of their
functions in Buxtehude’s basso ostinato psalm settings and in my counting methodology.
50
This is a prominent enough correlation that I also observed this in Buxtehude’s ostinato
works before encountering Kee’s article. See chapter 4. Piet Kee, “Astronomy in Buxtehude’s
Passacaglia: Measure and Number in Ostinato Works,” The Diapason 75 (1984): 27–28.
19
as a possible vehicle for figurate-number symbolism.
51
This may be because Kee’s numerical
interests are often ideologically much larger than the specific piece at hand, as seen in this
description of a figurate triangle of the numbers one through thirty-six:

[Each] enlargement of the [figurate] triangle below—especially that with the first
four numbers—produces a number which is of fundamental importance in nature
and in culture. The numbers 3 and 6 lead to the duodecimal system, manifest in
the cosmos and in time: 12 signs of the zodiac, 12 months, etc. The number 10
leads to the decimal system, found for instance in the human body: 10 fingers,
toes, etc.
52

But in his discussion of the “root” or “radical” numbers one through six in relation to the
numerically explicit triangular seal of the Societät der Musickalischen Wissenschafften (of which
Bach was a member), interestingly, Kee does not mention that six is a triangle number.
53
I would
add one more feature to his argument, to reinterpret his already convincing data with just a small
adjustment: beginning the sequence of triangular numbers from one (unity), rather than three, the
first in the sequence to “look” triangular,
54
adds dimension to Kee’s findings involving the
number twenty-eight.
55
As the triangle number upon which his larger argument hangs, twenty-
eight thus becomes the seventh triangle number in the natural sequence—meaning, it is not just a

51
For example, Kee, “Astronomy,” 27.
52
Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato Works,”
28.
53
Kee, “Astronomy,” 27. In fact, it is the third triangular number in the natural sequence, so
it creates a triangle with three points per side.
54
The number one satisfies the generating formulae for every polygonal number. See chapter
4.
55
Although it does not look like a triangle when expressed visually, as a point, the number
one is the first triangular number, by definition. One satisfies every generating equation of
figurate (therefore constructible) number, so it should be counted as the first of any equation it
satisfies. This is part of its mathematical “divinity” as the unity of all numbers, from which
multiplicity springs.
20
mathematically “perfect” number, but also theologically “perfect,” as a visual-spatial rendering
of Werckmeister’s (3 x 7) “Trinity in divinity.”
56

Kee’s reading of Buxtehude’s Passacaglia provides a possible interpretation that could
help a performer make registration, timing, or other expressive decisions, by creating a
programmatic arc for performance.
57
But because the triangular-number arrangement as the
number twenty-eight is similarly demonstrable in other Buxtehude works, including the ones this
dissertation handles,
58
the moon’s connection to this piece specifically remains more abstract
than the objective mathematical significance the perfect number itself carries, especially also as
the seventh triangular number. But of all possible external connections to suggest, Kee’s choice
of astronomy makes biographical sense: Buxtehude wrote a now-lost set of seven keyboard
suites, each a meditation on the qualities and characteristics of a different planet.
59
Buxtehude
also demonstrates an affinity for the number seven in his publishing habits: in a stroke of what
Kerala Snyder calls “bold originality,” Buxtehude published his two collections of sonatas for
violin, viola da gamba, and basso continuo—among his few publications in general—as groups
of seven sonatas, instead of the usual six.
60
In her discussion of this unusual feature, Snyder

56
Not in literal product of 3 and 7, but as the seventh figure in a sequence of three-sided
geometric shapes. For explanations of Werckmeister’s meanings of numbers, see chapter 3.
57
Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato Works,”
30–32.
58
The basso ostinato section of Sicut Moses exaltavit serpentem in deserto (BuxWV 97) is
an excellent example. See chapter 7.
59
For instance, did Buxtehude care about the number twenty-eight because of the lunar
cycle, or did part of his interest in the planets and the lunar cycle depend on their numerical
perfection in the cosmos? In alchemy and Rosicrucianism, the moon also symbolizes the
feminine energy that acts as an essential foil for the sun. It is possible that this piece really does
map the lunar cycle, but it is simultaneously possible that Buxtehude’s interest in crafting the
piece as such came from a different direction from pure astronomy. For historical context and
information about the lost keyboard suites, see Jeffrey Cooper, “The Seven Planets in Bach,
Buxtehude, and a Dresden Ballet of 1678” (DMA diss., University of Houston, 2017).
60
Snyder, Dieterich Buxtehude: Organist in Lübeck, 284.
21
notes that Buxtehude favored groupings of seven elsewhere, including in his Membra Jesu Nostri
cycle, in addition to the lost keyboard suites and the Passacaglia’s ostinato statements.
61
But for
the first two of these, the subjects themselves already dictated divisions by seven. By contrast,
Buxtehude “imposed the number seven on the sonata collections,” and Snyder notes that the key
arrangement of the first set—F major, G major, A minor, B-flat major, C major, D minor, and E
minor—as a linear scale, represents the extension of the hexachordum molle to seven notes. The
keys of the second set also form a a heptachord, but not ordered linearly like the first set.
62

1.3 – Pietism and Rosicrucianism in Bach and Buxtehude Studies
For scholars of Buxtehude’s vocal music, any observations about his mystical tendencies
typically find their focus in the German Pietist movement rather than in counterpoint or alchemy.
A new argument about Buxtehude’s possible Pietism arises roughly once every twenty to thirty
years, beginning with the 1965 publication of Martin Geck’s dissertation Die Vokalmusik
Dietrich Buxtehudes und der frühe Pietismus. In summary: Geck suggests that Buxtehude
belonged to a Pietist circle whose members aimed to deepen their personal faith experience, and
thus a Pietist appeal to the senses inspired Buxtehude’s lyricism in sacred song.
63
The most
recent argument to echo Geck’s work is by Clemens van den Berg, in a 2018 article in which he
argues that Buxtehude’s use of “synaesthesia” in Membra Jesu Nostri reflects distinctly Pietist
influence.
64

61
Snyder, 285.
62
Snyder, 285.
63
Martin Geck, Die Vokalmusik Dietrich Buxtehudes und der fruḧe Pietismus (Kassel:
Bar ̈ enreiter, 1965).
64
Clemens G. van den Berg, “Dissecting Jesus: The Spiritual Role of the Senses in
Buxtehude’s Cantata Cycle Membra Jesu Nostri (1680),” Junctions: Graduate Journal for the
Humanities 3, no. 1 (2018): 31.
22
While it is true that Buxtehude drew many texts from Pietist or Pietist-leaning authors,
including John Rist, Angelus Silesius, Heinrich Müller, Thomas Fritzsch, and Johann Wilhelm
Petersen, Kerala Snyder raises strong conflicting evidence: a cornerstone of the Pietist movement
was a drive to ban from the church service precisely the compositional genres that form the
majority of Buxtehude’s output.
65
Theophil Großgebauer (1627-1661), professor of philosophy
and theology in Rostock and deacon at the local St. Jakobi Church, details this proposed ban in
his 1661 Wächterstimme aus dem verwüsteten Zion, which describes cleansing Lutheran church
music of Latin texts, Italianate stylistic influence, excessively artful organ music, and all cheerful
music during communion. Among these offenses, he particularly condemns settings of biblical
texts in which verses “are torn apart and chopped up into little pieces through swift runs of the
throat,” which exactly describes Buxtehude’s vocal settings’ pervasive coloratura and generally
short textual excerpts.
66
Likewise, Großgebauer’s descriptions of organists who detract from the
congregation’s faith experience could apply to no fewer than three generations of North-German
organists (“There the organist sits, plays, and shows his art; in order that the art of one person be
shown, the whole congregations of Jesus Christ is supposed to sit and hear the sound of pipes”).
These Pietist attacks on orthodox Lutherans’ use of music in worship elicited equally
impassioned responses, including Hector Mithobius’s Psalmodia christiana (Jena, 1665), which
includes a frontispiece depicting a music-centered worship scene: an organ stands in place of an
altar, a lutenist and violinist can be seen in the organ loft (as was often the case in St. Mary’s in
Lübeck), balconies are filled with instrumentalists and singers, and a conductor directs from the
center of the church, among the congregation. Biblical verses (some in prose, others just listed by

65
Snyder, Dieterich Buxtehude, 146.
66
Snyder, Dieterich Buxtehude, 146–49.
23
chapter and verse number) decorate the scene as reminders of God’s desire for man to praise him
with instruments and voices.
67

With the benefit of more recent Pietism scholarship, I would like to nuance this outlook
slightly, and in the process clarify—or helpfully complicate—some of the salient terminology. In
surveying the last twenty years of Pietism-related scholarship, Tanya Kevorkian has
demonstrated that different groups of North-German Pietists held highly distinctive musical
beliefs and engaged in equally distinctive musical practices. Thus, there was no “one set of
Pietist attitudes toward music,” and Kevorkian therefore suggests amending any lingering
“simplistic views” of Pietism as “hostile to music and the arts”; as her work shows, much of the
“harsh Pietist rhetoric” about music has more recently been proven “at odds” with actual German
Pietist practice.
68
Meanwhile, in Pietist historiography, many twentieth-century historians
emphasize the adverse economic conditions following the Thirty Years’ War as the primary
reason for Pietism’s cultural emergence. Kevorkian concurs that this indeed comprises “one
root” of Pietism that influenced Lutherans in the 1660s and 1670s—especially as a “critique of
contemporary cultural consumption,” based on “Old Testament prophecies of divine vengeance”
and the “New Testament’s apocalyptic outlook.”
69
But by the 1680s, when Pietism became a
broadly recognized social movement, several northern trade centers, including Hamburg and
Lübeck, were in the middle of an “economic boom,” a vast contrast to other cities’ economic
situations. This disparity effectively negates past attempts to describe Pietism as a singular

67
Reproduced in Snyder, Dieterich Buxtehude, 148.
68
Tanya Kevorkian, “Pietists and Music,” in A Companion to German Pietism, 1660-1800,
ed. Douglas H. Shantz, vol. 55, Brill’s Companions to the Christian Tradition (Leiden and
Boston: Brill, 2015), 171.
69
Kevorkian, 172.
24
response to a unified socio-cultural climate.
70
Moreover, certain ideological overlaps between
Pietism and non-Pietist Lutheranism, for instance an emphasis on accessible pedagogy and a
“richly felt emotional attachment to Christ,” mean that too-broad definitions of Pietism falsely
categorize such things as specifically “early Pietist,” when they were important for most German
Lutherans.
71
Kevorkian suggests that a similar issue extends to confusion about definitions of
music within Pietist historiography as well:

When Pietists and other contemporaries talked about “music” or “church music,”
they meant what we would call art music and dance music. In the Baroque era,
this included the church and secular cantata, organ preludes and interludes,
secular instrumental music, and of course opera and dance. Contemporaries did
not consider hymns, chants, or the simple organ accompaniment of hymns to be
“music”...[and the] dividing line between the hymn and secular music was also
not absolute.
72

Precisely because of these terminological concerns, in reopening questions of Buxtehude’s
Pietist influences, most compelling recent discoveries have concerned his music itself—
specifically, his vocal works and their texts—without focusing directly on the question of his
personal Pietism. Many of Buxtehude’s texts are unidentified or otherwise obscure, which has in
part led to very few of his vocal works’ being widely studied or performed, apart from his
Membra Jesu Nostri.
73
But these texts likely harbor remaining clues to Buxtehude’s extra-
musical intellectual influences, including possibly Pietist ones. To this end, Olga Gero has made
arguably the most important Buxtehude discovery of the last decade: the previously unidentified
text to Buxtehude’s cantata Fallax mundus comes from a Jesuit emblem book, Anton II Wierix’s

70
Kevorkian, 172–73.
71
Kevorkian, 176.
72
Kevorkian, 174–75.
73
Olga Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude,”
Early Music 46, no. 2 (2018): 235.
25
Cor Iesu amanti sacrvm.
74
This collection contains eighteen engravings, each depicting a
different stage of the faithful heart’s journey to mystical union.
75
On the title page (Figure 1.1),
Ignatius of Loyola and Franz Xavier embrace an enormous person-sized heart, which appears as
the main “character” in all of the engravings. An undying flame emanates from a single valve at
the top of the heart, just below the trademark Jesuit “IHS” insignia, standing for Ieusus Humilis
Societas and Iesus Hominum Salvator.

74
Gero, “Text and Visual Image,” 236.
75
One wonders whether these eighteen plates have any possible connection to Count Michael
Maier’s eighteen rungs of the Alchemical Ladder that lead to the Philosophers’ Stone—the
alchemical analog to unio mystica. For an explanation of the ladder rungs, see Hereward Tilton,
The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of Count Michael
Maier (1569-1622) (Berlin; New York: Walter de Gruyter, 2003), 98.
26

Figure 1.1. Anton II Wierix, title page from Cor Iesu amanti sacrvm (ca. 1585/6).

This discovery, adding to a growing list of “un-Lutheran” appearing works in his œuvre, deepens
questions about Buxtehude’s religious and professional life, regarding his personal faith,
Abendmusik activities, and his audiences’ and patrons’ conceptions of and uses for his music.
Gero wonders, “Were these pieces to be used in Lutheran public worship or in private devotion
at courts or collegia musica? Are these pieces Catholic or Lutheran, or do they belong to a third
category that mingled elements of Catholic and Lutheran devotion?”
76
Beyond this, the
emblematic nature of the devotional manual in question suggests intentional emphasis, either in

76
Gero, “Text and Visual Image,” 235. Gero never explicitly mentions Pietism, but her
evidence and argumentation imply it without her officially entering the debate.
27
conception or implied religious use, on contemporary visual material. This is the case for other
Buxtehude works as well: two verses from Membra Jesu Nostri appear in seventeenth-century
Passion engravings, including “Quid sunt plagae istae in medio manuum tuarum” (Zecharaiah
13:6) in the series Septem Christi Iesu servatoris nostri effusions sanguinis by Dominicus Cuctos
(ca. 1576-1625) and “Illustra faciem tuam” (Psalms 10:16) in an engraving of Veronica’s Veil by
Hieronymus Wierix, Anton’s brother.
77
As I further explain in chapter 7, a famous Passion
engraving by Julius Goltzius after Maarten de Vos also contains the text to Buxtehude’s Sicut
Moses exaltavit serpentem in deserto (BuxWV 97),
78
alongside certain symbols strongly
associated with seventeenth-century Rosicrucianism—the “Rosicrucians” being an esoteric
Christian society with which I ultimately argue that Buxtehude was in some way involved. The
heart “character” in Cor Iesu amanti sacrvm also has a visual Rosicrucian analog: Daniel
Cramer’s Rosicrucian emblem book Emblemata Sacra (1624) contains a similar progression of
heart images, each depicting a transformative process the faithful heart undergoes on the path to
unification with Jesus.
79
Figure 1.2 shows Cramer’s heart “character” roasting in the fire of faith;
from its single valve, it releases the resulting “pleasing aroma” of Christ up to God the Father,
accompanied by a quotation from Corinthians to this end.

77
Gero, “Text and Visual Image,” 245.
78
Gero, “Text and Visual Image,” 242.
79
Daniel Cramer, Emblemata Sacra (Frankfurt: Lucae Jenissi, 1624).
28

Figure 1.2. Daniel Cramer, Emblem VIII from Emblemata Sacra (1624).

In both the public sphere and surviving print sources, seventeenth-century Rosicrucians
shared some mystical Pietist beliefs, but their ostensible interest in social and personal reform
did not contain artistic restrictions.
80
More importantly, my geometrical findings in Buxtehude’s
ostinato works align consistently with Rosicrucian theology, particularly a neo-Pythagorean
concept of the sanctity of the numbers one, three, four, seven, and ten, as well as efforts to
numerically cast concepts of eternity and mystical union in a joining of triangles, squares, and

80
On the contrary, the founding Rosicrucian documents appear to celebrate music in a
Paracelsian sense of Harmonia. See chapter 2.
29
circles. I would like to echo a possibility that Snyder presented in 1987, quoting Joyce Irwin’s
text on Bach’s perhaps analogous relationship to Pietism and Pietist authors:

Significantly, several of Müller’s writings were found among J. S. Bach’s books
in the following century. His Göttliche Liebes-Flamme, Geistliche
Erquickstunden and Schlußkette und Kraft-Kern are listed in the inventory of
books in Bach’s possession at the time of his death. If, as seems to be the case, we
can distinguish within the broader term “Pietism” between a practical impulse
toward ecclesiastical and pedagogical reform and a devotional impulse inclined to
mysticism, both Bach’s relation to Pietism and Pietism’s relation to music become
less paradoxical. The opposition to artistic music in church was centered in the
reform movement, whereas Bach’s affinity was limited to the devotional
movement.
81

Like Irwin’s argument, my Rosicrucianism theory effectively releases both composer and
historian from irreconcilable paradox. Rather than a counterargument to Martin Geck’s
Buxtehude-Pietism thesis, this runs parallel: the alchemical elements of David Yearsley’s
contrapuntal findings, the visual symbolism of Olga Gero’s textual discoveries, and the mystical
aspects of available Pietist arguments could consonantly be remnants of one cohesive
Rosicrucian theology.
Along these lines, I would like to suggest three new ideological meeting points that were
not feasible in scholarship just a few decades ago: first, a possible alignment between Pietism
and North-German musical practice, another between seventeenth-century German Pietism and
Rosicrucianism, and connecting these, a final meeting point between North-German musical
practice and Rosicrucianism. These comparisons expose complex issues with which to contend,
including definitions of both Pietism and Rosicrucianism, the solidity of any divides between
them, and historiographical difficulties inherent to the elements of intentional secrecy in the

81
Joyce Irwin, “German Pietists and Church Music in the Baroque Age,” Church History 54,
no. 1 (1985): 39. Quoted in Snyder, Dieterich Buxtehude, 147.
30
social histories of both. But fundamentally, I propose that Geck and I are describing different
outgrowths from the same evidentiary root system, with terminology being the biggest difference
between our conclusions.
82

Without any specific argument for or against Buxtehude’s contact with Rosicrucianism,
David Yearsley has made the biggest contribution to date in research about Buxtehude and
seventeenth-century occult philosophy in general, through his study and contextualization of late
seventeenth-century contrapuntal techniques as esoteric symbols. Yearsley’s dissertation,
“Ideologies of Learned Counterpoint in the North German Baroque” and later book Bach and the
Meanings of Counterpoint function as encyclopedic field guides for “Hamburg school”
counterpoint’s formation and transmission of extra-musical meaning.
83
As Yearsley
demonstrates, North-German theorists of the period practiced counterpoint for non-musical
edification, most commonly related to alchemy.
84
Buxtehude’s close friend Johann Theile was so
entrenched in the practice of alchemy- and mysticism-infused “secret” counterpoint that he held
a “mythical status” among North-German musicians as “the father of contrapuntists.”
85
Certain
details in Theile’s counterpoint tracts also suggest his knowledge of at least one alchemical

82
The language and scholarship surrounding Rosicrucianism in the 1960s were neither
present nor nuanced enough for Geck to have seriously considered them. Free from “occult”
connotations, Pietism was more visible to twentieth-century exoteric scholarship, and therefore
more comfortable in which to lodge evidence of mystical inclinations and authors like Arndt.
Even Frances Yates’s pioneering 1970s work on the subject contains some serious issues only
exposed by research after 1990. See Carlos Gilly, Cimelia Rhodostaurotica (Amsterdam: BPH,
1995), 22; 75–76.
83
See chapter 2.
84
David Gaynor Yearsley, “Ideologies of Learned Counterpoint in the Northern German
Baroque” (PhD diss., Stanford University, 1995), 38.
85
Yearsley, “Ideologies of Learned Counterpoint,” 23–24.
31
treatise: Atalanta fugiens (1617)
86
by Michael Maier, who was also the most outspoken German
Rosicrucian apologist of the early 1620s.
87

Numerology and Rosicrucianism have converged in seventeenth-century musicology at
least once before: in the mid-twentieth century, bits and pieces of Rosicrucian ideals found
themselves intertwined with the outskirts of Bach number-scholarship, later put in print in a 1985
study by Kees van Houten and Marinus Kasbergen:

Johann Sebastian Bach was born on the 21st March 1685 or 21 3 307 in the
Rosicrucian calendar. He died on the 28th July which in Rosicrucian terms is 28 7
372. This leads to an improbable but inescapable conclusion: it appears that Bach
employed the epitaph of Christian Rosencreuz in the Sinfoniae. In the Magnificat
the epitaph encircles 28+7 and in the last three organ sonatas it encircles the
number 372. In relation to this inscription we find in one case 28 7 and in the
other case 372, the date and year of Bach’s death when calculated by the
Rosicrucian calendar…In other words Bach accurately registered the date of his
death in relation to the epitaph long before the actual event…The connection
Bach – Rosicrucian (epitaph) – date of death becomes more and more evident and
the numbers involved are very relevant to Bach himself and have a fundamental
symbolic meaning. A special chapter is devoted to the number 23,869, the total
sum of the days of Bach’s life.
88

Here, Rosicrucianism has become a focal point of the authors’ argument, but logical connections
between the numerical, musical, and biographical information they record likely suggest some

86
David Yearsley, “Alchemy and Counterpoint in an Age of Reason,” Journal of the
American Musicological Society 51, no.2 (1998): 225–26. Atalanta fugiens is also the first
alchemical treatise to extensively draw metaphorical connections between alchemical operations
and musical-contrapuntal ones. For a complete digital edition with accompanying commentary,
see Tara Nummedal and Donna Bilak, eds., Furnace and Fugue: A Digital Edition of Michael
Maier’s “Atalanta Fugiens” (1618) with Scholarly Commentary (Charlottesville: University of
Virginia Press, 2020), https://doi.org/10.26300/bdp.ff.
87
Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of
Count Michael Maier (1569-1622).
88
Kees van Houten and Marinus Kasbergen, Bach en het getal (Zutphen: De Walburg Pers,
1985), 50–54. This translation appears in Tatlow, Bach and the Riddle of the Number Alphabet,
1.
32
kind of coincidence rather than “inescapable” causation. But more importantly, the “Rosicrucian
calendar” on which the authors base their argument does not actually exist: Rosicrucianism’s
core is entirely and intentionally fictional, based on precepts just unbelievable enough to be
understood as intentional allegory.
89
For instance, in the Confessio Fraternitatis, the original
Rosicrucian authors claim that their fictional founder, Christian Rosenkreutz, was born in 1378.
90

For a society championing their vision of Christian reform within an already post-Reformation
Christianity, they meant 1378 to refer to the Papal Schism, a time of Christian brokenness
necessitating a new redeemer. Using it as a literal “calendar” would therefore suggest a
misunderstanding of the founding Rosicrucian texts.
91
For this and other factual issues, van
Houten and Kasbergen’s study is sometimes cited as an example of musical numerology’s
possible pitfalls, including by Tatlow in Bach and the Riddle of the Number Alphabet.
92
This has
probably discouraged Rosicrucianism-related investigations of Bach-era music, especially those
involving numerology.
93
But as I will show in chapter 2, the original Rosicrucian phenomenon

89
See chapter 2 for an outline of some of these elements, especially those involving numbers
(like dates) and astronomy.
90
[Anonymous], Confessio Fraternitatis (Kassel, 1615).
91
For excellent translations of all three founding documents, see Joscelyn Godwin,
Christopher McIntosh, and Donate Pahnke, trans., Rosicrucian Trilogy: The Three Founding
Documents in New Modern Translation (Newburyport, Massachussetts: Weiser Books, 2016).
For historical background, see Hereward Tilton, “The Rosicrucian Manifestos and Early
Rosicrucianism,” in The Occult World, ed. Christopher Partridge (New York, New York:
Routledge, 2015), 128–40. Further explained in chapter 2.
92
Tatlow, Bach and the Riddle of the Number Alphabet, 1.
93
This is my personal opinion, based on many conference-paper questions and informal
discussions with colleagues. In these contexts, I have noticed that most modern preconceptions
about Rosicrucianism align with nineteenth-century iterations in the United States (later known
as the “Rosicrucian Order, AMORC”), not the original seventeenth-century documents or
historical context. Relatedly, modern misconceptions of Rosicrucianism as “occultist” (rather
than just occult) can sometimes play into this issue. For information about the modern order, see
https://www.rosicrucian.org/. For an in-depth look at all historical versions of Rosicrucianism in
context, see Tobias Churton, The Invisible History of the Rosicrucians: The World’s Most
Mysterious Secret Society (Rochester, Vermont: Inner Traditions, 2009).
33
was surprisingly far-reaching in central Europe and England,
94
so much so that elements of
Rosicrucian doctrine ended up dictating real political events and providing a traceable
ideological foundation for elements of what would become Rationalist intellectual thought.
95

Although van Houten and Kasbergen’s Rosicrucian study chronologically coincided with
the study of Pietism in 1980s Bach scholarship, Rosicrucianism and Pietism do not coincide in a
single Bach or Buxtehude study. But the surface goals of both groups are fundamentally
consonant, in idealizing an intensified spiritual life achievable only through equally intensified
personal devotion and social reform. The two movements also share foundational literature:
German theologian Johann Arndt (1555-1621)—whom twentieth-century historians consider an
integral, though posthumous, part of 1680s Pietism—also deeply influenced Johann Valentin
Andreae (1586-1654), probable author of the first Rosicrucian manifestos.
96
Conversely,
Andreae also contributed to the body of what would eventually be called “Pietist” literature, in
adding commentary to Arndt’s famous Four Books of True Christianity (ca. 1605-10).
97
The four
“books” to which the title alludes are Christ, the Bible, the human conscience, and “the Grand
Universal Book of Nature”—a concept that features prominently in the founding Rosicrucian
documents. When Arndt became superintendent general for Lüneburg, he and Andreae also
corresponded in 1614, the year the first Rosicrucian manifesto was published.
98

94
Alyke Zwaantina de Vries, “The General Reformation Divini et Humani: The Rosicrucian
Call for Change, Its Sources, and Early Impact” (PhD diss., Nijmegen, Netherlands, Radboud
University Nijmegen, 2020), 1–8.
95
Discussed in chapter 2. See also de Vries, 18–24.
96
See chapter 2 for a summary of the relevant authorship issues.
97
de Vries, “The General Reformation Divini et Humani: The Rosicrucian Call for Change,
Its Sources, and Early Impact,” 180.
98
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 89.
34
Thus, early branches of Pietism and Rosicrucianism closely resemble one another, both in
specific literary influences and in their goals of intensifying bonds with Christ through equal
parts heightened personal piety and large-scale social reform. The most important distinctions
between Pietism and Rosicrucianism before and during Buxtehude’s lifetime, however, concern
the latter’s language surrounding resurrection and the apparent rejection of personal sin as a
theological basis. That is to say that most branches of Rosicrucianism, though still claiming
Christ’s crucifixion and resurrection as a starting point for devotional contemplation, do not
necessarily find its focus in the faithful’s sin for which Christ suffered on the cross. Rather, as an
idealized reform program, seventeenth-century Rosicrucianism illuminates the beauty of
crucifixion and resurrection as a mystical union of opposites—in this case, life and death and
heaven and earth—and the spiritual magic of transformation and renewal. Therefore, if
Buxtehude might have been Rosicrucian (or composing for someone who was), then “Pietist vs.
Lutheran orthodox,” “Pietist vs. Rosicrucian” and “Rosicrucian vs. Lutheran orthodox” lines of
questioning create false dichotomies; instead, we should ask why, when, and how Buxtehude
textually and musically acknowledges transformative aspects of divine unification.
99
Informed by
the authors and sources I have outlined here, these questions position my work in a corner of
Buxtehude scholarship largely unexplored in modern musicology. Bringing numerical aspects of
Buxtehude’s craft to the fore, with an openness to established and new occult fascinations in his
milieu, holds the potential to more precisely understand his compositional structures—and by
extension his creative process—than ever before.

99
My analyses treat exactly these questions, in documenting evidence for a consistent
connection between texts handling mystical union, ostinato basses, and a distinctly Rosicrucian
concept of eternity and cyclic transformation between death and rebirth.
35
CHAPTER 2
Seventeenth-Century Alchemy, Rosicrucianism, and Theological Mathematics

2.1 – Seventeenth-Century Alchemy, Christianity, and Numerology
In pre-Enlightenment contexts, boundaries between the spheres of “religion” and “science” were
more ambiguous and fluid than in today’s secular culture; essentially, before any widespread
Western drive to categorize disciplines based on foundations in empiricism or faith, no such
divides existed. Western esoteric pursuits, concerned with probing divine realities for
transcendent knowledge or seeking spiritual salvation through the study of nature’s “hidden”
laws, could move freely between scientific and theological discourse. If God created everything,
including nature, then nature’s secrets must be of similarly divine origin, and in this way “mirror
the mysteries of the divine economy.”
1
As a pursuit situated at the precise intersection of science
and religion, alchemy was already by 1600 considered an “occult” science, for its alleged domain
beyond the experiential world and visible causal reality. Thus, this “occult” designation was
meant only to refer to those hidden parts of nature that appear to yield powerful, observable
effects. “Natural magic” was available only to magi (wise men) whose deep knowledge of the
universe and “purity of spirit” brought them close enough to God to be able to probe both the
visible and invisible realms, and to thus effect transformation by manipulating “spirits,” both
material and immaterial.
2

1
Wouter J. Hanegraaff, Western Esotericism: A Guide for the Perplexed, Bloomsbury
Academic, Guides for the Perplexed (London and New York, 2013), 21.
2
Penelope Gouk, “Transforming Matter, Refining the Spirit: Alchemy, Music and
Experimental Philosophy around 1600,” European Review 21, no. 2 (2013): 147,
https://doi.org/10.1017/S1062798712000324.
36
Alchemy and Judeo-Christian thought and literature experienced a long history of
intermingling in the Christian West. As a pseudo-spiritual pursuit at many points in its long
history through the seventeenth century, alchemy as a practice can mean, and intersect with, a
variety of disciplines—an inherently multivalent state of being that lends itself to equally
multivalent interpretations. The first alchemy we have a record of, in third-century BCE
Hellenistic Egypt, concerns purely material operations, things such as coloring metals to look
like gold or pearls, which eventually led to early experiments in the transmutation of base metals
into nobler ones, an act known then as chrysopoeia (gold-making). These traditions were
eventually taken up and reshaped by the Arabs and Persians starting in the eighth century CE,
when the Sufi Jabir ibn Hayyan first mentions a theory of a mercury-sulphur composition for the
Philosophers’ Stone, within which one also finds the first notion of a substance able to
simultaneously elevate base metals and cure human diseases. The earliest copy of the Emerald
Tablet of Hermes, a foundational alchemical text for later generations in many capacities,
including gold-making, medicine, and aspects of personal transformation, dates from this
period.
3

In the twelfth century, around when the Christian West learned about alchemy (via
translations from Arabic to Latin),
4
there appears to have existed contemporaneous alchemical
literary interest in “spirits.” Sometimes, however, the term referred to volatile substances like

3
Peter J. Forshaw, “Isn’t Alchemy a Spiritual Tradition?,” in Hermes Explains: Thirty
Questions about Western Esotericism, ed. Wouter J. Hanegraaff and Peter J. Forshaw
(Amsterdam: Amsterdam University Press, 2019), 105.
4
The first of these, attributed to the Christian monk Morenius, De compositione alchimie
(1144), refers to itself as “a book divine and completely filled with divinity.” Peter Forshaw
describes its contents as primarily sounding “like laboratory practice,” but interspersed with
“enigmatic” statements, for example: “Truly, this matter is that created by God which is firmly
captive within you yourself, inseparable from you, wherever you be, and any creature of God
deprived of it will die.” See Forshaw, “Isn’t Alchemy a Spiritual Tradition?,” 106.
37
mercury and had little to do with the alchemist’s own “spiritual” path, but other times to alchemy
as an inner science, involving spiritual transformation regardless of laboratory work, as in the
case of Andalusian scholar and mystic Ibn ‘Arabi (1165-1240).
5
It is important to distinguish this
kind of broad metaphorical thought, concerning things like “spirits,” transformation, myth, and
allegory, from the Jungian “spiritual alchemy” popularly known today.
6
Jung’s “spiritual
alchemy” is a psychological alchemy entirely without physical applications. A person therefore
uses “spiritual alchemy” purely as a means of contemplating and achieving spiritual growth,
broad interpretation of which can accidentally lead to the misconception that all alchemy is
“really” about spiritual transformation.
7
Alchemical symbolism can doubtless be used for
teaching and understanding Jungian psychology. But from a seventeenth-century historical
perspective, Jung’s theories do not provide an informed lens for understanding earlier
alchemists’ thought processes about spirits and spirituality.
In the Middle Ages, alchemy and Christian theology begin to intermingle, particularly in
ways employing the story of Christ as an analogy for various laboratory processes. We find
documentation of this by the twelfth century, when both alchemists and theologians began to
consider and document connections between alchemy and Christianity. In so doing, some used
alchemy as a way of demonstrating theological concepts, others used theological thought to
guide alchemical experimentation, and many others compared the events of creation and other
biblical events to chemical phenomena or hypothesized about alchemical-medicinal tinctures’

5
Forshaw, “Isn’t Alchemy a Spiritual Tradition?,” 105.
6
C. G. Jung, Psychology and Alchemy, trans. R. F. C. Hull, Complete Digital Edition, vol.
12, The Collected Works of C. G. Jung (Princeton, New Jersey: Princeton University Press,
1968).
7
Wouter J. Hanegraaff, Esotericism and the Academy: Rejected Knowledge in Western
Culture (New York: Cambridge University Press, 2012), 195.
38
efficacy, based on the bodies of “extraordinary” Judeo-Christian characters like Adam, the
Virgin, and various saints. Each of these operations now falls under the category of “Theo-
Alchemy,” a broad term referring to any alchemical approach directly relating religious thought
and metaphor to physical laboratory practice.
8
Other pre- and post-Reformation alchemists were
interested in using the fruits of the concrete physical operations themselves toward spiritual ends,
not just in intellectual abstraction, but as special tinctures designed to protect the faithful during
the End Times.
9

Thus, in Early Modern Europe, alchemical metaphor blended with and drew from
Christian imagery, yielding rich opportunities for new Christian understanding and even proof of
basic Christian truths. Often, this involved analogous connections between the stages of Jesus’s
life and chemical-transformation stages in recipes for the Philosophers’ Stone, both of which
alchemists believed involved necessary pain, torment, and redemptive death before the ultimate
reward of resurrection.
10
John of Rupescissa, the fourteenth-century Franciscan monk and
alchemist, became a central figure in the formation and propagation of this tradition. In

8
Forshaw, “Isn’t Alchemy a Spiritual Tradition?,” 106.
9
Tara Nummedal, “Alchemy and Religion in Christian Europe,” Ambix 60, no. 4 (2013):
311–12, https://doi.org/10.1179/0002698013Z.00000000036.
10
Before and during the seventeenth century, alchemists described the chemical
transformation of base substances (prima materia) into the Philosophers’ Stone (also called the
Magnum opus or “Great Work”) as occurring over certain stages or phases, each of which invited
allegorical interpretation and expression. These range from as few as four stages involving colors
(blackening, whitening, yellowing, and reddening) to as many as twelve or eighteen stages,
usually involving imagery of a king and a queen, or the sun and the moon, as opposites to be
joined in their “Chemical Wedding” (conjunctio) and then purified after and through the birth of
their homunculus (the Stone itself). In order to initiate the purifying stages, the materials must be
“blackened” or otherwise “killed” prior to the first distillation, which results in vapors rising, as
if “resurrected.” For further explanation of the alchemical stages see Hereward Tilton, The Quest
for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of Count Michael Maier
(1569-1622) (Berlin; New York: Walter de Gruyter, 2003), 65–66. Also see Lyndy Abraham, A
Dictionary of Alchemical Imagery (Cambridge: Cambridge University Press, 1998), 110–13.
39
interpreting earlier writings by pseudo-Arnald of Villanova, Rupescissa draws connections
between distillation, the third stage of the Philosophers’ Stone’s transformation, and the
crucifixion. As the mercury dissolves at the bottom of the vessel while its resulting vapors rise to
the top, Rupescissa describes witnessing Christ’s ascension: “mercury is placed in the bottom of
the vessel...because what ascends from there is pure and spiritual, and converted into powdery air
and exalted in the cross of the head of the alembic just like Christ.”
11
Other examples of his
include descriptions of the red stone’s encasement in the alchemical vessel as looking like
“Christ inside the sepulcher,” which once freed from the vessel “ascend[s] from the sepulcher of
the Most Excellent King, shining and glorious, resuscitated from the dead and wearing a red
diadem...”
12
Imagery of this type appears not only elsewhere in prose, but in full visual
illustration, as in the still-famous 1550s volume Rosarium philosophorum, originally published
as part of a compendium of alchemical texts.
13

After the sixteenth century, however, the relationship between alchemy and
institutionalized religion became tense in many public contexts in the Christian West.
14
This was
not unprecedented: the fourteenth century, for example, saw Pope John XXII (1316-1334)
condemn alchemical practices in his 1317 bull “Spondent quas non exhibent,” and several
Catholic orders banned their members from pursuing alchemy, for fear that intense knowledge of

11
John of Rupescissa, Liber lucis, as cited and translated in DeVun, Prophecy, Alchemy, and
the End of Time, 113. Quoted and further explained in Nummedal, “Alchemy and Religion,”
314–15.
12
Leah DeVun, Prophecy, Alchemy, and the End of Time: John of Rupescissa in the Late
Middle Ages (New York: Columbia University Press, 2009), 118.
13
Cyriacus Jacob, ed., De alchimia opuscula complura veterum philosophorum, quorum
catalogum sequens pagella indicabit. 2 vols. (Frankfurt am Main, 1550).
14
Nummedal, “Alchemy and Religion in Christian Europe,” 321–22.
40
the art put it in divine competition with scripture.
15
Still, alchemists continued to explore
connections between their craft and Judeo-Christian characters and events, though not always
openly, both through alchemy-infused biblical exegesis and by reimagining their laboratory craft
as reenactments of crucifixion, resurrection, and the End Times. Unquestionably, the
Reformation played a large role in the development and propagation of alchemical and biblical
thematic intermingling. The nascent “biblical literalism” so characteristic to Protestantism in
most forms pushed alchemists to discover more literal and perceivable connections between their
laboratory and religious activities, while the development of new orthodoxies (Protestant and
Catholic alike) simultaneously and paradoxically pushed such developments further and further
out of the realm of sanctioned orthodox practice.
16

Significant to this study’s larger aims, sixteenth- and seventeenth-century Lutheranism,
of all denominations, was most open to alchemical-Christian thought and practice. To be sure,
what Wouter Hanegraaff calls the “ancient wisdom narrative”—Christian doctrine’s infusion
with pagan wisdom, a union between the theology of the One Church and more ancient ideals—
came about in Roman Catholic circles well before the Council of Trent, Protestants regarded this
notion an “unacceptable heresy.” And yet, the “alchemical-wisdom” alternative attracted a
specifically Lutheran audience.
17
Martin Luther himself openly lauded alchemy as a “philosophy

15
For further context for these and other examples, see William R. Newman, “Technology
and Alchemical Debate in the Late Middle Ages,” Isis 80 (1989): 339–41 and Nummedal,
“Alchemy and Religion in Christian Europe,” 321.
16
Nummedal, “Alchemy and Religion in Christian Europe,” 321–22.
17
Hanegraaff, Esotericism and the Academy: Rejected Knowledge in Western Culture, 194.
For instance, (at p.194) Hanegraaff says, “The question of why alchemical modes of thinking
could be so appealing to Lutherans (but rarely to Calvinists) is important, and should be explored
in greater detail than is possible here.” This is indeed interesting, considering the alchemical
ideals behind the original Rosicrucian movement in early seventeenth-century Tübingen—a
movement we now think was conceived by Calvinists, not Lutherans, in its earliest form.
41
of the ancients,” and found its virtues of “decocting, preparing, extracting, and distilling herbs”
fully consonant with Christian faith, in which alchemy’s “allegory and signification” are
“exceedingly fine, touching the resurrection of the dead at the last day.”
18
While Luther did not
practice alchemy, his understanding of actual visual events that take place in the alchemist’s
laboratory proves the art’s broad audience and widespread cultural saturation:

For, as in a furnace the fire extracts and separates from a substance the other
portions, and carries upward the spirit, the life, the sap, the strength, while the
unclean matter, the dregs, remain at the bottom, like a dead and worthless carcass;
even so God, at the day of judgment, will separate all things through fire, the
righteous from the ungodly. The Christians and righteous shall ascend upward
into heaven, and there live everlastingly, but the wicked and the ungodly, as the
dross and filth, shall remain in hell, and there be damned.
19

When combined with alchemical thought, seventeenth-century alchemy beyond Luther’s lifetime
birthed some of the most important intellectual works and movements of what we now call
“Western Esotericism,” including late seventeenth-century Rosicrucianism and Christian
Theosophy, based on the school of Jacob Böhme and his followers.
20
Such strong affinity for
alchemical thought was by no means a given among all Christian sects. For example, Jesuits
were generally wary of alchemy, believing that a material lust for gold could put souls at risk, or
that alchemical concepts of transmutation and other theories of matter might compromise or
challenge Catholic teachings about the Eucharist. Some seventeenth-century Jesuits, including
Athanasius Kircher and J. Marcus Marci (Dean of Medicine at the University of Prague),

18
Nummedal, “Alchemy and Religion in Christian Europe,” 311.
19
Martin Luther, “Of the Resurrection,” Book DCCLX, The Table-Talk of Martin Luther,
trans. William Hazlitt (London: George Bell and Sons, 1878), 826. For the original Latin, see
Martin Luther, D. Martin Luthers Werke: kritische Gesamtausgabe [Abt. 2]. Vol 1, Tischreden
(Weimar: H. Böhlaus Nachfolger, 1912-1921), 1149. Translation from Nummedal, 311.
20
Hanegraaff, Esotericism and the Academy: Rejected Knowledge in Western Culture, 194.
42
exhibited more openness than others to alchemical precepts. Still, one wonders how open such
scholarly figures might have been if alchemical ideals more privately encroached on their faith.
21

In contrast to the post-Reformation Catholic experience, Lutheran identity on the whole
was founded on theological and social-experiential grounds of individual observation,
transformation, and perseverance through faith in the face of life-and-death adversity, without an
authoritative institutional safeguard beyond personal will. The basic concept of alchemical
transmutation lends itself naturally to this particular worldview: divorced from the authority of
Roman Catholicism’s centuries-long tradition, the seventeenth-century Lutheran thinker relied
on “personal conscience” to lead to the path of “regeneration,” on which they believed Christ’s
redemptive divine light to obliterate the shadow of sin and ignorance. Unlike in Catholic
orthodoxy, the soul’s transformation from darkness to light would not constitute an “escape”
from the body’s earthly existence; instead, according to Jacob Böhme’s Lutheran-inspired
philosophy,
22
the transformed soul lives on after death, with Christ, as a “regenerated spiritual
body of light.”
23
This emphasis on physical experience thus brought Lutheran theology into
alignment with alchemical phenomenology observable and manipulable in the laboratory.
Seventeenth-century alchemy inherited certain numerological traditions from earlier
allegorical tracts—for instance, in the convention of visualizing and communicating their craft as
quantities of steps and ladder-rungs to climb.
24
At the same time, alchemists’ assumed sanctity of

21
Nummedal, “Alchemy and Religion in Christian Europe,” 321. See also Martha Baldwin,
“Alchemy and the Society of Jesus in the Seventeenth Century: Strange Bedfellows?,” Ambix 40,
no. 2 (1993): 41–64.
22
Representative of North German Rosicrucianism during Buxtehude’s lifetime
23
Hanegraaff, Esotericism and the Academy: Rejected Knowledge in Western Culture, 195.
24
This is often evident in treatise titles, for example Michael Maier’s Scala Arcis
Philosophicae. See Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in
the Work of Count Michael Maier (1569-1622), 98.
43
certain numbers
25
rendered music, as a “rational” art also able to move the “spirits,” uniquely
poised to bridge the numerical and spiritual-chemical realms. Such became music’s explicit
alchemical place in the textual tradition established by experimental physician Philippus
Aureolus Theophrastus Bombastus von Hohenheim (1493-1541), more commonly known as
“Paracelsus,” who pioneered alchemy as a primarily medicinal practice.
Because of his subversive and radical ideas, Paracelsus was sometimes called the “Luther
of medicine,”
26
but his ideas eventually earned attention and funding from some of Europe’s
most influential courts, including Holy Roman Emperor Rudolf II and the German Prince Moritz
von Hessen. The alchemists at Rudolf’s court in Prague were among the most influential of both
the sixteenth and seventeenth centuries, including Oswald Croll, Heinrich Khunrath, and Michael
Maier, who would later become not only the most outspoken German Rosicrucian apologist, but
the first to explicitly equate alchemical precepts with musical contrapuntal “transformations” of
canon and invertible counterpoint.
27
Prince Moritz of Hessen’s personal Paracelsian physician,
Johannes Daniel Mylius, published some of the most important Rosicrucian tracts of the 1620s
and also wrote and published lute music.
28
Thus, while Paracelsus himself never wrote anything

25
For instance, the number seven: the number of planets and metals.
26
Paracelsus rejected this idea, though, as in his Paragranum: “With what mockery have you
made me a caricature, calling me the Luther of physicians…I am Theophrastus and I am more
than he with whom you compare me. I am myself and I am the king of physicians (monarcha
medicorum).” See Alyke Zwaantina de Vries, “The General Reformation Divini et Humani: The
Rosicrucian Call for Change, Its Sources, and Early Impact” (PhD diss., Nijmegen, Netherlands,
Radboud University Nijmegen, 2020), 126.
27
Michael Maier, Atalanta Fugiens, hoc est, Emblemata nova de secretis naturae chymica,
accommodate partim oculis et intellectui, figuris cupro incises, adjectisque sententiis,
Epigrammatis et notis, partim auribus et recreationi animi plus minus 50 Fugis musicalibus
trium Vocum, quarum duae ad unum simplicem melodiam distichis canendis peraptam,
correspondeant, non absque, singulari jucunditate videnda, legenda, meditanda, intelligenda,
dijudicanda, canenda et audienda (Oppenheim: Johann Theodor de Bry, 1617).
28
Gouk, “Transforming Matter, Refining the Spirit,” 146. It makes sense that Paracelsian
views, of all alchemical subsects, would become intertwined with the Rosicrucian movement,
44
about music’s potential powers in the laboratory, one notices multiple appearances of musically
engaged, Paracelsian alchemists in Moritz’s court—including the prince himself, who practiced
alchemy and became an accomplished amateur composer.
29

In this discussion, Heinrich Khunrath’s (1560-1605) Amphitheatrum sapientiae aeternae
(Amphitheatre of Eternal Wisdom), first printed in 1595,
30
provides the single most important
piece of iconography, and one of the best-known images in Western Esotericism (Figure 2.1).
31

because Paracelsian medicine promised a specifically “intellectual balsam” for religious and
political unwell This became particularly enticing—and dire—in the decade of the Rosicrucian
manifestos, all written within five years before the start of the Thirty Years’ War in 1618.
29
Gouk, 148.
30
It was republished in 1609, four years after Khunrath’s death, and this second edition is
most often cited in modern scholarship.
31
Peter J. Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations
on Cabala, Music, and Alchemy,” ARIES - Journal for the Study of Western Esotericism 10, no.
2 (2010): 170, https://doi.org/10.1163/156798910X520584.
45

Figure 2.1. Heinrich Khunrath, ‘Lab-Oratorium,’ Amphitheatrum sapientiae aeternae (1609).

Highlighting musical imagery as its centerpiece, Khunrath’s engraving of the alchemist’s
workspace unites elements of Christian doctrine, numerical symbol, cabalistic influence,
Pythagoreanism, Paracelsian medicine, and Greek mythology with physical alchemy. Alchemical
publications over the following decades will also thread together Rosicrucian doctrine with
music, via known allusion to precisely this image and treatise. The engraving provides one of the
46
earliest visual depictions of an alchemist’s laboratory, a century after alchemists began using the
term “laboratory” to refer to their physical spaces for natural-philosophical discovery. In contrast
to our modern notions of the purpose and physical circumstances of chemical labs, Khunrath’s
takes the form more of a private meditation temple than anything else–an “inner sanctum.”
32
This
image is surprisingly dualistic (or tripartite, counting the central table), considering that
alchemical and Christian theological doctrine often thoroughly intertwine in textual descriptions:
here, the right side features chemical apparatus, suggesting scientific operations in the physical
realm, while the left side shows Khunrath (or a stand-in for general learned philosopher)
kneeling in prayer at an altar, representing work and transformation in the metaphysical realm.
The end goal: the alchemist’s soul’s unio mystica with God. Together, this laboratory-oratory
image represents the two possible paths to divine unification, which a true Christian
“Theosopher” (lover of Godly wisdom) merges through spiritual medicine. Thus, it invites the
viewer to ruminate on the boundaries (or lack thereof) between science and magic, by portraying
the laboratory and oratory as two distinct stations within the alchemist’s single space of
knowledge-seeking.
33

Central to Khunrath’s image, and in the foreground, sits a table of musical instruments,
exactly equidistant between the laboratory and oratory, through which Khunrath invites the
viewer to “enter” the scene.
34
Further, this central placement suggests a “third kind” of natural
magic, somewhere between the physical and metaphysical realms, which music mediates to

32
Gouk, “Transforming Matter, Refining the Spirit,” 147.
33
There is some debate about whom the pictured alchemist may represent (i.e., King David,
Pythagoras) in addition to Khunrath himself. See Gouk, 147–48.
34
Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations on
Cabala, Music, and Alchemy,” 172.
47
palpable effect on body and soul, all without visible cause.
35
This power-without-apparent-cause,
as a particular trademark of natural magic within seventeenth-century occult philosophy, music
takes one step further: its powers constitute a form of “mathematical magic,” in their powers to
turn rational proportion into harmonious sounds capable of moving the human and animal
spirits.
36
Of these three stations in Khunrath’s engraving, music acts as a harmonious, uniting
force between the oratory and laboratory. In one of Khunrath’s other works, Vom hylealischen
Chaos (1597), he even goes so far as to brand ‘utterly un-Philosophical’ those who deign to
‘separate Oratory and Laboratory from each other.”
37

This image and its oratory-laboratory imagery gained traction later in the century, as
evident in the work of Abraham von Franckenberg (1593-1652), first-generation student and
biographer of Jacob Böhme (1575-1624), the famous Rosicrucian mystic, Lutheran theologian,
and Hermetic theosopher. In his posthumous treatise Raphael oder Artzt-Engel (1676),
Franckenberg’s chapter handling “Kabalistic or Spiritual Medicine” includes a table (Figure 2.2)
intended to map correspondences between “Kabala,” “Magia,” and “Chymia.” Franckenberg
unites these arts with the single suffix “-orium” at the bottom, and we discover from prefixes
connected to each column above that each column refers to a specific location: “Kabala,”
“Magia,” and “Chymia” belong in the “Oratorium,” “Auditorium,” and “Laboratorium,”
respectively.
38
It is worth noting that in Franckenberg’s table, Mathematics mediates between

35
Gouk, “Transforming Matter, Refining the Spirit,” 149.
36
Gouk, 149.
37
Khunrath, Vom hylealischen Chaos, 252. Translated in Forshaw, “Oratorium–Auditorium–
Laboratorium,” 171.
38
Franckenberg, Raphael oder Artzt-Engel, 27. For further explanation see Forshaw,
“Oratorium–Auditorium–Laboratorium,” 169–70.
48
Theology and Physics, just as the musical realm (Auditorium) serves as meeting point between
the oratory and laboratory here and in Khunrath’s Amphitheatrum.
39

Figure 2.2. Abraham von Franckenberg, table from Raphael oder Artzt-Engel (1676) and
transcription.

Turning back to Khunrath’s engraving, observing Franckenberg’s table makes us look at
the musical elements in a new light, especially the instruments themselves. In constituting
Khunrath’s “Auditorium” as mediators of prayer and experiment and the metaphysical and
physical, they invite a wealth of interpretations. Modern scholars tend to agree that, as a
collection, they symbolize harmony between both the microcosm and macrocosm, and humanity
and the cosmos, in the sense of Paracelsian magic. The larger concept upon which this idea
rests—that the cosmos itself is an example of harmony, in ratio and balance, one traces as far

39
Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations on
Cabala, Music, and Alchemy,” 172.
49
back as Plato’s Timaeus, which famously echoes the Pythagorean notion of the heavens and
human soul as being held together by harmony itself.
40
This cosmic Harmonia is evidently
important to Khunrath, because he uses the term repeatedly to describe the microcosm and
macrocosm, Christ and the Stone, and crosswise relationships among them. He says, “Only one
experienced in both [oratory and laboratory] will comprehend the ‘analogical harmony’
(Harmonia analogica) between Christ, Son of the Microcosm, and the Philosophers’ Stone, Son
of the Macrocosm,”
41
and suggests that this harmonious relationship is central to both Christ and
the Stone’s ontologies (“if the one exists, so does the other,” and “Oh, wondrous Regenerative
harmony of the Macro and Microcosm”).
42

This language prefigures that of another Paracelsian physician and philosopher Robert
Fludd (1574-1637), whose images from his treatises on The History of the Macrocosm and
Microcosm (1617-1619) provide further depth to this discussion. One such image (Figure 2.3)
depicts the universe as the monochord of antiquity, divided into two octaves from Gamma-ut (G)
to gg, with each planet assigned its own tone, ascending higher and higher in pitch the farther
from Earth its orbit (here, Earth is both the musical fundamental and center of the universe).
43

40
Gouk, “Transforming Matter, Refining the Spirit,” 151.
41
Heinrich Khunrath, Amphitheatrum Sapientiae Aeternae Solius Verae: Christiano-
Kabalisticum, Divino-Magicum, Nec Non Physico-Chymicum, Tertriunum, Catholicon (Hanau:
Guilielmus Antonius, 1609), 97. See also Heinrich Khunrath, Magnesia Catholica
Philosophorum (Magdeburg: Johan Botcher, 1599), 30.
42
Khunrath, Amphitheatrum Sapientiae Aeternae, 54, 192, 197. See Forshaw, “Oratorium–
Auditorium–Laboratorium,” 172.
43
Gouk, “Transforming Matter, Refining the Spirit,” 151.
50

Figure 2.3. Robert Fludd, divine monochord and man as microcosm, Utriusque cosmi...historia
I and II (1619).

In a related image, Fludd shows a human as the microcosm, whose body has itself become a
monochord (note the musical string stretching along the length of his body), governed and
divided by the same musical proportions ruling the macrocosm. The string in this sense, while
meant to remind the reader of musical harmony in general, also represents the dynamic spiritus
that unites body and soul together, and these with the spiritus mundi (world soul), which threads
mortal existence with astrological influence, and the path along which the human soul emanates
from and returns to the divine, in the process attaining enlightenment.
44

44
Gouk, 153–54.
51
Thus, in Fludd one finds even more meanings behind Khunrath’s musical instruments, for
instance in the form of the spiritus mundi, through which all of the cosmos resonates. Probably
the most famous way of illustrating this kind of cosmic sympathetic resonance before the
seventeenth century was to put two in-tune lutes in proximity; when a string on one lute is struck,
the corresponding one on the other visibly and audibly resonates. Sixteenth-century Paracelsian
magi saw this invisible thread of sympathetic connection between distanced resonating bodies as
an example of “occult power in nature,” in which that sympathy is readily apparent, yet the
actual impetus remains “imperceptible to the unaided human senses.”
45
These plucked
instruments, then, can also symbolize the vibrating harmonies of heaven and earth, reminding the
beholder of the foundational Hermetic precept found on the Amphitheatrum’s title page: “that
which is BELOW is like that which is ABOVE; And that which is ABOVE is like that which is
BELOW.” At the same time, the presence of exactly four instruments likely alludes to a
harmonious union of the four elements, or the four bodily humors.
46

The two instruments closest to the Khunrath’s earthly “laboratory” are fretted—perhaps
representing the quantitative “measure, number, and weight” of Wisdom 11:21, and visually
echoed in the physical scales and weights located just behind these instruments in the image,
along with an open book with visible musical staves. This biblical phrase was popular among
both alchemists and cabalists, including Michael Maier, who in his Cantilenae intellectuales
(1622) would later write that, “by a certain number, weight and measure all celestial and
terrestrial bodies rejoice in as it were a real blending of musical harmony, as do spiritual

45
Gouk, 154.
46
Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations on
Cabala, Music, and Alchemy,” 173.
52
creatures…led by its melodies and symphonic intervals.”
47
These two fretted instruments, the
lute and cittern, were also especially popular among literate amateurs around 1600, and, as
mentioned earlier, Paracelsian physician Daniel Mylius published at least one collection of lute
music (1622), which confirms the idea of their placement more towards the “earthly” realm of
Khunrath’s scene.
48
Meanwhile, the harp and lyre (lyra da braccio) on the left—with ideological
ties to formidable figures like King David, Apollo, and Orpheus, all of whom famously used
music to superhuman spiritual effect—are relegated more to the oratory.
49

Lastly, the number of strings on each of Khunrath’s instruments might provide another
layer of numerological symbol. Both Forshaw and Gouk note in their readings of the engraving
that the instruments’ string complements do not correspond to their real-life norms, even
allowing for known regional variation: Khunrath’s harp has eight strings, his cittern and lute
each have five, and his lyre has four. These numbers directly spell the number of steps contained
in each perfect interval beyond the unison, as contained in the Pythagorean Tetraktys (octave - 8,
fifth - 5, and fourth - 4), which Pythagoreans believed to be the mathematical fabric of the
universe, in the ratios 1:2, 2:3, and 3:4.
50

Thus, in Khunrath’s Paracelsian practice, the musical instruments are not incidental; their
physical centrality in the scene symbolizes their ideological centrality to his seventeenth-century

47
Michael Maier, Cantilenae Intellectuales, in Triadas 9. Distinctae, de Phoenice Redivivo,
Hoc Est, Medicinarum Omnium Pretiosissima (Rostock: Mauritius Saxon, 1622). Translated in
Forshaw, “Oratorium–Auditorium–Laboratorium,” 173. Gouk agrees with virtually all of these
symbolic connections in her reading. See Gouk, “Transforming Matter, Refining the Spirit,” 154,
for a corroborative retelling drawing more from natural magic than from alchemy and cabala.
48
Gouk, “Transforming Matter, Refining the Spirit,” 154.
49
For an outline of the possible mythological connections made by earlier cabalists and
philosophers like Ficino and Agrippa, see Forshaw, “Oratorium–Auditorium–Laboratorium,”
175.
50
Gouk, “Transforming Matter, Refining the Spirit,” 155.
53
Christ-centered alchemy, as the ultimate mediators of prayer and practice. In this way,
Khunrath’s musical instruments serve yet another vital purpose, beyond their illustration of the
concept of Harmonia or of physical weights and measures as a faction of the alchemist’s
physical experience. Throughout the engraving, Khunrath points to music as spiritually
medicinal, specifically—yet another element of this scene that would become important to
Rosicrucianism within five years of its publication. Khunrath probably inherited this concept of
music-as-medicine from Renaissance Neoplatonist Marsilio Ficino (1433-1499), who asserted
music’s unique ability to heal the spiritus, which mediates the body (healed by medicine) and the
soul (healed by theology). According to Ficino, this occurs through music’s being of the same
“fine substance” as the spiritus, which itself also unites heaven and earth as an energetic channel
for astrological power—the same spiritus that according to Paracelsus also participates in
matter’s alchemical transformation.
51
Michael Maier, meanwhile, tells the story of the birth of
Harmonia, daughter of Venus (copper) and Mars (iron), in his Arcana arcanissima (1613).
52
In
Maier’s alchemical allegory, Harmonia is conceived in Vulcan’s steel net, and as the product of
copper and iron, she represents the alchemist’s “harmonically composed” philosophical
medicine.
53

Khunrath is clear about which spiritual musical medicine he condones: in order to
properly “chase away sadness and evil spirits,” according to the inscription on Khunrath’s
tablecloth, the best aural medicine is “Sacred music”—ideally the Psalms of David—because

51
Gouk, 149.
52
Michael Maier, Arcana Arcanissima, Hoc Est Hieroglyphica Aegyptio-Graeca (London,
1614).
53
Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations on
Cabala, Music, and Alchemy,” 180–81.
54
through them the “Spirit of Jehovah gladly sings in a heart filled with pious joy.”
54
The pile of
partbooks behind the musical instruments therefore alludes to polyphonic psalm-settings,
perhaps even one to Psalm 145, to which careful examination finds Khunrath’s psalter open
before the alchemist, shown kneeling in prayer at the oratory. This emphasis on Psalms is not
accidental: in other parts of the Amphitheatrum, Khunrath cites St. Paul’s advice to the Ephesians
(5:18) to be “filled with the Holy Spirit, speaking to yourselves in psalms and hymns and
Spiritual canticles, in your hearts to the LORD,”
55
among other examples of music’s spiritual
power, whether through allusions to the book of Psalms or to fellow Christian Cabalist Giovanni
Pico della Mirandola’s “hymns of Orpheus,” allegedly of unparalleled efficacy in “natural
magic.”
56

I would like to suggest that Khunrath’s apparent regard for Psalms above all other forms
of prayer specifically for their musical efficacy is significant. The Psalms, through which
Khunrath believed the Holy Spirit moved and allowed David to communicate with God, likewise
provided the magus a pathway to occult knowledge of the universe’s hidden forces. The Psalms
mediated the material and immaterial worlds with music, whose chemical likeness to the spiritus
contained the power to unify heaven and earth.
57

54
In Ficino’s Neoplatonic philosophy, music alleviates humoral imbalance, because
harmonious sounds reorganize the disordered spirits, restoring proper balance between body and
soul. See Gouk, “Transforming Matter, Refining the Spirit,” 149–51 for an explanation of this
concept’s multivalent relationship to melancholia.
55
Khunrath, Amphitheatrum Sapientiae Aeternae, 157.
56
Khunrath, 74. Some of these references may also relate to exorcism, as suggested by the
Agrippa-related phrase in the engraving, that one should “not speak of God without light” (Ne
loquaris de deo absque lvmine). See Forshaw, “Oratorium–Auditorium–Laboratorium,” 174 and
176.
57
Gouk, “Transforming Matter, Refining the Spirit,” 156.
55
Khunrath’s Amphitheatrum was his best-known work; if Johann Theile indeed knew
alchemical tracts of similar fame to Michael Maier’s Atalanta fugiens,
58
then he likely also knew
the Amphitheatrum. This would especially be true of confirmed alchemical aficionados such as
Johann Gottfried Walther (1684-1748)—J. S. Bach’s relative and Werckmeister’s friend and the
inheritor of manuscript editions of Buxtehude’s works and some personal letters—even into the
mid-eighteenth century.
59
As much as for any of these musicians, Khunrath’s belief that the
Psalms were the most powerful praise of God would have resonated with Buxtehude, a devout
Lutheran composer regularly in the musical service of God. He also would have been well versed
in the Psalms as a functional church musician, and half of his extant ostinato works are psalm
texts. The number of ostinato psalm settings might well have been higher, since many of his
works have been lost.
As I will note later in the chapters analyzing Buxtehude’s ostinato psalm settings, each of
the texts in question contains ideas of eternity and constancy that alone invite an ostinato
rendering to some extent. But with insight into Paracelsian ideas of the Psalms as especially
powerful vehicles for theosophical knowledge of Christ—and of music’s own power of
medicinal healing and divine unification—Buxtehude’s choice to set these psalm texts with
repeating bass-patterns grows conceptional dimension. With understanding of these texts’ (and
music’s) hidden powers of uniting the microcosm and macrocosm through sounding weights and
measures, number and proportion, Buxtehude lends these psalm settings a musical rhetoric of
eternity and perpetuity, as a symbolic underlayer as ardent in its praise as the literal text.

58
As David Yearsley has argued. See David Gaynor Yearsley, “Alchemy and Counterpoint
in an Age of Reason,” Journal of the American Musicological Society 51, no. 2 (1998): 220–22.
59
Yearsley, 217–18.
56

2.2 – Numbers and Geometry in Rosicrucian Allegory
The term “Rosicrucianism” is extraordinarily difficult to define. Faced with literature so rife with
deception, both intentional and not, a reader looking for “truth” eventually must concede that
fabrication itself is among the deepest essences of the Rosicrucian phenomenon.
60
Thus, when
discussing Rosicrucian sources and characters, it is important to distinguish between “waves” of
Rosicrucian influence through specificity about time and place, and to realize that for even the
most central doctrinal issues, multiple generations of Rosicrucian-related authors find multiple
ways of reaching the same result. Meaning, in discussing number symbols, different branches of
Rosicrucianism might believe in the sanctity of the same numbers, but those numbers’ exact
meanings might differ from text to text, thereby converging on that same larger conclusion from
different directions—usually Pythagorean, Christian, cabalist, or alchemical. Buxtehude’s most
often-used numbers appear in the original Rosicrucian manifestos with implied symbolic import.
While these numbers are also biblically significant, concordances between elements of
Rosicrucian documents and Buxtehude’s chosen texts in which the same numbers feature
prominently suggest that there are more ideological threads present than just Lutheran theology.
It is the preponderance of circumstantial and textual evidence that suggests he would have been
aware of these symbols as specifically Rosicrucian, rather than simply a product of any one
disparate influence on its own.
The founding documents of the “original” Rosicrucian movement, all three anonymous
and of variously disputed origins, claim a more fantastical genesis story for Rosicrucianism than

60
Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of
Count Michael Maier (1569-1622), 116.
57
could possibly be true. According the Fama Fraternitatis (1614), the movement’s founder,
Christian Rosenkreutz (b. 1378), traveled to the East to obtain divine knowledge to bring back to
Germany, and after establishing the Rosicrucian Brotherhood in the early fifteenth century based
on that knowledge, lived to age 106 and predicted the discovery of his perfectly intact body in
his secret tomb of eternal wisdom, precisely 120 years later.
61
These founding documents, now
typically called the “Rosicrucian manifestos,” were distributed in the form of three anonymous
pamphlets printed in Kassel in the second decade of the seventeenth century, effectively on the
eve of the Thirty Years’ War (1618-1648): the Fama Fraternitatis (Fame, or Infamy, of the
Fraternity, 1614), the Confessio Fraternitatis (Confession of the Fraternity, 1615), and the
Chymische Hochzeit: Christiani Rosencreutz (Chemical Wedding of Christian Rosencreutz,
1616). The provocative pamphlets called for large-scale religious, scientific, and political reform
and heralded the imminent coming of a new era, in which a Paracelsian-inspired Hermeticism
and humanist Lutheranism would intellectually and spiritually redeem society from the shackles
of “papism.”
62
Despite using such inflammatory anti-Catholic words—and then going so far as to
proclaim the Pope to be the Antichrist in the opening of the Confessio Fraternitatis
63
—the
anonymous authors do not object to Catholicism.
64
Indeed, the characters at the epicenter of the
Rosicrucian pamphlets and their most famous first-wave responses were from vastly different

61
[Anonymous], “Fama Fraternitatis, 1614,” in Rosicrucian Trilogy: The Three Original
Rosicrucian Publications in New Modern Translation, trans. Christopher McIntosh and Donate
Pahnke McIntosh (Newburyport, Massachussetts: Weiser Books, 2016), 25.
62
Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of
Count Michael Maier (1569-1622), 118.
63
[Anonymous], “Confessio Fraternitatis, 1615,” in Rosicrucian Trilogy: The Three Original
Rosicrucian Publications in New Modern Translation, trans. Joscelyn Godwin (Newburyport,
Massachussetts: Weiser Books, 2016), 41.
64
Many modern scholars describe the movement’s Christian orientation as “supra-
confessional.” See Hereward Tilton, “The Rosicrucian Manifestos and Early Rosicrucianism,” in
The Occult World, ed. Christopher Partridge (New York, New York: Routledge, 2015), 129–30.
58
Christian backgrounds: Johann Valentin Andreae (who wanted the Lutheran-reformed Duke
August II to lead his utopian Christian society) and Tobias Hess were both from Lutheran
Tübingen, while the manifestos themselves printed in Calvinist Kassel. Dr. Adam Haslmayr (ca.
1562-1631), an early respondent to a pre-publication manuscript edition of the Fama,
65
was a
Catholic, but asked the Calvinist Prince August von Anhalt to lead his branch of the Rosicrucian
movement. Though on opposing sides, the Paracelsian physicians and alchemists Michael Maier
and critic Andreas Libavius were both Lutherans, and Christoph Besold a latent Catholic
convert, while another famous sparring pair, Robert Fludd and Marin Mersenne, were Anglican
and Catholic, respectively.
66

Across such diverse confessional backgrounds, the manifestos’ authors announce their
belief in strengthening similarities rather than differences between Christian sects and direct any
inflammatory Pope-Antichrist rhetoric not toward Catholicism, but rather toward the dogma of
thoughtless subordination to intermediary authorities between man and God. In the manifestos,
what they have to say “…will of course be of little use to the unthinking world,” full of those
who “cling to the old teachings, esteeming the Pope, Aristotle, and Galen—indeed everything
that has the appearance of a codex—more than the clear and manifest light.”
67
Predictably, these
views created friction with orthodoxy across denominations, and the alleged persecution the
original Rosicrucian brethren faced at the hands of the Jesuits comprised just one reason why the

65
The pre-publication and publication history of these texts is so convoluted (probably
intentionally so, to heighten their mystery and further conceal their origin) that Haslmayr’s
Answer was printed in 1612, two years before the text to which it responds. See de Vries, “The
General Reformation Divini et Humani: The Rosicrucian Call for Change, Its Sources, and Early
Impact,” 2.
66
de Vries, 366–67.
67
[Anonymous], “Fama Fraternitatis,” 16.
59
authors remained anonymous.
68
Putting their utopian agenda above risk of secrecy-pledge
violations, the authors of the Fama Fraternitatis summarize their ecumenical Christian aim,
demanding deep thought and anticipation of the coming new age, in these opening sentences:

We the Brethren of the Fraternity of the R.C. extend our greetings, love, and
prayers to all who read this our Fama in a Christian spirit.
God, the all-wise and all-merciful, having in recent times so abundantly
poured out his mercy and goodness to humankind that knowledge of his Son and
of nature is becoming more and more widespread and we can justly rejoice in a
forthcoming happy time, He has not only revealed half of the unknown and
hidden world and laid before us many wondrous and hitherto never experienced
works and creations of nature, but has also caused certain highly illuminated
minds to come forth, who might partially renew the arts, which have become
debased and imperfect, so that finally Man might understand his true nobility and
splendor, in what sense he is a microcosm, and how far his art extends into
nature.
69

This utopic “mega-vision”
70
for a Christian society founded on natural-philosophical wisdom
rather than blind “papism,” backed by convincing millenarist apocalyptic visions, immediately
captured the central-European imagination. Acting as “mission statements” for divine and earthly
reform, yet carefully devoid of precise details of how that transformation would occur, the texts
carried universal appeal through their openness to interpretation by anyone and everyone feeling
disheartened about the state of society and their local political and religious leadership.
71
In
response, hundreds of people flooded the scene with texts defending the Rosicrucian cause
against criticism, some going so far as to claim to be Rosicrucian prophets, or most commonly

68
This Jesuit “persecution” was actually true in the case of Dr. Adam Haslmayr, whom the
Jesuits imprisoned despite his being Catholic. See Joscelyn Godwin, “Introduction to the
Confessio Fraternitatis,” in Rosicrucian Trilogy: The Three Original Rosicrucian Publications
in New Modern Translation (Newburyport, Massachussetts: Weiser Books, 2016), 35–40.
69
[Anonymous], “Fama Fraternitatis,” 16.
70
de Vries, “The General Reformation Divini et Humani: The Rosicrucian Call for Change,
Its Sources, and Early Impact,” 377.
71
de Vries, 209.
60
begging the authors of the original pamphlets to reveal themselves, to officially induct
sympathizers into the brotherhood so that it may organize and realize the group’s vision.
Considering the over 400 written responses within a decade of the publication of the Fama,
scholars now aptly refer to this early explosion of Rosicrucian interest as the “Rosicrucian
furore.”
72

Much of the modern scholarship on the Rosicrucian movement focuses on authorship and
chronology questions surrounding the founding documents.
73
While these issues remain largely
peripheral to the present study, a few important points inform a mathematical-theological gaze.
For one, scholars generally agree that Lutheran mathematician and theologian Johann Valentin
Andreae (1586-1654) had a hand in all three of the manifestos, with The Chemical Wedding
possibly being entirely of his design.
74
The Fama Fraternitatis and the Confessio Fraternitatis,
however, certainly had more authors—likely at least Andreae’s close friends and teachers, the
lawyer Tobias Hess (1586-1614) and jurist Christoph Besold (1577-1638).
75
What little
biographical information Hess left us includes evidence of “deep study of sacred numbers, of
Kabbalah and biblical numerology.”
76
His well-known interest in number symbolism and
millenarist calculations. In these he found strongest inspiration in the mathematical prophesies of

72
de Vries, 209.
73
For an excellent overview of this mass of scholarship, see de Vries, 14–20.
74
This is an extraordinarily complex issue. See de Vries, 165–73. For the sake of simplicity,
and to allow for inconsistencies in printed record and the possibility of further authors, I will still
refer to “authors” (plural) for The Chemical Wedding, as I do for the Fama and the Confessio.
Even if The Chemical Wedding’s authorship is somewhat less disputed, we cannot ascertain
Andreae’s collaboration or lack thereof. Andreae also eventually distanced himself from the
Rosicrucian furore, to protect himself from the “screaming and fanatical mob” that he had
participated in creating. He never gave up on Christian utopian dreams for large-scale reform,
but instead channeled his ideas into (not anonymous) fictional publications. See de Vries, 202–3.
75
Godwin, “Introduction to the Confessio Fraternitatis,” 36.
76
Tobias Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious
Secret Society (Rochester, Vermont: Inner Traditions, 2009), 68.
61
Simon Studion (1543-1605?), who predicted Christ’s Second Coming as set to occur in 1623 and
wrote of similar Christian reform ideas to Hess’s in his Naometria (completed 1604).
77

While the Rosicrucian origin story is probably largely allegorical, the manifestos’ arrival
in the German political and intellectual scene both resulted from and later affected real events.
By 1600, central Europe had built up a volatile “atmosphere of prophetic expectation,”
78
in
which the populace was primed for earthly reform foretold either by celestial events, scriptural
calculations, or a combination of them. This climate can only have increased the manifestos’
power, as Christian allegory interwoven with actual, observable astronomical occurrences, when
many contemporary astronomers believed “new stars” and conjunctions to signal beginnings of
new eras. The signs of “Serpentarius and Cygnus” that the authors of the Confessio Fraternitatis
mention were actual celestial events, the first being a bright star in the constellation of Cygnus
(visible from 1600 and named “P Cygni”).
79
Then in December 1603, Johannes Kepler (1571-
1630) observed a close conjunction of Saturn and Jupiter in Pisces—so close that it involved
only one degree of angular separation between planets, a distance equivalent to just twice the
diameter of the sun, to the observing eye.
80
When three conjunctions occur in one year, it is

77
Simon Studion, “Naometria” ([Württemberg], 1604), MS. Cod. Theol. et phil. qt. 23a-b,
Stuttgart, Württembergische Landesbibliothek, http://digital.wlb-stuttgart.de/purl/bsz411974165.
This work was never published, but it circulated widely in manuscript form. It also includes
sheet music for an allegorical ceremonial fanfare at the end, set to music by Studion’s colleague
Johannes Brauhart. For more on Hess’s interest in Sudion, see de Vries, “The General
Reformation Divini et Humani: The Rosicrucian Call for Change, Its Sources, and Early Impact,”
39.
78
Christopher McIntosh, “Introduction to the Fama Fraternitatis,” in Rosicrucian Trilogy:
The Three Original Rosicrucian Publications in New Modern Translation (Newburyport,
Massachussetts: Weiser Books, 2016), 6.
79
de Vries, “The General Reformation Divini et Humani: The Rosicrucian Call for Change,
Its Sources, and Early Impact,” 62.
80
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 22.
62
called a “triple conjunction,” and surviving evidence suggests that one occurred specifically
between Saturn and Jupiter in Pisces, between May and December of the year 7 BCE—then
thought to historically coincide with Christ’s birth. Kepler cross-checked his findings with the
records of Jewish astronomer Rabbi Isaac Abarbanel, author of The Wells of Salvation (1497), a
well-known commentary on the book of Daniel. Abarbanel calculated that conjunctions of
Saturn and Jupiter occur every twenty years, but that the closeness of the conjunction, and its
occurrence in Pisces specifically, made it a mahberet ‘asumah, a “mighty conjunction,” which
signifies the birth of great prophets, miracle workers, and possibly the Messiah.
81
Remarkably, a
few months later Mars joined the conjunction, which reached its highest intensity in September
1604, in Sagittarius, which Kepler calculated had similarly occurred not only at Christ’s birth
around 7 BCE, but also at six other “epoch-marking” events, including those related to Adam in
4032 BCE, Enoch in 3227 BCE, the Great Flood in 2422 BCE, Moses in 1617 BCE, Isaiah in
812 BCE, and Charlemagne in 799 CE. After this, in October 1604, a supernova exploded as
Saturn and Jupiter neared conjunction in Sagittarius; it remained visible for almost a year in the
constellation of Serpens, the snake—the “Serpentarius” mentioned in the Confessio.
82
This also
completed the “fiery trigon” (or “triangle”) mentioned in the Fama Fraternitatis (“the fiery
triangle, whose flames will now shine more brightly and give the final illumination to the
world”):
83
the Sabian astronomer Abu Ma’shar al-Balki (b. 787 CE) divided the twelve signs of
the zodiac into four “trigons,” each related to one of the four elements, and these most recent
celestial events had occurred in the fire-related trigon of Ares, Leo, and Sagittarius.
84
By Abu

81
Churton, 23.
82
Churton, 24.
83
[Anonymous], “Fama Fraternitatis,” 20.
84
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 25.
63
Ma’shar’s calculations, including those taken from his Latin-translated Introductorium Minus,
the most widely used astronomy textbook in late-Medieval European universities, these Great
Conjunctions occurred every twenty years in their zodiac-cycle of twelve. After 12 x 20 (240)
years in one trigon, the conjunctions then take place in the next trigon, so after 4 x 240 (960)
years, the cycle of conjunctions thus completes and begins anew. But Abu Ma’shar thought that
only the conjunctions of Jupiter and Saturn predict times of great change on earth.
85

The 1604 supernova excited other famous astronomers, including Helisaeus Roeslin
(1545-1616) and Galileo Galilei (1564-1642). Although Kepler in his treatise On the New Star
(1606) ultimately claimed that the 1604 supernova’s appearance at that particular moment
indicated nothing special beyond “blind chance,” Kepler’s colleague David Fabricius (1564-
1617), like many others, believed it to “signify peace as well as a change of the [Holy Roman]
Empire for the better.”
86
For anyone who followed Abu Ma’shar and Rabbi Isaac Abarbanel, this
new series of fiery-trigon conjunctions marked the beginning of a new period of change; for the
Rosicrucians, these events unquestionably constituted the “final illumination” prophesied to start
the earth’s “final period,” as predicted in Revelation.
87
This was widespread and ardent enough a
Protestant political belief as well—specifically in the “expectation of a great leader” who would
swiftly “usher in a new age”—that they effected real political change:
88
enough people placed
this kind of “millenarian” hope onto Elector Frederick V of the Palatinate,
89
that their

85
de Vries, “The General Reformation Divini et Humani: The Rosicrucian Call for Change,
Its Sources, and Early Impact,” 65.
86
de Vries, 62.
87
de Vries, 65.
88
McIntosh, “Introduction to the Fama Fraternitatis,” 7.
89
Married to Elizabeth, daughter of James I of England.
64
enthusiastic influence likely factored into his “rash decision to accept the Bohemian crown,”
fiercely believing that “the millennium was at hand.”
90

These astronomical and millenarian underpinnings reveal that number and mathematics
provide keys for understanding the Rosicrucian manifestos’ history- and astronomy-engaged
code. 1604, the year of the great supernova, features prominently in the Rosicrucian origin story
provided in the Fama, but it requires a short calculation: if Christian Rosenkreutz was born in
1378 and allegedly lived to be 106, then his tomb was constructed in the year of his supposed
death, 1484. This would date the tomb’s prophesied discovery, exactly 120 years later, in 1604.
Like the 1604 astronomical occurrences, the dates 1378 and 1484 refer to real events: for a
society championing their vision of Christian reform within an already post-Reformation
Christianity, the year 1378 conspicuously symbolizes the Papal Schism, a time of Christian
brokenness necessitating a new redeemer. 1484, then, symbolizes both the birth of Martin
Luther, a first redeemer whose unfinished work or missteps the ecumenical Rosicrucian “Golden
Age” would finally realize,
91
but also the beginning of what Tobias Hess, borrowing from
Brocardo, called the 120-year “period of repentance.”
92
And lastly, it is also through number that
the authors most directly signal their work’s fictional nature: Paracelsus was not born until 1493,
so if Rosenkreutz’s tomb was sealed in 1484, it could not possibly have believably contained the
works by “Theophrastus” that the authors mention finding within (“Each side [of the vault] had a

90
Frances A. Yates, The Rosicrucian Enlightenment (London: Routledge & Kegan Paul,
1972), 35.
91
de Vries, “The General Reformation Divini et Humani: The Rosicrucian Call for Change,
Its Sources, and Early Impact,” 34.This date is sometimes given for Luther’s birth, as his first
full year of life after being born in November 1483.
92
de Vries, 173–74.
65
door to a chest containing various things, especially all our books…including the Vocabulary of
Theophrastus Bombastus of Hohenheim…”).
93

While no unified “Rosicrucian numerology” exists, it is through the aforementioned
numerical clues that the manifestos invite numerical interpretation. Later in the seventeenth
century, Jacob Böhme’s followers incorporated earlier traditions of alchemical and cabalistic
numerology into a Rosicrucian-inspired framework, resulting in extant “Rosicrucian” manuscript
sources combining “original” Rosicrucian doctrine with “wonder-number” exegesis on the
sanctity of certain numbers, many of which correspond to numbers Buxtehude uses to structure
his compositions.
94
Throughout the manifestos, the authors write on different symbolic levels for
different audiences. From the abundance of numerical detail (i.e., dates, numbers of years
between events, ages, lists of numbered axiomata, etc.), they must assume at least one such level
to be numerically engaged.
Numbers permeate all three founding Rosicrucian documents; if there isn’t actually some
kind of numerical cipher to decode, the authors want the reader to think that there is, which
constitutes a kind of numerological play unto itself. To complement the astronomical
geometrical shape already mentioned (the “trigon” providing the world’s “final light,”)
95
they
express their concept of the Christianized ancient wisdom that provides the backbone for their
utopic vision similarly geometrically. In one of the now most-famous sentences of all three

93
[Anonymous], “Fama Fraternitatis,” 27.
94
For example: Anonymous, Einfältig ABC-Büchlein der Rosenkreuzer, Manuscript, from
Staats- und Universitätsbibliothek Hamburg, codex in scrinio 21, paper,
http://digitalisate.sub.uni-
hamburg.de/nc/detail.html?id=1901&tx_dlf%5Bid%5D=15792&tx_dlf%5Bpage%5D=2
(accessed July 30, 2019). See chapter 4 for a comparison of this text with a textual anomaly in
Herr, wenn ich nur Dich hab’ (BuxWV 38).
95
[Anonymous], “Fama Fraternitatis,” 20.
66
manifestos, the authors describe their “pansophist dream of encapsulating the whole of human
knowledge within one overarching schema”
96
in geometrical terms:

Thus it should not be said: “This is true according to philosophy but false
according to theology,” for everything which Plato, Aristotle, Pythagoras, and
other recognized as true, and which was decisive for Enoch, Abraham, Moses,
and Solomon and which above all is consistent with that wonderful book the
Bible, comes together, forming a sphere or ball in which all the parts are
equidistant from the center.
97

This geometrical language describing perfection as a sphere or globe draws loosely from
the theological-geometrical of Nicolas Cusanus (1401-1464),
98
while acutely reminding
one of the sixteenth-century works of French poet Guillaume de Salluste Du Bartas,
whose works Andreae was known to have studied, “as directed by Christoph Besold.”
99

Du Bartas’s Devine Weekes and Workes appeared in English in 1608, translated by the
Jacobean poet Joshua Sylvester, and contains the following geometrical description:

See here the Solids: Cubes, Cylinders, Cones,
Pyramids, Prisms, Dodecahedrons:
And there the Sphere, which (World’s Type)
comprehends
Itself in itself; having neither midst nor ends…
100

96
Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work of
Count Michael Maier (1569-1622), 119.
97
[Anonymous], “Fama Fraternitatis,” 30. Emphasis mine.
98
For example, his De Geometricis Transmutationibus (1445). This imagery factors heavily
into my analysis of Herr, wenn ich nur Dich hab’ (BuxWV 38) relative to “Squaring the Circle.”
See chapter 4.
99
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 133–34.
100
Reproduced here from Churton, 133.
67
Beyond geometrical allusion, most of the mentions of specific numbers in the
Fama involve the Brotherhood’s founder, Christian Rosenkreutz, for whom the numerical
references provide covert characterization. This mostly manifests in Rosenkreutz’s
numerically specific life chronology, in numbers of years between events. For example,
he is five years old when his impoverished parents place him in a monastery to ensure his
education in Greek and Latin,
101
then much later in life, exactly five years pass before he
attempts societal reform.
102
At age sixteen, he travels to Damcar, but only exactly one
year later, when he is seventeen, does he know enough Arabic to “translate into good
Latin the Book M.,”
103
from which he “took his physics and mathematics.”
104
Then, he
founded the Brotherhood with exactly “three of his brethren” from his first monastery,
thereby yielding a fraternity “initially with four persons only.” When they decided to
expand, “in all they were eight in number.”
105
At this point, the eight brethren agreed on
“six articles,” the last of which stipulates that “The Brotherhood should remain
undisclosed for one hundred years.” After agreeing on the six articles, five of the brothers
left, leaving three brothers (including CR), so that “for all the days of his life he always
had two brethren with him.”
106

101
[Anonymous], “Fama Fraternitatis,” 17.
102
[Anonymous], “Fama Fraternitatis,” 20.
103
This probably refers to the Liber mundi, the “book of the world” or the Book of Nature,
which Paracelsus and his followers frequently mention. In the Rosicrucian story, the authors
mention this book relative to both Paracelsus and Christian Rosenkreutz, as a way of “co-
opt[ing] Paracelsus as a forerunner of Rosencreutz and the Rosicrucian cause.” See de Vries,
“The General Reformation Divini et Humani: The Rosicrucian Call for Change, Its Sources, and
Early Impact,” 136.
104
[Anonymous], “Fama Fraternitatis,” 17.
105
[Anonymous], “Fama Fraternitatis,” 21.
106
[Anonymous], “Fama Fraternitatis,” 22.
68
The authors’ description of Rosenkreutz’s tomb contains more number-mentions, both
geometric and arithmetic. They describe the entrance to the tomb as a “vault of seven sides and
corners, each side being five feet wide and eight feet high,” while a bright light in the exact
“center of the ceiling” illuminated the “small round [brass] altar.”
107
It was inscribed, “Jesus all
things to me” (in Latin), with “four figures, enclosed in a circle,” circumscribed [in Latin]:

1. A void exists nowhere.
2. The yoke of the law.
3. The Liberty of the Gospel.
4. God’s glory is inviolable.
108

Next, they describe the vault as having “seven sides” and “twice seven triangles,” while the
whole structure was of “three parts”: “the ceiling or heaven,” itself further “divided into
triangles, running from the bright center toward the seven sides,” then the seven walls, and the
ground. Each side was “divided into ten quadrilateral sections,” and the floor was “also divided
into triangles.”
109

But perhaps most symbolic of all is the engraving on the vault’s door, with the prophecy:
“AFTER 120 YEARS I SHALL OPEN.”
110
The authors reiterate this number multiple times,
including at the end of the eulogy they find Rosenkreutz’s corpse holding: “...he created a
miniature world, corresponding in all motions to the greater one…he was hidden here by his own
kind for 120 years.”
111
The number 120 provides a case study in the biblical and astronomical
numerology in which initiated seventeenth-century readers would have found meaning. One

107
[Anonymous], “Fama Fraternitatis,” 25–26.
108
[Anonymous], “Fama Fraternitatis,” 26.
109
[Anonymous], “Fama Fraternitatis,” 26–27.
110
[Anonymous], “Fama Fraternitatis,” 25.
111
[Anonymous], “Fama Fraternitatis,” 28.
69
meaning comes from Genesis: “Then the LORD said, “My Spirit shall not abide in

man
forever, for he is flesh: his days shall be 120 years,”
112
and the 1607 Geneva English Bible
contains commentary that 120 years was also the amount of time God gave humankind to repent,
before God would destroy the earth, further citing Peter 3:20, which refers to the Deluge from
which Noah was saved.
113
The number 120 was also featured in Giacomo Brocardo’s Mystica et
prophetica libri Geneseos interpretatio (The mystical and prophetical interpretation of the book
of Genesis),
114
with which another suspected author of the manifestos, Tobias Hess, knew.
115

Brocardo also believed the date of Luther’s birth (November 1483) to mark the start of the “last
age,” which would last 120 years, based on Abu Ma’shar’s prediction that the coming
conjunction of Saturn, Jupiter, and Mars in the constellation of Scorpio in 1484 would see the
birth of a prophet who would “supersede the prophet of Islam”
116
These 120-year prophecies thus
popularly anticipated late 1603, when Kepler observed the conjunction of Saturn and Jupiter that
became a triple conjunction in 1604, punctuated by the famous supernova in Serpentarius in the
October of that year. Information in the later Confessio Fraternitatis confirms this kind of
allegorical reading: the authors give the year of Rosenkreutz’s birth as 1378 (the Great Schism of
the Catholic Church) and his life length as 106 years—meaning, he would die in 1484, the
beginning of Luther’s life and Brocardo and Abu Ma’shar’s prophesied beginning of the new
age, exactly 120 years before the 1604 supernova and alleged discovery of Rosenkreutz’s tomb

112
Gen. 6:3 (ESV)
113
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 125.
114
Jacopo Brocardo, Mystica et Prophetica Libri Geneseos Interpretatio (Bremen: Theodor
Gluichstein, 1585).
115
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 125.
116
Churton, 125–26.
70
and “compendium of the universe.”
117
And finally, the authors’ emphasis on 120 further recalls
calculation tables in Simon Studion’s infamous Naometria (itself completed in 1604, mentioned
earlier), whose last plate includes a “wheel of the heavens” (Figure 2.4) intended to track
comets.
118

Figure 2.4. Simon Studion, “wheel of the heavens” from Naometria (1604).

117
Churton, 126–27.
118
Studion, “Naometria,” 1790. (Fold-out chart between pp.1790 and 1791 of Part II.)
71
This wheel, comprised of seven candelabra (representing the seven angelic ages), seven swords,
and two pyramids, Adam McClean calculated to have forty nodes in sixteen levels, with each
level intended to measure an interval of 120 years.
119

Throughout the Fama, the authors also repeatedly intimate math’s moral preeminence, in
contexts that suggest they believe math and numbers to hold truth and divine wisdom. One of the
few things they tell the reader about Christian Rosenkreutz’s intellectual activities beyond
alchemy (“he could have boasted of his art, especially that of the transmutation of metals”), is
that he “spent a considerable time preoccupied with mathematics and…constructed many fine
instruments from all branches of this art.”
120
More explicitly, they earlier describe the “truth” of
“theology, physics, and mathematics” as working against the “old enemy” of “cunning and
malevolence,”
121
and soon after, that Christian Rosenkreutz’s study of “mathematics [from the
Book of the World]...ought to have been joyfully received by the world,” though the people were
not ready to receive his wisdom with “love,” without “resentment.”
122
And finally, the signed
eulogy allegedly found Rosenkreutz’s immaculate corpse holding in its tomb, lists the initials of
several “circles” of brothers. Among these, only three have listed professions, other than Brother
R.C. junior, inheritor of [the House] of the Holy Spirit:
123
Painter/Master-Builder (Brother

119
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 126. The plate also includes the seven planets, seven churches, twelve tribes of Israel,
twelve disciples, and the twelve precious stones and two cornerstones on which will be founded
the New Jerusalem (Rev. 21:24). Unfortunately, McClean’s explanatory text is not currently
available, but Tobias Churton explains McClean’s findings.
120
[Anonymous], “Fama Fraternitatis,” 20.
121
[Anonymous], “Fama Fraternitatis,” 16.
122
[Anonymous], 17.
123
Later in the seventeenth century, Jacob Böhme’s followers often refer to the “School” or
“College” of the “Holy Spirit,” specifically in texts claiming to be Rosicrucian, but originating
from a different lineage than these founding documents. See Rafael T. Prinke, “Lampado Trado:
From the Fama Fraternitatis to the Golden Dawn,” The Hermetic Journal 30 (1985): 5–14.
72
B.M.P.A.), Kabbalist (Brother G.G.M.P.I.), and Mathematician (Brother P.A.), who is listed first
in the “second circle” of names.
124

Three other number-related mentions in the Fama, perhaps significantly all in moments
of superlative praise, the authors allude specifically to harmony or music. First, in their recount
of Christian Rosenkreutz’s learned travels in Fez, the authors describe the foundations for his
schooling in “magia” and “Kabbalah” as being in “exact harmony with the whole world.”
125
Just
following this comes an artful description of appreciation for the “unity,” in whom the entire
macrocosm and microcosm is contained, all ruled by musical harmony:

Thence arises the recognition of the beautiful unity whereby, just as every seed
contains the whole tree and its fruit, so likewise the whole world is contained in
miniature in every human being, with his religion, politics, health, bodily parts,
natural traits, speech, words and works—all of which partake of the same tune
and melody as God, heaven, and earth.
126

Later, in discussing Paracelsus (“Theophrastus”) and painting a picture of him as too great a sage
for his contemporaries to recognize, the authors laud his “profoundly present…harmonia of
thought,” which he would have “communicated…to the learned,” had they been “worthy of the
higher art.”
127
And finally, in their description of Rosenkreutz’s tomb, full of “mirrors,” they cite
among the treasures “little bells” and “certain marvelously artistic songs.”
128

The previous examples come only from the first manifesto; the second and third
manifestos, one numerological step beyond this, are textually organized around numerical
principles. In the Confessio, the authors tell us this outright after foreshadowing it in the Fama,

124
[Anonymous], “Fama Fraternitatis,” 28.
125
[Anonymous], “Fama Fraternitatis,” 18.
126
[Anonymous], “Fama Fraternitatis,” 18.
127
[Anonymous], “Fama Fraternitatis,” 20.
128
[Anonymous], “Fama Fraternitatis,” 27.
73
explicitly using its design of thirty-seven statements as its most basic descriptor (“our Confessio,
in which we set out thirty-seven reasons why we now reveal our Brotherhood…”).
129
In The
Chemical Wedding, the authors make it structurally apparent on different levels, with the most
obvious being repeated “sevenfold” items in the plot. The Confessio, which includes many
phrases taken directly from Studion-inspired Tobias Hess’s work, provides a foil to the
fantastical Fama’s “tall tales” with straightforward Rosicrucian doctrine.
130
In the Fama, the
authors also refer to the Confessio three times, and tell the reader that they have done so (“Here
for the third time we refer to our Confessio, for what we reveal here is for the benefit of those
who are worthy”).
131
The authors also state the Confessio’s numerical structure, both in the Fama
and again in the introduction, in which they advertise thirty-seven “rationes” (reasons) for
bringing their message to the world, spread over fourteen chapters. This numerical structure is
hidden, though, as the thirty-seven reasons are “interspersed” with the rest of the prose, rather
than formatted into a discrete list.
132

The Confessio’s intentional misalignment between chapter number and “reason” number
therefore creates a numerical puzzle in the Latin text, whose solution lies in the punctuation.
After the authors’ introduction, exactly thirty-three sentences end with a period (rather than a
comma, colon, semicolon, etc.) over the course of the fourteen chapters; these, along with four
statements ending in question marks, make thirty-seven.
133
For a mathematically engaged
audience, the authors hint that this reading is correct: following this scheme, the thirty-seventh

129
[Anonymous], “Fama Fraternitatis,” 23.
130
Godwin, “Introduction to the Confessio Fraternitatis,” 36.
131
[Anonymous], “Fama Fraternitatis,” 25.
132
[Anonymous], “Confessio Fraternitatis,” 42.
133
For all of the rationes in numbered-list form, see Godwin, “Introduction to the Confessio
Fraternitatis,” 37.
74
“reason” is also the opening sentence of the final (fourteenth) chapter, suggesting intentional
alignment. Beyond this, the Fama primes the reader to look for the statements that this process
yields, based on the “four figures, enclosed in a circle,” in Rosenkreutz’s tomb (“A void exists
nowhere. The yoke of the law. The Liberty of the Gospel. God’s glory is inviolable.”)
134
Like the
thirty-seven statements ending in periods or question marks in the Confessio, these Latin phrases
are short combinations of both subject-verb sentence fragments or even shorter, possessive
descriptors.
Like the Confessio Fraternitatis, The Chemical Wedding of Christian Rosenkreutz (1616)
contains an underlying numerical structure. As alchemical scholar and archivist Adam McClean
observes, even a “mere cursory reading” detects the work’s sevenfold “symbolic architecture.”
135

A quick glance at any page indeed finds what appears to be as many allusions to the number
seven as possible, perhaps to signal a deeper numerological underpinning below the surface.
There are so many instances of sevens in the story, in fact, that to recount them all would
essentially involve reproducing the entire thing. In addition to the seven-day arc of the narrative,
just a few examples include things such as the escape rope falling to an imprisoned Christian
Rosenkreutz exactly seven times; on the Sixth Day, Rosenkreutz and his companions ascend
seven floors of the Tower of Olympus, guided by seven ships, accompanied by a Sirens’ song of
seven verses; the “Weighing Ceremony” on the Third Day employs seven weights; the short
comedy at the exact center of the story (the middle of the Fourth Day) contains seven acts; and
the Altar in the Fourth day is likewise sevenfold in its inclusion of “six ritual objects,” with the

134
[Anonymous], “Fama Fraternitatis,” 26.
135
Adam McClean, “Introduction and Commentary,” in The Chemical Wedding of Christian
Rosenkreutz, trans. Joscelyn Godwin, Magnum Opus Hermetic Sourceworks 18 (Boston: Phanes
Press, 1991), 113.
75
altar itself serving as the first or seventh.
136
Each of the story’s seven days also contains a further
sevenfold structure, in the form of seven separate events, which the reader encounters and can
divide as such easily, “without any artificiality.”
137

These sevenfold items permeating the story of The Chemical Wedding alert the reader to
yet more just under the surface—most of which only require counting items, but often spread
across the narrative, without being named as specifically “seven.” Some of these include
Rosenkreutz’s seven tests he must pass, as well as the seven items he carries with him on his
journey to and through the Wedding. Requiring a bit more intensive decoding, though, are the
seven weights in the Weighing Ceremony, upon whose symbolic meaning scholars disagree, but
McClean’s reading includes each weight corresponding to one of the Seven Virtues. McClean
comes to this conclusion partially through mathematical calculation involving the pattern of
characters and the weights each’s character apparently earns, noting that they form the “precise
total of possible mathematical combinations of seven qualities taken 1, 2, 3, 4, 5, and 6 at a
time,” and the people the judges deem most “successful” in weight exchange seven riddles.
138

Probably not lastly (but sufficient for illustrating this point), the “Chemical Wedding” itself—the
apex of the story’s drama—involves beheading seven people in total (in addition to the Bride and
Bridegroom, in whose castle Christian encounters seven rooms, one counts two sets of Kings and
Queens and the Moor who performs the beheading.
139
Thus, without ever needing to tell the

136
McClean, 113.
137
McClean, 120–122. McClean analyzes each day relative to an “archetypal sevenfold
pattern” common to alchemical literature, and which convincingly holds across the narrative’s
larger arc, in addition to each individual day. See McClean, 121–22 for the analysis itself.
138
McClean, “Introduction and Commentary,” 114–16.
139
While this all-encompassing emphasis on the number seven illustrates The Chemical
Wedding’s numerical structure, the complexity of that structure has not yet been fully exhausted
in scholarship. A seemingly infinite number of possible exegetical layers exist, at least one
involving the number three. For example, the main arc of seven days further seems to divide
76
reader what the number seven might mean, the authors stimulate the reader’s numerological
interest and spark thought about the possible layers of symbols present.
As mentioned previously, part of the historical complication these manifestos present is
their constant intermingling of allegory with real people and events. Two such allusions occur in
The Chemical Wedding, both with numerical implications, an obvious one being to John Dee and
the other, more elusive one to Heinrich Khunrath (also obliquely suggested in the Fama). On the
First Day, the invitation letter Rosenkreutz receives contains John Dee’s (1527-1608/9)
Hieroglyphic Monad. A reader familiar with Dee’s explanation of the monad as his composite
symbol for the unity of the cosmos, his 1564 Monas Hieroglyphica,
140
would remember that Dee
conceived of the symbol as being specifically of sevenfold design—thus, the authors likely place
it into the narrative to signal to Rosenkreutz that his journey (and the story itself) will be
similarly sevenfold.
141
Their allusion to Heinrich Khunrath’s Amphitheatrum is much less
obvious, but is confirmed by an earlier mention in the Fama.
142
First, the Latin phrase found on

itself into three phases of three days, one central day, and three final days: probably alluding to
the formation, the central fruition, and final outer expression of a “spiritual impulse” or
successful experiment in the alchemist’s laboratory, explanation of which typically overlays
sevens and threes in this way. For more on these “skeleton frameworks upon which the
alchemists hung their symbols,” see McClean, 114–16.
140
John Dee, Monas Hieroglyphica (Antwerp: Willem Silvius, 1564).
141
McClean, “Introduction and Commentary,” 113–14.
142
Despite coming from similar Paracelsian traditions and espouse many of the same spiritual
ideas, the authors of the Confessio directly tell the reader not to believe Khunrath (“the
“amphitheatrical” comedian, a man most ingenious in deceit. The enemy of human happiness
mingles such things with the good seed, to make it harder to believe the truth. Truth is simple
and naked; Falsehood is specious and adorned with fringes of divine and human wisdom”).
Considering these similarities, and those specifically between Khunrath’s Amphitheatrum and
The Chemical Wedding, one senses that the authors include this as a diversionary tactic, to keep
authorities guessing, lest the ideas in the manifestos align too closely with their “real” scholarly
work attached to their real names. It seems just as likely, though, that Khunrath himself
interspersed truth and untruth in his works to guard alchemical secrets, which the authors of the
Confessio simply point out as examples of the spiritual treacheries of misconstruing alchemy as
only a material art. For the original context in the Confessio, see [Anonymous], “Confessio
77
the title page of the first editions of The Chemical Wedding also appears in Khunrath’s 1597
treatise entitled Chaos, warning that “Mysteries made public become cheap.”
143
But more
strikingly, one finds clear similarities between the events of The Chemical Wedding and the nine
plates of Khunrath’s Amphitheatrum. McClean demonstrates direct concordances, for instance,
between the seven steps shown in Khunrath’s Gate of the Mysteries and the Weighing
Ceremony, Khunrath’s plate showing the initiate “besieged by calumniators” and The Chemical
Wedding’s scene in the Hall of guests. Or especially Khunrath’s “Heptangular Fortress of
Alchemy,” which the Bridegroom’s Castle in The Chemical Wedding architecturally recalls, with
its seven sides and three gates. The “correct” gate through which to enter the Fortress—there are
twenty-one (7 x 3) options, but only the door of Christian devotion and righteousness leads to the
inner sanctum—in Khunrath’s image sports John Dee’s Hieroglyphic Monad (like the Bride and
Bridegroom’s invitation), while both the Bridegroom’s Castle and Khunrath’s laboratory contain
musical instruments.
144
Khunrath’s final engraving shows Christ within the Cosmic Rose, a
symbol of the resurrected (rather than the suffering) Christ upon which Rosicrucianism’s vision,
and name, for a similarly reborn Europe rests.

2.3 – Rosicrucian Numerical Theology in Seventeenth-Century Mathematics
The initial Rosicrucian manifestos only allude to the importance of mathematics in a well-
ordered Christian society, without laying out any specific mathematical precepts as proposition
societal reform. Still, central Rosicrucian ideals intersected with seventeenth-century

Fraternitatis,” 50. This is just one of many such paradoxes and inconsistencies within and among
the manifestos.
143
McClean, 156.
144
McClean, 156–57.
78
“mainstream” mathematics in significant ways. Johannes Faulhaber, born in Ulm in 1580, serves
as a prime example of a mathematician working with both “pure” math and biblical numerology
during the same decade as the publication of the Rosicrucian manifestos. Faulhaber’s early
career was not particularly remarkable: he opened a school in Ulm as a Rechenmeister
(reckoning-master, teacher of arithmetic) after finishing his schooling. In 1604, he published his
first book, Arithmetischer Cubicossischer Lustgarten (Arithmetic Cubicossic Pleasure Garden), a
collection of cubic problems and his method for solving them, as his response to Cardano’s 1545
Ars Magna on the same subject. But shortly thereafter, his life took a series of tumultuous turns,
related to biblical-numerical prophesies that Faulhaber would later publish in pro-Rosicrucian
mathematical tracts. According to Ulm records, in 1606 Faulhaber began to tell his court
landlord, Noah Kolb, and Johann Bartholome, a local preacher, about certain calculations he had
made that would suggest an imminent Day of Judgment. The two men were so enthralled with
these discoveries that Bartholome allegedly “ordained and initiated” Faulhaber with prayers and
rituals to strengthen his resolve, after which Faulhaber officially presented in Ulm, Memmingen,
Augsburg, and Hamburg his numerical figurings prophesying mankind’s demise. These beliefs
soon led to Kolb’s imprisonment and execution in 1615, and Faulhaber’s imprisonment and
apparent rejection by the church after his release. The new preacher appointed in 1611, Peter
Hueber, then refused Faulhaber Communion because he suspected the mathematician of
sorcery.
145
The Fantastereyen (fantastical ideas) themselves that led to Faulhaber’s arrest
consisted primarily of mystical and cabalistic number speculations, based on formulas he
initially developed for his “pure” mathematical calculations of polygonal and pyramidal

145
Ivo Schneider, “Between Rosicrucians and Cabbala - Johannes Faulhaber’s Mathematics
of Biblical Numbers,” in Mathematics and the Divine: A Historical Study, ed. T. Koetsier and L.
Bergmans (Amsterdam: Elsevier, 2005), 313.
79
numbers. He included several of these among his 160 cubic problems in the Arithmetischer
Cubicossischer Lustgarten, though without mention of anything biblical.
146

Faulhaber founded nearly all of these mathematical contributions on “figurate” numbers.
Figurate (also called “figural” or “figured”) numbers are sets of regularly spaced points that
naturally form geometric shapes, or “figures.” Knowledge of these numbers dates back at least to
the time of Pythagoras, when this was the usual mode of representing all quantities—as series of
pebbles or other units in the sand, formed into closed-sided or closed-sided and solid shapes.
Figurate numbers were therefore central enough to Greek number theory that a vast number of
surviving Greek texts treat them, the most famous of these authored by Nicomachus of Gerasa
(ca. 100 CE), Theon of Smyrna (ca. 130 CE), Diophantus of Alexandria (ca. 250 CE), and
Iamblichus (ca. 283-330 CE).
147

Faulhaber’s biblical and mathematical interest in these numbers was so great that P. J.
Federico refers to him not just as a figurate-number enthusiast but a “devotee.”
148
Faulhaber
introduces the most basic figurate numbers—polygonal numbers—into his Lustgarten, along
with pyramidal numbers based on them, to approach cubic problems in the “coss-tradition,” the
algebraic method of German Rechenmeisters.
149
In short: polygonal numbers are sums of the first

146
Schneider, 313.
147
P. J. Federico, Descartes on Polyhedra: A Study of the De Solidorum Elementis, ed. G. J.
Toomer, vol. 4, Sources in the History of Mathematics and Physical Sciences (New York;
Heidelberg; Berlin: Springer-Verlag, 1982), 83. For a discussion of these numbers’ adoption as
theological symbols in the first several centuries of Christianity, see Joel Kalvesmaki, The
Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity (Washington,
DC; Cambridge, MA and London: Center for Hellenic Studies, Trustees for Harvard University;
Harvard University Press, 2013). For further explanation of figurate numbers in Buxtehude’s
compositional practice, see chapter 4.
148
Federico, 32.
149
Ivo Schneider, “Textbooks of German Reckoningmasters in the Early 17th Century,”
Journal of the Cultural History of Mathematics 2 (1992): 47–52.
80
n terms of arithmetic sequences with first term 1 and difference d, with the name for the resulting
polygonal number depending on the value of d, specifically from the value d + 2. This means
that d = 1 yields triangular numbers, d = 2 quadrilateral (tetragonal) numbers, and so on. Figure
2.5 shows the shape relationship between the simplest of these figurate sequences, triangular and
quadrilateral numbers.
150

Figure 2.5. Triangular and quadrilateral numbers, as constructed from the given generating
functions, with points labeled by counting number (taken from Schneider, “Between
Rosicrucians and Cabbala,” 315).

Faulhaber’s later publications build upon these polygonal and pyramidal numbers to include
more complex figurate structures such as dodecahedronal and prismatic numbers, as in his 1622
Miracula Arithmetica
151
and 1631 Academia Algebrae.
152
Applying a range of methods including

150
For a more detailed explanation of these figures, see Schneider, “Between Rosicrucians
and Cabbala - Johannes Faulhaber’s Mathematics of Biblical Numbers,” 314–15.
151
Johann Faulhaber, Miracula Arithmetica. Zu Der Continuation Seines Arithmetischen
Wegweisers Gehörig. (Augsburg: David Franck, 1622).
152
Johann Faulhaber, Academia Algebrae. Darinnen Die Miraculossische Inventiones/ Zu
Den Höchsten Cossen Weiters Continuiert Und Profitiert Werden. Dergleichen Zwar Vor 15.
Jahren Den Gelehrten Auff Allen Universiteten in Gantzem Europa Proponiert, Darauff
Continuiert, Auch Allen Mathematicis Inn Der Gantzen Weiten Welt Dediciert, Aber Bißhero/
Noch Nie so Hoch/ Biß Auff Die Regulierte/ Zensicubiccubic Coß/ Durch Offnen Truck
81
calculus of differences, Faulhaber uses these figurate structures to produce formulae for
arithmetic progressions of higher order and sums, including sums of powers of natural numbers
up to the exponent seventeen.
153

Faulhaber’s formulae treat polygonal and pyramidal numbers from the perspective of
arithmetical series, taking into account the different figures’ numbers of sides. Faulhaber directs
his formulae towards special numbers mentioned in the Bible, as a way of finding secret
concordances between them. One of the most important of these to Faulhaber was also the
Rosicrucian-favored 120, from Genesis 6:3, around which Faulhaber created a “completely new
invention”—now known as the method for finding pyramidal numbers—which he presents as the
following formula for the pyramidal number with base of thirteen sides:
154

(11n
3
+ 3n
2
- 8n) / 6

When n = 4, this gives 120, which is also the fifteenth triangular number. Another “Wunderzahl”
(wonder-number) is 490, the seventy weeks (490 days) of Daniel 9:24-27. He gives the formula
of the pyramidal number with base of fifty sides:

(16n
3
+ n
2
- 15n) / 2

Publiciert Worden. Welcher Vorgesetzet Ein Kurtz Bedencken/ Was Einer Für Authores Nach
Ordnung Gebrauchen Solle/ Welcher Die Coß Fruchtbarlich/ Bald/ Auch Fundamentaliter
Lehrnen Und Ergreiffen Will. (Augsburg: Johann Ulrich Schönigk, 1631).
153
Schneider, “Between Rosicrucians and Cabbala - Johannes Faulhaber’s Mathematics of
Biblical Numbers,” 315.
154
Presented here in modern notation, as transcribed in Federico, Descartes on Polyhedra: A
Study of the De Solidorum Elementis, 117.
82
This yields 490 when n = 4. He also uses these formulae to connect biblical numbers to
sixteenth-century events, as well as to predict future ones. For instance, he gives this formula for
the pyramidal number with base of 154 sides:

(152n
3
+ 3n
2
- 149n) / 6

When n = 4, this gives 1530, the date of the Augsburg Confession. Some of the other polygonal
numbers that Faulhaber treats in this manner are: 666, the number of the beast in Revelation
13:18 (666 is also the thirty-sixth triangular number); 1335, the number of days in Daniel 12:12
(the thirtieth pentagonal number); and 2300, the number of days in Daniel 8:14 (the twentieth
tetradecagonal number).
155

Like Faulhaber and other European intellectuals alive during the initial Rosicrucian
furore, René Descartes (1596-1650) found the Fama Fraternitatis enticing, particularly its
promise of an all-encompassing and restorative, coming new age. Specifically, Descartes
believed this promise to signal the arrival of a new form of absolute mathematics—an art that
would unify and perfect all human knowledge. Descartes likely channeled his reading of the
manifestos through mathematics in this way because in his view number was the most consistent
and trustworthy tool for the human mind; as the foundations of God’s language, numerical truths
remain impervious to human irrationality, senses, and opinions.
156
He therefore assumed that

155
Most of these operations were not actually brand new to Western mathematics, though
Faulhaber honestly believed them to be at the time. But building upon these earlier formulae in
dimensional complexity, he was definitely the first to treat what we now call “hyperpyramidal
numbers.” See Federico, Descartes on Polyhedra: A Study of the De Solidorum Elementis, 117.
156
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 268–69.
83
either the Rosicrucian brothers already knew this new mathematics—in which case Descartes
hoped to seek them out and learn it—or that they were calling upon someone to discover it, and
that he could be that person.
157

Descartes was at the apex of his Rosicrucian interest when he and Faulhaber met in 1619,
when Descartes was temporarily living near Ulm. From a modern perspective, Faulhaber’s
biblical-numerical prophecies would seem incompatible with Descartes’s concept of
mathematics as “consistency and certainty” fully separable from subjective interpretation.
158
But
Descartes held Faulhaber in high regard, and Descartes’s own work with pyramidal numbers
reflects his interest and confidence in Faulhaber’s specific technical methods.
159
Descartes was
well aware of the esoteric nature of Faulhaber’s interest in these topics: in a diary entry from
January 1619, Descartes mentions studying Faulhaber’s “table resembling the German Cabala,”
containing “corporeal numbers” (polygonal and pyramidal numbers constructed by mathematical
series) of significant numbers in the Bible.
160

This table was Faulhaber’s 1615 response to the Rosicrucian manifestos, crafted years
before Faulhaber met Descartes.
161
Shortly after meeting Faulhaber, Descartes made his own
chart of the same types of corporeal numbers. Both mathematicians’ charts include the same six
polyhedral numbers, and both use the same terms, “ponds” and “radix,” to describe certain
values.
162
This close resemblance is unusual enough within Descartes’s output that scholars

157
Churton, 269.
158
Churton, 272.
159
Federico, Descartes on Polyhedra: A Study of the De Solidorum Elementis, 30.
160
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 273.
161
Churton, 274.
162
Federico, Descartes on Polyhedra: A Study of the De Solidorum Elementis, 30.
84
believe this sufficient for approximate dating to this year of his life.
163
This and similar evidence
suggests that Descartes’s work on polyhedral numbers was at least founded upon Faulhaber’s
formulae, if not a direct result of Faulhaber’s suggestion, even if cabalistic aspects did not
interest Descartes—as modern rhetoric surrounding these events invariably assumes:

One cannot imagine Descartes being impressed by Faulhaber’s cabalistic lore, nor
is it likely that Descartes first learned about figurate numbers from
him...However, [Descartes] would no doubt have been interested in the algebra
involved, and it is reasonable to infer that Faulhaber’s enthusiasm may have
inspired him to begin to think about the subject and to evolve some new ideas.
Furthermore, Faulhaber’s equations of pyramidal numbers may well have been
the starting point for Descartes’ treatment of pyramids.
164

Thus, Rosicrucian ideals likely influenced Descartes’s mathematical thought and trajectory in
1619 and into the early 1620s. Descartes later denounced any connection to Rosicrucian ideas,
however, perhaps out of embarrassment that their prophecies never came true. As part of this
distancing, Descartes truthfully claimed that he “could find nothing [mathematically] certain in
[the Rosicrucian] doctrines”—which makes sense, considering that the manifestos, for all of their
numerical innuendo, never explicitly state mathematical precepts.
165

Even outside of Descartes’s mathematical work, Rosicrucianism left marks on his
philosophical writings. Around the time he was in Ulm, he directs one notebook fragment
specifically to the “distinguished brothers of the Rose Croix in Germany,” to whom he forwards
a Rosicrucian-sounding, optimistic argument for developing “the means of solving all the
difficulties in the science of mathematics” and to “see how the sciences are linked together”

163
Federico, 30.
164
Federico, 118.
165
Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society, 271.
85
simply and logically, just like “a series of numbers.”
166
Descartes also called these sketches The
Mathematical Treasure Trove of Polybius, Citizen of the World—a title that Tobias Churton has
demonstrated relates to the title and characters of a play within Johann Valentin Andreae’s satire
Mennipus (1617).
167
Perhaps even more surprising to modern readers, however, are the full
sections of Descartes’s famous Discourse on Method that borrow themes from the Rosicrucian
manifestos. One of the most obvious is Descartes’s image of building a house as a metaphor for
constructing a person’s intellectual perspective. He says, essentially, that it would be foolish for
someone wanting to improve a town to indiscriminately raze everything—thereby ruining the
broader established order for everyone—instead of simply rebuilding his own house first. This
image comes directly from the Fama Fraternitatis, in which the architect “Brother N.N.”
diligently makes repairs to his own house, only to find hidden within its walls the perfect
“compendium of the universe”—the secret to an enlightened, uplifted society.
168

In this way, one can trace elements of Cartesian philosophy to Rosicrucianism’s
messages of social and intellectual reform, and elements of Cartesian mathematical experiment
to Faulhaber’s cabalistic, millenarian algebra. Churton further argues that Descartes’s decision to
become a professional mathematician was in part informed by this and other contact with
Rosicrucian thought.
169
But in carrying his Faulhaber-inspired mathematical projects to the next
stages of development, Descartes ultimately questioned the more subjective aspects that had
provided most if not all of Faulhaber’s conviction.
170
To Faulhaber, mathematics and cabala were

166
Churton, 271.
167
Churton, 277.
168
Churton, 271–72.
169
For example, see Churton’s discussion of Descartes’s three Rosicrucian “Olympian
dreams” of November 1619. Churton, 275.
170
Churton, 276.
86
so connected as to be essentially the same pursuit: when Faulhaber used “cossic” (German
algebraic) numbers of “higher powers,” he believed this in multiple senses of the word, including
that his mathematical operations carried messages to him from “superior beings.”
171
Descartes,
however, saw advantages in separating Faulhaber’s technical and cabalistic elements.
172

Descartes’s personal efforts in this regard probably hastened a larger rationalist cultural interest
in freeing number from numerological symbolic impulses. In a larger sense, then, Descartes’s
contact with and eventual distancing from these early Rosicrucian influences likely helped secure
his place as a founder of the modern scientific method.
173

Unlike Faulhaber and Descartes, adult witnesses to the initial Rosicrucian furore,
Gottfried Wilhelm Leibniz (1646-1716) represents a later generation of thinkers fascinated by
Rosicrucian ideals and documents during the final decades of the seventeenth century,
contemporary to Buxtehude’s circle of friends. Compared to Descartes, Leibniz’s esoteric
interests have also been better documented in twentieth- and twenty-first-century scholarship.
174

Marcia Scuchard explains that despite complications inherent to research into Rosicrucianism
itself, persistent evidence of Rosicrucian thought within Leibniz’s work steadily drives Leibniz-
related scholarship in a Rosicrucian direction:

The continuing controversy over Leibniz’s association with Rosicrucianism points
to the difficulty of scholarly investigation of societies that were determinedly
secret. However, as each new volume of [Leibniz’s] collected works appears, the

171
Churton, 274.
172
Churton, 275.
173
This is ironic on multiple levels. For instance: if, according to Descartes, God
communicates most clearly through number, why would it be necessary for the mortal Descartes
to dictate what numbers can and cannot mean? For further exploration of this and related ironies,
see Churton, 275–76.
174
For an overview of Leibniz and Hermeticism, both in his works and within Leibniz
historiography, see Allison P. Coudert, Leibniz and the Kabbalah (Dordrecht: Kluwer Academic
Publishers, 1995).
87
evidence of his lifelong interest in Rosicrucian-style science (especially
kabbalistic mathematics and Hermetic chemistry) makes it harder to avoid the
issue.
175

Indeed, Leibniz was an avid religious and political thinker, with views aligned with the utopic
Christian vision outlined in the Rosicrucian manifestos. He must have known them well and read
them carefully, because he also proposed the first viable answer to an intricate mathematical
riddle posed in The Chemical Wedding.
176
Though by the 1690s Leibniz no longer believed that
the fraternity described in the Fama Fraternitatis was a real group of organized activists, he
believed deeply in the possible reality of implementing Rosicrucian goals in his actual society.
177

In a post-Thirty Years’ War Germany rife with religious controversy and shifting international
alliances, Leibniz optimistically looked for ways to unify and synthesize smaller differences
between political and religious factions, in favor of a possible—but not yet realized—greater
ecumenical good. Although he was a practicing Lutheran, Leibniz indeed succeeded in reaching
across confessional divides, to eventually become widely respected in Catholic circles.
178

175
Marcia Keith Scuchard, “Leibniz, Benzelius, and the Kabbalistic Roots of Swedish
Illuminism,” in Leibniz, Mysticism and Religion, ed. Allison P. Coudert, Richard H. Popkin, and
Gordon M. Weiner, vol. 158, International Archives of the History of Ideas (Dordrecht; Boston;
London: Kluwer Academic Publishers, 2013), 84.
176
McClean, “Introduction and Commentary,” 125. On the Fourth Day, Christian
Rosenkreutz asks the Virgin (who serves as his guide) her name. She answers with a riddle
involving numbers, letters, and proportional relationships between them. Leibniz proposed the
solution “ALCHYMIA,” which today is considered the definitive solution.
177
Scuchard, “Leibniz, Benzelius, and the Kabbalistic Roots of Swedish Illuminism,” 84.
178
Frank J. Swetz, “Leibniz, the Yijing , and the Religious Conversion of the Chinese,”
Mathematics Magazine 76, no. 4 (October 2003): 276,
https://doi.org/10.1080/0025570X.2003.11953194.
88
Like the Rosicrucians Andreae, Hess, Studion, and Faulhaber—but also Athanasius
Kircher and Marin Mersenne
179
—before him, Leibniz theorized about God and humanity through
meaningful connections between mathematical, metaphysical, and religious thought, inspired by
the works of Ramon Lull and Nicholas of Cusa.
180
Cusa informed Leibniz’s belief in infinity as a
uniting place for contradictory forces, where the largest possible number joins with the
smallest—one; in this system, all numbers are therefore contained in both infinity and one, as the
ultimate unity.
181
Leibniz, like Cusa, thus believed God to be both that infinite quantity and
unifier of all quantities—the number one, from which every other quantity springs. And like
Cusa and the authors of the Fama Fraternitatis, Leibniz visualized these divine relationships
geometrically, specifically as spheres and circles.
182

Leibniz relegated most of his mathematical-theological explorations to combinatorics, the
earliest European manifestations of which also specifically concerned Judeo-Christian theology.
In the Jewish tradition, for example, the mystical Sefer Yetsirah (Book of Creation) contains
calculations for the numbers of ways that the twenty-two letters of the Hebrew alphabet can be
arranged, according to the rules of different counting systems. This also includes counting
possible permutations of letters up to 11! (eleven factorial), since eleven is the most number of
letters in any single word in the Hebrew Bible.
183

179
Eberhard Knobloch, “Mathematics and the Divine: Athanasius Kircher,” in Mathematics
and the Divine: A Historical Study, ed. T. Koetsier and L. Bergmans (Amsterdam: Elsevier,
2005), 343.
180
Swetz, “Leibniz, the Yijing , and the Religious Conversion of the Chinese,” 276.
181
Swetz, 277.
182
Swetz, 277.
183
Robin Wilson and John Fauvel, “The Lull before the Storm: Combinatorics in the
Renaissance,” in Mathematicians & Their Gods: Interactions between Mathematics and
Religious Beliefs, ed. Snezana Lawrence and Mark McCartney (Oxford: Oxford University
Press, 2015), 92.
89
In Christian combinatorics, one traces virtually all exploration through the seventeenth
century back to the thirteenth-century Catalan mystic Ramon Lull (or Llull).
184
Through
combinatorics, Lull aimed to unite all of human knowledge within one system, and to teach
Christian theology so logically through it as to be able to instantly convert people on contact with
its truth.
185
Lull based his method on the idea that all knowledge is founded upon finite principles
or categories; by creating every possible combination of those categories, he could construct all
possible knowledge. To this end, he created circular diagrams to organize possible divine
attributes (“dignities”), which included Bonitas (goodness), Potestas (power), Sapientia
(wisdom), and others. He also devised formulas—in which certain letters stood for words,
phrases, or sentences—which he then formed into algebraic combinations via rotating wheels.
When further adorned with meaningful colors and symbolic geometric shapes, the result was
Lull’s “combinatorial theological tapestry of fantastic complexity.”
186

Leibniz wrote his Lull-inspired Dissertatio de Arte Combinatoria (Dissertation on the
Combinatorial Art) in 1666, at age twenty. This work closely resembles Mersenne’s and
Kircher’s Lullist works, in details of discussion of permutations and combinations, but also its
claim to prove God’s existence “with complete mathematical certainty” through these
operations.
187
After Leibniz, Lull was never again so influential in Western mathematics.
Leibniz’s deep Lullist exploration of combinatorics, in pointing him toward what would become
his version of calculus in the 1670s, pushed mathematics’ known limits to an unprecedentedly
deep theological level, in allowing closer encounters with infinite values than ever before. But

184
Wilson and Fauvel, 89.
185
Wilson and Fauvel, 93.
186
Wilson and Fauvel, 94.
187
Wilson and Fauvel, 99–100.
90
ironically, these same operations’ newfound practicality within applied fields like physics would
simultaneously ensure Lull’s—and theology’s—obsolescence within Enlightenment-
era mathematical inquiry.
188

Like the founding Rosicrucians, Faulhaber, Descartes, and Leibniz each in his own way
considered links between mathematics and Rosicrucian theology in exploring pyramidal numbers
and combinatorics. Many of the same Rosicrucian ideas that captivated them persist even to this
day, through Descartes’s and Leibniz’s hands in shaping the modern scientific method and our
understanding of infinity, if not also humanity’s internet-era encyclopedic impulse to amass and
unite current human knowledge into a modern “compendium of the universe.” Reframing
seventeenth-century Rosicrucian intellectual contributions in this way should complicate, if not
fully dissolve, prevalent conceptions of “occult” mathematical theologies as purely archaic,
mystical, and impractical. By eliminating artificial boundaries between esoteric and exoteric
historiography within these seventeenth-century mathematicians as people, one can more fully
understand their philosophical and religious interests outside of a teleological focus on
mathematical applications. There, one finds Rosicrucianism woven into the fabric of even
“Enlightened” mathematical thought. If Buxtehude’s circle of friends had contact with and
interest in Rosicrucian mathematical theologies, we should find that neither surprising nor
subversive.

188
Wilson and Fauvel, 101. In many twenty-first century conceptions of mathematics, the
field of combinatorics epitomizes “detached” analytical thought, for precisely its “hands-off”
nature. It is therefore interesting to think about its entire Western early development as having
been theological, mystical, and directly connected to cabalist practice, all for the same reason.
91
CHAPTER 3
Contextualizing the Hamburg School of Contrapuntists

Buxtehude did not leave us much biographical information, but details about his friends—and
certain compositions circulated among them—provide clues about the content of their
interactions. The goal of this chapter is to examine these friendships, in order to better
contextualize Buxtehude’s compositional practices, especially extra-musical interests that might
have informed them.
With the exception of Andreas Werckmeister, who remained geographically separated
from the rest of Buxtehude’s circle of friends for the duration of their relationship, Buxtehude’s
main professional contacts while he lived in Lübeck (starting in 1668) belonged to the “Hamburg
school” of contrapuntists.
1
In this chapter I first outline Buxtehude’s multifaceted friendships
with these Hamburg musicians, then detail Buxtehude’s relationship with Johann Theile, and
conclude with a section about Andreas Werckmeister’s mathematical concepts of music and
theology, in order to contextualize these beliefs within his publications and relative to those of
other members of Buxtehude’s social circle.

3.1 – Buxtehude’s Hamburg Circle: Weckmann, Bernhard, and Reincken

After arriving in Lübeck to begin his post as organist at the Marienkirche, Buxtehude traveled
very little; but when he did it was to Hamburg, for “musical and intellectual stimulation—and for

1
David Gaynor Yearsley, “Ideologies of Learned Counterpoint in the Northern German
Baroque” (PhD diss., Stanford University, 1995), 21.
92
entertainment.”
2
Hamburg, sixty kilometers southwest of Lübeck, was by 1660 reachable by
daily coach service on two lines, and on two possible roads, one passing through Oldesloe and
the other through Schönberg to the south. During the summer, this trip was possible in just one
day, and even in winter it required only one overnight stop.
3
Thus, with travel to Hamburg
relatively easy, Buxtehude built relationships with some of Hamburg’s leading musicians, a
roster that had experienced major changes during Buxtehude’s years working in Helsingør in the
1660s: Johann Adam Reincken (1643-1722) replaced his teacher Scheidemann as organist of St.
Catherine’s. Christoph Bernhard (1628-92) had at Matthias Weckmann’s (ca. 1619-74)
recommendation become cantor at Hamburg’s Latin School, the Johanneum. Bernhard and
Weckmann (organist at Hamburg’s St. Jacobi) were friends who both worked for Heinrich
Schütz in Dresden for six years starting in 1649.
4

Buxtehude knew Christoph Bernhard, or at least his composition Prudentia prudentiana
by 1671, when Buxtehude wrote two works of learned counterpoint on the chorale “Mit Fried
und Freud ich fahr dahin” (BuxWV 76-1), for the funeral of Meno Hanneken, Lübeck
superintendent.
5
Both Kerala Snyder and David Yearsley agree that Buxtehude modeled this
work directly on Bernhard’s (also a funerary piece).
6
Thus, the only surviving evidence points
more to professional admiration than to a personal friendship between them.

2
Kerala J. Snyder, Dieterich Buxtehude: Organist in Lübeck, 2nd ed. (Rochester, NY:
University of Rochester Press, 2007), 107.
3
Snyder, 108.
4
Snyder, 108.
5
For an extensive analysis of the contrapuntal and musical-rhetorical symbolism in these
works, see David Gaynor Yearsley, “Towards an Allegorical Interpretation of Buxtehude’s
Funerary Counterpoints,” Music & Letters 80 (1999): 183–206.
6
Snyder, Dieterich Buxtehude: Organist in Lübeck, 109. Bernhard wrote this for Rudolf
Capell and published it in 1669. For further explanation of the relationship between these works
by Bernhard and Buxtehude, again see Yearsley, “Towards an Allegorical Interpretation of
Buxtehude’s Funerary Counterpoints,” 198–200.
93
Bernhard’s job at the Johanneum included major civic duties, including serving as
Director musices for the whole city of Hamburg, which included directing concerted music in all
of Hamburg’s principal churches (St. Peter’s, St. Catherine’s, St. Nicholas’s, and St. Jacobi).
7

Among Bernhard’s most lasting contributions, however, was the work he did for Weckmann’s
collegium musicum (founded 1660), which according to Mattheson’s Ehrenpforte included “fifty
people, all of whom contributed,” with pieces regularly imported from as far away as “Venice,
Rome, Vienna, Munich, Dresden, etc.,” leading to such renown that the “greatest composers
tried to attach their names to it.”
8
The group’s interest in new music likely attracted Buxtehude to
participate as both performer and composer, and would have provided ample reason for some of
his known Hamburg trips.
9

Of all of these Hamburg musicians, Buxtehude appears to have been closest with Johann
Adam Reincken, the famous organist of St. Catherine’s, a position he held for so long that he still
had it in 1720, when J. S. Bach visited Hamburg.
10
According to Ulf Grapenthin, Buxtehude and
Reincken must have met by 1670, but if Kerala Snyder is correct that they shared Scheidemann
as their teacher, then they would have known each other as early as the 1650s.
11
Two details from
their friendship provide hints to Buxtehude and Reincken’s shared interest in visual puzzles,
anagrams, and numbers. Building on the work of Christine Defant
12
and others, and using

7
Snyder, Dieterich Buxtehude: Organist in Lübeck, 108.
8
Snyder, 108–9.
9
Snyder, 109.
10
Snyder, 110.
11
Ulf Grapenthin, “Die »beyden damahls extraordinair berühmten Organisten, Herren
Reincken und Buxtehuden« und ihr gelehrter Freund Johann Theile,” Buxtehude-Studien: Im
Auftrag der Internationalen Dieterich-Buxtehude-Gesellschaft (IDBG) 4 (2021): 14–15.
12
Christine Defant, “Johann Adam Reinckens ‘Hortus Musicus’ - Versuch Einer Deutung
Als Metapher Für Die Hochbarocke Musikauffassung in Deutschland,” Die Musikforschung 42
(1989): 128–48. Also, Christine Defant, Instrumentale Sonderformen in Norddeutschland - Eine
Studie Zu Den Auswirkungen Eines Theologenstreites Auf Werke Der Organisten Weckmann,
94
Werckmeister as a main historical source, Ulf Grapenthin illuminates not only potential number
symbolism in Reincken’s ordering and construction of the sonatas comprising his 1688
collection Hortus Musicus, but proportional connections between that structure and visual
elements of the collection’s frontispiece, through which Reincken alludes to the perfect
consonances as ratios.
13
These details suggest that Reincken worked to coordinate foundational
proportional aspects of his musical “garden” with their visual rendering,
14
and he appears to do
so proudly: on this same frontispiece, he calls himself “Organi Hamburgensis ad D. Cathar.
celebratissimi Directore” and brazenly etches his initials into the foundations of the pictured
pillars supporting the grandiose structure.
15
Lastly, in a laudatory poem to commemorate
Reincken’s second marriage (to Anna Wagener, in 1685), a mutual friend of Buxtehude and
Reincken, Heinrich Rogge (1654-1701), mentions Buxtehude in three of thirteen stanzas. He
does this to both praise their collective friendship and Buxtehude’s and Reincken’s
compositional skills for “choirs, organs and keyboards,”
16
while somewhat comically
apologizing to Buxtehude for apparently commandeering his musical wedding-gift to Reincken.
The gift was an augmentation canon containing a clever anagram of Reincken’s name (spelled

Reincken Und Buxtehude, vol. 41, Europäische Hochschulschriften 36 (Frankfurt a. M, Bern,
New York, Paris: P. Lang, 1990).
13
Ulf Grapenthin, “Beziehungen Zwischen Frontispiz Und Werkaufbau in Johann Adam
Reinckens Hortus Musicus von 1688,” in Proceedings of the Weckmann Symposium: Göteborg,
30 August - 3 September 1991 (Göteborg: Göteborg, Dept. of Musicology, 1993), 199–210.
14
This, then, supports visual analyses of other artifacts Reincken left us, including
Voorhout’s painting. And with so much care evidently put into his own frontispiece for at least
this collection, a connection between the frontispiece to Atalanta fugiens and Voorhout’s
painting, which Reincken commissioned, seems even more probable. For a recent confirmation
of this commission, see Grapenthin, “Die »beyden damahls extraordinair berühmten Organisten,
Herren Reincken und Buxtehuden« und ihr gelehrter Freund Johann Theile,” 14.
15
Snyder, Dieterich Buxtehude: Organist in Lübeck, 111–12.
16
For a transcription and analysis of the stanzas in question, see Grapenthin, “Die »beyden
damahls extraordinair berühmten Organisten, Herren Reincken und Buxtehuden« und ihr
gelehrter Freund Johann Theile,” 18.
95
“Reinken”), praising the composer as “ein Kern” (a kernel, seed) of compositional brilliance—an
anagram Rogge repeats verbatim in the poem, to describe this stolen gift. While this attribution
has been challenged at least once in print for its roundabout nature,
17
yet another wedding gift
from the same event has been associated with Buxtehude since 1921, again identified primarily
by wordplay. In the gifted version of the composition, Buxtehude only identifies himself in code,
as “Deo Beante” (“God Blesses,” but also the initials “D. B.”) from “Lübeck.” While the
composition itself does not survive, only the title, in a catalog entry, this title matches the text to
Buxtehude’s handwritten aria now known as BuxWV 19.
18
Ultimately, while neither attribution
can be confirmed, the spirit of puzzles, code-names, and similar trickery appear known and
shared between Reincken and Buxtehude as part of their friendship, when employing identical
tools of learned counterpoint and canon that they developed as colleagues in the Hamburg
school.

3.2 – Johann Theile: Learned Counterpoint, Canon, and Alchemy
As David Yearsley’s work has illuminated, German music theorists during and before J. S.
Bach’s lifetime practiced counterpoint for reasons outside of musical composition, including
alchemy.
19
That this narrative is largely absent from post-Enlightenment historiography, in
Yearsley’s words, “speaks to the great distance between the positivism of our age and the rich

17
Grapenthin, 19–20.
18
Grapenthin, 20–21.
19
David Yearsley’s contribution to this subject is truly encyclopedic. I will reproduce here
only the essential items for a reader fully unfamiliar with the concept. For more detail, see
Yearsley, “Alchemy and Counterpoint in an Age of Reason”; Yearsley, “Towards an Allegorical
Interpretation of Buxtehude’s Funerary Counterpoints”; Yearsley, “In Buxtehude’s Footsteps,”
Early Music 35 (2007): 339–53; Yearsley, “Ideologies of Learned Counterpoint in the Northern
German Baroque.”
96
play of meanings so important to Baroque musical thinkers.”
20
The nucleus for innovation and
preservation of ties between counterpoint and alchemy and Hermetic philosophy was
Buxtehude’s close friend Johann Theile (1646-1724), an avid experimental contrapuntist whose
work indicates a certain “gnosis” of counterpoint as transformative magic. Among Buxtehude’s
sparse surviving biographical detail is confirmation that he and Theile extensively exchanged
ideas, so much as to elicit confusion and debate after Buxtehude’s death about who actually
mentored whom.
21
Theile was by far the most famous advocate of learned counterpoint in the
late seventeenth century: through his teaching and compositions he gathered a “mythical status”
and was hailed by later generations as “the father of contrapuntists.”
22
After spending the entirety
of 1673 alongside the older Buxtehude in Lübeck, he also authored by far the most blatantly
“alchemical” book of counterpoint and canon before Bach: the Musikalisches Kunstbuch
(“Kunstbuch” meaning a book of Hermetic knowledge or magic).
23
Several surviving copies of
Theile’s work begin with a ten-voice canon entitled the Harmonischer Baum (The Harmonic
Tree) (Figure 3.1), similar to representations of the arbor philosophica, a famous symbol of
Hermetic philosophy.
24
David Yearsley has proven the text’s celebration of a love-filled wedding
not to invoke a human wedding, but rather the “chemical wedding” of mercury and sulphur,
primary ingredients in recipes for the Philosophers’ Stone, or eternal enlightenment-through-
transmutation.
25
The assortment of individual compositions that form this collection date from
the 1670s and 80s, when Buxtehude likely wrote all of the works that this study handles.

20
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 38.
21
Snyder, Dieterich Buxtehude, 112–24. Discussed toward the end of this section as well.
22
Yearsley, “Ideologies of Learned Counterpoint,” 23–4.
23
David Yearsley, “Alchemy and Counterpoint in an Age of Reason,” Journal of the
American Musicological Society 51, no.2 (1998): 225–26.
24
Yearsley, “Alchemy and Counterpoint,” 234–38.
25
Yearsley, “Alchemy and Counterpoint in an Age of Reason,” 235–37.
97

Figure 3.1. Johann Theile’s “Harmonischer Baum” from the Musikalisches Kunstbuch (left) and
Athanasius Kircher’s “Arbor Philosophica” from Ars magna sciendi, 1669 (right).

Members of Theile’s counterpoint circle found a plethora of ideological connections
between alchemy and contrapuntal procedure, especially canon and double counterpoint. For
some, such as Georg Österreich,
26
who studied with Theile and later collected Buxtehude’s vocal
music, these musical techniques reflected the “order of God” (Ordnung Gottes), and through

26
Yearsley emphasizes the importance of Österreich’s “lengthy, untitled treatise dated
1722,” which compiles counterpoints by Förtsch, Theile, Bernhard, Berardi, and Bononcini. See
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 8.
98
them one could thus concretely realize the “inexplicable essence of God’s creation.”
27
Johann
Philipp Förtsch, another Theile pupil and later central figure in Hamburg civic musical life,
28
saw
this type of musical practice as the purest form of music’s “unfathomableness”
(Unergründlichkeit der Musik), and Österreich’s student Heinrich Bokemeyer—leader of the last
generation of Theile’s followers, who inherited some of Buxtehude’s compositions from
Österreich—considered learned counterpoint to encompass the “mystery of harmony”
(mysterium harmonicum).
29
Bokemeyer believed “perpetual” canons to be especially powerful
metaphors for God’s creation of the universe, and he carried this and similar mystical views of
counterpoint into the mid-eighteenth century, long after they had gone out of fashion.
30

Bokeymeyer’s own treatise, Elaboratio dissonantiarum nach den Fundamental Reguln des sel.
Herrn Theilen, which he wrote after Theile’s death in 1725, attests to this ideological longevity.
Bokemeyer’s lasting “overzealous enthusiasm” for learned counterpoint eventually sparked his
multi-part written confrontation with Johann Mattheson over learned counterpoint’s value, in
Mattheson’s article reproducing their correspondence, “Die Canonische Anatomie.” Even in title,
Mattheson signals his anti-Paracelsian worldview: Paracelsian tradition explicitly forbade
physical dissection, for its threat to the spirit’s power in reducing a being to only physical parts,
and therefore valuing only visible natural forces.
31
Yearsley vividly describes Mattheson’s
surgical intentions:

27
Yearsley, “Towards an Allegorical Interpretation of Buxtehude’s Funerary Counterpoints,”
202.
28
And possibly the more correct identification for “Auditus” in Johann Voorhout’s 1674
Musical Party, according to Kerala Snyder. See section 3.3 of this chapter.
29
Yearsley, “Towards an Allegorical Interpretation of Buxtehude’s Funerary Counterpoints,”
202–5.
30
Yearsley, “Alchemy and Counterpoint in an Age of Reason,” 215–17.
31
Yearsley, 223.
99
…Mattheson’s polemic was meant to be a kind of rational dissection of canon, a
careful, well-lighted examination that would expose learned counterpoint’s
metaphysical underpinnings as a dangerous illusion. The enlightened scientist
would draw back the shroud of secrecy and cut into the corpse of canon,
demystifying the strange creature once and for all…Eighteenth-century devotees
of Hermetic science would have known that for “anatomists” such as Mattheson,
occult explanations were inimical to truth; to embrace anatomy was to assume
that no causes were hidden, and that the body, and by extension the universe,
could be understood on a purely physical level, without the aid of magical
insight.
32

Despite Bokemeyer’s eventual admission of defeat in this debate,
33
number enthusiast Johann
Adolph Mizler later honored Bokemeyer’s contributions to learned counterpoint by inducting
him as the fourth member of his famous Societät der Musikalischen Wissenschaften in 1739.
34

The theorists in Theile’s “Hamburg school” of counterpoint had loftier goals than
practicality; only later would J. S. Bach regularly find “practical” uses for the operations Theile
and his circle studied and celebrated, including things such as augmentation, diminution,
inversion, and retrograde inversion. It is not that the Hamburg theorists did not understand the
possible applications for these procedures in aurally pleasing contexts; rather, they chose to study
counterpoint exhaustively, “at a length which went far beyond its relevance” to other musical
genres, so that the point became the study itself, “for its own sake”
35
For all that scholars still
may not know about this circle’s secret contrapuntal practices, we can be sure of this intentional
impracticality, as a central tenet of their philosophy about which they were not subtle. In his
treatises, Theile purposefully distinguishes between the “Musicus Practicus” and the
“Contrapunctist,” to further divide his two possible audiences by the loftiness of their

32
Yearsley, 223.
33
It remains unclear how genuine Bokemeyer’s surrender really was. See Yearsley, 209.
34
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 9–10.
35
Yearsley, 60–61.
100
contrapuntal pursuits. Do not be fooled: any allusion to the more pedestrian “Musicus Practicus”
was not Theile’s way of increasing his work’s reach by suggesting its usefulness in the
“practical” arena. Quite the opposite, he does this only to glorify the apparent “rupture between
theory and practice,” in order to solidify counterpoint’s status as an art so lofty as to be
“unknown” to virtually every famous musician outside of Theile’s circle.
36

Whether or not his claims to “unknown” contrapuntal secrets were true, the sense of
intentional isolation from mainstream musical thought and practice that Theile rhetorically
assigned to the “Contrapunctist” became central to the group’s understanding of counterpoint
and its carefully curated, sequestered place within their larger musical activities. Theile turned
the counterpoint that he had learned from Schütz as practical skills explicitly into an impractical
and esoteric intellectual commodity: to the true Contrapunctist, counterpoint was an elite pursuit
“whose special knowledge gave its members a certain sense of superiority,” so that “what had
been a necessity was now a curiosity.”
37
The title page to Theile's Curieuser Unterricht von
denen doppelten Contrapuncten exemplifies this cultivated sense of idealized obscurity:

Curious lesson in double counterpoint which clearly explains the construction of
such pieces, and demonstrates these with previously unknown concepts of the art,
which were all unknown to all the famous German masters and have been thought
to be impossible to practice.
38

36
Yearsley, 62.
37
Yearsley, 62.
38
Johann Theile, Curieuser Unterricht von denen doppelten Contrapuncten…worinnen gantz
deutlich derselben Vertfertigung verfasset, und mit nach vorher niemals bekanten Kunstgriffen
gezeiget wird, ...welche auch denen allen berühmten teutschen Meistem vorher nicht bekant
gewesen, und vor unmöglich zu practiciren gedacht hat. Manuscript, Staatsbibliothek zu Berlin,
Mus. ms. theor. 917, part II, titlepage. Yearsley notes that Georg Österreich was this
manuscript’s copyist, so it is possible that he, not Theile, was responsible for the title given here.
If that is the case, it forwards an even longer extension of this kind of “secrecy” and exclusionary
rhetoric surrounding learned counterpoint well into the first quarter of the eighteenth century.
See Yearsley, 61.
101

Theile’s contrapuntal tracts and compositions circulated among and united both the
“brotherhood” and peripheral enthusiasts and patrons in Lübeck and Hamburg. In Lübeck, Theile
published a collection of six stile antico masses dedicated to its twenty-four donors—mostly
musicians and businessmen from Lübeck, including Buxtehude, but only Reincken from
Hamburg—and Christoph Bernhard wrote an opening laudatory statement praising Theile’s
knowledge of old-style counterpoint.
39
In his printed tribute to his twenty-four patrons, Theile
arranges their names into a circle (Figure 3.2) resembling Rosicrucian-style mandalas, including
Simon Studion’s famous “candelabra” or “wheel of the heavens” from his Naometria (1604).
40

Figure 3.2. Theile’s twenty-four patrons for his 1673 Stile antico masses (left) vs. Studion’s
“wheel of the heavens” from Naometria, 1604 (right).

39
Snyder, Dieterich Buxtehude: Organist in Lübeck, 113.
40
Simon Studion, “Naometria” ([Württemberg], 1604), MS. Cod. Theol. et phil. qt. 23a-b,
Stuttgart, Württembergische Landesbibliothek, http://digital.wlb-stuttgart.de/purl/bsz411974165.
Discussed in chapter 2.
102

If Reincken’s interest in learned counterpoint extended to his own compositions, beyond
helping to fund Theile’s, he did not leave many examples: as Yearsley notes, Reincken’s fugues
in Hortus Musicus only require knowledge of invertible counterpoint at the octave.
41
But in
addition to his financial support of Theile’s masses, he owned two counterpoint manuscripts that
included two different versions of Sweelinck’s Compositions Regeln, the earlier of which
Reincken himself had copied in 1670. In addition, the contents of these manuscripts included a
work entitled Erste unterrichtung zur Compesition [sic]; Arcana geheimnißen oder handtgriffe
der wahren wißenshafft der Composition, that handled imitative counterpoint and canon; and an
unattributed treatise by Theile called “Kurtze doch deütliche Regulen von denen duppelten
Contrapuncten.” Probably written between the mid-1670s and 1691, Theile’s treatise includes a
four-voice double canon in augmentation (“Canon Duplex à 4 per augmentation”) that strikingly
resembles the one Buxtehude wrote in Johann Valentin Meder’s autograph book in 1674
(BuxWV 123).
42

In addition to Buxtehude’s financial support of Theile’s Lübeck stile antico masses,
accounts suggest that he and Theile were close, both personally and professionally, as
Buxtehude’s laudatory poem printed in the prefatory material to Theile’s St. Matthew Passion
makes clear.
43
After Buxtehude’s death, Theile claimed to have been Buxtehude’s teacher during
that year in Lübeck, and Mattheson’s obituary for Theile in 1725 corroborates this with the

41
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 60.
42
Snyder, Dieterich Buxtehude: Organist in Lübeck, 112–13.
43
This work was also published in 1673, like his stile antico masses, when Theile was with
Buxtehude in Lübeck. See chapter 5 for possible Rosicrucian wordplay in Buxtehude’s poem.
For a transcript and poetic modern translation, see Elizabeth Mackey, “The Sacred Music of
Johann Theile” (PhD diss., Ann Arbor, Michigan, University of Michigan, 1968), 317–18. For a
facsimile, see Denkmäler der deutschen Tonkunst, vol. 17 (Leipzig: Breitkopf & Härtel, 1904),
109.
103
following assessment: “Next [Theile] went to Stettin, and there he instructed organists and
musicians; he also did this in Lübeck, and was an informator of the well-known Buxtehude, of
the organists Hasse, and of the municipal musician Zachau, among others.”
44

Based on Buxtehude and Theile’s similar ages and compositional sophistication, Snyder
has argued that, though Theile and Buxtehude would have certainly extensively discussed
counterpoint over the course of their friendship, Theile could not have been Buxtehude’s
teacher.
45
In a 2021 article about Reincken, Buxtehude, and Theile’s musical and intellectual
relationship in the 1670s, Ulf Grapenthin disentangles terminological issues surrounding the
relationships implied by “student” and “teacher” in seventeenth-century Germany.
46
In further
differentiating these from Matthesson’s term, “informator,” Grapenthin concludes that as
Buxtehude’s “informator,” Theile likely functioned as a peer-collaborator-teacher in
combination, in the way that high-level specialists in different areas might consult with one
another, without unilaterally ranking one as singular “teacher.” According to Grapenthin’s
archival research,
47
Theile fulfilled many diverse roles for many different musicians of equally
diverse ages and ranks during his official posts in different German locales across his career. The
skills he shares as “informator” to these students include everything from oboe lessons to
advanced composition techniques and the “arcana” of multiple-voice counterpoint, to
“traditional” early music-education lessons to noble youth.

44
Johann Mattheson, Criticae Musicae Tomus Secundus (Hamburg, 1725), 57; Translation
from Snyder, Dieterich Buxtehude: Organist in Lübeck, 113.
45
Snyder, Dieterich Buxtehude: Organist in Lübeck, 113.
46
Grapenthin, “Die »beyden damahls extraordinair berühmten Organisten, Herren Reincken
und Buxtehuden« und ihr gelehrter Freund Johann Theile.”
47
Grapenthin, 26–27.
104
Considering Theile’s circle’s emphasis on secrecy and “impractical” stile antico and
philosophical counterpoint, one might find their contemporaneous achievements as innovators in
the very public sphere surprising. Their theoretical concerns appear to have run parallel to their
practical music-making, as progressive pacesetters of Germany’s “new style.”
48
Around the time
of Weckmann’s death in 1674, Elector Johann Georg II asked Bernhard to return to Dresden;
with both musical giants gone, Reincken once again became Hamburg’s leading organist until
Vincent Lübeck’s arrival in 1702. Bernhard’s successor, Joachim Gerstenbuttel, did not continue
Bernhard’s tradition of public concerts, though. The “resulting vacuum”
49
made space for
Theile’s remaining circle to set their sights on new ventures, leading to their founding the
Hamburg Opera in 1678, the first public opera house outside of Italy, which presented at least
one hundred performances per year.
50
Theile was the Opera’s first Kapellmeister, with Förtsch
taking over as its most prominent composer in the late 1680s.
51

Despite the Hamburg school’s efforts to separate their learned and popular styles, both
Theile and Buxtehude leave thematic clues to their interest in alchemical ideas, if not specifically
Rosicrucian ones, in public works whose libretti survive without music. For Theile, this was the
first of his operatic ventures, which Christoph Bernhard and Buxtehude both helped support
financially and Buxtehude attended regularly. This first opera was Theile’s biblical Singspiel:
Der erschaffene, gefallene und wieder aufgerichtete Mensch (Adam und Eva) (The Created,
Fallen, and Resurrected Human, or Adam and Eve). The work begins with the Creation of the

48
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 10.
49
Snyder, Dieterich Buxtehude: Organist in Lübeck, 115.
50
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 10–11.
51
For an overview of the opera’s repertoire during these decades, see George J. Buelow,
“Hamburg Opera during Buxtehude’s Lifetime: The Works of Johann Wolfgang Frank,” in
Church, Stage, and Studio, ed. Paul Walker (Ann Arbor: UMI, 1990), 138–40.
105
universe from chaos, dramatized by characters portraying personified versions of the four
elements.
52
This detail, along with clear titular emphasis Resurrection (redemption, renewal)—
listed even before the main characters—resonates with specifically Rosicrucian ideals beyond
just alchemical ones.
53
The title’s three-part description also aligns with three statements about
our souls’ earthly journey, “found” in Christian Rosenkreutz’s tomb and reprinted at the end of
his eulogy in the Fama Fraternitatis (1614):
54

WE ARE BORN IN GOD,
WE DIE IN JESUS,
WE LIVE AGAIN IN THE SPIRIT.
55

3.3 – A New Reading of Johannes Voorhout’s Musical Party
The strongest material evidence for the close friendship between members of the Hamburg
school comes from a painting by Johannes Voorhout (Figure 3.3), executed in Hamburg in 1674

52
Margaret Ross Griffel, “erschaffene, gefallene, und wieder aufgerichtete Mensch, der
(Adam und Eva),” in Operas in German: A Dictionary, Revised edition, vol. 1 (Lanham:
Rowman& Littlefield, 2018), 130.
53
It also recalls the manifestos’ emphasis on Adamic wisdom. For instance, from the Fama:
“Our Philosophia is nothing new but is the same which Adam received after his fall and which
Moses and Solomon applied.” [Anonymous], “Fama Fraternitatis, 1614,” in Rosicrucian Trilogy:
The Three Original Rosicrucian Publications in New Modern Translation, trans. Christopher
McIntosh and Donate Pahnke McIntosh (Newburyport, Massachussetts: Weiser Books, 2016),
30. The “Coming return of Adamic wisdom” is also one of the thirty-seven rationes in the
Confessio. Joscelyn Godwin, “Introduction to the Confessio Fraternitatis,” in Rosicrucian
Trilogy: The Three Original Rosicrucian Publications in New Modern Translation
(Newburyport, Massachussetts: Weiser Books, 2016), 38.
54
[Anonymous], Fama Fraternitatis, oder Entdeckung der Bruderschafft deß löblichen
Ordens deß Rosen Creutzes/ Beneben der Confession Oder Bekantnuß derselben Fraternitet/ an
alle Gelehrte und Haüpter in Europa geschrieben (Kassel, 1614). For context, see chapter 2.
55
[Anonymous], “Fama Fraternitatis,” 28. Both the text and large-scale key scheme in Sicut
Moses exaltavit serpentem in deserto (BuxWV 97) follows this same trajectory. See chapter 7.
106
but not known to musicologists until 1975.
56
Now housed at the Museum für Hamburgische
Geschichte, the painting was formerly known as the Häusliche Musikszene (Domestic Music
Scene), but is now called Musizierende Gesellschaft in Hamburg, or simply Musical Party in
English. Most scholars agree that it was likely commissioned by Reincken to commemorate his
friendship with Buxtehude.
57

Figure 3.3. Johannes Voorhout, Musical Party, 1674, Hamburg, Museum für Hamburgische
Geschichte.

56
Snyder, Dieterich Buxtehude: Organist in Lübeck, 115.
57
Grapenthin, “Die »beyden damahls extraordinair berühmten Organisten, Herren Reincken
und Buxtehuden« und ihr gelehrter Freund Johann Theile,” 14.
107
Voorhout’s painting, which also contains Buxtehude’s only known image, has proved a
complex identification puzzle. On the surface, its subject and imagery seem clear enough, but
certain oddities create stumbling blocks for determining who is real, who is allegorical, and even
more basically, who is whom. The painting shows Reincken seated at the harpsichord—an
identification that is certainly true, based both on Gottfried Kneller’s portrait of Reincken and his
well-documented enjoyment of Japanese silk brocade kimonos (all the rage in northern Germany
and Holland at that time). To Reincken’s left, another man plays the viola da gamba and looks in
his direction.
58
To the right of the harpsichord sits yet another man, appearing somewhat younger
than the two other musicians to his left, holding a hand to his ear, his mouth open and a sheet of
paper on his lap. For decades, beginning with Christoph Wolff’s reading of the scene, scholars
generally identified this man as Buxtehude, and the viola da gamba player as Johann Theile—
based on their friendship and Theile’s being known as a viol player.
59
But Grapenthin has since
redated Reincken’s birthyear to 1643 from Mattheson’s given 1623, which would make the then
thirty-seven-year-old Buxtehude the oldest member of the Reincken-Buxtehude-Theile friend
group at the time of the painting’s completion in 1674.
60
Next to the listening man, a woman
lutenist joins in the music-making, and behind the harpsichord dances another couple. To the far
left, we find the painter himself, and a black page-boy offers Reincken some grapes—a symbol
of sensual pleasure and wealth.
61

58
Snyder, Dieterich Buxtehude: Organist in Lübeck, 110.
59
Christoph Wolff, “Das Hamburger Buxtehude-Bild,” Musik und Kirche 53 (1983): 8–19.
60
Snyder, Dieterich Buxtehude: Organist in Lübeck, 110.
61
Gisela Jaacks, “Wer ist Wer? und weitere Rätsel. Zur Diskussion um das sogenannte
Buxtehude-Bild von Johannes Voorhout,” in Buxtehude jenseits der Orgel. Akademie für Alte
Musik – Hochschule für Künste Bremen, ed. Michael Zywietz (Graz: Akademische Druck- und
Verlags-Anstalt, 2008), 57–68.
108
Thus, because the painter and the page-boy are not necessarily a coordinated pair,
Heinrich Schwab suggests that one might think of the painting as containing three main pairs:
Buxtehude and Reincken, the dancing couple, and the listener and the lutenist, the last of which
Schwab identifies as an allegorical “Auditus” and “Musica.”
62
In this reading, Theile is not in the
painting, which makes sense if one considers these characters’ relative social positions at the
time: as Hofkapellmeister to the Duke of Schleswig-Holstein at Gottorf, Theile would have been
even higher ranking than civic musicians Reincken and Buxtehude, so if he appeared in the scene
it would be strange for him not to be named in the dedication.
63

The dedication in question appears on the piece of paper on the listening man’s knee,
alongside a musical composition. The composition, believed to be in Reincken’s handwriting, is
a canon for eight voices at the unison, setting a Latin textual excerpt from Psalm 133: “Behold,
how good and how pleasant it is for brethren to dwell together in unity!”
64
Then following this,
the inscription: “In hin: dit: Buxtehude: et Joh: Adam Reink: fratr[um].” Wolff based his original
identification on the convention of placing named dedicatees in the center of a portrait; in this
case, with the harpsichord dominating the middle of the canvas, Voorhout’s choices would have
been to either keep Reincken and Buxtehude together but off-center, or to separate them. Several
important discoveries since Wolff’s original hypothesis, in addition to Reincken’s re-dating,

62
Heinrich W. Schwab, “Johannes Voorhouts Gemälde ‘Häusliche Musikszene’ (1674). Zum
Problem Der Identifikation Dietrich Buxtehudes,” in Musikvidenskabelige Kompositioner.
Festkrift Til Niels Krabbe, 1941-3. Oktober-2006 Kopenhagen (København: Det Kongelige
Bibliotek i kommission hos Museum Tusculanum Forlag, 2006), 55–73. See also Heinrich W.
Schwab, “Wenn ‘Brüder Einträchtig Beieinander Wohnen’: Zur Bildlichen Darstellung
Buxtehudes Auf Dem Gemälde von Johannes Voorhout (1674),” in Dieterich Buxtehude: Text -
Kontext - Rezeption, ed. Wolfgang Sandberger and Volker Scherliess (Kassel; New York:
Bar ̈ enreiter, 2011), 11–32.
63
Snyder, Dieterich Buxtehude: Organist in Lübeck, 111.
64
Snyder, 110.
109
suggest that Voorhout chose the former path. He appears to have indicated the pair’s importance,
however, by making them larger and with heads roughly on the same level (Schwab’s “Auditus
and Musica” are in the foreground, just in front of the harpsichord), and this also keeps
Buxtehude’s and Reincken’s names, left to right, in the order in which the dedication lists them.
The final clue, however, lies in the viol player’s left hand, in which he conspicuously fingers his
initials, as the pitches “D” and “B-flat” (“B” in German) on the fretboard—fret two on the C-
string and fret one on the A-string. Buxtehude is not known to have played the viol, but his
activities outside of his organ playing work and the Marienkirche’s accounting records are not
well known in general. Kerala Snyder reminds us:

That Buxtehude is not known to have played the viola da gamba does not argue
against this identification [of Buxtehude as the viol player in Voorhout’s
painting]. Other famous keyboard players also played stringed instruments,
notably Nicolaus Bruhns and Johann Sebastian Bach. Buxtehude left a
magnificent body of music scored with viola da gamba, and his professional
colleagues, the Lübeck municipal musicians, took pride in their ability to play
multiple instruments.
65

Primarily because it contains Buxtehude’s only known image, this painting has received a wealth
of close scholarly attention such as that cited here. And yet, the identification issue is still not
entirely closed. While most sources after 2007 accept a reading of the middle-right figure as just
the allegorical “Auditus,” not all do. As recently as 2019, for example, David Yearsley again
refers to the figure as “Johann Theile” in a footnote, while also suggesting that the lutenist might
be Reincken’s wife.
66
The former identification is still unlikely, unless Voorhout altered facial

65
Snyder, 110–11.
66
David Yearsley, Sex, Death, and Minuets (Chicago: University of Chicago Press, 2019),
279–80. Admittedly, the Theile identification was not Yearsley’s focus here: instead, he
bemoans the fact that nearly all readings of the painting–and of paintings of this period in
general–just assume that women are mere studio props: “...it seems hard to believe that a painter
110
features in order to make all of the men look more similar to each other—for instance, in order to
suggest extra “brotherly” identification with one another. The recent discovery of a
contemporary portrait of Theile now contradicts all claims to his appearance in the painting.
67

Looking at the available evidence, I conclude that both Schwab’s and Wolff’s “Auditus”
identifications are correct, but that something else is also at play.
While both the musical composition and dedication on the “Auditus” figure’s knee have
proven crucial to solving other aspects of the identification puzzle, they also contain major
implications for this study’s understanding of Buxtehude’s number symbolism as related to
Rosicrucian ideas. From a Paracelsian perspective in the works of Heinrich Khunrath, multiple
aspects of the canon and dedication find concordances with Rosicrucianism-adopted tenets of
Paracelsian philosophy. The most obvious of these is the repeated use of the word “brothers” to
describe Buxtehude and Reincken. Both the psalm text of the canon and the dedication—both of
which appear in Latin, like psalm-text inscriptions in the Rosicrucian manifestos and in
Khunrath’s treatises—contain direct references to “brotherhood.” The fact that the text is a psalm
text also recalls Khunrath’s claim that the psalms are the most important prayer tools an
alchemist keeps in his “lab-oratory,” in praise of God.
68
Then, the Reincken-penned music to set

of Voorhout’s talent and standing would have been engaged at considerable expense to fill up an
entire corner of the picture space with mere staffage, rather than with a member of Reincken’s
familial and musical circle…Why is it so often assumed that a woman’s role in a painting is
merely pictorial or mythological, that the depicted female is merely included because she is
pretty, compositionally useful, a muse or a goddess or some other iconographic prop?”
67
Arndt Schnoor, “Ein Unbekanntes Porträt von Johann Theile (1645/46-1724),” in
Dieterich Buxtehude: Text - Kontext - Rezeption, ed. Wolfgang Sandberger and Volker
Scherliess (Kassel; New York: Bar ̈ enreiter, 2011), 33–34.
68
Peter J. Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations
on Cabala, Music, and Alchemy,” ARIES - Journal for the Study of Western Esotericism 10, no.
2 (2010): 169–95, https://doi.org/10.1163/156798910X520584. See also my discussion in
chapter 2.
111
this psalm text celebrating “brothers” in “unity” is a canon—an alchemically-charged procedure
in itself
69
—also points to the “high level of their relationship.”
70
This canon’s number of voices
and interval also signify “brotherly unity”: the “original” number of first-generation Rosicrucian
“brothers” was eight,
71
while the unison signifies divine proportional perfection, or “unity”—
here also wordplay, as both canon’s text and its voices’ intervallic relationship to one another.
In part, the canon’s numerical, intervallic, and textual features lead to my own
identification hypothesis, which serves as a meeting point for competing elements in past
readings of the painting. In addition to the party’s on-duty workers—the painter (far left) and
page boy (middle)— there are four male figures who look as though they should be named (for
only two names given in the dedication) because the painting shows what art historians call a
“continuous narrative”—meaning, both Buxtehude and Reincken each appear twice. Wolff
suggests this possibility for both the lute player and Reincken (reimagined as the pair in the
back), but not also for Buxtehude.
72
Although, as Snyder mentions that this kind of “double
portraiture was not uncommon”
73
in the late seventeenth century, it was a self-consciously arcane

69
Yearsley, “Alchemy and Counterpoint in an Age of Reason.”
70
Snyder, Dieterich Buxtehude: Organist in Lübeck, 112.
71
Eight is also Werckmeister’s number of “fullness,” as a trinitarian rendering of Christ (2)
as a cube). Discussed later in section 3.4.
72
Wolff, “Das Hamburger Buxtehude-Bild.”
73
Snyder, Dieterich Buxtehude: Organist in Lübeck, 111. Snyder does not believe him to be
Buxtehude, however. She compellingly argues that if this “Auditus” figure is a historical person
other than Theile, because of the issue of class and rank mentioned earlier, he would more likely
be Johann Philipp Förtsch (1652-1732). By 1674, Förtsch had just arrived in Hamburg, as a
twenty-two-year-old tenor in the Kantorei, and already by this point demonstrated keen interest
in learned counterpoint. Snyder points out that, at this young age (as a “junior member of the
‘fraternity,’”), it would not be strange for him to go unnamed in the painting’s dedication.
Förtsch would become one of Theile’s most important students, eventually succeeding him as
Kapellmeister to Duke Christian Albrecht in 1680. Förtsch also would go on to produce works of
learned counterpoint, both theoretical and compositions, most notably a unified collection of
thirty-two canons on the chorale “Christ, der du bist der Helle Tag,” along with his theoretical
Musicalischer Compositions Tractat, which devotes its longest section to invertible counterpoint
112
style—just like the procedures of canon and invertible counterpoint that this “brotherhood”
celebrated at its core. Perhaps not coincidentally, this same “continuous narrative” visual
technique also communicates the entire Myth of Atalanta and Hippomenes in the frontispiece for
Michael Maier’s Atalanta fugiens.
74

Interpreting the dancing man in the background as another Reincken and the listening
“Auditus” as another Buxtehude unifies the painting’s message: the dedication celebrates the
“brotherly unity” of just these two men. Here Voorhout shows them in what is simultaneously a
lively party atmosphere and a continuous-narrative celebration of their Godly vocations (making
music together, in praise of God) and for their earthly pleasure. Voorhout also shows Reincken
as somewhat of a womanizer and Buxtehude as a listener, enjoying music’s auditory sensuality
safely—at least non-erotically—as allegorized with his woman companion of “Musica” herself.
Both scenarios would match known details about these men’s proclivities in real life.
75
Certain
costuming elements would also confirm this double “continuous narrative” reading: in addition
to each pair’s similar hair and facial features, especially nose and eyes for Reincken and mouth
and nose for Buxtehude, both “Reinckens” appear to wear the same long tie, while both

and canon. For more about its contents, including the important seventeenth-century Italian
sources from which Förtsch draws, see Yearsley, “Ideologies of Learned Counterpoint in the
Northern German Baroque,” 7–8.
74
Michael Maier, Atalanta Fugiens, hoc est, Emblemata nova de secretis naturae chymica,
accommodate partim oculis et intellectui, figuris cupro incises, adjectisque sententiis,
Epigrammatis et notis, partim auribus et recreationi animi plus minus 50 Fugis musicalibus
trium Vocum, quarum duae ad unum simplicem melodiam distichis canendis peraptam,
correspondeant, non absque, singulari jucunditate videnda, legenda, meditanda, intelligenda,
dijudicanda, canenda et audienda (Oppenheim: Johann Theodor de Bry, 1617).
75
Mattheson’s obituary for Reincken relates that he was a “constant lover of women and of
the Rats-Weinkeller,” and that in his will he did not forget “the unknown ladies whom he had in
his house until his death.” Indeed, in offering grapes to Reincken at the harpsichord, the black
page…is inviting him to taste of sensual pleasure.” See Snyder, Dieterich Buxtehude: Organist
in Lübeck, 111.
113
“Buxtehudes” wear the same neck ruffles and red wristbands. A close look at each pair’s head
placement also finds a horizontal and a vertical line in opposition, between heads: Buxtehude
and Reincken (left to right) and the “other” Buxtehude and Reincken (bottom to top) visually
create a deconstructed cross. This balances the painting as a whole while keeping each pair’s
heads close together, as would befit the Christian “brotherhood” in the dedication.
One original counterargument to the “Auditus” figure’s identification as Buxtehude is
that he does not look at Reincken in coordinating whatever music they make.
76
But with the
visual “cross” in mind, as in, when one visually pairs the music-making Buxtehude and Reincken
as one and then, separately, the “earthly” Buxtehude and Reincken as one, their gazes move in
pleasingly opposing directions across the room—one that would suggest this pairing to be
intentional, with each woman character acting in similar visual opposition to the other.
77
And a
reason this continuous-narrative reading was not considered earlier was Wolff’s then-reasonable
assumption that Reincken was not as much of an aficionado of learned counterpoint as we now
know he was.
78
Reincken owned at least one treatise by Theile at the time of his death, though it
is not labeled as such, but has since been positively attributed to him. And like Theile, Reincken
used words such as “secret” and “hidden” to describe contrapuntal operations in his own titles
and annotations.
79
For these two “brothers” in Voorhout’s painting, their shared interest in

76
Snyder, 111. Snyder believes that “an allegorical interpretation of the man with the canon
as ‘Auditus,’ also suggested by Wolff in addition to his identification with Buxtehude, has much
to recommend it, particularly with respect to his lack of eye contact with Reincken.”
77
For applicable theories involving such issues of relative position in portraiture, see Harry
Berger, “Fictions of the Pose: Facing the Gaze of Early Modern Portraiture,” Representations 46
(1994): 87–120.
78
This is in addition to an array of new information, such as the discovery of the portrait of
Theile and of Buxtehude’s fretboard initials.
79
Snyder, Dieterich Buxtehude: Organist in Lübeck, 112–13; Yearsley, “Ideologies of
Learned Counterpoint in the Northern German Baroque,” 54.
114
learned counterpoint constitutes a strong enough Hamburg-school bond, not requiring another
composer in the frame for validation.

3.4 – Andreas Werckmeister

Thereby, we can perceive what a grandiose subject the mathematical discipline is,
whereby we can rise to the heavens, as it were. Whoever also has the knowledge
of God through Christ, and thereby glimpses the wonders of his Creator through
the light of nature, he must all the more be moved to praise the Omnipotent One.
With great amazement one beholds how the wondrous secrets of nature and other
lofty matters can be discovered through mathematics…
80

– Andreas Werckmeister, Musicalische Paradoxal-Discourse (1707)

In terms of publication record, the most significant member of Buxtehude’s circle of friends in
an investigation of Buxtehude’s social and intellectual influences is music theorist, composer,
and organist Andreas Werckmeister (1645-1706). Werckmeister, who came from a family of
Thuringian church musicians, served as organist in Hasselfelde and Elbingerode, and in 1675
moved to Quedlinburg to become organist at St. Servatius, the chapel of Anna Sophia I, Abbess
and Countess Palatine. In Quedlinburg, where he also published most of his musical-theoretical
works, Werckmeister assumed another post as organist at St. Wiperti in 1677. In 1696 he became
organist of St. Martin’s church in Halberstadt, where he served until his death in 1706. By the
time of his final post in Halberstadt, where he was also appointed Royal Prussian Examiner of

80
Andreas Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A
Well-Tempered Universe, trans. Dietrich Bartel, Contextual Bach Studies (Lanham: Lexington
Books, 2017), 64–65. For the original, see Andreas Werckmeister, Musicalische Paradoxal-
Discourse (Quedlinburg: Theodor Philipp Calvisius, 1707), 19. For all future citations of this
source, I will draw from and cite Dietrich Bartel’s English translation, with Calvisius’s original
page number in brackets, like this: [MPD p.19]
115
Organs in the Principality of Halberstadt, he was already famous not only as an examiner but as
innovator-proponent of a series of circulating temperaments, about which he started publishing
in 1681, in the Orgel-Probe (“or a brief description of how and in which form organs should and
are to be accepted, tested, examined, and delivered to churches from an organ builder,”
Quedlinburg: Theodor Calvisius). Michael Dodds estimates that by 1702, Buxtehude had
probably known Werckmeister personally for as many as twenty years.
81

In this section, I aim primarily to explain Werckmeister’s perspective, sources, and
literary influences, since his beliefs and instructions are much better documented than
Buxtehude’s. This provides a window into the possible content of their decades-long friendship
and correspondence, and therefore helps reconstruct a significant portion of Buxtehude’s likely
non-Hamburg influences. I will also outline Werckmeister’s concept of number in music, both in
and before his oft-cited 1707 Musicalische Paradoxal-Discourse,
82
to situate these offerings
within his larger output. This includes a brief discussion of his interest in Hermeticism,
especially confluences of these with practical and theological issues in his treatises. In view of
their close friendship and shared professional interests, these Hermetic leanings warrant a more
Hermetic-sensitive investigation of Buxtehude’s texts and musical-numerical devices as well.
His and Werckmeister’s friendship required intentionality to uphold at a distance, for so many

81
Michael R. Dodds, “Columbus’s Egg: Andreas Werckmeister’s Teachings on Contrapuntal
Improvisation in Harmonologia Musica (1702),” Journal of Seventeenth-Century Music 12, no. 1
(2006): 2.2, https://sscm-jscm.org/v12no1.html.
82
The numerically explicit sections of this treatise frequently appear as foundational
primary-source material in modern number-symbolism studies, but without the luxury of space
for this degree of context. For example, see Carol Jarman, “Buxtehude’s Ciacona in C Minor and
the Nicene Creed,” The Musical Times 146 (2005): 58–69; Piet Kee, “Astronomy in Buxtehude’s
Passacaglia: Measure and Number in Ostinato Works,” The Diapason 75 (1984): 27–33;
Grapenthin, “Beziehungen Zwischen Frontispiz Und Werkaufbau in Johann Adam Reinckens
Hortus Musicus von 1688.”
116
years, with many opportunities for source-sharing. And finally, I will elucidate Werckmeister’s
relationship to Buxtehude’s Hamburg-school friends, particularly regarding contrapuntal devices
that on the surface appear to connect Werckmeister with Buxtehude, Theile, and Reincken, but
that have proven contentious in modern scholarship.
As Werckmeister’s student, friend, and author of the composer’s biographical entry in his
1732 Musicalisches Lexicon, Johann Gottfried Walther provides a network of crucial links
between central themes and characters within this study, both already explicated and to come in
later analysis chapters: Werkmeister and alchemy, Werckmeister and J. S. Bach, and
Werckmeister and Buxtehude. Although no physical letters survive, it is thanks to Walther that
scholars even know about their habit of written correspondence. In a letter to Heinrich
Bokemeyer in 1729, Walther mentions that Werckmeister, his teacher and friend, had “honored
[him] … with some letters and keyboard works by Buxtehude,” the latter of which were in
German organ tablature, in Buxtehude’s own hand.
83
These are particularly tantalizing details
from the perspective of Buxtehude studies, when the majority of Buxtehude’s extant
compositions in the Düben Collection are not manuscripts, but scribal copies. Without knowing
the content of Buxtehude’s and Werckmeister’s letters to each other, one assumes that they held
common interests as high-profile church organists in their respective cities. In addition to
compositional and contrapuntal techniques, any number of these topics, such as organ tuning and
construction, could have sustained lively written correspondence.
84

83
For a discussion of the benefits of organ tablature for organizing a composition’s
mathematical structure, see chapter 4.
84
Dodds, “Columbus’s Egg: Andreas Werckmeister’s Teachings on Contrapuntal
Improvisation in Harmonologia Musica (1702),” 2.2.
117
Throughout Werckmeister’s long publishing career, a strong thread connecting his
projects is an open reverence for Pythagorean ideas of number and mathematics, as building
blocks of the universe and the language through which the divine communicates in the mortal
realm. Musically, his treatises therefore reflect his ardent belief in a musically designed cosmos
and a cosmologically designed music, unified by this divine preeminence of number and
proportion. Thus, his works stand among the last to champion music in an “ancient” sense, and
on foundational aspects of music’s meaning and purpose Werckmeister writes more as a
historian than as his own contemporary. In understanding and writing about music as primarily a
mathematical and scientific pursuit belonging more to the Quadrivium than the Trivium, he
evokes Pythagorean and Platonic ideals that inherently privilege compositional design above
audible, sensual pleasure. To Werckmeister, as to Plato and Pythagoras, numerical order alone
forms the basis of Harmonia, the divinely ordained balance between microcosm and macrocosm,
and a mathematical mirror between music and humanity, corporeal reality, and the motion and
balance of the universe.
85
Thus, Werckmeister’s often articulated belief that ratio is the ultimate
“arbiter” of harmony also recalls the Boethian concept that true mastery of musica, however
natural a force to humanity as all-encompassing mathematical truth, comes by way of intellectual
understanding, through proper contemplation.
86
These concepts, particularly as filtered through
the works of St. Augustine, form a distinctly Christian foundation in Werckmeister’s
understanding of music and the universe: just as one best contemplates unity and creation itself
via contemplation of ratio, it is music’s numerositas (“numberliness”) that makes it an effective

85
Dietrich Bartel, “Introduction to the Musicalische Paradoxal-Discourse,” in Andreas
Werckmeister’s Musicalische Paradoxal-Discourse: A Well-Tempered Universe (Lanham:
Lexington Books, 2017), 3.
86
Bartel, 4.
118
vehicle for Christian revelation. To both Augustine and Werckmeister, music was a scientia bene
modulandi—a science of good measure—in which contemplation of musical-numerical
proportion in this Christian light instills in one’s life a sense of the same divine order that
dictates Pythagorean ratio as universal truth.
87

In relaying information to his reader, Werckmeister imbues his prose with copious
citations that tell us a fascinating story of his reading habits and library contents. He most
frequently cites fifteenth- and sixteenth-century authors, and his sources from this period show
the “whole spectrum of the Renaissance.”
88
Most of his sources after this period are German,
which Pieter Bakker attributes to the destruction wrought by the Thirty Years’ War, in which
eastern Germany “especially suffered,” enough to make library updates challenging.
89

These citations, which bespeak his intellectually omnivorous reading habits, Michael
Dodds aptly dubs “a curious mixture of Medieval thought and the avant-garde.”
90
Dietrich Bartel,
too, describes Werckmeister’s œuvre as “riddled with obscure references, peppered with all
kinds of innuendo,” the simultaneous breadth and minutiae of which assumes in his reader
complete fluency in biblical detail, Latin and Greek, and all manner of contemporary and ancient
literature involving theology, philosophy, and other disciplines.
91
In all cases, the core of

87
Bartel, 4.
88
Pieter Bakker, Andreas Werckmeister: The Historical Positioning of His Writings, trans.
Pleuke Boyce (Schraard: Kunst en Wetenschap, 2015), 7–8,
https://www.academia.edu/12304029/Andreas_Werckmeister_the_Historical_Positioning_of_his
_Writings. Pieter Bakker’s inventory of Werckmeister’s citations includes “fourteen classical,
fifteen late-classical and early Christian and twelve medieval writers, twenty-nine writers from
the first part of the 17th century and nineteen contemporary ones. From the period between 600
and 1400 only six writers are mentioned, among them the realist Anselmus and the Franciscans
Roger Bacon and Nicolaus de Lyra, who opposed Thomism.”
89
Bakker, 8.
90
Dodds, 3.1.
91
Dietrich Bartel, “Preface,” in Andreas Werckmeister’s Musicalische Paradoxal-Discourse:
A Well-Tempered Universe (Lanham: Lexington Books, 2017), xiv–xv.
119
Werckmeister’s philosophy is a regard for music as a speculative and mathematical, scientific,
and deeply theological pursuit. But Dodds notes that counter to this “old-style” understanding of
music as Quadrivium-bound, calculable art simultaneously runs a progressive bent toward
innovation in tangible musical practice. This is most apparent in matters of temperament,
tonality, contrapuntal techniques, and improvisation, experimental exploration of which
Werckmeister justifies on the “grounds that a creative artist not be fettered by arbitrary
constraints.”
92

In his laudatory poem (Figure 3.4) to Werckmeister in the introduction to Harmonologia
musica (1702), Buxtehude highlights precisely this dichotomy of prowess between speculative-
theological musical philosophy and practical applications. Also a clever, pun-filled acrostic on
Werckmeister’s name, Buxtehude’s poem recognizes Werckmeister’s knowledge of music
theory and praises his interest in glorifying God through music and in using music solely for
pure, Christian worship:

92
Dodds, 3.1.
120

Figure 3.4. Buxtehude’s poem in Werckmeister’s Harmonologia musica (1702).

(Whoever views a work of art rightly does not disdain it anonymously, speaks
freely without sheer cunning, in a Christian way, as is right, for when it comes to
the test, the work must praise the master. He, my friend has thought well, in the
book, and excerpted what is useful to art, honestly and unfeignedly, he has also
become work-master, praiseworthy in the order of muses)
93

Throughout Werckmeister’s published treatises, one finds frequent iterations of a thematic thread
of mathematics, theology, and especially their union in divinely ordained measure indicative of
Christian virtue and godliness. Although some of his thoughts about these ideas’ precise
implications for music theory and practice—especially temperament—shift slightly over the
course of Werckmeister’s career, their thematic presence remains ubiquitous from the 1680s
until the 1707 posthumous publication of his final treatise, the Musicalische Paradoxal-
Discourse (“or extraordinary speculations on how music has an elevated and divine origin”).

93
Andreas Werckmeister, Harmonologia musica, oder kurtze Anleitung zur misicalischen
Composition (Frankfurt and Leipzig, 1702; reprint, Hildesheim, 1970), introduction (my
translation). Reprinted with a different translation in Snyder, 127.
121
The first such treatise of Werckmeister’s to tackle overtly numerical ideas was his second
published, the Musicae mathematicae Hodegus curiosus (Quedlinburg, 1686 and 87), which
primarily concerns music theory’s mathematical and theological foundations, or, as the long title
states, “…not only the natural properties of the musical proportions as calculated on the
monochord, but also how through the same proportions, natural and correct reasoning can be
made about musical composition.” Similarly, his next treatise, Musicalische Temperatur
(Quedlinburg, 1686/87 and 91), constitutes a “clear and truly mathematical explanation” of
temperaments “with the aid of the monochord,” which in the last edition he illustrates with a
massive, two-foot-long copper engraving of a monochord.
94
Then, his 1691 Der edlen Music-
Kunst Würde, Gebrauch, und Miss-brauch (On the dignity of the noble art of music, its use and
misuse, according to Holy Scriptures and various ancient and reconfirmed pure church-
teachings) evidently concerns sacred music, but as usual, with mathematical underpinnings.
Werckmeister’s discussion of consonance and dissonance and order and disorder in chapter 4, for
example, hinges upon “the whole of Harmony [being] contained in the numbers 1, 2, 3, 4, 5, 6,
and 8,” but also on “Nature,” who “does not want to stray too far from the unity,” and
“Harmony,” whose “various orders [of measured height or depth of pitch] strive after equality”
in the unison, the ratio 1:1.
95

94
Bartel, “Introduction to the Musicalische Paradoxal-Discourse,” 11.
95
“…den die gantze Harmonia bestehet in den Zahlen 1. 2. 3. 4. 5. 6. und 8.”; “Also können
wir wieder mercken, daß die Natur nicht zu weit von der Aequalität schreiten…”; “Also sehen
wir, wie in der Harmonie vielerley Ordnungen müssen in acht genommen werden, welche alle
nach der aequalität streben.” For a discussion of some these issues of harmony, proportion, and
“generative unity,” especially relative to Bach’s works and drawn from this treatise of
Werckmeister’s specifically, see Ruth Tatlow, Bach’s Numbers: Compositional Proportion and
Significance (Cambridge: Cambridge University Press, 2015), 85–88.
122
While mostly about temperaments and Werckmeister’s theories of dissonance, his next
treatise, Hypomnemata musica (Quedlinburg, 1697), is also heavily numerical. As part of
Werckmeister’s explanation for what he will later explicitly call equal temperament and promote
as superior to both meantone and well-tempered but unequal options, he takes the reader through
intense mathematical discussion of the intervals, including a chapter on the properties of the
“harmonic numerals.” He also includes a chapter on what Dietrich Bartel calls “the age-old
question of ratio versus sensus,” in which Werckmeister ultimately concludes that while both the
mathematics and audibility of music are necessary for “determining acceptable temperaments
and harmonies,” it is steadfast number (ratio) that makes the final ruling, as an infallible check to
what the less reliable ear perceives.
96

Even Werckmeister’s most amusing treatise in concept and execution, the Cribrum
musicum (“or musical sieve, in which certain deficiencies of a half-educated composer are
presented, and in which the good is sieved and separated from the bad”), still incorporates these
profoundly serious themes, but expressed throughout in comically pompous and at times
polemical language: while aiming primarily to correct compositional errors using as a model an
anonymous, badly written (“embarrassing!,” “weak!,” “wretched!”) fugue that Werckmeister
allegedly “had been sent” as part of a larger work, immediately preceding presentation of the
“erroneous fugue,” chapter 3 contains a section about how “God put everything into good order,
the nature of music must also be as such which is proved through the numbers.”
97

96
Bartel, “Introduction to the Musicalische Paradoxal-Discourse,” 11.
97
This treatise also contains chapter 52 of Johann Kuhnau’s musical-satirical work, the novel
Der musicalische Quack-Salber (“charlatan”). In this chapter, “Der wahre Virtuose und
glückselige Musicus,” Caraffa, the novel’s titular charlatan, receives a letter from a pastor
defining the “true virtuoso and blissful musician” in exactly 64 tenets about the fundamentals of
music. In light of Werckmeister’s and his historical sources’ own numerological predilection,
particularly involving 3s and 4s, one wonders whether the number of tenets (4
3
) bears any
123
Among his eclectic citations and often found alongside Lutheran theologians, Christian
figures like St. Augustine, and ancient Greek philosophy, Werckmeister makes frequent esoteric
numerological references that an Enlightenment critic would find inconvenient, in the context of
an otherwise “rational” or “scientific” theoretical approach. Many such references include direct
occult philosophy and philosophers, as I will show later. But number-engaged music theorists are
especially important in this numerical investigation. Probably the most overt and personal of
these references center on Baryphonus. Direct quotes from personal letters to and from
Baryphonus appear in two of Werckmeister’s treatises previously mentioned: Musicae
mathematicae hodegus curiosus (1687) and Cribrum musicum (1700). The former contains
scattered details of correspondence between Baryphonus and (separately) Calvisius, Schütz,
Scheidt, and Grimm, while the appendix of Cribrum musicum contains other details of
exchanges between Baryphonus and Schütz and Baryphonus and Scheidt.
98
We do not know how
or why Werckmeister had access to Baryphonus’s personal correspondence; Benjamin Dobbs
guesses that at some point during his tenure in Quedlinburg, Werckmeister (on account of
physical and occupational proximity) was gifted some of Baryphonus’s personal effects.
99

Werckmeister’s ability to paraphrase ideas or even reproduce quotations from Baryphonus’s
letters would suggest that he was in sustained physical possession of the documents.

significance of order, reason, and virtue, either in Kuhnau’s original work or in Werckmeister’s
repurposing of it.
98
Benjamin M. Dobbs, “A Seventeenth-Century Musiklehrbuch in Context: Heinrich
Baryphonus and Heinrich Grimm’s Pleiades Musicae” (PhD diss., University of North Texas,
2015), 38. Werckmeister also cites Baryphonus’s Pleiades musicae in the Paradoxal-Discourse.
See Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 85. [MPD p.42]
99
Dobbs, “A Seventeenth-Century Musiklehrbuch in Context: Heinrich Baryphonus and
Heinrich Grimm’s Pleiades Musicae,” 39.
124
Chapters 11 and 37 of Werckmeister’s Musicae mathematicae hodegus curiosus also
present accounts of letters from Calvisius to Baryphonus, both of which concern issues of
notating intervals as proportions. In the first of these instances, Werckmeister draws support
from Calvisus for the notion that the smaller number in a given proportion should always be
placed above the larger one:
...it is not suitable that the larger number be put above or below, but because
proportions take their origin from unity, and seeing that in music all sounds spring
forth from the unison, it is more natural to set the smaller number above, an
opinion that Calvisius also expressed in a letter to Baryphonus. But it is, before all
else, to be taken into account that the smaller should not be exchanged with the
larger, sometimes above, sometimes below.
100

In the latter instance, Werckmeister again cites letters to and from Baryphonus and Calvisius as
part of a larger argument for expressing intervals as proportions, but this time, specifically
because numerical representation aids in visualizing harmonic variety, which he believes
desirable.
101
But within Werckmeister’s works, citations of correspondence between Baryphonus
and Schütz are more prevalent than correspondences between Baryphonus and any of the other
aforementioned people. These citations appear in three places, once in Cribrum musicum and
twice in Musicae mathematicae hodegus curiosus, as enhanced authority for claims that

100
Andreas Werckmeister, Musicae Mathematicae Hodegus Curiosus, Oder Richtiger
Musicalischer Weg-Weiser (Quedlinburg: Theodor Philipp Calvisius, 1686), 34. “Heiran ist nicht
viel gelegen / daß die grosse Zahl oben oder unten gesetzet werde / weil aber die proportiones
ihren Ursprung aus der Unität nehmen / und in musicis ex unisono alle soni entspringen / ist es
natürlicher, die kleinere Zahlen oben zusetzen: Welcher Meinung auch Calvisius in Epistola ad
Baryphonum; Doc hist vor allen Dingen in ach tzu nehmen / daß nicht die kleinern mit den
grössern bald unten bald oben verwechselt warden.” For further explanation and another
translation, see Dobbs, “A Seventeenth-Century Musiklehrbuch in Context: Heinrich
Baryphonus and Heinrich Grimm’s Pleiades Musicae,” 40–41.
101
Werckmeister, Musicae Mathematicae Hodegus Curiosus, Oder Richtiger Musicalischer
Weg-Weiser, 108.
125
Werckmeister himself likely thought contentious.
102
Werckmeister’s reliance on Baryphonus’s
and Schütz’s authority is significant, in that it would suggest respect that Werckmeister himself
not only holds, but that he apparently expects of his readers. In addition to providing a
numerically engaged lineage connecting Werckmeister with the Hamburg school—both Theile
and Bernhard studied with Schütz—perhaps Schütz also harbored a special interest in numerical
theology and its possible musical renderings.
103

Werckmeister’s numerical understanding of the universe permeates his writings. He
outlines these views most explicitly in his 1707 Musicalische Paradoxal-Discourse, in which he
interprets each counting number alone and in harmonic combination. Werckmeister’s meanings
for the numbers one through ten can be summarized as follows: 1 (“unity”) represents God the
Father, 2 (“dividing number”) Christ, 3 – the Trinity (or the Holy Spirit), 4 – the angels and
triadic sonorities, 5 – man and his five senses, 6 – animals and creation, 7 – the cross and the
Spirits of God, 8 – the trinity (as a cube) and full harmony, 9 – the “key” to both Paradise and
Satan, and 10 (the “circle number”) – completeness, and God’s Law.
104
Werckmeister also
ascribes meanings to Pythagorean ratios. Just as the perfect unison (1:1) represents the
foundation of all music, he understood it as symbolic of God’s perfection as the foundation of all
things.
105
The octave (2:1), then, represents the union yet distinction between God the Father and

102
Dobbs, “A Seventeenth-Century Musiklehrbuch in Context: Heinrich Baryphonus and
Heinrich Grimm’s Pleiades Musicae,” 41–42.
103
This question lies outside of the scope of a Buxtehude-centered gaze, but it remains
provocative in the scope of seventeenth-century musicology and historiography. Schütz also set
some of the more unusual texts Buxtehude set, including in the only other known seventeenth-
century setting of the text for Sicut Moses exaltavit serpentem in deserto. See chapter 7.
104
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 127–31. [MPD pp.92–97] Also summarized in Dietrich Bartel, Musica
Poetica: Musical-Rhetorical Figures in German Baroque Music (Lincoln: University of
Nebraska Press, 1997), 14–15.
105
Werckmeister, 127–31. [MPD pp.92–97]
126
Christ, and between the heavenly and earthly. Of these ratios, Werckmeister repeatedly notes the
special importance of the perfect fourth (4:3), for bridging the trinity (1:2:3) and the triad (4:5:6).
Only the “holy” and “secret” number seven is absent from harmonic ratios, which, according to
him, only enhances and proves its holy mystery, which no one but the spirit of God can
understand.
106

In this understanding of music, which Werckmeister finds in “theological numerals” and
explicitly calls “musical theology,” Werckmiester is not the author but rather the magnanimous
messenger: he passes on to his reader only that “which God himself has placed in nature, in order
that we may further probe and discover for our and our neighbor’s sake.”
107
Because
Werckmeister finds “the origin of music” in God, he believes that it is through the harmonic
numerals that “we can harmonize eternally with God.” He therefore describes the concordance
between God and the human soul in proportional terms: “for just as all numerals which are
closest to the unison result in a harmony with the same, so, too, can all people who do not
distance their spirit from God harmonize with him.”
108

Modern critics of numerological Bach scholarship often center their criticism on
Werckmeister, because he is so often cited for exactly these ideas in his Paradoxal-Discourse.
Scholars arguing against using him as a numerological source typically either claim that he refers
to numbers on a purely theoretical basis—explicitly not for practical use in composition—or that

106
Werckmeister, 130. [MPD pp.95–96] It is also believed that Buxtehude wrote a set of
(now lost) sonatas, each a meditation on the qualities and characters of the seven planets. See
Piet Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato Works,”
The Diapason 75 (1984): 19–21.
107
Werckmeister, 55. [MPD p.6]
108
Werckmeister, 73. [MPD p.28]
127
in their original contexts, Werckmeister’s numbers only refer to intervals.
109
Careful examination
of his numerical explanations in the Paradoxal-Discourse, however, reveals neither to be the
case. The most prominent counterexample is his treatment of the number seven throughout the
treatise. If Werckmeister were only interested in numbers as expressions of intervals, he would
not emphasize the number seven’s importance, nor explicitly explain its mystical significance as
deriving from its inaudibility to mortal ears.
110
In his prefatory material, Werckmeister is also
very precise about numbers’ intervallic vs. individual meanings:

[it is] necessary to disclose to the esteemed reader who is not familiar with the
principles of musical mathematics (for its understanding flows from this science),
that he may know what a musical proportion be, in order that he not confuse the
musical scale with the proportional numerals, and mistake the one for the other.
111

In chapter 13, he later offers a practical (i.e., not purely theoretical) idea for simplifying German
tablature by expressing note durations with “arithmetical values.”
112
When he does not specify
“arithmetical” values, he does not automatically refer to musical intervallic proportion. When
Werckmeister speaks about numbers’ meanings, he most often refers to proportion in general,
and then applies this to musical interval, usually to forward arguments about music’s theological
basis:
...all consonances as well as the motions of meter and beat are purely those
proportional numerals which are closest to the unison or equality...Because music
is a matter of clarity and order, and as such is nothing other than a pattern and
construct of God’s wisdom, a human being ...will naturally be moved to joy when

109
Pieter Bakker, Modern Numbers: Source References in the Numerical Research of Bach’s
Musical Structures, trans. Pleuke Boyce (Schraard: Kunst en Wetenschap, 2015),
https://www.academia.edu/15734670/Modern_Numbers_Source_References_in_the_Numerical_
Research_of_Bachs_Musical_Structures.
110
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 62. [MPD p.15]
111
Werckmeister, 59. [MPD p.12]
112
Werckmeister, 109. [MPD p.70]
128
this construct and wisdom of his benevolent Creator is instilled into his ears and
subsequently his heart and affections through such reverberating numerals.
113

And again, in proving links between God and man’s soul, as mediated by numbers and music,
Werckmeister makes each of these leaps explicit, rather than conflating number and interval, as
his modern critics argue he does habitually:

In proceeding further, we discover that the Almighty God has not only created all
things harmonically, but subsequently has commanded humans to construct all
things harmonically, as illustrated in the proportions concerning length, height,
and breadth. For example, Noah’s ark was three hundred cubits long, fifty wide,
and thirty high. Should this be transferred to the monochord, it would result in the
harmonic triad C g’ e’’. Similarly, the Ark of the Covenant, the Mercy Seat, the
Table, the Tabernacle, the Temple of Solomon, and all constructions were built
harmonically according to the musical proportions through God’s command.
Should this have occurred by chance and without cause? Certainly not!
114

Here, number inhabits multiple roles (“length, height, breadth”) dictated by God, which He then
applies to musical interval, via mathematical proportion. In “constructing all things
harmonically,” Werckmeister invokes all proportion—God’s proportion, the human body’s
proportion, biblical structures’ proportion—of which audible music is but one manifestation.
This is a theology and whole worldview based in mathematical preeminence, as God’s
foundational language, rather than a narrow understanding of numerical power as only contained
in musical interval.
Werckmeister was by no means unusual for these beliefs about number as the fabric of
the cosmos—he was just more explicit and insistent about it, later than most of the other theorists
with whom his number-centric cosmology resonated. The most famous of these theorists during

113
Werckmeister, 70. [MPD pp.24–25]
114
Werckmeister, 74. [MPD p.29]
129
Werckmeister’s lifetime, and certainly known to both him and the Latin-educated Buxtehude,
Jesuit priest Athanasius Kircher was similarly interested not only in the mystical and musical
meanings of individual numbers, but also in calculus, the basic arithmetical operations to which
numbers may be subjected, to enhance their theological interplay. Kircher’s Arithmologia and his
Ars Combinatoria contain thorough description of his mathematical logic system, in which he,
like Werckmeister, notes the theological value of basic arithmetic.
115
For example, in addition to
the number twelve’s perhaps obvious connection to the twelve Apostles, he suggests that twelve
should simultaneously be understood as a combination of three and four that then symbolizes the
spreading of Trinitarian belief over the four corners of the earth.
116
He also discusses
combinatorics, but Werckmeister, just one step beyond in connecting such operations to music,
goes so far as to enumerate all of the possible consonances created by the sequence of the seven
numbers “1, 2, 3, 4, 5, 6, and 8,” describing their twenty-one combinative pairs as the product of
three and seven, and for this reason, explicitly, a “Trinity in divinity.”
117
Buxtehude, who served
as accountant for Lübeck’s Marienkirche during his long tenure as organist and music director,
might have held similar interest in arithmetic’s theological value, beyond its natural role in
musical intervallic proportion.
118

115
Robin Wilson and John Fauvel, “The Lull before the storm: combinatorics in the
Renaissance,” in Mathematicians & their Gods: Interactions between mathematics and religious
beliefs, ed. Snezana Lawrence and Mark McCartney (Oxford: Oxford University Press, 2015),
97–99.
116
Jean-Pierre Brach, “Mystical arithmetic in the Renaissance: from biblical hermeneutics to
a philosophical tool,” in Mathematicians & their Gods: Interactions between mathematics and
religious beliefs, ed. Snezana Lawrence and Mark McCartney (Oxford: Oxford University Press,
2015), 106–7.
117
Werckmeister, Musicalische Paradoxal-Discourse, 96–97.
118
Buxtehude’s close friend Johann Adam Reincken refused a similar accounting position in
his organ post in Hamburg, likely because he did not need the extra money, rather than because
he found the job incompatible with his musical pursuits.
130
As in Kircher’s works, surrounding Werckmeister’s discussion of numbers and “musical
theology” in his treatises, one finds frequent references to Hermetic philosophy and
philosophers—this is intriguing, considering evidence of alchemical and Rosicrucian
numerology in Buxtehude’s works,
119
and of Michael Maier’s influence in Theile’s.
120
One of the
most striking characteristics of Werckmeister’s language and citations in his treatises is the
freedom with which he, a Lutheran church-employee, mingles Judeo-Christian wisdom with
Hermetic and Paracelsian precepts, presumably finding them consonant with one another. He
directly mentions Paracelsus at one point, suggesting that one familiar with biblical verse
understands the power of celestial music: “That which Theophrastus Paracelsus and innumerable
other philosophers wrote concerning the wondrous effects of the heavenly bodies shall remain
unsaid at this point, for the effects are already familiar to us through Holy Scriptures.”
121
Soon
after, alluding again to Paracelsian authors (“philosophers”), Werckmeister invokes the Hermetic
precept “as above, so below,” after describing music as a “sub-constellation” that harnesses its
power from possessing the “same order as that of the constellations”:
122
“However, no one who
has proper knowledge regarding natural phenomena will refute that lower things, including
humans, are governed by higher things such as the constellations, which has long been affirmed
by so many philosophers.”
123

Werckmeister’s numerological sources for his Paradoxal-Discourse are even more
overtly esoteric in established ties to alchemy, Rosicrucianism, and Paracelsian philosophy.

119
See chapters 4–7.
120
Yearsley, “Alchemy and Counterpoint in an Age of Reason,” 22–27.
121
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 68. [MPD p.22]
122
Werckmeister, 69. [MPD pp.23–24]
123
Werckmeister, 72. [MPD p.26]
131
Werckmeister claims that of all of the “many learned men and philosophers” (alchemists) who
have “written concerning the character, nature, and mystery of the numerals,” he recommends
that his reader consult Georg Philip Harsdörffer’s Mathematische und philosophische
Erquickstunden, Agrippa’s De occulta philosophia (book 2), and Giordano Bruno’s De Monade
et Numero.”
124
As part of Werckmeister’s introduction to his own interpretation of the numbers
one through ten, he recommends that one look at Johann Christian Lange’s 1702 Theologia
Christiana in Numeris (Christian theology in numerals) for further explanation of the ways in
which “God has revealed his wisdom and harmony very clearly to us through the
numerals.”
125
Lange’s work is essentially a Christian theosophical meditation on each of the
numbers one through ten (their shape, appearances in scripture, secret meanings, etc.),
126

complete with cabala-inspired images and word diagrams strongly resembling those found in
Rosicrucian sources (discussed elsewhere in the present study, for their connections to
Buxtehude’s texts and numerical symbols), dating from as early as 1604 and as late as 1700.
The fluency that Werckmeister demonstrates in these occult topics and authors tells us
something important, if uncomfortable in pursuit of neat epistemological categories. From this,
one reaches at least three possible conclusions: either Werckmeister was unusual in this occult
fluency and he was a worse teacher than his technically careful explanations would suggest,
insomuch as he would self-consciously speak over his readers’ heads; or, he was unusual in his
knowledge of Hermetic sciences, but he pedagogically believed that the uninitiated reader has

124
Werckmeister, 60. [MPD p.12]
125
Werckmeister, 126. [MPD p.91]
126
Johann Christian Lange, Theologia Christiana In Numeris. Das Ist: Sonderbahre
Darstellung, Wie Die Fürnehmsten Haupt-Stücke Christlicher Gottes-Gelehrtheit...in Dem
Denario Der...Pythagorischen Tafel, Oder in Den Grund-Zahlen Aller Zahlen von 1 Bis
10...Fürgebildet Und Enthalten Sind (Franckfurt; Leipzig, 1702), http://resolver.staatsbibliothek-
berlin.de/SBB0001CCF300000000.
132
something important to learn from these occult sources, by proxy; or, this kind of fluency was
not necessarily unusual in Werckmeister’s time and place. In addition to being the simplest
conclusion, this last one best supports his argumentation style: he typically draws upon these
occult authors seemingly to boost his own credibility, especially in matters he expects his reader
to find challenging. Thus, one concludes that he these sources themselves to be convincing,
rather than contentious.
Surprisingly, the biggest modern controversy surrounding Werckmeister’s relationship
with Buxtehude does not concern Hermetic philosophy or numerology, but rather specifics of
contrapuntal practice. The circumstances of Buxtehude’s 1702 testimonial in Harmonologia
musica remain unknown; but on the surface, the treatise advertises instructions for contrapuntal
operations that, in similarity to practices of his counterpoint “brotherhood” with Theile and
Reincken, would seem to interest Buxtehude. Werckmeister’s full title explains the work’s aims:
HARMONOLOGIA MUSICA or Brief Introduction to Musical Composition. How
one can compose and improvise simplex counterpoint using the rules and symbols
of thoroughbass with the special aid of three chords or hand positions, and
through this have the opportunity to advance and to make variations at the
keyboard and in composition; together with instruction on how one may make or
arrange double counterpoint and all sorts of canons, or fugas ligatas, through
special devices and advantageous techniques, all on the basis of mathematical
and musical foundations; brought to press and published by Andreas
Werckmeister of Benneckenstein in Thuringia, currently organist in the main
parish church of St. Martin in Halberstadt.
127

127
Andreas Werckmeister, Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen
Composition (Quedlinburg: Theodor Philipp Calvisius, 1702). Full title: HARMONOLOGIA
MUSICA Oder Kurtze Anleitung zur Musicalischen Composition. Wie man vermittels der Regeln
und Anmerckungen bey den General-Bass einen Contrapunctum simplicem mit sonderbahrem
Vortheil durch drey Sätze oder Griffe Componiren, und extempore spielen: auch dadurch im
Clavier und Composition weiter zu schreiten und zu variiren Gelegenheit nehmen könne:
Benebst einen Unterricht, wie man einen gedoppelten Contrapunct und mancherley Canones
oder Fugas Ligatas, durch sonderbahre Griffe und Vortheile setzen und einrichten möge, aus
denen Mathemathischen und Musicalischen Gründen aufgesetzet und zum drucke herausgegeben
133

But in modern discussions, this treatise—and the appearance of Buxtehude’s laudatory poem in
this particular work of Werckmeister’s and not others—has prompted speculations and heated
debate about the extent and finer qualities of Buxtehude’s contrapuntal interests. Snyder and
Dodds both conclude that because Buxtehude used some of the specific contrapuntal methods
Harmonologia musica treats, that:

Buxtehude must have read Werckmeister’s composition treatise with great
interest, because it teaches the same techniques of invertible counterpoint and
canonic writing that he himself had cultivated—along with Bernhard, Theile and
Reincken—in the 1670s. Werckmeister gives examples of quadruple counterpoint
against a chorale melody and proposes the use of double sets of parallel thirds as
the key to all kinds of canons and double, triple, and quadruple counterpoint. This
is precisely the technique that Buxtehude had used in his canons for both Meder
and Reincken.
128

While Snyder is correct about technical similarities between Werckmeister’s counterpoint
method and Buxtehude’s gift-canons for Meder and Reincken,
129
David Yearsley, from a
Hamburg-school perspective, does not believe that Harmonologia musica “could have been of
much technical interest to [Buxtehude],” because it “[treats] only the most basic procedures in
the simplest of manners.”
130
I agree with Yearsley on this point: if Buxtehude was so close to the
source of the highest-level counterpoint in all of Europe, he could not possibly have learned
much “lofty” technique from the watered-down version of canon and counterpoint

Durch Andream Werckmeistern, Benicosteinensem Cheruscum, p.t. Organisten in der Haupt-
Pfarr-Kirche zu St. Martini in Halberstadt.
128
Snyder, Dieterich Buxtehude: Organist in Lübeck, 127.
129
For more examples of this in Buxtehude’s catalog, see Dodds, “Columbus’s Egg: Andreas
Werckmeister’s Teachings on Contrapuntal Improvisation in Harmonologia Musica (1702),” 5.
130
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 80–81.
134
Werckmeister’s Harmonologia musica contains.
131
But in the extremity of his viewpoint,
Yearsley overlooks the possibility that Buxtehude still could have appreciated the treatise for
other reasons, including precisely this ease and practicality, without regard for “the gulf”
between theory and practice that separates Werckmeister from the Hamburg school.
132
In this
light, both Yearsley’s and Snyder’s arguments remain well-founded and opposed, but become
not actually irreconcilable: Buxtehude, as much a church musician as a counterpoint “brother,”
could have appreciated Werckmeister’s practical offering even if Werckmeister’s expression of
theoretical precepts faltered, relative to the lofty level of the explicitly impractical Hamburg-
school exercises.
The rift between Yearsley’s and Snyder’s readings assumes that both Theile and
Werckmeister held similar beliefs about the perils of disseminating (“before swine”) this
contrapuntal information, which they probably did not. In Harmonologia musica, Werckmeister
aims only to give his reader the tools to use music for proper Christian worship. He also
expounds on the value of simplicity, and the ultimate, most profound simplicity—the unity,
1:1—is his vision of the Godhead itself, which ultimately forms his central argument for equal
temperament.
133
While resting on more profound “mathematical and musical foundations,”
Werckmeister’s contrapuntal strategies in Harmonologia musica succeed in this practicality,
through their accessibility to readers with only rudimentary keyboard technique and their aim of
aiding church organists in improvisation. Werckmeister addresses the treatise to this audience, as

131
Yearsley, 77–78. As Yearsley even more forcefully states, “Indeed, Bokemeyer’s
admonition against throwing pearls before swine bring to mind Werckmeister’s treatment of this
hallowed subject.”
132
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 79.
133
Dietrich Bartel, “Andreas Werckmeister’s Final Tuning: The Path to Equal
Temperament,” Early Music 43 (2015): 503–12.
135
he frequently reminds the reader, with asides such as “But again I say that I have not wanted to
write anything here for experienced, erudite, and virtuosic people, nor for uncomprehending
slanderers, but only for beginners and music-lovers.”
134
The necessity of sharing helpful
information with one another is a recurring theme throughout his treatises. For instance, he
similarly expounds on “neighborly” education, while hinting at possible different levels of
understanding within the information he presents, in this passage from his Paradoxal-Discourse:

...our well-intentioned thoughts should be presented to our neighbor with all due
respect (as every Christian is obliged to do), and would that everyone should
serve his neighbor with his own talent…We are human beings, and are indebted
to serve each other with our respective talents: “Not everyone can do all
things.”
135

Passages like these contextualize and soften some of Werckmeister’s more abrasive language
toward opacity that Yearsley reads as “pejorative,” or as evidence that Werckmeister believes
learned counterpoint to be “arcane and useless.”
136
For instance, Yearsley reads the theorist’s
descriptions of older Zarlinian counterpoint as having “many dark rules” (viel dunckele
Regeln)—a few of which he reproduces for his reader just “out of curiosity” (zur Curiosität)—as

134
Werckmeister, Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen
Composition, 184. “Ich sage aber noch einmahl, dass ich vor exercirte, hochverständige, und
virtuose Leute, auch vor die unverständigen Lästerer, nichts wil geschrieben haben, allein, nur
vor die Incipienten, und Music-Liebende.” Dodds notes that “’Incipienten’ here denotes not rank
beginners (the book does not after all address such fundamentals as scales, intervals, and key
signatures), but rather musical apprentices who possess basic knowledge and are ready to
advance further…Thus in the main body of the treatise he addresses such topics as thoroughbass,
the modes, transposition, and the requisite traits of the church organist—traits that include the
ability to improvise fugues and chorale settings.” See Dodds, “Columbus’s Egg: Andreas
Werckmeister’s Teachings on Contrapuntal Improvisation in Harmonologia Musica (1702),” 3.2.
135
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 55–56. [MPD, p.7]
136
Yearsley, 79.
136
antagonistic.
137
But I think Werckmeister, in a “neighborly” way, intends this language only to
exaggerate his own method’s simplicity. And simple it is: he offers an almost automated method
of generating double counterpoint from parallel thirds, one “above” (in the right hand) and
another “below” (in the left) the main theme to be treated.
138
Especially compared to the “secret”
and “lofty” works of “untiring diligence” by Theile,
139
Werckmeister’s many descriptions of this
method, with its “convenient advantages” (bequeme Vortheile),
140
read like do-it-yourself
counterpoint advertisements, promising instant canon and double counterpoint “without
difficulty” (ohne Muhe).
141
As an advertiser, he probably therefore intends the following
description not to disparage Zarlino, but merely to emphasize his own method’s comparative
ease:

The rules that Zarlino and his followers have given are too extensive and obscure,
and one cannot easily grasp their meaning in a moment. But our [method/rules]
are infallible and consist of patterns in which a third is always placed above and
below…
142

To Yearsley, Werckmeister’s “keyboard-oriented approach”
143
shows “a certain lack of
intellectual rigor...[implying that] that which cannot be easily understood…is not really worth

137
Werckmeister, 111.
138
Note the possible Hermetic allusion to “above” and “below.”
139
Yearsley, 78.
140
Werckmeister, Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen
Composition, 95.
141
Werckmeister, 125.
142
Werckmeister, Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen
Composition, 119. “Die Regeln so Zarlinus und seine Nachfolger davon gegeben haben / sind
gar weitfläuffig und obscur, daß man sich in einem Moment nicht leichte besinnen wird. Unsere
aber bestehen aus den Sätzen / wann unten und oben allezeit eine Tertia gesetzet wird / so kan es
nicht fehlen…”
143
Yearsley, 80.
137
the trouble of learning.”
144
It is true that Harmonologia musica does not claim intellectual rigor;
but if read in a magnanimous tone, in a spirit of pedagogical accessibility, the combative edge
that Yearsley perceives in Werckmeister’s descriptions of learned counterpoint fades. Again, in
his Paradoxal-Discourse, as an even more theological work, Werckmeister expounds on both
music’s “divine mysteries” and the importance of simplifying this fact for all levels of
appreciation:
That music or harmony finds its origin in God and is a marvellous gift of the
Creator to humans is known and understood not only by many blessed and
learned theologians, but even the wise heathens recognized this through the light
of nature. However, should the simple garnish little light and knowledge of such
eminent and divine mysteries, even though such eminent matters can be discerned
from music and harmony, we will now in all simplicity register a few things for
their own good and better understanding. God grant that it may be employed to
his glory and to the edification of our neighbor.
145

If Theile’s and Zarlino’s “dark rules” require initiation and cultivated idealized secrecy, then
Werckmeister does not play their game, and thus cannot win or lose. His treatise serves exactly
the opposite purpose of the Hamburg school’s intentional contrapuntal secrecy: Werckmeister
designs his explanation only to address practical aspects of composition and improvisation,
presumably as simply as possible, with as broad a reach as possible.
As Yearsley has demonstrated, the Hamburg school was as concerned with
counterpoint’s intentional impracticality and secrecy as an art “above all other arts” as its actual
techniques.
146
Thus, any competitive effort in this arena would require initiation and an
understanding of “secret” and “lofty” counterpoint’s rhetoric. On the surface, Werckmeister

144
Yearsley, 79.
145
Werckmeister, 59. [MPD p.11]
146
Yearsley, 60–61.
138
indeed appears to be the “Musicus Practicus” to whom Theile disparagingly refers. As an author
and church musician expected to compose and improvise pleasing music on command,
Werckmeister writes for a very public, rather than a very secret, audience. And yet, much of his
language surrounding counterpoint’s value suggests that he did, in fact, know and believe in
“lofty” contrapuntal secrets. Perhaps he encountered them through correspondence with
Buxtehude or any other Hamburg contacts in the “brotherhood”—including those who
eventually inherited some of Buxtehude’s works and letters from him. Werckmeister’s
Neoplatonist description of invertible counterpoint as reflective of cosmological order (also from
Harmonologia musica) suggests a more philosophically profound understanding of counterpoint
than do his simple technical explanations:

The heavens are now revolving and circulating steadily so that one (body) now
goes up but in another time it changes again and comes down. This circulation is
therefore to be found in and on the earth and also in microcosm in man. As the
philosophers say, high is low and low is high. We also have these mirrors of
heaven and nature in musical harmony, because a certain voice can be the highest
voice, but can become the lowest or middle voice, and the lowest and middle can
again become the highest.
147

If Werckmeister believed so strongly in counterpoint’s cosmological profundity and wanted to
protect its true secrets, then would his dressing it up as a “simple” and “easy” not cleverly fortify
walls between counterpoint’s “true” meaning and the uninitiated? One remembers the hopeless
“fools” the Rosicrucian authors describe, who think that alchemy is “just” about gold-making,
based only on the preponderance of available recipe-books.
148

147
Werckmeister, Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen
Composition, v. Transcribed and translated in Yearsley, “Alchemy and Counterpoint in an Age
of Reason,” 212.
148
[Anonymous], “Fama Fraternitatis,” 31. The authors say, “Concerning the godless and
accursed gold-making, this has gotten so out of hand in our time that many greedy gallows-birds
139
Buxtehude has gotten caught in the modern philosophical crossfire, as a hinge between
these two different contrapuntal worlds. This is useful to think about, considering the tension in
his compositions between audible and inaudible compositional structures.
149
His music reflects
an understanding of learned counterpoint consistent with the Hamburg school’s teachings, yet
this music “to be heard” also constantly risks divulging Theile’s secrets, in frequent appearances
of readily audible canonic techniques.
150
Practical, technical contrapuntal operations on their
own are probably the only possible intersection between Werckmeister and the Hamburg school.
But this does not mean that both groups’ trajectories in this analogy are diametrically opposed—
especially in revering music as expressions of divine wisdom on earth.
Ultimately, Werckmeister’s treatises and his numerical theology therein give the modern
reader a glimpse of the final flowering of a much longer lineage of Hermetic thinkers fascinated
by numerical consistency in the microcosm and macrocosm, and musical expressions thereof,
rooted in a mathematical understanding of God. If he is eclectic or peculiar in this way (as
Bakker states in no uncertain terms),
151
that in no way dilutes his potential influence on
Buxtehude’s numerical thought. The same is true for Snyder, Dodds, and Yearsley’s debate
about the reasoning behind Werckmeister’s contrapuntal techniques in Harmonologia musica:
Buxtehude can have parallel conversations both with his Hamburg friend-group and
Werckmeister, and take something from each, without disrupting the goals and projects of the

practice great knavery with it…There are also simple people at this time who are of the opinion
that the transmutation of metals is the apex and summit of philosophy…We hereby publicly
declare this to be false. To the true philosophers, gold-making is a trivial matter and a side issue,
in comparison with which they have a thousand better skills.”
149
Perhaps most starkly in Herr, wenn ich nur Dich hab’ (BuxWV 38). See chapter 5.
150
Yearsley, “Ideologies of Learned Counterpoint in the Northern German Baroque,” 18.
151
Bakker, Andreas Werckmeister: The Historical Positioning of His Writings, 8.
“Werckmeister isn’t so much a prototype representing the most important writers of his time and
surroundings, but rather an example of the group of organists and cantors who didn’t write.”)
140
other. Moreover, despite their breadth and wide-ranging citations, Werckmeister’s treatises,
especially the Paradoxal-Discourse, were not intended to be exhaustive composition textbooks.
They also increasingly become temperament-related manifestos towards the end of his
Werckmeister’s life, and his reasoning for turning to equal temperament is mathematical, based
on his “axiom” that “The closer something is to its origin, the more perfect it is; therefore, the
further proportions are removed from their origin or the unison, the more imperfect they are.”
152

In this cosmological scheme, humans can only learn so much about composition: “Humans are
not in fact the originators of music but only the tools which God uses for his own purpose. God
is directly and indirectly the author of all music in this earthly life.”
153
Thus, frustrating as it may
be, the fact that Werckmeister, for all his numerical exegesis, does not explicitly tell composers
how to invoke numbers in their compositions makes sense. If God has through His works proven
numerical preeminence, to Werckmeister, a composer’s task should be to praise God with
number within his means, even if that does not extend beyond simply understanding the
theological importance of the counting numbers and their proportions. If numbers are a
foundational truth of the universe, then those predisposed to understanding and using them
through a mathematical gift can use them however they can, as a form of praise. For others,
“good” composition itself, as an inherently numerical activity, will still glorify God through
sounding ratios as intervals—that is, if employed in a “Christian way,” as Werckmeister makes
clear and Buxtehude’s poem for him praises above all else: “For music is an image of God, and

152
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 60. [MPD p.13] See also Bartel, “Andreas Werckmeister’s Final Tuning:
The Path to Equal Temperament.”
153
Werckmeister, Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, 72. [MPD p.26]
141
God cannot better be glorified than through his own power, order, and edicts which he himself
has dispensed.”
154

154
Werckmeister, 75. [MPD p.31]
142
CHAPTER 4
Analyzing the Basso Ostinato Psalm Settings:
Introduction, Methodology, and Examples from Laudate pueri Dominum (BuxWV 69)

4.1 – Buxtehude’s Vocal Music
Buxtehude’s vocal works are amazingly diverse, covering a range of genres, scoring,
compositional styles, length, and texts. At an estimated 122 total,
1
more of his vocal
works survive than any chamber or keyboard works; yet they have until the last decade
represented the minority of Buxtehude scholarship.
2
Extant vocal compositions (in four
languages) include ensembles as small as solo voice, solo stringed instrument, and
continuo (BuxWV 64 and 98) and as large as six choirs of nine voices, fifteen
instruments, and continuo (BuxWV 113). In terms of length, Buxtehude’s discrete works
range from a short, ten-measure strophic aria and ritornello (BuxWV 105) to three
chorale strophes of 525 total measures (BuxWV 41).
Kerala Snyder attributes this wide variety to Buxtehude’s relative compositional
freedom in his job: his positions never required him to write vocal music, so he wrote all
“quite apart from his official duties as organist.”
3
One finds this fact especially
compelling in the scope of this dissertation. Intentionality behind the numerical
structures and coordinated alchemical subtext presented in the remaining chapters would

1
This is according to the Buxtehude-Werke-Verzeichnis (BuxWV), including
adjustments such as removing sources of doubtful authenticity plus two parody works
(same music, only the texts changed), but then in turn counting the Membra Jesu Nostri
cantatas as seven discrete works. See Kerala J. Snyder, Dieterich Buxtehude: Organist in
Lübeck, 2nd ed. (Rochester, NY: University of Rochester Press, 2007), 137.
2
Olga Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich
Buxtehude,” Early Music 46, no. 2 (2018): 235.
3
Snyder, Dieterich Buxtehude: Organist in Lübeck, 137.
143
require an element of serious personal investment, far beyond routine execution for
public—and only aural—appreciation during services.
If vocal writing had been part of Buxtehude’s routine weekly obligations, one
might gather a different concept of their specialness than this study presupposes. It is
possible that Buxtehude used numbers as part of his general compositional process,
including the most mundane,
4
but this is not the prevailing impression after a close
examination of his ostinato psalm settings. The skill and energy that this level of
engineering would require indicates the specialness of these works as a subgenre of
Buxtehude’s œuvre. The fact that he could approach their composition with relative
textual and constructional freedom supports this idea, in that his creative boundaries
would have come either from him or from individual patrons on whom he did not rely
for basic income.
5

Most of Buxtehude’s extant vocal works, both ostinato and not, contain German
or Latin texts: eighty-six in German and thirty-three in Latin survive. While this
preponderance of Latin texts might seem strange for a Protestant composer, Kerala
Snyder’s archival research shows that Latin-texted works were commonly performed at
Lübeck’s Marienkirche,
6
and these comprise most of the printed music in the church’s
old music library. Gustav Düben also preferred Latin-texted works: the Düben collection

4
Future projects will explore this possibility, in determining which numerical
operations from Buxtehude’s basso ostinato vocal works also appear in his organ works
probably intended for services, to build upon the numerical analyses of Carol Jarman and
Piet Kee.
5
For information about Buxtehude’s funding sources for projects, see Snyder,
Dieterich Buxtehude: Organist in Lübeck, 61–65.
6
Snyder, 138. For instance, many of the works performed in the Marienkirche
festival services of 1682-83, during Buxtehude’s tenure there as organist and music
director.
144
preserved all but one of Buxtehude’s Latin-texted works, and this linguistic preference
probably explain’s Buxtehude’s choice of Latin text for his 1680 Membra Jesu Nostri
(dedicated to Düben).
7

Buxtehude’s ostinato psalm settings represent an intersection of two significant
aspects of his œuvre. He drew texts for twenty-five of his surviving works from the
Psalms, leading Kerala Snyder to deem them his “most important biblical source.”
8
Of
these, only three compositions setting a complete psalm text survive—BuxWV 17, 23,
and the Laudate pueri Dominum (BuxWV 69) analyzed later in this chapter. As another
subset of his output, Buxtehude’s basso ostinato vocal works “cut across the genres of
concerto and aria.” Snyder categorizes BuxWV 38, 57, 69, and 92 as concertos, and
BuxWV 70 and 62 as arias, with the latter actually designated “Aria” in its manuscript
sources. BuxWV 57, 69, 70, and 92, meanwhile, all bear the title “Ciaccona,” in various
spellings. Both “ciaccona-arias” set poetry by Ernst Christoph Homburg, while the texts
of the “ciaccona-concertos” all vary more widely.
9
Buxtehude scores these six ciacconas
for one, two, three, and four voices with instruments.
10

7
Snyder, 137–38.
8
Unlike Schütz and others, Buxtehude did not set many complete psalms. See
Snyder, 138.
9
These texts include a German psalm, a Latin poem, a complete Latin psalm, and an
unidentified Latin devotional text.
10
Snyder, Dieterich Buxtehude: Organist in Lübeck, 173.
145
4.2 – Counting Methodology and Buxtehude’s Organ Tablature
Throughout all of my analyses, my main methodological tenets involving numbers and
calculations include four points. I will first print the condensed list here, then explicate
relevant components of the first two items in the next section. Mathematical explanations
related to the third point comprise the next numbered chapter-section (4.3):
1. In counting notes, the numbers I indicate in my analyses all refer to
sounding pitches, not total note-heads; in instances of ties, I include
only the articulated note in my calculations.

2. The numbers I include belong to the following categories: measure
number, note number, and ground-iteration number.

3. The mathematical operations to which I subject any note, ground-
iteration, or measure number include factorization, digit addition, ratio
division, and “figurate” number formation. These are all common
procedures well known in the seventeenth century.

4. In annotated musical examples, note numbers and measure numbers
are in Arabic numerals, while ground-iteration numbers are in
uppercase Roman numerals.

Further Explanations:

1. In counting notes, the numbers I indicate in my analyses all
refer to sounding pitches, not total note-heads.

I count in this way because German organ tablature, likely Buxtehude’s preferred
notation method,
11
operates in this manner. Even toward the end of the
seventeenth century, music printing in Germany was difficult and inconsistent;

11
The manuscripts of Buxtehude’s that Walther owned were in tablature. In general,
it held the advantage of saving space (and therefore paper) and of aligning the parts more
legibly than other methods. See Snyder, 313.
146
one maintained significantly better control over quality, accuracy, and legibility in
manuscript than one could in moveable-type.
12
Copperplate engraving was much
more accurate, but it was also expensive and not commonly available in Germany
until the eighteenth century.
13

German organ tablature notation (Example 4.1) was an efficient
manuscript-only solution, excellent for providing compact overviews of both
keyboard and ensemble music in letter notation. There are three parts in this
system: letters designate pitch class, letter case designates octave, and rhythm
signs show the location and duration of notes. This notation shows measures
through long horizontal lines that group all of the notes in a given measure
together. The rhythm signs are comprised of vertical strokes to indicate separate
notes, and horizontal strokes to designate note value. While it can be challenging
to determine octave at times (these measure lines function as octave lines as well),
virtually every other parameter was clearer in this notation than in contemporary
German printed music.
14

12
Smaller note values were difficult to print, and the results were difficult to read.
See Snyder, 313–14.
13
Snyder, 314.
14
Snyder, 315. For a direct tablature-to-staff transcription with features labeled, see
Snyder, 316–17.
147

Example 4.1. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), opening
in organ tablature from the Düben Collection.

Perhaps not coincidentally, it is also much easier to count notes in this tablature
system than it is in staff notation.
15
This is the case for two reasons: the pitch and
rhythms are separated such that the note flags are already grouped into countable
sets, and the relatively condensed format means that the rhythmic flags in
different voices are more vertically aligned than individual notes typically are in
Buxtehude-contemporary staff-notation publications.

15
I mean this in light of the fact that both Walther and Werckmeister owned
Buxtehude’s manuscripts specifically in tablature. See chapter 3.
148
2. The numbers I include belong to the following categories:
measure number, note number, and ground-iteration number.

According to Walther’s 1732 Lexicon, the “bar” (Tact/Takt)
16
is the appropriate
measurement unit for calculating the approximate length of a composition during
planning stages. In Bach’s Numbers, Ruth Tatlow also demonstrates evidence of J. S.
Bach’s keeping track of measure numbers in his sketches and revisions.
17
In both
Buxtehude’s Herr, wenn ich nur Dich hab’ and Quemadmodum desiderat cervus, I have
found possible evidence of Buxtehude’s keeping track of measure numbers, but also
note-numbers. This often manifests in inaudible note repetitions under melismas, near
places of central importance to a work’s larger numerical structure. As in this example
(just one of many), perhaps Buxtehude realizes that he is just a note away from his
numerical target, so he picks up an extra one (the d repetition, Example 4.2):

Example 4.2. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), m. 70.

16
Ruth Tatlow, Bach’s Numbers: Compositional Proportion and Significance
(Cambridge: Cambridge University Press, 2015), 113–14.
17
Tatlow, 102–29.
149
4.3 – Figurate Numbers and Alchemical Geometry: A Primer
Although Walther does not mention quantities of notes as any typical measurement of a
work’s length, in all three ostinato psalm settings the number of notes in the actual
ostinato bass is significant, as all are “figurate”
18
numbers.
Figurate numbers comprise one of the oldest areas of Western mathematical
inquiry, dating back to the Pythagoreans of the sixth century BCE, but they also
fascinated seventeenth-century mathematicians and mystics.
19
As their name suggests,
figurate numbers are “figures” in that they can be visually arranged into geometrical
structures of regularly spaced points. Today, these numbers are primarily investigated by
student mathematicians, since interest in figurate numbers—and in number theory more
broadly—significantly declined during the Enlightenment drive toward applied fields.
Still, no better tool exists for teaching basic relationships between geometry and
arithmetic.
20

The Pythagoreans put special value in the number one—the “monad”—as the
fundamental from which all things emanate. They saw every possible geometric
arrangement as being composed of unit, and it is for this reason that figurate numbers
provided their most automatic quantifying methods, often as physical pebbles on the

18
Also called “figural” or “figured.” See chapter 2 for connections between these
numbers and seventeenth-century Rosicrucianism.
19
For example, Pascal uses figurate numbers extensively in his 1653 Treatise on the
Arithmetic Triangle, and “Pascal’s Triangle” is itself a type of exponential rendering of
figurate numbers. He used his triangle also to explore the numbers’ figurate,
combinatoric, and binomial relationships, which eventually led him to probability theory.
See C. Boyer, “Pascal’s Formula for the Sums of Powers of the Integers,” Scripta
Mathematica 9 (1943): 237–44.
20
David Shane, “Figurate Numbers: A Historical Survey of an Ancient
Mathematics,” Monarch Review 5 (2018): 10.
150
ground.
21
This “monad” serves as the first number of all figurate sequences—an idea that
resonated well with monotheistic alchemists of later eras.
22
Every arithmetic figurate
number exists in the monad as part of the monad; the monad, in turn, is the only number
that appears in and as every geometric figure.
23

Of all figurate numbers, triangular numbers are considered the most basic, as the
fewest number of “monad” points required to create a solid plane in space is three.
24

Every successive triangular number adds a row of one more point than the previous row
contains. Figure 4.1 gives the first seven triangular numbers.

Figure 4.1. The first seven triangular (triangle) figurate numbers.

The Pythagoreans believed the fourth figurate triangle in this sequence to be the most
special, because it quantifies ten—a number through which the monad “returns,” as the
digits one through nine begin another cycle.
25
They named this triangular number the

21
Shane, 11.
22
See chapter 2.
23
Shane, “Figurate Numbers,” 12.
24
For information about formulae for these numbers, and how early mathematicians
developed them, see Janet L. Beery, “Formulating Figurate Numbers,” BSHM Bulletin:
Journal of the British Society for the History of Mathematics 24, no. 2 (2009): 78–91,
https://doi.org/10.1080/17498430902820879.
25
In base ten. This effectively evokes a trinitarian notion of “three in one” as well, in
the three-sided figure also embodying both generating and “circular” monadic properties.
151
Tetraktys after the four rows—each containing an ascending “sacred” number—one
(monad), two (dyad), three (triad), and four (tetrad)—of its the skeletal structure. These
numbers, interpreted as geometrical forms also tell the story of creation and propagation,
from the monad to the tetrad, and from the monad to the decad (Figure 4.2).
26

Figure 4.2. Correspondences between the lines of the Tetraktys and the formation of a
three-dimensional tetrad (modern graphic by Malin Fitger, 2020).

Closely related to triangular numbers are so-called “perfect numbers”—also well known
in the seventeenth century, including among European musicians.
27
For instance, without
explaining how or why a composer should know or use these in compositional practice,
28

Walther includes an entry for “Numerus perfectus” in his 1732 Lexicon.
29
Perfect
numbers are positive integers that are both the sum and product of its divisors, excluding

26
Ursula Szulakowska, “Geometry and Astrology in Late Medieval and Early
Renaissance Alchemy,” in The Alchemy of Light: Geometry and Optics in Late
Renaissance Alchemical Illustration, vol. 10, Symbola Et Emblemata (Leiden: Brill,
2000), 16.
27
Of these, the numbers six and twenty-eight appear frequently in foundational
scaffolding within Buxtehude’s works. For example, see the comparison of the Herr,
wenn ich nur Dich hab’ bass line with the one in Sicut Moses exaltavit serpentem in
deserto, in chapter 7.
28
Very much like Werckmeister in his Paradoxal Discourse. See chapter 3.
29
Tatlow, Bach’s Numbers: Compositional Proportion and Significance, 103.
152
the number itself. For example, both of these statements are true: 6 = 1 + 2 + 3, and 6 = 1
x 2 x 3. The sequence of perfect numbers begins: 6, 28, 496, 8128, etc., and all perfect
numbers are also triangular figurate numbers.
30

The second figurate arithmetic progression, with each figure essentially
comprised of two diagonal triangles sharing a middle line, generates shapes of four
equilateral sides, or “square” numbers.
31
Figure 4.3 shows the first five square numbers.
Figure 4.4, from a seventeenth-century treatise,
32
shows the interwoven relationships
between triangle numbers and square numbers, and between both of these and “higher
order” pyramidal structures crafted from them, in the style of Rosicrucian mathematician
and cabalist Johannes Faulhaber (discussed in chapter 2).

Figure 4.3. The first five quadrilateral (square) figurate numbers.

30
This is a cornerstone of Kee’s argument about triangular-number grounds. See Piet
Kee, “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato Works,”
The Diapason 75 (1984): 27–33. See also Piet Kee, Number and Symbolism in the
Passacaglia and Ciacona: A Forgotten and Hidden Dimension (United Kingdom: John
Loosemore Center Buckfastleigh, 1988).
31
Shane, “Figurate Numbers,” 13. Of all figurate numbers, this one is the most
prevalent in modern terminology, when used as a verb (i.e., to “square” a number in this
form of number theory effectively means generating a figurate square of that number of
points per side.
32
See chapter 2.
153

Figure 4.4. [Johannes Remmelin], figurate numbers from Mysterium Arithmeticum,
1615 (taken from Schneider, “Between Rosicrucians and Cabbala,” 317).

In addition to the basic triangle and square numbers, the most important figurate numbers
within Buxtehude’s ostinato works are called “star” numbers—a special kind of figurate
number, whose centered points naturally form a Star of David, which is also a type of
regular hexagram.
33
By the seventeenth century, this hexagram was well established as a

33
Unless otherwise labeled, modern diagrams taken from
https://ibmathresources.com/2015/01/20/stellar-numbers-investigation/ (accessed April
20, 2022).
154
symbol of union-in-duality, expressed as interlocking upward and downward triangles.
34

These dualities typically included body and spirit, heaven and earth (like the Hermetic
philosophy “as above, so below”), and humanity and God. The more “terrestrial” square
and triangle numbers typically stood for the four elements and the tripart body, spirit, and
soul, respectively.
35

Figure 4.5. The first four “star” (stellar) figurate numbers.

In this diagram of the first four “star” numbers (Figure 4.5), one observes each smaller
star “nesting” within the one just larger than it, a phenomenon easily observed when the
stars are connected into closed shapes (like they are here) rather than left as free points.
This particular figuration also hints to a special feature of two of the star numbers: the

34
Szulakowska, “Geometry and Astrology in Late Medieval and Early Renaissance
Alchemy,” 13.
35
For more information about these geometrical symbols, including the story of their
passage into the Theosophical movement centuries after the Rosicrucian furore, see
Malin Fitger, “The Tetractys and the Hebdomad: Blavatsky’s Sacred Geometry,”
Correspondences 8, no. 1 (2020): 73–115.
155
numbers thirty-seven and seventy-three. These two numbers contain certain unique
properties within the first twenty-five million prime numbers, involving their being
“contained” within one another, as well as palindromic features. I will detail these at
various points throughout chapters 5 and 6. Evidence of this line of thought exists
abundantly in Johann Lange’s Theologia Christiana in Numeris. Buxtehude’s friend
Andreas Werckmeister specifically recommends this tract for learning about properties of
numbers.
36
Figure 4.6 exemplifies Lange’s mystical geometry, with the two leftmost
figures featuring repeated iterations of stars within each other—and different ways of
counting them—across multiple configurations.

Figure 4.6. Johann Christian Lange, Mystical geometrical figures from Theologia
Christiana in Numeris (1702).

The circles in Lange’s two rightmost figures reflect at least two major avenues of
mystical-geometrical influence: the cabalistic calculation charts of Ramon Lull,

36
See chapter 3.
156
thirteenth-century Catalan mystic,
37
and the other a trend within alchemical literature as
early as the late Hellenistic period of conceiving the alchemical process as circular. This
cyclical process, so ancient alchemists thought, began with perfection as the origin of all
matter in God, and ended in perfection, as “spiritualized” matter.
38
Figure 4.7 features the
alchemical “Ouroboros,” the dragon or serpent who eats its own tail, continuously
poisoning and healing itself with its own alchemical power, and taking the physical form
of a never-ending circle.
39
Figure 4.8 unites many of the images already presented,
including squares and triangles as synonymous with the numbers four and three; both of
these shapes contained within a circle, whose wings and ouroboros atop it suggest
eternity. The androgyne,
40
meanwhile, signifies the reconciliation of opposites in the
“chemical wedding,” as does the allusion to “Squaring the Circle” (signified by the
compass and straight edge), as a symbol for divine unification and eternal
enlightenment.
41
All of these geometrical images feature prominently in the works treated
in chapters 5 through 7.

37
See chapter 2.
38
Szulakowska, “Geometry and Astrology in Late Medieval and Early Renaissance
Alchemy,” 14.
39
Lyndy Abraham, A Dictionary of Alchemical Imagery (Cambridge: Cambridge
University Press, 1998), 207.
40
For an excellent explanation of the REBIS and queer bodies in alchemical and
Christian history, see Leah DeVun, The Shape of Sex: Nonbinary Gender from Genesis to
the Renaissance (New York: Columbia University Press, 2021). Also see David Rollo,
Kiss My Relics : Hermaphroditic Fictions of the Middle Ages (Chicago: University of
Chicago Press, 2011),
http://ebookcentral.proquest.com/lib/socal/detail.action?docID=765343.
41
See chapter 5.
157

Figure 4.7. Michael Maier, Emblem XIV, “This is the Dragon that eats its own tail (the
Ouroboros),” from Atalanta fugiens (1617).

Figure 4.8. Heinrich Nollius, the REBIS (sacred androgyne) holding a compass and
straight edge and standing on a geometrical representation of the numbers one, three,
and four, from Theoria Philosophiae Hermetica (1617).

158

4.4 – Pythagorean-Ratio Examples: Laudate pueri Dominum (BuxWV 69)
In her overview of Buxtehude’s ostinato works, Kerala Snyder details two observations
containing provocative clues to the potential specialness of this subgenre. Snyder first
notes that, because an ostinato structure “imposes a high degree of unity on a work,” it
serves as a “surprising choice for a concerto, which normally glories in its diversity.”
42

Soon after, she mentions that “Buxtehude used an ostinato bass, both strictly and loosely,
in portions of several other vocal pieces, most frequently in an ending “Amen” or
“Alleluia.”
43
Based on my analyses, I have concluded that Buxtehude uses ostinato
structure more for mathematical reasons than for audible aesthetic ones.
44
Laudate pueri
Dominum (BuxWV 69) provides a useful case study to this end, through its multiple
intersecting marks of the “specialness” to which Snyder nods. First, it contains a full
psalm text, rather than just a fragment:
45

Laudate pueri Dominum, laudate nomen
Domini.

Sit nomen Domini, sit benedictum ex hoc
nunc et usque in saeculum, a solis ortu
usque ad occasum.

Laudabile nomen Domini excelsus super
omnes gentes Dominus et super coelos
gloria eius.

Quis sicut Dominus, Deus noster, qui in
altis habitat et humilia respicit in coelo et
in terra, suscitans a terra in opem de
Praise ye the Lord, praise, O ye servants,
praise the name of the Lord.

Blessed be the name of the Lord from this
time forth and for evermore. From the
rising of the sun unto the going down of
the same, the Lord’s name is to be praised

The Lord is high above all nations, and
his glory above the heavens.

Who is like unto the Lord our God who
dwelleth on high, who humbleth himself
to behold the things in heaven and in the

42
Snyder, Dieterich Buxtehude: Organist in Lübeck, 173.
43
Snyder, 175.
44
See chapter 7.
45
Snyder, Dieterich Buxtehude: Organist in Lübeck, 138.
159
stercore erigens pauperum, ut collocet
eum cum principibus populi sui, qui
habitare facit sterilem in domo matrem
filiorum laetantem.

(Psalm 113)

Gloria Patri et filio et spiritui Sancto sicut
erat in principio et nunc et semper et in
saecula saeculorum.

Amen.
earth? He raiseth up the poor out of the
dust and lifteth the needy out of the
dunghill, that he may set him with the
princes of his people. He maketh the
barren woman to keep house and be a
joyful mother of children.
(Psalm 113)

Glory be to the Father and to the Son and
to the Holy Spirit; as it was in the
beginning, is now and forever shall be,
world without end.

Amen.

The Laudate pueri Dominum is also one of just two surviving works of Buxtehude’s
scored for full viol consort.
46
The other is his Membra Jesu nostri (BuxWV 75), a cycle
of seven Passion works, each a meditation on a different body part of the crucified Christ.
Buxtehude appears not to have conceived it for church or Abendmusik performance, or
any specific occasion, but rather as a personal expression of his faith.
47
For this reason,
scholars often compare it to Schütz’s Cantiones sacrae and J.S. Bach’s funeral motets.
48

Buxtehude’s autograph manuscript is in tablature, and includes a tender dedication to his
Gustav Düben. In “Ad Cor” (To [His] Heart), the sixth of the seven pieces, the viol

46
For information about the viol as an alchemical symbol, see chapters 2 and 6. For an
overview of possible affective meanings behind Buxtehude’s viol consort works,
especially in lamento contexts, see Eva Linfield, “The Viol Consort in Buxtehude’s
Vocal Music: Historical Context and Affective Meaning,” in Church, State, and Studio:
Music and Its Contexts in 17th-Century Germany, ed. Paul Walker (Ann Arbor,
Michigan: UMI Research Press, 1990), 163–92.
47
David Cox, “Buxtehude and His Passion Music,” The Musical Times 112, no. 1537
(1971): 233, https://doi.org/10.2307/956401.
48
Ryan Andrew Board, “Buxtehude’s Membra Jesu Nostri: A Study in Baroque
Affections and Rhetoric” (DMA diss., University of Missouri-Kansas City, 2006), 68.
160
consort, in addition to providing the only ostinato interludes in the cycle, musically serve
as Christ’s heartbeat.
49

In this work, too, the viols serve an important purpose as markers of ground-
iteration numbers, through their unified entrances. This numerical structure rests on the
ostinato figure, whose eight-measure line is so long as to “[stretch] the ability of the ear
to perceive it.”
50
The ground begins immediately with a cadence on A before modulating
to F major. After several rising and falling scalar figures, it then creeps back to D minor,
by way of a C to C-sharp pivot, before it ends with a seamless cadence into a D minor
restart. Example 4.3 shows the full ostinato length, in context.

49
There is certainly a wealth of symbolism, numerical and otherwise, to investigate in a
future project treating this discrete piece, as well as the full Passion cycle.
50
Snyder, 175. The range is also unusually large, spanning a thirteenth, from a B-flat
just below middle C to the D two octaves lower.
161

Example 4.3. Buxtehude, Laudate pueri Dominum (BuxWV 69), first page, showing
complete ostinato.

B
B
B
B
B
B
B
?
?
b
c
c
c
c
c
c
c
c
c
b
b
b
b
b
b
b
b
b
c
c
c
c
c
c
c
c
c
Soprano 1
Soprano 2
Viol 1
Viol 2
Viol 3
Viol 4
Viol 5
Violone
Basso
Continuo
&
&
&
B
B
B
B
?
?
∑
∑
‰
j
œ . œ
œ
. œ œ œ
‰
J
œ . œ
œ
.
œ œ œ
‰
j
œ
. œ œ .
œ # œ œ
‰
j
œ
.
œ
œ
. œ œ œ
‰
J
œ
.
œ œ
.
œ œ œ
‰
J
œ
.
œ œ
. œ œ œ
œ
œ
œ œ
œ
12 Repetatur
∑
∑
‰
j
œ
.
œ œ
œ
‰
J
œ
‰
J
œ
. œ œœ
‰
J
œ
‰
J
œ
. œ œ
œ
‰
J
œ
‰
J
œ
.
œ œœ ‰
J
œ
‰
j
œ
.
œ œ
œ
‰
j
œ
‰ j
œ
. œ œ
œ
‰
j
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ .
œ œ
œ œ œ
œ
œ
œ
œ .
œ œ
œ œ œ œ
.
œ
œ
œ
œ
œ
œ
œ œ
œ
. œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
∑
.
œ œ
. œ œ
œ
œ
.
œ œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
J
œ
≈
R
œ
œ
œ
œ
œ œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
5
∑
∑
œ
‰
J
œ n
. œ
œ b
. œ
œ
œ
œ
œ
œ
.
œ
œ
œ
.
œ
J
œ
œ
‰
j
œ
œ Œ Ó
œ
Œ Ó
œ
œ
œ
œ
œ œ #
œ
œ
œ
œ
œ œ #
∑
∑
. œ
œ
œ .
œ
œ
œ
œ
. œ
J
œ
. œ
œ
œ
œ
œ
œ .
œ
œ
œ
œ
œ
∑
∑
.
œ
œ
œ
. œ
œ
œ
.
œ
œ
œ
. œ
œ
œ
∑
∑
œ
œ
œ .
œ œ
. œ œ
.
œ œ
œ
œ
œ .
œ # œ
. œ œ
œ
œ œ œ
œ
Œ
.
œ
J
œ
œ #
œ
Ó Œ
œ
.
œ
J
œ
œ
œ
œ
.
œ
J
œ
œ
œ
œ
∑
∑
˙
‰
J
œ
.
œ
œ #
œ
œ
œ œ œ
œ
œ
œ
œ
œ
œ .
œ
œ
œ
œ
œ œ
œ
œ
œ
œ œ
œ
œ œ œ
œ #
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
‰
j
œ
.
œ
œ
. œ #
œ n
œ œ
Lau da te pu e ri, lau
Œ ‰ j
œ
œ œ
Œ
Lau da te
œ
Œ Ó
œ
Œ Ó
œ
Œ Ó
œ Œ Ó
œ
Œ Ó
œ
Œ Ó
œ
œ
œ œ
œ
- - - - -
- -
Laudate pueri Dominum
Dieterich Buxtehude
BuxWV 69
© 2022 Malachai Komanoff Bandy. All Rights Reserved.
Chiaccona à 8: doi Soprani, 6 viole di gamba e B.C.
162
Numerically, this work serves as a compact case study for Buxtehude’s emphasis
on the numbers three, seven, twelve, and twenty-one, and on Pythagorean ratio and
figurate number. First, the bass pattern’s modulation scheme divides its forty-seven notes
into a grouping of ten notes (the first two measures) and thirty-seven notes (the remaining
six measures). In figurate numbers, this joins the Tetraktys with the “star” number thirty-
seven.
Throughout, the viols serve as large-scale numerical timekeepers. They enter at
the beginning (rather in the middle or at cadences) of the ground at: measures 1, 17 (the
third iteration of the ground), 49 (the seventh iteration), 73 (the tenth iteration, Example
4.4), 89 (for the twelfth iteration). Thus, textually and musically important events occur
on measure numbers that either end with seven, or that are multiples of seven. Probably
the most obvious of these is the added “Gloria Patri” section of the text, interrupting what
began as a declamatory restatement of the opening material on measure 73, on the
downbeat of measure 77 (Example 4.5). The viol entrance in measure 73 also coincides
with both the tenth iteration of the ground and the twelfth unified, declamatory consort
entrance, the only one to contain (as a kind of half-reprise) material from the piece’s first
and last statements.
163

Example 4.4. Buxtehude, Laudate pueri Dominum, mm. 71-75.

Example 4.5. Buxtehude, Laudate pueri Dominum, mm. 76-78.

&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
67
œ
œ
œ
œ
œ
œ
œ
j
œ
≈
r
œ
œ
œ
œ
œ
tan
œ œ
œ
œ
œ
œ
œ
‰
J
œ
tem, lae
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
tan
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
Œ
œ œ œ
œ
œ
œ
tan tem ma trem fi li
œ œ
Œ Ó
tem
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ œ #
œ
œ
‰
j
œ
œ
œ
œ
œ
œ
œ
œ
œ
o rum lae tan
œ œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
ma trem fi li o rum, fi li
∑
∑
∑
∑
∑
∑
.
œ
œ
œ
. œ
œ
œ
- - - - - - - - - -
- - - - - - - - - - - -
- -
&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
71
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ # œ
‰
J
œ
œ
œ
Œ
o rum, lae tan tem,
∑
∑
∑
∑
∑
∑
.
œ
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ .
œ œ
‰
J
œ
œ
œ
œ œ
œ #
œ
œ .
œ
œ
lae tan
∑
∑
∑
∑
∑
∑
œ #
œ
œ
œ
œ
œ
˙
Ó
tem.
˙
Ó
tem.
‰
j
œ . œ
œ
. œ œœ
‰
J
œ . œ
œ
.
œ œœ
‰
j
œ
. œ œ .
œ # œœ
‰
j
œ
.
œ
œ
. œ œœ
‰
J
œ
.
œ œ
.
œ œœ
‰
J
œ
.
œ œ
. œ œœ
œ
œ
œ œ
œ
∑
∑
‰
j
œ
.
œ œ
œ
‰
J
œ
‰
J
œ
. œ œ œ
œ
‰
J
œ
. œ œ
œ
‰
J
œ
‰
J
œ
.
œ œ œ ‰
J
œ
‰
j
œ
.
œ œ
œ
‰
j
œ
‰ j
œ
. œ œ
œ
‰
j
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ .
œ œ
œ œ œ
œ
œ
œ
œ .
œ œ
œ œ œ œ
.
œ
œ
œ
œ
œ
œ
œ œ
œ
. œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
- - - - -
- - - - -
9 Laudate pueri Dominum
&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
76
∑
∑
.
œ œ
. œ œ
œ
œ
.
œ œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
J
œ
≈
R
œ
œ
œ
œ
œ œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
œ
œ
œ
œ œ
‰
j
œ
Glo ri a, glo ri a pa tri et
œ œ
œ œ œ œ œ œ
‰
J
œ
Glo ri a, glo ri a pa tri et
œ
Œ Ó
œ
Œ Ó
œ Œ Ó
œ Œ Ó
œ
Œ Ó
œ
Œ Ó
œ
œ
œ
œ
œ œ #
. œ
œ
œ
œ
.
œ
œ
œ œ
œ
fi li o et spi ri tu i
. œ
œ
œ
œ
œ
œ
œ
œ œ
œ #
œ
œ
fi li o et spi ri tu i
∑
∑
∑
∑
∑
∑
.
œ
œ
œ
. œ
œ
œ
œ œ
œ n
œ #
œ œ
œ
œ
san cto si cut e rat in prin
œ # œ
œ
œ
œ
œ
œ
œ
san cto si cut e rat in prin
∑
∑
∑
∑
∑
∑
.
œ
J
œ
œ
œ
œ
- - - - - - -
- - - - - - - - - - - - - -
- - - - - - -
&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
80
. œ œ
œ
‰
J
œ n
œ #
ci pi o et nunc,
.
œ
œ œ
Œ ‰
j
œ
ci pi o et
Œ ‰
j
œ
œ
‰
j
œ
Œ ‰
J
œ .
œ
J
œ
Œ ‰
J
œ œ
‰
J
œ #
Œ ‰
J
œ
œ
œ ‰
j
œ
Œ ‰
j
œ œ
‰
J
œ
Œ ‰ j
œ
œ
‰
j
œ
œ #
œ
œ
œ
œ
œ
‰
J
œ œ
‰
j
œ
œ
œ
et nunc, et nunc et
œ
‰
j
œ
œ œ
Œ
nunc et sem per,
œ
‰
j
œ
œ
‰
j
œ
œ
‰
J
œ
œ
‰
J
œ
œ
‰
J
œ
œ ‰
j
œ
œ
‰
j
œ
œ ‰
J
œ
œ ‰
J
œ
œ
‰
j
œ
œ
‰
j
œ
œ
‰
j
œ
œ
œ
œ œ
œ
œ
œ
Œ ‰
j
œ
œ
œ
sem per, et nunc et
‰
J
œ
.
œ œ
œ œ
Œ
et nunc et sem per
œ
Œ Ó
œ Œ Ó
œ
Œ Ó
œ
Œ Ó
œ Œ Ó
œ
Œ Ó
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
sem per et in se cu
Œ
. œ œ
œ
œ
œ
œ .
œ œ
et in se cu
Ó Œ ‰
J
œ
Ó Œ ‰
J
œ
Ó Œ ‰
J
œ
Ó Œ ‰
j
œ
Ó Œ ‰
J
œ
Ó Œ ‰
j
œ
œ
œ
œ
œ
œ
œ
œ
œ
- - - - - -
- - - - - -
10 Laudate pueri Dominum
164
Finally, in a moment of meaningful Pythagorean-ratio placement, the “et in terra”
concludes on measure 49 (7 x 7) (Example 4.6).

Example 4.6. Buxtehude, Laudate pueri Dominum, mm. 47-50.

This is the exact measure-number middle of the piece, which therefore marks a 2:1
ratio—Werckmeister’s “heaven and earth” ratio—across the work. Buxtehude casts this
with the actual words “heaven” and “earth,” such that those words span an octave in the
upper voice. This effectively creates a string of simultaneous 2:1 divisions, by three
different metrics (measure number, octave disposition, and numerological symbol),
thematically united in the literal text. Each of the techniques described here appears—
with even deeper symbolic implications—in the remaining works this study treats.

&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
43
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
œ
œ
œ
œ
al
∑
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ œ
tis ha bi
œ œ œ
œ
œ
œ
œ
œ . œ
œ
qui in al tis ha bi
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ
œ
œ
Œ Œ
œ
œ
tat et hu
œ
.
œ
œ .
œ œ œ
œ
tat et hu mi li a, hu
∑
∑
∑
∑
∑
∑
œ
œ
œ
œ
œ œ #
. œ
œ
œ
.
œ
œ
.
œ
œ
mi li a re spi cit in
. œ
œ
œ
Œ
. œ œ
mi li a re spi
∑
∑
∑
∑
∑
∑
.
œ
œ
œ
. œ
œ
œ
- - - - - - - - - -
- - - - - - - - - -
&
&
&
B
B
B
B
?
?
b
b
b
b
b
b
b
b
b
S1
S2
Vdg1
Vdg2
Vdg3
Vdg4
Vdg5
Vlne
BC
47
œ
œ œ
œ œ . œ
œ #
coe lo, in coe lo et in
œ œ
œ œ . œ
œ
œ
œ
cit in coe lo et in ter ra,
∑
∑
∑
∑
∑
∑
.
œ
J
œ
œ
œ
œ
œ œ
‰
j
œ
œ œ
. œ
œ #
ter ra, in coe lo et in
‰
J
œ
œ œ
Œ
.
œ
œ
in coe lo et in
∑
∑
∑
∑
∑
∑
œ #
œ
œ
œ
œ
œ
œ œ
Ó
ter ra
œ œ
Ó
ter ra
. œ œ . œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
. œ œ
. œ œ
œ
œ #
œ
œ
œ
œ
œ
œ
. œ œœ œ
J
œ # ‰ Œ
.
œ œ
œ œ
œ
.
œ œ
.
œ œœ
œ
œ œ œ œ
.
œ œ
œ œ
œ œ
œ
œ
œ
œ œ
œ
. œ œ œ œ œ
œ
œ
œ
œ
œ
œ
œ
su sci tans a ter
Ó
. œ œ œ
œ #
œ
œ
su sci tans a
œ
œ
. œ œ
œ
Œ
œ
œ
œ n
œ #
. œ œ
œ Œ
.
œ œ œ œ œ
Œ
œ
œ
œ
œ
œ
Œ
œ œ œ œ œ Œ
œ
œ
œ œ
œ
Œ
œ
œ
œ œ
œ
- - - - - -
- - - - - - - -
6 Laudate pueri Dominum
165
CHAPTER 5
Herr, wenn ich nur Dich hab’ (BuxWV 38)

Herr, wenn ich nur Dich hab’ (BuxWV 38) is one of two settings Buxtehude wrote of Psalm 73,
both scored for soprano, violins, and continuo. This, the shorter setting, is one of the few extant
basso-ostinato vocal works in Buxtehude’s œuvre.
1
In typical sacred-concerto style, each phrase
of text receives different melodic material, and the piece closes with a florid and imitative
“Alleluia.” The ostinato pattern consists of a three-measure ground, two half-notes per measure,
sounding a total of twenty-four times. Its shape forms two parallel scalar figures, each the other’s
inversion, separated at beginning and end by a perfect fourth (Example 5.1).

Example 5.1. Dieterich Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), ostinato bass.

Buxtehude’s text also contains an anomaly: the original psalm reads “Theil,” which the
organ tablature clearly replaces with “Heil.” These words are often rhymed in Lutheran mystical
poetry, but to my knowledge this feature is unique in seventeenth-century settings of this text.

1
While some of his through-composed works include brief sections of bass ostinato, only six
of completely ostinato design survive.
166

Herr, wenn ich nur dich hab’
so frag ich nichts nach Himmel und Erden,
wenn mir gleich Leib und Seel verschmacht
so bist du doch Gott allezeit
meines Herzens Trost und mein Heil. Alleluia
(Psalm 73 vv. 25 and 26)

Lord, if I only have you,
then shall I desire nothing from heaven and earth;
though both my flesh and soul may fail,
God will be for evermore
my heart’s consolation and my salvation. Alleluia

(Psalm 73 vv. 25 and 26)

Beyond the bass pattern, there are frequent appearances, in combination, of
Werckmeister-favorite numbers seven and three. The most conspicuous is the work’s seventy-
three total measures, considering the text—Psalm 73. Seven iterations of the opening vocal
melody also occur across three voices (soprano and both violins) throughout the first section of
text, while sevens and threes “punctuate” the soprano’s phrase endings, with “Erden,” the last
word of this section, as the twenty-seventh note (three cubed) in measure 7, on the third ground
iteration (Example 5.2). The soprano’s final “Erden” demarcates the first of several large-and-
small-scale congruences: just as the piece is seventy-three measures long, the first line of text
ends at exactly seventy-three notes in the vocal (and first violin) line, while the “Alleluia”
section contains a mirror-image thirty-seven bass notes.

Example 5.2. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 6-8 (left) and mm. 21-22 (right).
167
Combinations of the numbers four and three prove even more structurally prevalent. The
first section of text has forty-three bass notes,
2
while the last section begins on measure 43, and
the ground dictates that measure 34 houses the twelfth iteration (3 x 4). In a hypobolic downward
leap of an octave plus a perfect fourth (4:3) on bass note thirty-four, the soprano’s vocal entrance
ends in an abruptio after the word “Himmel,” before recasting the opening figure in a melodic
arc of a perfect fourth (4:3), up and down (Example 5.3). These numbers also appear in large-
scale ratio: the “Alleluia” section’s situation on the nineteenth ground repetition (of twenty-four
total) creates an all-encompassing 4:3 ratio
3
over the work (Example 5.4).
4

2
Carol Jarman and Stephen Ackert cite forty-three as the sum of “CREDO” (3+17+5+4+14)
in the natural-order number alphabet, well known in Bach gematria scholarship. In this same
system, forty-three also equals the initials of Buxtehude’s life motto: “Non homnibus, sed Deo”
(“not for man, but for God”). One perhaps finds Werckmeister’s Pythagorean reading of these
digits more compelling, considering the plethora of number-alphabets in use in the seventeenth
century and thus the inevitably large possibility for error. For a case for forty-three as “CREDO,”
see Carol Jarman, “Buxtehude’s Ciacona in C Minor and the Nicene Creed,” The Musical Times
146 (2005): 59.
3
In almost “magic square”-like fashion, on the word “Alleluia” in m. 55, the digits of the
note numbers in all voices also add to 55. On the downbeat of measure 49, the sum of all note-
numbers’ digits, again, add to 49—or 33 without counting the structurally inevitable note-
number in the bass. In the final note of the piece, all of the voices’ note-number digits add to
43—and 33, once again, without the bass. For information about magic squares, see Eberhard
Knobloch, “Mathematics and the Divine: Athanasius Kircher,” in Mathematics and the Divine: A
Historical Study, ed. T. Koetsier and L. Bergmans (Amsterdam: Elsevier, 2005), 333–46.
4
Note: this musical example (5.4) contains a note discrepancy in the last sixteenth note in the
vocal line on the third beat of measure 55. Instead of a repeated d, it should probably be an e, but
the tablature and transcribed parts both have smudges obscuring parts of just that note. Please see
the Appendix for any note questions.
168

Example 5.3. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 12-20.

Example 5.4. Buxtehude, Herr, wenn ich nur Dich hab’, mm. 53-56.

169
Recall that according to Werckmeister 4:3 bridges the gap between the “Trinity” and the
“earthly” triads. For a piece whose text centers on the notion of comfort and salvation coming
from God alone, this “Alleluia” placement—numerically mirroring its textual function—
simultaneously divides and elides God’s word and mortal praise.
The features I have introduced thus far comprise just a portion of a much larger riddle at
play concerning coordinated figurate numbers, ratio, and the infamous mathematical
impossibility known as “Squaring the Circle.” It is in this capacity that the work’s proliferation
of threes and fours, in combination with the number seven, generates its most intense
mathematical subtext, most of which stems from “figurate” numbers. The most important to this
work are “triangle” numbers (such as three and six), “square” numbers (such as four and
sixteen), and “star” numbers—a special breed whose centered points form a Star of David (a
“hexagram”) (Figure 5.1). The sequence of star numbers begins: 1, 13, 37, 73, and so on.

Figure 5.1. Triangle, square, and star “figurate” numbers.

By Buxtehude’s time, this hexagram was well established in cabalistic and alchemical literature
as a symbol of union-in-duality, expressed as interlocking upward and downward triangles
(Figure 5.2). These dualities included body and spirit, heaven and earth (as in the Hermetic
philosophy “as above, so below”), and man and God. Recall the piece’s 4:3 “Alleluia”
170
demarcation, which allots thirty-seven bass notes for the “Alleluia” over the work’s seventy-
three measures. This places star numbers thirty-seven and seventy-three, the third and fourth in
the natural sequence, in simultaneous congruence and opposition, yielding a kaleidoscopic union
of 4:3 ratios on four different scales: intervallic, measure number, note number, and “star-
number”-sequence.

Figure 5.2. Hexagram as a union of opposing triangles.

Of all known star numbers, thirty-seven and seventy-three contain extraordinary
properties that their coexistence in this “Alleluia” section and the other works this dissertation
treats
5
suggests that Buxtehude knew. Within the first twenty-five million prime numbers, thirty-
seven and seventy-three—the twelfth and twenty-first primes—are the only reversible primes
whose places on the prime-number line are also reversible (digit order: 37 and 73, 12 and 21).
They are also the only star numbers in which one is geometrically contained within the other in
not one, but two ways: in the hexagram seventy-three, thirty-seven comprises both the inlaid
hexagon and inlaid hexagram (Figure 5.3).

5
See chapter 6.
171

Figure 5.3. Thirty-seven and seventy-three as two “star” numbers contained in a single star, in
two ways: thirty-seven as inner hexagon (left) and as inner star (right).

This is more than reflection: one quantity is physically contained in its palindrome. It takes little
extrapolation to see theological-textual implications of this property, biblically (“I am in the
Father, and the Father is in me,” John 14:11, to name just one), but particularly considering
contemporary fascination with microcosm and macrocosm, expressed as triangles and other
geometrical patterns (Figure 5.4), inherited and translated from earlier centuries most famously
by Robert Fludd.
6

6
Joscelyn Godwin, Robert Fludd: Hermetic Philosopher and Surveyor of Two Worlds
(London: Thames and Hudson, 1979). See also Ursula Szulakowska, “Geometry and Astrology
in Late Medieval and Early Renaissance Alchemy,” in The Alchemy of Light: Geometry and
Optics in Late Renaissance Alchemical Illustration, vol. 10, Symbola Et Emblemata (Leiden:
Brill, 2000), 13–27.
172

Figure 5.4. Hexagram details from Kircher, Arithmologia, 1665 (left) and Robert Fludd,
Utriusque cosmi, 1619 (right).

5.1 – A Mysterious Rosicrucian Manuscript in Hamburg
A Christian-identified polymath, Robert Fludd became the most outspoken English Rosicrucian
apologist of his lifetime. Like their Pietist contemporaries, seventeenth century Rosicrucians
believed in an intensified Christian life achievable through equally intensified personal devotion
and social reform.
7
Rather than focusing on the faithful’s sin for which Christ suffered, they
presumably celebrated the beauty of crucifixion and resurrection as a mystical union of
opposites—here, life and death and heaven and earth—with transformative aspects of alchemy
and divine unification centering their theology.
8

7
See chapter 1 for a more detailed explanation of their beliefs, especially relative to Pietism.
See chapter 2 for an overview of their manifestos.
8
Throughout Buxtehude’s œuvre, one finds an overt connection between texts handling
mystical union, ostinato basses, and a distinctly Rosicrucian concept of eternity and cyclic
transformation between death and rebirth.
173
In this light, a Rosicrucian manuscript
9
at the Staats- und Universitätsbibliothek Hamburg
intensifies links between textual and numerical features in Herr, wenn ich nur Dich hab.’ This
manuscript appears to be an early version of what would eventually be revised, combined with
several similar manuscript sources, and published in the 1780s as Geheime Figuren der
Rosenkreuzer aus dem 16. und 17. Jahrhundert.
10
A recurring motto in this manuscript aligns
closely with Buxtehude’s extracted lines of Psalm 73 (but replaces “having” with “gnosis”) and
occurs in conjunction with the “wonder-numbers” three and four specifically: “Mensch erkenne
Gott und dich: Im Himmel und auf Erden gebricht dir nichts” (Man, know God and thyself, and
you shall need nothing from heaven or earth) (Figure 5.5). Hexagrams also abound, depicting
heavenly-earthly union, and some reflect the “transformation” of threes and fours into sevens. To
at least this branch of Rosicrucianism,
11
true “Heil” (“salvation”) springs from mystical union,
achievable through the contemplation of the numbers three, four, and seven—the same numbers
upon which Buxtehude bases his composition. Paleography dates this manuscript to around
1700, when Buxtehude spent all of his free time, however scarce, in its city of Hamburg.

9
[Anonymous], “Einfältig ABC-Büchlein Der Rosenkreuzer” (Manuscript, Staats- und
Universitätsbibliothek Hamburg, ca 1700), codex in scrinio 21, http://resolver.sub.uni-
hamburg.de/goobi/HANSh1310.
10
For a complete publication history and possible other sources for this manual, see Walter
Schneider, “‘Diese Schrift muss von Innen heraus und von Aussen hinein verstanden werden’:
Die Lehren der Rosenkreuzer aus dem 16. und 17. Jahrhundert und ihre Publikationsgeschichte,”
Rosenkreuzer Lehrtafeln 4 (2007): 2–12.
11
See chapter 2 for an explanation of the complications inherent to defining Rosicrucianism.
174

Figure 5.5. Anonymous, excerpt from the “Einfältig ABC-Büchlein Der Rosenkreuzer,”
Rosicrucian manuscript in the Staats- und Universitätsbibliothek Hamburg, ca. 1700 (above),
with detail from this same text below; textual similarity to Herr, wenn ich nur Dich hab’ is
marked at the top.
175
While there has been some question since the early twentieth century as to whether the
manuscript sources for the Geheime Figuren der Rosenkreuzer aus dem 16. und 17. Jahrhundert
are really Rosicrucian (only some versions explicitly mention Rosicrucianism),
12
this Hamburg
copy claims to be in its title: it contains the “teachings of the Rosicrucian brothers, for young
students who will daily practice in the school of the Holy Spirit, simply and with pictures painted
to practice with. In the natural and theological light by a brother of the Rosy Cross.” Many of the
drawings and figures themselves also contain explicit Rosicrucian identification. The central
figure on plate 14, “The Secret Wonder-Number 1-2-3-4,” for example is labeled “The Rosy
Cross according to philosophy and theology. The secret, hidden Rosy Cross which the world
does not know and still has much to say about.” On plate 23, “The Heavenly and Earthly Eve,”
one finds “Rosae Crucis Venite” among the inscriptions, along with reference to the first
Rosicrucian manifesto, the Fama fraternitatis: “Videamini Collegium ad Spiritum Sanctum”
(May you see the College of the Holy Spirit).
13
On the sixteenth and seventeenth plates, two
circles divided into four crosswise sections stand side by side, one with letters denoting the
Father, the Son, the Holy Ghost, and Man, and the other with the four elements (the first is
labeled the “divine,” “heavenly” Rosy Cross, and the other the “natural,” “temporal” Rosy

12
One of these other manuscripts, found in Wrocław, is thought to be the original from
which others were copied. That version can be more confidently dated 1650, and it contains none
of the errors that some others do. The Hamburg copy is closest to this, of all other extant
versions. It is possible that all of these manuscripts stem not from the earliest Rosicrucians
publishing around 1615, but from a parallel Rosicrucian group that shared much of their beliefs,
originating from the Jacob Boehme school. See Rafael T. Prinke, “Lampado Trado: From the
Fama Fraternitatis to the Golden Dawn,” The Hermetic Journal 30 (1985): 5–14.
13
Eve is shown mediating “Theory” and “Practice,” an intersection of which is central to a
seventeenth-century engraved portrait of Basil Valentine that Buxtehude also might have known,
based on the repeated appearance of star numbers in conjunction with the text “living water” in
one of his psalm settings. See the analysis of Quemadmodum desiderat cervus (BuxWV 92)
following this one.
176
Cross). On plate 13, the letters R and C denote two more quadrant-circles, labeled “The
cabalistic figure, the real reason for the wondrous number of God 1-2-3-4” and “The enclosed
Rosy Cross about which the world knows to speak, apparent to our eyes, evident, and the secret
of all secrets in Heaven and on Earth.” Finally, the very last plate tells us that the union of divine
and earthly nature is weighed on the “scales of the R. C.”
Whether Buxtehude or his friends knew this particular source, these coincidences suggest
a Rosicrucian concordance between seemingly disparate biographical and creative details:
Johann Theile’s alchemical interests, Buxtehude’s “un-Lutheran” texts, and Werckmeister’s
theological numbers in this and an array of other Buxtehude works. And as previously mentioned
in chapter 3, if Buxtehude did find himself associated with the Rosicrucian brotherhood, then the
canon sitting in the center of the painting containing his only known image piques one’s interest,
in its text’s celebration of “brotherly unity.”
14

5.2 – “Theil” vs. “Heil”: A Poem
In the face of any doubt to the intentionality of the “Theil” and “Heil” switch in Herr, wenn ich
nur Dich hab’, one only needs to examine Buxtehude’s laudatory poem for Johann Theile,
published in the prefatory material to Theile’s St. Matthew Passion in 1673, the same year that
he spent entirely in Lübeck alongside Buxtehude (Figure 5.6):

14
The eight-voice canon at the unison sets a Latin text from Psalm 133: “Behold, how good
and how pleasant it is for brethren to dwell together in unity!” This is followed by the
inscription: “In non: dit: Buxtehude: et Joh: Adam Reink: fratr[um].” Snyder provides a concise
summary of the identification issues of the characters in the scene. See Snyder, Dieterich
Buxtehude, 110.
177

Figure 5.6. Dieterich Buxtehude, Laudatory poem for Johann Theile, printed in Theile’s St.
Matthew Passion (1673).

Shall I write for noble Theile
In his honor verses new?
Gladly: if I were successful,
‘t would be merely friendship’s due.
Yet in this I must be wanting,
Letting learned men do the writing.

He, the honored, will be praised
Duly by men skilled and wise;
Even if by envy crazed,
There be some he fails to please,
Yet his praise shall be victorious
And from strife emerge all glorious.
178
Princes oft derive great pleasure
From the things he writes and rhymes,
Sound abroad his talent’s measure,
Letting kindly glowing beams
Shine upon the lovely verses
Which with skillful hands he traces.

So go forth, thy fame e’er winning
Through thy craft, O famous Theil.
Send thy songs from earth to heaven
Man’s salvation to extoll.
Christ, whose death will liberate thee,
Will instruct thee to live rightly.
15

The last stanza includes two relevant wordplay features: one on Theile’s name as both referring
to the composer and the word “portion” (the same meaning and context as its typical use in
Psalm 73), and the other in a rhyme between the words “Theil” and “Heil,” here as “berühmter
Theil” and “Menschen-Heil.” These are the same words and rhyme that Buxtehude uses to
modify Psalm 73 in the text to Herr, wenn ich nur Dich hab’.
Other shared words between the psalm text and Buxtehude’s poem create the same
context that I argue informed Buxtehude’s use of “Heil” in the Herr, wenn ich nur Dich hab’: in
both contexts, this “Theil”-“Heil” swap specifically flanks an allusion to “heaven” and “earth,”
and by extension recalls the Hermetic axiom “As above, so below.” In the anonymous Hamburg
Rosicrucian manuscript, and in the text to Herr, wenn ich nur Dich hab’, all three of the words
“Heil,” “Himmel,” and “Erden” appear in the same phrase. Here in Buxtehude’s poem, with all
three of these plus the original psalm’s “Theil” all together, he essentially left a key to his
thought process. This would confirm his intention in making the same pun in Herr, wenn ich nur
Dich hab’—a detail easily missed to those not initiated in this kind of alchemy-infused Christian

15
Poetic translation from Elizabeth Mackey, “The Sacred Music of Johann Theile” (PhD
diss., Ann Arbor, Michigan, University of Michigan, 1968), 318.
179
rhetoric. Between these two appearances of the same pun, it makes one wonder whether
Buxtehude and Theile more broadly used Theile’s name as a stand-in for the word “proportion,”
rather than just “portion.” Linguistically equating “proportion” with “salvation” would befit the
work’s mathematical commentary to this effect.

5.3 – “Squaring the Circle”
The last dimension of Herr, wenn ich nur Dich hab’ left to examine unites these mathematical
and textual features, in a distinctly alchemical and Rosicrucian sense: the issue of “Squaring the
Circle.” Of all open problems in the history of mathematics, none straddles pure geometry,
algebra, number theory, theology, and alchemy so equally yet contentiously. The challenge, first
posed by ancient Greek geometers (and not proven impossible until the nineteenth century)
16

goes as follows: using a compass and a straight edge, construct from a circle a square equal in
area to it, in only a finite number of steps.
17
These confines link the problem directly to figurate
numbers, in the algebraic processes through which one must go to determine the relative lengths
of “constructible” shapes. Meanwhile, it is no wonder that this problem, concerned with
transmutation, and regimented by finite operations and mortal tools, would by the fifteenth
century develop close ties to theology,
18
and by the seventeenth become synonymous with
alchemical pursuit of the Philosophers’ Stone, or, to Rosicrucians, union with the divine.

16
Davide Crippa, The Impossibility of Squaring the Circle in the 17th Century: A Debate
Among Gregory, Huygens, and Leibniz (Cham, Switzerland: Birkhäuser (Springer Nature
Switzerland AG), 2019).
17
This last step essentially dictates the problem’s impossibility, because of the infinite nature
of pi as a “transcendental” number (neither algebraic nor constructible).
18
See Nicholas of Cusa’s De Geometricis Transmutationibus (1445), for example.
180
In 1617, alchemist and leading German Rosicrucian apologist
19
Michael Maier published
Atalanta fugiens, an alchemical emblem book containing fifty engravings illustrating alchemical
principles, each of which receives a title, caption, epigram, discourse, and musical canon.
20

Figure 5.7. Michael Maier, Emblem XXI, “Make of the Man and Woman a Circle,” from
Atalanta fugiens (1617).

19
By the time he finished this text, Maier was becoming an avowed Rosicrucian, after
initially dismissing the brotherhood’s message at the time of their first publications. See
Hereward Tilton, The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work
of Count Michael Maier (1569-1622), (Berlin; New York: Walter de Gruyter, 2003), 113–27.
20
David Gaynor Yearsley, “Alchemy and Counterpoint in an Age of Reason,” Journal of the
American Musicological Society 51, no. 2 (1998): 234–38. As David Yearsley has shown,
Johann Theile’s Musikalisches Kunstbuch bears close resemblance in format, epigram, linguistic
style, all in connection with canonic composition—enough to suggest that Theile was aware of
this text. See chapter 3 for further biographical and philosophical context.
181
Of all fifty plates, only plate 21 (7 x 3) directly mentions the Philosophers’ Stone—the end goal
of the alchemical process, and Rosicrucian metaphor for the union of heaven and earth.
The image (Figure 5.7) shows a master constructing a large circle around a man and woman
(symbolizing duality), whom he has already enclosed in a circle, square, and triangle. Relevant to
our earlier discussion, note the hexagram at his feet. Above the emblem, the caption reads,
“Make of the man and woman a Circle, of that a Quadrangle, of this a Triangle, of the same a
Circle and you will have the Stone of the Philosophers.”
21
The epigram below it contains more
detailed instructions:

Around the man and woman draw a ring,
From which an equal-sided square springs forth.
From this derive a triangle, which should touch
The sphere on every side: and then the Stone
Will have arisen. If this is not clear,
Then learn Geometry, and know it all.
22

The last few lines of Maier’s “discourse” explain the spiritual and mathematical nature of the
union-in-duality that springs from circle-squaring:

In like manner the Philosophers would have the Quadrangle reduced into a
Triangle, that is, into a Body, Spirit and Soul…Then the Triangle will be perfect,
but this again must be changed into a Circle…and six the first of the perfect
numbers is absolved by one, two having returned again to a unity in which there is
Rest and eternal peace.
23

21
Michael Maier, Atalanta fugiens: hoc est, emblemata nova de secretis naturæ, chymica,
accomodata partim oculis & intellectui, figuris cupro incisi, adiectisque sententiis, epigrammatis
& notis, partim auribus & recreationi animi plus minus 50 rugis musicalibus trium vocum
(Oppenheim, 1617), 93.
22
Maier, Atalanta fugiens, 93.
23
Maier, Atalanta fugiens, 93.
182
Immediately, this last excerpt contains striking textual similarities to Buxtehude’s work: the
three-part “body, spirit, and soul” recall the psalmist’s “flesh” and “soul” that may “fail,” but that
will in spirit be perfected by God’s salvation, which yields eternal “Trost” (comfort, solace). But
perhaps even more fascinating is the numerical content, which seems to prescribe the
composition of Buxtehude’s ostinato, in terms of duration, note value, barring, melodic contour,
and interval. First, a “quadrangle” of four-beat, duple time is “reduced into a triangle” by
division into three measures. Then, this triangle is made “perfect” by subdivision into six notes
(six, a triangle number, is the first numerus perfectus). But melodically, we see in this triangle a
constructed duality, in its two groupings of three conjunct notes each. Finally, this is “changed
into a circle” by invertible line and interval, which renders the ostinato linearly circuitous, with
each grouping of three notes separated from itself on both ends by a 4:3 ratio—a joining of the
first square and triangle numbers, expressed in melodic “unity” (Example 5.5).

Example 5.5. Buxtehude, Herr, wenn ich nur Dich hab’, ostinato bass as 4-3-2-1 (four beats,
three measures, two notes and two groups of three-note scales, unity in circular path).

With this “perfect” triangular and circular ground ruling the piece, it becomes all the more fitting
that the text “meines Herzens Trost” (my heart’s contentment) is bookended by two square
numbers: m. 49 (7 x 7) and bass note 100 (10 x 10).
24
Also, recall that the work’s crucial textual

24
Precisely on the soprano’s word “Trost” in m. 49, all of the note-numbers’ digits add to 22,
the value of the letter “X” in the natural-order number alphabet. I am generally a gematria
183
division points occur on numbers that co-mingle the “triangle” three and “square” four, and that
when the “Alleluia” section begins at the precise 4:3 division point, it macrocosmically mirrors
the ground’s own triangle-square division.
Maier’s numerical tropes also appear in the work’s note total of 1,357: this further breaks
down to 145 bass notes and 1,212 non-bass notes. In the bass, the number of complete ground
iterations yields a 12 x 12 square of 144 notes, which is then “completed” into a circle on its final
note, 145, a unique number in two embedded “circularities.”

First, 145 equals the sum of its own
digits’ factorials (one of only two numbers to do so). The number thus mathematically
“generates” itself using only its own elements, its digits, just as ostinato patterns self-generate
through predetermined measurements. Second, in repeatedly reducing any positive integer to the
sum of its digits’ squares, as many times as possible, all numbers will eventually reduce to one
of two values: one (“unity”) or 145. 145 therefore serves as three-digit gateway to an endless
cycle of two-digit integers that will continually “return to unity” in reducing to one another.
Meanwhile, the non-bass notes’ 1,212 notes are comprised of twelve factors: 1, 2, 3, 4, 6, 12,
101, 202, 303, 404, 606, and 1,212. In addition to these individual numbers’ importance to both
Werckmeister and Maier, note the digits’ unusual sequential repetition—another layer of
“circularity” (Figure 5.8).

skeptic, but it is fairly well documented that Heinrich Biber used twenty-two as a cross symbol.
Its appearance here may be entirely coincidental, but the note-numbers’ “real” sum (as whole
numbers, not digits) is 733. In numerical counterpoint to this coincidence, the downbeat of
measure 22 elicits significant note-numbers in the upper voices: seventy-three, forty-nine,
seventy-three, on the forty-third bass note.
184

Figure 5.8. Herr, wenn ich nur Dich hab’: note-totals, factorization structure, and juxtaposed
circular and square properties.

Finally, the total 1,357 notes—the composition’s “area,” as it were—is comprised of
digits whose separation by a value of two spells the generating function for the square-number
sequence.
25
This means that the “circular” repetitions I have explicated, evident simultaneously
on different scales from ostinato upward, ultimately culminate in a total note-value whose
factorization structure is entirely circular, but whose digits are made of square building-blocks.
Squaring the circle is indeed impossible with a compass and straight edge over finite steps, but in
Herr, wenn ich nur Dich hab’, Buxtehude achieves it at virtually every possible compositional
level—with one pen, three lines of text, four voices, six bass notes, and seventy-three measures

25
1 + 3 + 5 + 7 = 16, or 4
2
.
185
Herr, wenn ich nur Dich hab’, like Buxtehude’s remaining two basso ostinato psalm settings,
contains coordinated textual and mathematical features suggesting Rosicrucian-favored themes
of completeness, eternal constancy, and desire for mystical union with the divine. The other two
compositions, while in some ways less intricate in layers of symbol and geometrical allusion,
fluently “speak” the same numerical language. The numerical elements that form the foundation
of Herr, wenn ich nur Dich hab’ solidify it as the mathematical benchmark within Buxtehude’s
œuvre: palindromic numerical sequences, figurate-number formations, large and small 1:2 and
3:4 ratios, and regular alignment between note and measure number at textual division points.

186
CHAPTER 6
Quemadmodum desiderat cervus (BuxWV 92)

Buxtehude likely composed his setting of Quemadmodum desiderat cervus, for tenor, two
violins, and continuo, in the 1670s.
1
He appears to have drawn the work’s text from multiple
Latin sources, both biblical and poetic.
2
As is evident from the title of the piece, the first half of
the text is the opening of Psalm 42/41. In the second half, we find lines borrowed from Psalm
118/117: 24, intermingled with pseudo-Augustinian phrases likely borrowed from an
unidentified contemporary devotional manual. Portions of Buxtehude’s text appear verbatim in
Andreas Musculus’s (1541-1581) sixteenth-century Precationes ex veteribus orthodoxis
doctoribus. This manual was widely used among both German Protestants and Catholics,
musicians included—Heinrich Schütz drew many texts from it for his Cantiones sacrae (1625)
and set this version of “Quemadmodum” in part II of his Kleine geistliche Konzerte (1639).
3
But
Buxtehude’s text only partially matches these sources; certain fully intact phrases of Musculus’s
commentary are present in Schütz’s setting, but not in Buxtehude’s version.

1
The Düben Collection dates their score 1676-77, but other sources suggest ranges as late as
1680-90. For example, see Sara Eckerson, “On Buxtehude’s Quemadmodum Desiderat Cervus,”
FORMA DE VIDA: Revista Do Programa Em Teoria Da Literatura Da Universidade de Lisboa,
A ARTE ALEGRE #5, 13 (May 2018): (online), https://formadevida.org/seckersonfdv13.
2
This is unusual; the vast majority of Buxtehude’s extant poetic texts are German. See
Kerala J. Snyder, Dieterich Buxtehude: Organist in Lübeck, 2nd ed. (Rochester, NY: University
of Rochester Press, 2007), 137.
3
Snyder, 139.
187

The first half of the psalm’s text evokes at once both “thirst” and visual desire, while the
second half revels in the “joy” of mystical union for which the faithful soul yearns. From the
start, the imagery of the deer provides a mundane, visceral backdrop for the speaker’s repeated
spiritual reach toward the divine. In a Neoplatonic reading, this intermingling of “low” and
“high” senses creates a tension—and thus an opportunity for musical-rhetorical opposition—
between the earthly and the heavenly, all within the psalmist’s single voice and Buxtehude’s
single, unbending basso ostinato. In her 2018 analysis of Quemadmodum desiderat cervus, Sara
Eckerson notes a basic incongruity between the seeming sensual crescendo of the text and

Quemadmodum desiderat cervus ad fontes
aquarum, ita desiderat anima mea ad te, Deum,
sitivit anima mea ad te, Deum, fontem vivum.
Quando veniam et apparebo ante faciem tuam?
O fons, fons vitae,
vena aquarum viventium,
quando veniam ad aquas dulcedinis tuae?
Sitio, Domine, fons vitae es,
satia me, sitio te Deum vivum.
O quando veniam et apparebo, Domine, ante
faciem tuam?

(Psalm 42)

Putas me, videbo diem illam jucunditatis et
laetitiae, diem, quam fecit Dominus,
exultemus et laetemur in ea,
ubi est certa securitas, secura tranquillitas,
et tranquilla jucunditas,
jucunda felicitas, felix aeternitas,
aeterna beatitudo et beata Trinitas et Trinitatis
unitas, et unititis Deitas, et Deitatis beata visio
qua est gaudium Domini tui,
O gaudium super gaudium,
vinces omne gaudium

(Psalm 118; Unknown Source)

As the deer longs for springs of water,
so my soul longs for you, O God.
My soul thirsts for you, O God, a living spring.
When shall I come and appear before your face?
O spring, spring of life,
vein of living waters,
when shall I come to the waters of your sweetness?
I thirst, O Lord; you are the spring of life;
satisfy me; I thirst for you the living God.
O when shall I come and appear, O Lord, before your
face?

(Psalm 42)

You think on me: I shall see that day of joy and
gladness, the day which the Lord has made,
let us rejoice and be glad in it,
where there is certain security, secure tranquility,
and tranquil joy,
joyful felicity, felicitous eternity,
eternal blessedness, and the blessed Trinity and unity
of the Trinity, and a deity of unity, and a blessed
vision of the deity, Where is the joy of your Lord:
o joy above joy,
you shall conquer every joy.

(Psalm 118; Unknown Source)

188
Buxtehude’s rigid ostinato setting: the ground’s repeated resolutions do not match the “desire”
present in the text, and while the words “build toward a final sense of sublime [joy],” the music
stagnates.
4
I agree that most of the urgency and sensuality of Buxtehude’s text is only partly
present in audible components. The rest lies in the numbers that form its structure, an analysis of
which yields a more complete picture of the work’s symbolic landscape and intense subtext.
As I demonstrated in chapter 5, the “star”-number division between the numbers thirty-
seven and seventy-three forms vital scaffolding for Buxtehude’s setting of Psalm 73, Herr, wenn
ich nur Dich hab’. In combination with other numerical occurrences, this “Alleluia” division
point creates a large 3:4 ratio across the work and thus plays a role in the musical-dimensional
“Squaring the Circle.” But this single occurrence alone cannot prove foundational compositional
intentionality, however convincing its effect. The numerical elements in Herr, wenn ich nur Dich
hab’ are so thoroughly connected that it remains impossible to decide which of the many might
have served as Buxtehude’s first or central organizational impetus for the rest.
In Quemadmodum desiderat cervus, these same star numbers appear in such abundance
throughout the work that they must have served as Buxtehude’s main organizational goal from
the earliest planning stages. The two-measure ground’s construction provides a possible clue to
this end: like the ground bass of Herr, wenn ich nur Dich hab’, its number of notes (in this case,
ten) forms a special figurate triangle—the Tetraktys
5
—spanning one octave in range, sounding
for a total of sixty-five iterations across the work. This ten-note structure, as it progresses,
dictates that every new bass statement naturally begins on what after the first iteration is
simultaneously both note one and eleven. In bass-note quantities, this creates palindromic note-

4
Eckerson, “On Buxtehude’s Quemadmodum Desiderat Cervus.”
5
See chapter 4.
189
number digits at the beginning of each ground repetition in the hundreds. When examined
alongside the work’s text, these palindromic digits will later gather textual meaning and
symbiotically support that meaning as the piece progresses.

Example 6.1. Dieterich Buxtehude, Quemadmodum desiderat cervus (BuxWV 92), ostinato
bass.

On a larger scale than their triangular grounds, Herr, wenn ich nur Dich hab’ and
Quemadmodum desiderat cervus share a range of similar scaffolding, including coordination
between large- and small-scale ratio. In both works, this most often manifests in congruence
between note number and measure number. In Quemadmodum desiderat cervus, the end of the
first section of the text concludes with the words “anima mea” falls on bass note 111, while the
final section of the text (“O gaudium”) begins on measure 111.

190

Example 6.2. Buxtehude, Quemadmodum desiderat cervus, mm. 22-23 (top) and mm. 109-14
(bottom).

Likewise, this final section is twenty-one measures long, while the voice concludes twenty-one
bass notes from the end. The very first few vocal statements, too, feature scaled congruence with
the ground: the ostinato immediately leaps up an octave, and over its course, returns to the low
F; the voice follows the identical intervallic path over the course of the first statement, but
191
repeatedly returns to the octave-leap high F for “fontes aquarum,” the long “desiderat” in
measure 21, and most climactically, the end of the first line of text: “anima mea.”

Example 6.3. Buxtehude, Quemadmodum desiderat cervus, mm. 15-25.

As in Herr, wenn ich nur Dich hab’, in Quemadmodum desiderat cervus, Buxtehude uses
the Pythagorean ratios 4:3, 3:2, and 2:1 to mark the work’s central thematic and structural
features. For instance, to set portions of text primarily about mortal desire to meet the divine, 4:3
192
ratios run rampant, in the form of repeated motives outlining perfect fourths (4:3). For example,
the many settings of “ad te,” directly addressing God from earth to heaven, “bridge” this
distance, just as Werckmeister’s 4:3 ratio in theory bridges the “heavenly” and “earthly” triads.
6

Example 6.4. Buxtehude, Quemadmodum desiderat cervus, mm. 22-24 (left) and mm. 30-31
(right).

Like the large-scale 4:3 ratio that determines the climactic “Alleluia” division point in Herr,
wenn ich nur Dich hab’, the exact 2:1 midpoint of Quemadmodum desiderat cervus is readily
audible, by a sudden moment of calm separated on both sides by the frenetic motion that defines
the texture of the rest of the work.
7
But the textual midpoint, which divides the psalmist’s earthly
desires from the “gaudium” (joy) of mystical union with God, occurs not at this musical
geographic center but instead on the thirty-seventh ground iteration, on measure seventy-three.

6
See chapter 3.
7
In Buxtehude’s Laudate pueri, this same 2:1 ratio is similarly audible, but carries even
weightier textual implications within that work’s context. See Chapter 4.
193

Example 6.5. Buxtehude, Quemadmodum desiderat cervus, mm. 58-68.
194

Example 6.6. Buxtehude, Quemadmodum desiderat cervus, mm. 69-75.

Finally, the chromatic inflection on the word “felicitas” toward the end of the piece
provides an audibly striking moment of Pythagorean-ratio interaction with the text.
8

8
In what little literature exists about this piece, and despite differing interpretations, most
descriptions (ranging from program and liner notes to scholarly articles) mention this as a
moment of particular import or specialness.
195

Example 6.7. Buxtehude, Quemadmodum desiderat cervus, mm. 94-96.

Eckerson comments on this word’s “other-worldly” quality, but Werckmeister’s ratios offer a
more scientific explanation—one that we might consider something like “Pythagorean
hyperbole.”
9
Here, Buxtehude colors “felicitas” with not one, but two stacked 4:3 intervallic
ratios relative to the tonic. This “double” 4:3 makes this felicitous union with God twice as
distant and twice as audible, through chromatic inflection.
Palindromic numerical sequences and pitch patterns also permeate Quemadmodum
desiderat cervus. The “anima mea” closing the first section of both the text and Buxtehude’s
thematic setting comes on voice note 141 and bass note 111, while the first direct address of
God, “ad te,” falls on bass note 151. Near the end of the piece, Buxtehude also breaks the long

9
In contemporary musical-rhetorical figures, many theorists, including Buxtehude’s friend
Christoph Bernhard, considered transgressing the typical octave ambitus as “hyperbole,”
“transgressio,” or in the case of exceeding the bounds of a particular mode, “modus superfluus.”
By borrowing this term, I respond to the “otherworldly” effect of the lowered seventh scale
degree (E-flat above F tonic) others, including Eckerson, have noted, but explaining it not as an
altered seventh, but rather as two perfect fourths apart—to Werckmeister, then, two whole
bridges between the Earthly and Heavenly triads. For more information about hyperbole, see
Dietrich Bartel, Musica Poetica: Musical-Rhetorical Figures in German Baroque Music
(Lincoln: University of Nebraska Press, 1997), 303–7.
196
string of circulatio statements from measures 110 to 111 with a small palindromic melodic
figure, seven notes long, for only five syllables: as he later recreates in the final vocal statements,
we see five (“man”) repetitions of the word “gaudium,” in two of the last three vocal statements,
finally elevated to seven (“holiness”) as the last statement, to signify the precise moment of
climactic spiritual ecstasy. Finally, the vocal line’s first and last statements both contain thirty-
seven notes. In the rest of Buxtehude’s ostinato psalm settings, the length of the first texted
statement consistently corresponds to numbers of the greatest structural importance in the work.
Still, this particular palindromic effect, in mirroring the first and last statement note-count, is to
my knowledge unique within this repertoire.
As suggested earlier, many of these musical-textual-numerical features occur at note and
measure numbers that are also “star” numbers.
10
As in Herr, wenn ich nur Dich hab’, Buxtehude
juxtaposes specifically the palindromic star numbers thirty-seven and seventy-three, the third and
fourth in the sequence, at the central textual division point between Psalm 42 and the devotional-
manual excerpt. These numbers’ twice-palindromic qualities are especially fitting for a text
fixated on the act of “facing” (thirty-seven and seventy-three are the only reversible primes
whose places on the prime-number line are also reversible, in the first twenty-five million prime
numbers).
11

In a geometrical reading of a union of dualities, these occurrences numerically reinforce
the text, in the acts of “facing God,” “appearing before Him,” and reaching upward towards Him
in yearning for reflective acknowledgement. Indeed, star-number measure and note numbers

10
Figurate numbers whose centered points form a Star of David (a six-pointed, regular
hexagram). The generating equation is !
!
=6$($−1)+1. The sequence of star numbers
begins: 1, 13, 37, 73, 121, and 181.
11
See chapter 4 for visual examples of the star-number sequence; see chapter 5 for a graphic
demonstrating these special properties of thirty-seven and seventy-three.
197
provide every major textual and musical division point: the first mention of “facing God” (“ante
faciem tuam”) falls on bass note 181 and measure thirty-seven; the first “Deum” falls on bass
note 121, on ground iteration number thirteen; and the climactic “gaudium” statements begin
suddenly on measure 121. In the thirteenth measure of this final section of the piece, Buxtehude
elevates five (man) text-repetitions of “o gaudium” to seven (holiness) in this “joy that conquers
all joy”—all sounding in a final “hexagram” totaling thirty-seven notes in the vocal line,
mirroring the line’s thirty-seven-note opening passage.
12

6.1 – Hexagrams and Aqua vitae

One finds an illuminating combination of number symbolism, textual allusion to “living water,”
explicit reference to music and psalms, all mediated by theory and practice—the library and the
laboratory—in a seventeenth-century engraving printed by famed publisher of both alchemical
and musical works Jacques de Senlecque. Senlecque uses this same engraving on the title pages
for two different alchemical works: Jean Brouaut’s Traité de l’Eau de Vie ou anatomie théorique
et pratique du Vin (1646) and an edition of Basil Valentine’s Révelation des mystères des
teintures essentielles des sept métaux (1646/1668). Senlecque splits the engraving into a left-
hand and a right-hand panel, one depicting the “Occidental Philosopher” Basil Valentine (left)

12
These last examples cover a significant portion of the piece. Please see score in Appendix,
m. 107-end.
198
and the other the “Oriental Philosopher” Hermes Trismegistus (right), both at work in their
laboratories (Figure 6.1).

Figure 6.1. Jacques de Senlecque, title-page engraving, Basil Valentine’s Révelation des
mystères des teintures essentielles des sept métaux (1646/1668).

As Peter Forshaw has argued, Senlecque’s use of music as Harmonia to tie together so
many aspects of this engraving is directly inspired by Heinrich Khunrath.
13
A mention of the
“singular” achievements of Khunrath in Senlecque’s foreword to his reader in the Révelation des

13
See chapter 2.
199
mystères supports this interpretation.
14
One especially senses Khunrath’s influence in
Senlecque’s suggestion that music itself is chemically medicinal: a footnote to the whole
engraving, just below the viol, states that “Harmonia sancta, spirituum malignorum fuga seu
[Saturni] interperiei Medicina est’ (Sacred harmony chases away evil spirits, as medicine for the
very intemperate behavior of Saturn [shown as the planetary symbol]).
15

Throughout Senlecque’s engraving, the numbers one through seven quantify various
elements, and so serve to mediate the different facets of knowledge the engraving depicts. Above
Valentine, a shelf marked “Theory” (Theoria) holds seven books of incrementally taller and
taller spines, decorated with alchemists’ and mathematicians’ names, such as Geber, Lull, and
Valentine himself. Just below this, seven flasks of increasingly ascending heights line a shelf
marked “Practice” (Practica). Each flask is labeled with the name of a different solution central
to basic alchemical operations, with the graphic symbol for each hovering above its
corresponding flask. Immediately to the right of this, and continuing in perfect ascending
continuity, seven organ pipes appear directly above both the viol and Hermes Trismegistus, each
assigned a different planetary symbol in similar fashion to the flasks, under the musically and
theologically inspired phrase, “Psallite Domino in Chordis et Organo” (Play to the Lord on
Strings and Organ). The viol under these seven organ pipes, too, contains seven strings and seven
frets, all explicitly labeled with the Arabic numerals one through seven.
16

14
Peter J. Forshaw, “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations
on Cabala, Music, and Alchemy,” ARIES - Journal for the Study of Western Esotericism 10, no.
2 (2010): 169–95, https://doi.org/10.1163/156798910X520584.
15
Forshaw, 180. This is also musical wordplay involving “fuga” or canon. This is apt,
considering later, cultivated connections between alchemical practice and precisely this musical
technique. See chapters 2 and 3.
16
Forshaw, 179. This viol likely predates actual seven-string French viols by several
decades. As a philosophical object in this case, it might hold several symbolic meanings:
Forshaw suggests that Senlecque uses it perhaps to recall the stringed instruments in Khunrath’s
200
Much of this engraving thematically relates to Buxtehude’s approach to Harmonia in
compositions, effectively uniting elements of alchemy and theology, via the numerical arts of
music more broadly and of numerology more specifically. But one included symbol makes an
explicit connection to the dimensions of Quemadmodum desiderat cervus, both in terms of
literary symbol within the psalm and the geometrical underpinnings of Buxtehude’s musical
setting. The psalmist’s “living water,” “streams,” “fonts,” and even the “deer” all carry potent
alchemical meanings in the seventeenth century and earlier, each of which—in close textual
relationship with “living water” or “water of life” above all—creates a geometrical and symbolic
hinge between theme, engraving, text, and music.
In alchemy, Aqua vitae (living water or water of life) refers to two substances of different
chemical composition, but of similar philosophical power in the reconciliation of opposites. In
the most common sense, “living water” and “water of life” both refer to ethyl alcohol—or, even
more specifically, alcoholic spirits of the first distillation, as in once-distilled, rather than simply
once-fermented, wine. But it is also a name for “philosophical mercury” (mercurius), or the
“quintessence”—the “true Spirit so many have fought for,” so “desired of all Wise Men,”
according to alchemists as far back as Calid (d. eighth century CE) in his Book of Secrets.
17

engraving, but also notes that Senlecque mentions that the viol was “called Lyre in antiquity” in
his preface. I might add to this that “Lyre” connections would suggest its possible use as a
symbol for scientific measurement (via reason and Apollo), for Pythagorean ratio (as a series of
monochords), for Orpheus (who has his own Ficinian and Hermetic connotations), and for the
legend of Hermes himself crafting the first lyre out of sinews and a tortoise shell. It is worth
noting, in this light, that two turtles appear in the engraving’s diagonal corners (upper left and
lower right), and both are marked with the symbol for Saturn/lead, the base ingredient to be
elevated, perhaps with or into this harmonious medicine. For retellings of the Hermes-tortoise
legend, see Michael Maier’s Arcana Arcanissima, 4–5. For a modern analysis, see E. Borthwick,
“The Riddle of the Tortoise and the Lyre,” Music and Letters 51 (4), October 1970, 373–374.
17
Lyndy Abraham, A Dictionary of Alchemical Imagery (Cambridge: Cambridge University
Press, 1998), 9.
201
Noteworthy relative to the text of Psalm 42, in the psalmist’s equating thirst with a desire for
soul-God union, is this philosophical mercury’s use in the alchemical opus: it explicitly acts as a
“catalyst” or agent, which is necessary for the proper “Marriage between Body and Spirit”
according to Colson’s 1662 Philosophia maturata.
18
After equating the substance explicitly with
philosophic mercury, and in doing so providing yet another layer of possible theological symbol,
Colson further describes it as “our Fire always equally burning…working and producing many
wonders in the most secret Work of Nature.”
19
Artephius, meanwhile, refers to this same Aqua
vitae as the healing “dew of grace,” which purifies the blackened mass of the Stone post-
putrefaction, and which then precipitates the albedo (whitening) if “rightly ordered and disposed
with the body” of the transitioning Stone.
20
Because of these opposing characteristics, the most
common symbol for Aqua vitae in alchemical tracts is a hexagram—the same shape as the “star”
figurate numbers that provide the numerical foundation for Quemadmodum desiderat cervus—
which we find identifying the tallest flask on Valentine’s shelf of “practical” spirits (Figure 6.2).

18
Philosophia Maturata: An Exact Piece of Philosophy Containing the Practick and
Operatives Part Thereof in Gaining the Philosophers Stone (Lancelot Colson, London: G.
Sawbridge, 1662), 34.
19
Philosophia Maturata, 32.
20
Abraham, A Dictionary of Alchemical Imagery, 9.
202

Figure 6.2. Senlecque, “Aqua vitae” flask and hexagram detail from Valentine engraving
(1646/1668).

In seventeenth-century alchemical tracts of various nationalities, we find little if any
distinction between this “living” water and simply “water.”
21
As one of the four elements,
themselves sacred to any alchemist using Nature as the ultimate guide toward divine perfection,
“water” in recipes and exegetical texts also often signifies the “philosophical mercury” or
“matter of the sages” described previously under the name Aqua vitae. Especially interesting
from a Christian standpoint oriented toward creation, fall, and sacrificial rebirth, both Aqua vitae
and this “water” contain inherently opposing lethal and regenerative properties. It is for this
reason that “mastery” of such a chemical, in the coincidence of opposites, “brings peace.”
22

Whether or not “water” actually accomplishes a kind of death and rebirth in practical
experiments, this imagery of opposing forces is consonant with ethyl alcohol’s readily
perceivable properties to that effect. We find clues about this in its many nicknames explicitly

21
For instance, in Abraham’s dictionary, nearly all definitions containing the word “water”
are necessarily cross-listed, either because their definitions themselves are so similar or because
authors often define “water”-related terms with other terms also containing the word “water,”
“living” or not.
22
Abraham, A Dictionary of Alchemical Imagery, 213.
203
evoking opposites: the “water that does not wet the hands” and “fiery water,” for example, which
communicate what even a non-initiate immediately learns about ethanol—a substance cool to the
touch yet hot on the lips, throat, and wounds; liquid in the bottle yet only wet on surfaces for an
instant before turning to vapor.
23

To further connect this “water” to the “streams” and “fountains” in the text of Psalm 42,
in addition to receiving laudatory nicknames (“permanent water,” “water of grace,” “precious
water,” “divine water,” and “celestial water”), both “river” and “the fountain” are among
Abraham’s documented synonyms.
24
While not a synonym for Aqua vitae directly, “stream” also
refers to mercurial water, the “transforming arcanum,” specifically of the sort that was known to
harmonize the male and female spirits.
25
Specifically as related to “streams” in alchemical texts,
this union of opposites occurs via coagulation and dissolution—both of which this single
“stream” accomplishes, as one substance containing opposing chemical properties. For this
reason, the “chemical wedding” required for the Stone’s successful birth is sometimes described
as the joining of divergent streams, as in Herrick’s alchemical poem—far from a singular
example—“To the King and Queene, upon their unhappy distances”: “Like Streams, you are
divorc’d: but ‘twill come when / These eyes of mine shall see you mix agen.”
26

Finally, we confront the fleeing deer at the heart of Psalm 42’s text, whose earthly thirst
for the “streams of living water” the psalmist compares to his soul’s divine yearning.
27
According

23
Abraham, 214. Yet another nickname is “serpent.” This adds a potential layer of meaning
to my reading of Buxtehude’s choice and setting of his text for the cantata Sicut Moses exaltavit
serpentum in deserto. See chapter 7.
24
Abraham, 214.
25
Abraham, 191.
26
Lines 5-6. Abraham, 192.
27
The deer is also a much older Christian symbol, with ties to themes of beatification and
possibly idolatry. See Nicolò Morelli, “Petrarch’s Deer in Rerum Vulgarium Fragmenta 190 and
204
to Abraham’s survey of alchemical literature, for centuries before Buxtehude’s lifetime
alchemists used the deer, especially the stag, as “one of the best-known epithets for
Mercurius…[whose] fleeing…symbolizes Mercurius in his role as the intermediary soul which
unites the body and spirit of the Stone.”
28
For this reason, the deer was a popular alchemical
emblem, as in plates 2 and 8 of Salomon Trismosin’s Splendor Solis,
29
Sir George Ripley’s
“Emblematicall Scrowle,”
30
and in The Book of Lambspring,
31
this last with the epithet (in its
1678 reprint in The Hermetic Museum), “The deer desires no other name / But that of the Soul.”
32

the Visio Beatifica,” Italian Studies 76, no. 3 (2021): 237–53,
https://doi.org/10.1080/00751634.2021.1936799.
28
Abraham, A Dictionary of Alchemical Imagery, 52.
29
Salomon Trismosin, Splendor Solis (1582), Reprint (London: Kegan Paul, Trench and
Trubner, 1920), 30. See also Abraham, 52.
30
Sir George Ripley, “Emblematicall Scrowle” (Ashm. Roll 53A.1530, Bodleian Library,
n.d.).
31
Johannes Lambspring, “[Alchemistisches Lehrgedicht]” (1556), Ms P 2177,
Zentralbibliothek Zürich, 5r, https://doi.org/10.7891/e-manuscripta-6275.
32
A. E. Waite, ed., Hermetic Museum (1678), 1893 Edition, vol. 1 (York Beach, Maine:
Samuel Weiser, 1991), 280.
205

Figure 6.3. Salomon Trismosin, Stag decoration on plate VIII from Splendor Solis (1582).

Figure 6.4. Stag from Sir George Ripley’s “Emblematicall Scrowle” (n.d.).
206

Figure 6.5. Stag and unicorn, figure III from The Book of Lambspring (1556/1678).

6.2 – Trinity in Unity and Unity in Trinity
These pieces of textual symbolism reveal that in Psalm 42, beneath an already theologically
symbolic opposition-yet-concordance between fleshly desire for quenched thirst and the soul’s
heavenly desire for divine reconciliation, an alchemical narrative of similar power also
flourishes. In reapplying these symbolic double-meanings to Quemadmodum desiderat cervus, it
is important to remember that Buxtehude himself did not have to make these connections in
order for the text to carry this symbolism. For the initiate—from the extensive interrelatedness
among all the major terms in Psalm 42 (i.e., “deer,” “stream,” “font,” “living water,” “soul,”
“living spring,” etc.), early Christian alchemical symbolists might have drawn directly from
Psalm 42 when building this symbolic lexicon to describe and process the chemical reactions
occurring before them.
Buxtehude’s choice to unite alchemical aspects of Aqua vitae with the text’s other themes
of divine unification through star-number symbolism, however, was not the result of similar
207
“ready-made” textual symbolism. He would have had to connect the substance’s geometrical
symbol with numerical geometrical figurate-number renderings—potentially before writing a
note of the composition or determining that its number of ostinato bass notes (ten) should spell
the Tetraktys. One final image unites these alchemical and geometrical elements with wordplay
present in Quemadmodum desiderat cervus. The title page from an alchemical tract by Arthur
Dee, son of the famous John Dee, contains a drawing of a sun and moon inside of a hexagram
that geometrically unites their opposing powers (Figure 6.6). Above and below this hexagram,
the inscription reads: “Trinity in unity; Unity in Trinity.”
33

Figure 6.6. Arthur Dee, Title-page hexagram with chiastic “Trinity in Unity” inscription,
Arcana arcanorum (n.d.).

Just as the total number of measures in Herr, wenn ich nur Dich hab (seventy-three) spell its
psalm number, the “Trinitatis unitas” (Trinity in unity, or unity of the Trinity) in Quemadmodum

33
For an overview of Arthur Dee’s life and alchemical career, see Megan Piorko, “Chymical
Collections: Seventeenth Century Textual Transmutations in the Work of Arthur Dee” (PhD
diss., Georgia State University, 2020).
208
desiderat cervus appears in its 131 total measures, with the Trinity (3) inscribed into 1:1,
typically known as “unity” in contemporary mathematics.
34
At the same time, the ground’s two-
measure length yields a total of sixty-five iterations over these 131 measures. The sixty-fifth
prime number is 313, the “mirror inverse” of 131. This juxtaposition thus etches a “Trinity in
unity” and “unity in Trinity” into the work’s numerical ground-structure.
Even in the absence of verbal evidence that Buxtehude consciously intended every one of
these numerical features in Quemadmodum desiderat cervus, their overall coordination and
consistency points to a fundamental numerical design. Many of these synchronized moments,
such as the repeated perfect fourths and thirty-seven and seventy-three-measure division of the
text, are readily audible. But most evade the conscious ear, obscured only by the piece’s aural
fluency. This does not, however, impede Buxtehude’s numerical eloquence in portraying divine
union in large- and small-scale congruences, palindromic numerical and melodic sequences
concerned with “facing,” Aqua vitae-inspired star numbers, and of course the many large- and
small-scale 4:3 ratios that forge intervallic paths between the text’s ostensibly irreconcilable
earthly and heavenly realms. Just as God created all things according to measure, number, and
weight, Quemadmodum desiderat cervus offers a glimpse of cosmological unity, “spiritual”
perfection both theoretical and practical, and joy—harmonic, compositional, and indeed
mathematical.

34
This is widespread from ancient times through at least the eighteenth century, for example
by Descartes in his Géométrie and Fermat’s infinitary thought. See Rashid Rashed, Classical
Mathematics from Al-Khwārizmī to Descartes, trans. Michael H. Shank (London and New York:
Routledge, 2015), 244 and 327. Both of these examples come with robust ties to earlier Arab and
Islamic mathematicians who used the same “unity” terminology. There are explicit theological
implications for this when the same mathematicians write about “unity” as a number alongside
the idea of God’s “unity” as a metaphysical being. To find yet a third meaning in mathematics’
historiography, see Rashed’s chapter, “Algebra and its Unifying Role,” 105–48.
209
CHAPTER 7:
Beyond the Psalms: Further Numerical Applications within Buxtehude’s Works

If Theile and Reincken were relating music to alchemy, then Buxtehude may have
been as well, although he left no such clues. That is not to say that the composers
were necessarily performing experiments in a laboratory; alchemy involved
magical transformation, and it could take place chemically, spiritually, or
musically. What is the inversion of a four-part counterpoint if not a
transformation of a piece of music from one state to another? Whatever the depth
of their involvement with alchemy, in the pre-Enlightenment world of the
seventeenth century their experiments with learned counterpoint had a much
deeper meaning than the mere intellectual satisfaction of creating and solving
musical puzzles in their minds or on paper.
1

– Kerala Snyder, Dieterich Buxtehude (2007)

7.1 – Ostinato Basses as Musical-Numerical Rhetoric
I began this dissertation by outlining everything we still do not know about Buxtehude and his
works. The evidence I have since presented, however, suggests that Buxtehude’s basso ostinato
psalm settings, in their numerical properties and textual symbolism, contain more information
than earlier thought possible. While it is clear that Buxtehude was facile with numbers, this
combined biographical evidence suggests that he, like Werckmeister, understood numbers to be
symbolic vehicles, capable of providing meaning “beyond” themselves when employed as
compositional tools. Looking at the results of that numerical compositional process with this in
mind, and with a wider seventeenth-century scope more inclusive of the esoteric and mystical,
makes sense of certain well-documented clues. First, like his friends Theile and Reincken,
Buxtehude did show interest in alchemy; but that interest appears to be more textual and

1
Kerala J. Snyder, Dieterich Buxtehude: Organist in Lübeck, 2nd ed. (Rochester, NY:
University of Rochester Press, 2007), 113–14.
210
numerical than strictly contrapuntal. This study opens the door for more pointed contrapuntal
analysis than this narrow scope allowed, and canonic techniques do appear in all of the pieces I
have analyzed here. Next, as I demonstrated in chapters 3 and 5, Buxtehude was also good at
wordplay; he was probably as careful with his texts as with his numbers. That he spoke at least
seven languages would suggest that there is yet more symbolism and wordplay to be found in his
texts than scholars have documented. Lastly, we should think of Buxtehude as socially adroit, in
his ability to gather local support for his Abendmusik projects and in the close bonds he evidently
formed with members of the Hamburg circle, as we witness in his dedicatory pieces and poems
for them. Kerala Snyder by 2007 already suggested that we should update any “one-sided image
we might have had of him as merely a pious church organist,” citing the text of the 1670 canon
Buxtehude wrote for Meno Hanneken the younger: “Let us divert ourselves today, let us drink to
the health of my friend” (BuxWV 124).
2
Based on the controversy surrounding Werckmeister’s
Harmonologia musica outlined in chapter 3, to this we should add that Buxtehude likely
navigated potential ideological rifts between his Hamburg school friends and Werckmeister,
probably magnified relative to our modern debates about their differing contrapuntal
philosophies. Buxtehude’s intensive use of numerical and proportional symbols to set
alchemically resonant texts itself constitutes a meeting point between these two worlds. The
result, in Buxtehude’s hands, is a Werckmeister-inspired numerical rendering of alchemical
precepts; his music, meanwhile, also contains frequent canonic devices, presented in a

2
Snyder, 112.
211
“practical,” aurally pleasing manner.
3
I argue that it is by this aesthetic pleasantness that
Buxtehude’s numerical happenings mostly evade scrutiny.
4

The intricate numerical language in the structural designs of the compositions treated in
this study would suggest that they likely represent just the Tetraktys-shaped tip of Buxtehude’s
proverbial mathematical iceberg. The many numerical consistencies among the three psalm
settings—pairings of thirty-seven and seventy-three, proportional demarcations of 1:2 and 3:4,
and note groupings of seven and twelve by way of threes and fours—suggest Buxtehude’s quasi-
rhetorical use of number, transferrable from one piece to another. It is in this direction that I
suggest future studies should press. Beyond this, because of the numerical and textual
consistency with which Buxtehude uses ostinato patterns in mostly non-ostinato pieces,
5
I
propose that Buxtehude believed that ostinato patterns held some special importance, and that
this importance is either fully contained in, or best communicated through, number.
In the introduction to her article, “Metaphors of Time and Modernity in Bach,” Bettina
Varwig describes changing conceptions of time in the decades leading up to the mid-eighteenth
century:
6

3
As in, not exhaustive contrapuntal exercises for their own sake, but for practical use in
compositions likely intended for performance.
4
Ulf Grapenthin makes the same argument for Reincken’s use of number and proportion in
Hortus Musicus—that the music’s aesthetic beauty seems to contradict the strict numerical
underpinnings. I believe this applies to a much larger portion of Buxtehude’s catalog than we
currently know. Without a technical term for this, I often call this phenomenon the “nothing to
see here” effect. For Grapenthin’s argument, see Ulf Grapenthin, “Beziehungen Zwischen
Frontispiz Und Werkaufbau in Johann Adam Reinckens Hortus Musicus von 1688,” in
Proceedings of the Weckmann Symposium: Göteborg, 30 August - 3 September 1991 (Göteborg:
Göteborg, Dept. of Musicology, 1993), 199–210.
5
For example, ostinato figures appear at textually significant moments (always involving
eternity, psalmody, heaven and earth, or similar) in “Ad Cor” from Membra Jesu Nostri
(BuxWV 75), the Jubilate Domino (BuxWV 64), and others.
6
Bettina Varwig, “Metaphors of Time and Modernity in Bach,” The Journal of Musicology
29, no. 2 (Spring 2012): 155. This is a summary of and response to Karol Berger’s 2007 Bach’s
212

This shift, to summarize rather crudely, entailed a move from a premodern
cyclical to a modern linear notion of time—two geometrical metaphors that
translate time’s elusive qualities into concrete spatial shapes. In the earlier model,
human history is contained within a static conception of eternity, whereas the
second model places a premium on man-made teleological progress.
7

Whether or not this phenomenon took place in so cleanly delineated a fashion in reality, the idea
of a circular understanding of time is especially apt in the context of ostinato basses. This line of
thinking, especially paired with numerically consciousness analysis, will undoubtedly enable
more discoveries in Buxtehude’s other ostinato vocal works. Not every ostinato bass of
Buxtehude’s is as overtly “circular” in shape as the one in Herr, wenn ich nur Dich hab’, but the
act of repetition is itself inherently circular. These bass lines, then, provide additional
commentary to the texts they set—not just as possible readings as eternity and the passage of
time, but by perhaps representing the constancy of faith, continuous motion of the planets, or
steadfastness of Christian doctrinal truth.
In this way, Buxtehude’s ostinato compositions provide a paradoxically finite and infinite
space—a closed ecosystem for numerical play, in which the repetitions remind the observer of
time’s endlessness, while embedded numerical structures can hint even more pointedly at truly
infinite things, via geometrical figurations and ratio dimensions. In the melodic shape of their
bass lines, two of Buxtehude’s other ostinato works exhibit such features: in Jesu, meines Lebens
Leben (BuxWV 62), with a text about life’s constant path towards Jesus, the bass line is made of
two linear, descending tetrachords. To the ear, this gives the illusion of a never-ending scale,

Cycle, Mozart’s Arrow. The rest of Varwig’s article aligns with many of the geometrical and
philosophical questions raised in this dissertation. See especially her discussions about Saturn
and clocks, p. 160 onward.
7
Varwig, 156.
213
always proceeding stepwise. The bass line to Jesu dulcis memoria (BuxWV 57), by contrast,
casts “memory” as constant disjunct thirds, so that every few notes sound familiar, but the ear
cannot trace a coherent path. Numerically, these works also contain clues for future studies to
pursue, including texts featuring literal numbers (i.e., “a thousand times”) and large character
shifts occurring on the boundaries between certain possibly numerologically interesting measure
numbers (i.e., between 99 and 100). Liebster, meine Seele saget (BuxWV 70), meanwhile,
demonstrates frequent numerical oppositions between squares and hexagrams, especially the
numbers thirty-six and thirty-seven,
8
to set a text that Isabella van Elferen marks as a model of
“Lutheran ambivalence” in its Bridegroom narrative.
9
Understanding the bass lines themselves as
potentially symbolic—both numerically as often figurate numbers and as symbolic of eternity—
may be the first step toward understanding Buxtehude’s philosophies behind these and any
number of other works in his œuvre.
In theorizing these possible meanings of ostinato basses, one thinks of Leibniz’s
introduction to his definitions of “unlimited” and “limited” infinities:

Thus I call unlimited that in which no last point can be taken, if not on one side.
But by infinite I understand a quantity either limited or unlimited greater than any
quantity that can be assigned by us or that can be designated by numbers.
10

8
Thirty-six is both a triangular and quadrilateral number, while thirty-seven is a star number.
The final “Alleluia” in this work also forms a seven-by-seven “magic square,” to be further
explored in a future article.
9
Isabella van Elferen, “Spiritual and Mystical Love in Seventeenth-Century Vocal Music,”
in Mystical Love in the German Baroque: Theology, Poetry, Music (Lanham, MD: The
Scarecrow Press, 2009), 225–63.
10
Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth
Century (New York; Oxford: Oxford University Press, 1996), 144.
214
To Leibniz, both “infinities” are infinite—the unlimited infinities simply resist measurement, but
the limited quantities allow them. Buxtehude’s ostinato basses are perhaps both limited and
unlimited musical infinities: we can number each note, while their hints at eternity paradoxically
transcend human measurement.

7.2 – Example: Sicut Moses exaltavit serpentem in deserto (BuxWV 97)
The strongest evidence for Buxtehude’s rhetorical use of number and ostinato basses comes from
ostinato sections within otherwise through-composed works. When evidence of numerical
engagement coincides with such ostinato appearances, and particularly when these together
coincide with texts containing alchemical or Rosicrucian double-meanings, this supports the idea
that meaning, contained in ostinato and number, is almost linguistically transferrable between
compositions.
11
The best example of this I have found thus far is Buxtehude’s mostly through-
composed sacred concerto Sicut Moses exaltavit serpentem in deserto (BuxWV 97). This
composition exhibits consistent concordances between large- and small-scale proportion, while
its textual content communicates multiple layers of alchemical-Christian allegory. Throughout,
one also finds pointed implementation of the same numerical “figures” that I have shown form
the skeletal structures of the basso ostinato psalm settings. Numerically, this communicates
themes of divine unification and the reconciliation of opposites that also comprise the work’s
textual imagery. Ultimately, a close analysis finds a figurate-number internal structure as
consistent and dependable a feature in mystical interpretation as is the audible text.

11
These instances also demonstrate repeatable elements of my analytical method and suggest
a future possibility of coming close to reverse-engineering Buxtehude’s compositional process to
some extent.

215
The text of Sicut Moses exaltavit serpentem in deserto is comprised of two lines from the
book of John:

Sicut Moses exaltavit serpentem in deserto, ita exaltari
oportet filium hominis;

ut omnis qui credit in eum, non pereat, sed habeat vitam
aeternam. Amen.

(John 3:14–15)

Just as Moses raised up the serpent in the desert
(wilderness), so must the Son of Man be raised;

that whoever believes in him may not perish but have
eternal life. Amen.

(John 3:14–15)

While both its scoring (soprano, two violins, viola da gamba, and continuo) and textual brevity
all but define Buxtehude’s vocal œuvre, statistically this is an unusual text, set otherwise only
once in the seventeenth century, as a motet by Heinrich Schütz (SWV 68) in his Cantiones
sacrae (1625).
12
Buxtehude’s musical treatment simultaneously highlights the verse’s existing
parallelism while creating further division points within each half. The text on its own naturally
divides into just two main thematic segments, by line: “exaltation” (whether of serpent or man)
and “everlasting life” through belief in God. But Buxtehude’s choices of key area and meter—
and when to shift between them—further splits this paradigm into four total semi-lines, as two
sets of dualities—one of time signatures, the other of key areas. Interestingly, Buxtehude
distributes these musical features over the four textual lines such that aurally obvious changes in
key and meter do not align with the text’s central parallelism (see Figure 7.1). And as suggested
earlier, a basso ostinato instrumental interlude creates yet another “extra” division point. This
comes not at the text’s geographic center, but between the physical act of “exaltation” and man’s
spiritual pursuit of eternity.

12
Olga Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude,”
Early Music 46, no. 2 (2018): 241.
216

Figure 7.1. Dieterich Buxtehude, Sicut Moses exaltavit serpentem in deserto (BuxWV 97): Map
of keys and meter.

Microcosmically, the opening measures of the instrumental sonata encapsulate all
constructional elements that comprise the composition’s larger architecture. The first violin
melody on its own, for example, mirrors both the work’s textual content and key scheme: it rises
a perfect fourth (4:3) to D tonic, then falls to a B—like the middle section’s shift from D major
to B minor and back to D major—then rises back to D, with this “rising” motion emphasized
through chromatic inflection from C to C-sharp (Example 7.1).

Example 7.1. Dieterich Buxtehude, Sicut Moses exaltavit serpentem in deserto (BuxWV 97),
opening Adagio.

B
&
&
?
?
#
#
#
#
#
#
#
#
#
#
c
c
c
c
c
#
#
#
#
#
#
#
#
#
#
c
c
c
c
c
Soprano
Violino 1
Violino 2
Viola da
gamba
Basso
Continuo
&
&
&
?
?
∑
‰
j
œ œ
.
œ
J
œ n
‰
j
œ
œ
œ
œ
œ
‰
J
œ
œ
œ
œ
œ
‰
J
œ
œ
6
œ
œ
œ
Adagio
Sonata
∑
.
œ
J
œ a
˙
U
œ
œ
.
œ
œ˙
U
œ
œ
˙
U
œ
8 9
œ
6 7 \
˙
U
∑
‰
j
œ œ
.
œ
J
œ n
‰
j
œ
œ
œ
œ
œ
‰
J
œ
œ
n
œ
œ
œ
‰
J
œ
œ n
6
\
œ
œ
œ
6
p
[p]
[p]
[p]
∑
.
œ
J
œ a
˙
U
œ
œ
.
œ
œ˙
U
œ
œ
˙
U
œ
8 9
œ
6 7 \ \
˙
U
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
5
∑
∑
œ œ œ œ
œ
œ
‰
j
œ
∑
œ
4
œ
6
œ
œ
6
Allegro
∑
∑
œ
œ
‰
j
œ
œ
œ
œ
œ
.
œ
œ
∑
œ
œ
œ
5
6
œ
∑
œ œ œ œ
œ
œ
‰
J
œ
œ œ
œ ‰
J
œ
.
œ
œ
∑
œ
œ
œ
6
œ
3 4
∑
œ
œ
‰
J
œ
œ
œ
œ
œ
.
œ
œ
œ
œ œ œ œ œ . œ
œ #
∑
œ
œ
œ
5
œ
I
4
∑
œ
œ
œ
‰
j
œ
œ
œ
‰
J
œ
œ
‰
J
œ
œ œ œ œ
œ
œ ‰
J
œ
˙
. œ
J
œ
6
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
10
∑
‰
J
œ
œ
œ
œ
œ
.
œ
œ
œ
‰
j
œ
œ
œ
œ
œ
œ
‰
J
œ
œ
œ
œ
œ
. œ
œ
œ
œ
6
œ
œ
6
œ
7
œ
∑
˙
Ó
œ
œ œ œ
œ
œ ‰
J
œ
˙ Ó
˙
œ
œ
6
∑
∑
œ
œ
‰
J
œ
œ
œ
œ
œ
. œ
œ
∑
œ
œ
œ
5
6
œ
I
∑
œ œ œ œ
œ
œ
‰
J
œ
œ
œ
œ
‰
J
œ
.
œ
œ #
∑
œ
œ
œ
6
œ
I
4
∑
œ
œ
‰
j
œ
œ
œ
œ
œ
.
œ
œ
œ
œœœ
œ
œ
œ . œ
œ
∑
œ
œ
6
œ
5
6
œ
∑
œ
‰
J
œ
œ
‰
j
œ #
œ
œ
œ
‰
J
œ
œ
œ œ œ œ
œ
œ
‰
J
œ
˙
œ
œ
I
Sicut Moses exaltavit serpentem in deserto ita
Dietrich Buxtehude
©
à 4: Soprano con doi violini e viola da gamba
217
As in many of Buxtehude’s other compositions, the length of this first statement likewise
foreshadows the piece’s later numerical language. In this case, that violin motive is seven notes
long, but the opening adagio, in all voices, contains sixty-four (4
3
) notes, all of the same numbers
(three, four, seven, and sixty-four) that I will later show to dictate the piece’s larger structure.
Meanwhile, three-and-four numerical play also happens in meter: Buxtehude juxtaposes duple
and triple time in the notated 4/4 against what sounds initially like 3/4 with a pickup, in the
absence of downbeat reference. To the ear, even this figure’s immediate repetition does not
“correct” its duple-triple tension, but instead confirms it. And finally, the main point of imitation
in the following Allegro consists of a rising fourth (4:3) crossed over itself by a falling octave
(2:1), uniting in one motive all four numbers of Werkmeister’s “heaven” and “earth” ratios
(Example 7.2).
13
Together, this numerical sequence (1, 2, 3, 4) also forms the Greek Tetraktys,
unifying in one numerical figure—and, thus, its musical rendering—triangular and circular
elements.

Example 7.2. Buxtehude, Sicut Moses, Allegro fugal motive.

13
See chapter 3.
B
&
&
?
?
#
#
#
#
#
#
#
#
#
#
c
c
c
c
c
#
#
#
#
#
#
#
#
#
#
c
c
c
c
c
Soprano
Violino 1
Violino 2
Viola da
gamba
Basso
Continuo
&
&
&
?
?
∑
‰
j
œ œ
.
œ
J
œ n
‰
j
œ
œ
œ
œ
œ
‰
J
œ
œ
œ
œ
œ
‰
J
œ
œ
6
œ
œ
œ
Adagio
Sonata
∑
.
œ
J
œ a
˙
U
œ
œ
.
œ
œ˙
U
œ
œ
˙
U
œ
8 9
œ
6 7 \
˙
U
∑
‰
j
œ œ
.
œ
J
œ n
‰
j
œ
œ
œ
œ
œ
‰
J
œ
œ
n
œ
œ
œ
‰
J
œ
œ n
6
\
œ
œ
œ
6
p
[p]
[p]
[p]
∑
.
œ
J
œ a
˙
U
œ
œ
.
œ
œ˙
U
œ
œ
˙
U
œ
8 9
œ
6 7 \ \
˙
U
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
5
∑
∑
œ œ œ œ
œ
œ
‰
j
œ
∑
œ
4
œ
6
œ
œ
6
Allegro
∑
∑
œ
œ
‰
j
œ
œ
œ
œ
œ
.
œ
œ
∑
œ
œ
œ
5
6
œ
∑
œ œ œ œ
œ
œ
‰
J
œ
œ œ
œ ‰
J
œ
.
œ
œ
∑
œ
œ
œ
6
œ
3 4
∑
œ
œ
‰
J
œ
œ
œ
œ
œ
.
œ
œ
œ
œ œ œ œ œ . œ
œ #
∑
œ
œ
œ
5
œ
I
4
∑
œ
œ
œ
‰
j
œ
œ
œ
‰
J
œ
œ
‰
J
œ
œ œ œ œ
œ
œ ‰
J
œ
˙
. œ
J
œ
6
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
10
∑
‰
J
œ
œ
œ
œ
œ
.
œ
œ
œ
‰
j
œ
œ
œ
œ
œ
œ
‰
J
œ
œ
œ
œ
œ
. œ
œ
œ
œ
6
œ
œ
6
œ
7
œ
∑
˙
Ó
œ
œ œ œ
œ
œ ‰
J
œ
˙ Ó
˙
œ
œ
6
∑
∑
œ
œ
‰
J
œ
œ
œ
œ
œ
. œ
œ
∑
œ
œ
œ
5
6
œ
I
∑
œ œ œ œ
œ
œ
‰
J
œ
œ
œ
œ
‰
J
œ
.
œ
œ #
∑
œ
œ
œ
6
œ
I
4
∑
œ
œ
‰
j
œ
œ
œ
œ
œ
.
œ
œ
œ
œœœ
œ
œ
œ . œ
œ
∑
œ
œ
6
œ
5
6
œ
∑
œ
‰
J
œ
œ
‰
j
œ #
œ
œ
œ
‰
J
œ
œ
œ œ œ œ
œ
œ
‰
J
œ
˙
œ
œ
I
Sicut Moses exaltavit serpentem in deserto ita
Dietrich Buxtehude
©
à 4: Soprano con doi violini e viola da gamba
218
Looking more closely at the work’s larger structure, we find that various textual and
musical division points create numerical interplay within quantifiable features, specifically
involving the numbers three, four, and seven. The first metrical, key, and textual-thematic shift
occurs, for instance, on measure sixty-four (4
3
) and lasts sixty-four measures. But, as in the
melodic contour of the violin opening and key scheme, there are more palindromes. The meter
moves from 4/4 to 3/4, then from 3/4 to 4/4, but at a different rate from D major’s shift to B
minor and back. The measure-number structures also form palindromes in digits and exponents:
the instrumental sonata and final “Amen” are both twenty-five measures long, then the portions
containing the text “Sicut Moses” and “vitam aeternam” respectively are thirty-seven and
seventy-three measures, and the two sections interior to these are sixty-four (4
3
) and eighty-one
(3
4
) measures each (Figure 7.2). Across the 3/4 portion preceding the “Amen,” three full
repetitions of the section’s text occur over seventy measures (shown below as the area of bracket
overlap), punctuated by three four-measure iterations of only the phrase “but have eternal life.”

Figure 7.2. Sicut Moses: Map of keys, meter, and section lengths by number of measures.

But these details, however interesting on their own from a symmetry, balance, and
proportion perspective, remain beholden to an alchemical narrative below the surface. In its
219
original New Testament context, Buxtehude’s text is already symbolic, serving as meeting place
between the past and future: Christ foreshadows his own elevation on the cross while recalling
Moses’s brazen serpent that protected the Israelites from plague in The Book of Numbers (Figure
7.3):

From Mount Hor they set out by the way to the Red Sea, to go around the land of
Edom. And the people became impatient on the way. And the people spoke
against God and against Moses, “Why have you brought us up out of Egypt to die
in the wilderness? For there is no food and no water, and we loathe this worthless
food.” Then the Lord sent fiery serpents among the people, and they bit the
people, so that many people of Israel died. And the people came to Moses and
said, “We have sinned, for we have spoken against the Lord and against you. Pray
to the Lord, that he take away the serpents from us.” So Moses prayed for the
people. And the Lord said to Moses, “Make a fiery serpent and set it on a pole,
and everyone who is bitten, when he sees it, shall live.” So Moses made a bronze
serpent and set it on a pole. And if a serpent bit anyone, he would look at the
bronze serpent and live.
14

Figure 7.3. Michelangelo, Sistine Chapel serpent detail (1508).

14
Num. 21:4–9 (ESV).
220
Looking closely at the text, virtually every individual word in this passage features prominently
in contemporary alchemical discourse surrounding the concept of divine unification. An example
of this explicitly Christian imagery surrounding “elevation” as an alchemical operation appears
in Sir George Ripley’s 1591 The Compound of Alchymy, in the form of a passage likening
Christ’s elevation on the cross to the purification of metals. According to Ripley, this purification
eventually leads to consummation by both “man and wife” (i.e., duality, mercury and sulphur,
body and spirit, etc.), from which eternal life springs, in the form of the Philosophers’ Stone:

Proceede we now to the chapter of Exaltation,
Of which truly thou must haue knowledge pure,
But little it is different from Sublimation,
If thou conceiue it right I you ensure,
Hereto accordeth the holy scripture,
Christ saying thus, if I exalted be,
Then shall I draw all things vnto me.

Our medicine if we exalt right so,
It shalbe thereby nobilitate,
That must be done in manners two,
From time the parties be dispousate,
Which must be crucified and examinate,
And then contumulate both man and wife,
And after reuiued by the spirit of life.
15

Like Fallax mundus and several other Buxtehude works whose texts have been traced to emblem
books,
16
the text of Sicut Moses exaltavit serpentem in deserto also has an emblematic
counterpart, a crucifixion engraving by Julius Goltzius after Maarten de Vos (Figure 7.4).
17
This
engraving contains Buxtehude’s Latin text, but, atypical of most contemporary passion scenes,

15
Elias Ashmole, ed., Theatrum Chemicum Britannicum (London: J. Grismond, 1652), 178.
See also Lyndy Abraham, A Dictionary of Alchemical Imagery (Cambridge: Cambridge
University Press, 1998), 72.
16
Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude,” 236.
17
Gero, 242.
221
Adam’s corpse lies at the base of the cross, above a second text from John 12:24: “…unless a
kernel of wheat falls to the ground and dies, it remains only a single seed. But if it dies, it
produces many seeds.” In its original gospel context, this phrase originally comes as a prediction
of Jesus’s death. The line immediately preceding this seems to reflexively refer back to the text
of Sicut moses through the phrase, “The hour has come for the Son of Man to be glorified.”
18

Mary and John stand symmetrically on either side of the cross, and four virtues form a second
cross-pattern, crosswise to Christ’s own. The placement of Adam’s corpse and the cross’s high
horizontal beam create a visual frame around Jesus, above whom the holy spirit hovers, as a
dove.

18
Jn 12:23 (ESV).
222

Figure 7.4. Julius Goltzius, Crucifixion engraving after Maarten de Vos (ca. 1580).

In addition to noting Buxtehude’s possible contact with this engraving, Olga Gero suggests its
connection to the apocalyptic prophecy of the Resurrection of the Dead, based on the inclusion
223
of Adam’s body in the frame.
19
But yet another layer of specifically Rosicrucian symbol is at
play. First, we find the strongly Rosicrucian notion of “multiplicity springing from unity”
contained in the associated text about a dead “single seed” reproducing in abundance.
20
The
visual “frame” around Jesus, between the Holy Spirit and Adam, also distinctly recalls a
trademark Rosicrucian logo (Figure 7.5): an upside-down anchor to the heavens, framed by a
dove perched atop it and the horizontal bedrock of the Philosophers’ Stone at its base, with a
serpent—symbolizing Jesus, death, resurrection, and the nascent Stone—wrapped around the
anchor’s central bar. In its Rosicrucian context, this recalls both the healing rod of Asclepius and
Mercury’s caduceus.

Figure 7.5. Comparison of detail from Crucifixion by Goltzius, ca. 1580 (left) and printer’s
mark from The Chemical Wedding, 1616 (right).

19
Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude,” 242.
As explain in chapter 2, the Rosicrucian manifestos are founded in prophesies of the End Times,
including the prophecy to which Gero refers.
20
Jn 12:24 (ESV).
224

Turning back to Buxtehude’s textual imagery, we find a series of explicit alchemical
symbols allegorically connecting Moses, “exaltation,” and serpents. Although these symbols date
from centuries earlier, some of the most explicit iconography uniting these tropes come from
seventeenth-century alchemical publications. Such images are artifacts of the field’s chiastic
tradition of science-infused theological exegesis and theology-infused laboratory instruction.
21
A
cornerstone of this tradition, with evident interest in making connections between Judeo-
Christian and Egyptian wisdom, not only celebrated Moses as a great prophet, but credited him,
not Hermes Trismegistus, as the mythical founder of alchemy. Others believed them to be the
same person, as writes alchemist and physician George Starkey (1628-65), under the pseudonym
Eirenaeus Philalethes: “Hermes, surnamed Trismegistus, is generally regarded as the father of
[the alchemical] Art, but…some say he was Moses.”
22
And unquestionably, the Book of Genesis
and Hermes’ The Divine Pymander were the only creation texts to which serious alchemists
referred for elemental guidance.
23

While not a “character” per se, the act of “exaltation” elicits similarly hidden meanings.
In alchemy, “exaltatio” refers to the vaporization of the Stone, during which it is purified
through a reiterated cycle of dissolution and coagulation in its own “mercurial blood.” Johannes
Mylius, in his Philosophia reformata (Frankfurt, 1622) represents this process with the image of
a newlywed king and queen (sol and luna, sulphur and mercury), elevated five steps and flanked
by watchful lions, guarding the opus on its transformative journey (Figure 7.6).
24

21
For an overview, see Tara Nummedal, “Alchemy and Religion in Christian Europe,”
Ambix 60, no. 4 (2013): 311–22, https://doi.org/10.1179/0002698013Z.00000000036.
22
Abraham, A Dictionary of Alchemical Imagery, 130.
23
Abraham, 130–31.
24
Johann Mylius, Philosophia Reformata (Frankfurt: Lucas Jennis, 1622), 126.
225

Figure 7.6. Johannes Mylius, Exaltatio emblem from Philosophia reformata (1622).

Finally, we examine the most pervasive symbols in Sicut Moses exaltavit serpentem in
deserto: the alchemical serpent, the “prima materia” or ancient matter that the alchemist
transforms, with painstaking effort and more than a little luck, into the Philosophers’ Stone. In
George Ripley’s The Compound of Alchymy, the serpent is the corrupt metal that a second
“mercurial” serpent must destroy and reduce through putrefaction.
25
When properly inoculated,
one winged serpent (mercury) and one wingless (sulphur), encircle each other on the caduceus,
harmonizing male and female energies in their “chemical wedding.”
26

25
Found in Ashmole, Theatrum Chemicum Britannicum. See Abraham, A Dictionary of
Alchemical Imagery, 36.
26
Abraham, A Dictionary of Alchemical Imagery, 36.
226
This serpent-to-stone transformation serves as the primary feature in fourteenth-century
magister Nicholas Flamel’s Exposition of the Hieroglyphicall Figures or the Book of Abraham
the Jew, a likely fraudulent tract first published in 1612, but whose lack of ties to either Flamel
or to the fourteenth century did not compromise its widespread popularity.
27
According to its
introduction, the work purports to explain various figures Flamel came across in a certain
“guilded Booke, very old and large…not of Paper, nor Parchment…The cover of it was brasse,
all engraven with letters, or strange figures,” that an inscription stated belonged to “Abraham the
Jew.”
28
Flamel ultimately became so obsessed with deciphering the book’s language and images
that he set off for Spain in search of a “Jewish Priest in Some Synagogue” to help him translate
its contents.
29
On cue, Flamel finds Christian-converted-Jew, alchemist “Master Canches” on his
pilgrimage, who divulges the secret truths of transmutation to Flamel just before dying of an
unknown illness along the camino, exactly seven days into the pair’s journey back to France.
30

After returning to France alone, Flamel applies Canches’ wisdom, yielding enough successful

27
Laurinda S. Dixon, “Introduction,” in Nicolas Flamel: His Exposition of the
Hieroglyphicall Figures (1624), vol. 2, English Renaissance Hermeticism (New York: Garland
Pub., 1994), xiii–lviii. No original manuscript source for this treatise exists, and no extant
treatise before the sixteenth century cites Flamel at all. Thus, it is possible that it was written by
the treatise’s publisher, P. Arnauld de la Chevalerie, under the apparent pseudonym “Eirenaeus
Orandus.” Still, the fourteenth-century Nicolas Flamel was certainly a real person (his
tombstone, originally from the cemetery of St. Jacques, is now in the Musée de Cluny, after it
was found being used as a chopping board in a Paris grocery store). While the real Flamel might
well have been an alchemist, his superlative reputation in the field must have been a seventeenth-
century invention.
28
Nicholas Flamel, Nicholas Flammel, His Exposition of the Hieroglyphicall Figures Which
He Caused to Bee Painted Vpon an Arch in St. Innocents Church-Yard, in Paris. Together with
the Secret Booke of Artephius, and the Epistle of Iohn Pontanus: Concerning Both the Theoricke
and the Practicke of the Philosophers Stone. Faithfully, and (as the Maiesty of the Thing
Requireth) Religiously Done into English Out of the French and Latine Copies. by Eirenæus
Orandus, Qui Est, Vera Veris Enodans... (London: Thomas Snodham for Thomas Walkley,
1624), 6–8.
29
Flamel, 20.
30
Flamel, 23–25.
227
transmutations to build immense wealth and esteem. As repayment and commemoration, Flamel
erects a sculpted tympanum in 1413 (of course, “conveniently” destroyed by the seventeenth
century) at the Cemetery of the Innocents in the parish of St. Jacques de la Boucherie, with
imagery directly inspired by those found in the Book of Abraham the Jew.
31

While still alchemical in content, from the start Flamel’s aims are primarily theological;
and indeed, the cemetery tympanum the text describes contains only biblical imagery (though
with concealed alchemical implications), likely designed precisely to be interpretable by any
seventeenth-century layperson.
32
The text itself further confirms this, claiming that the tract’s
contained imagery

…may represent two things, according to the capacity and understanding of them
that behold them: First, the mysteries of our future and undoubted Resurrection, at
the day of Judgement, and coming of good Jesus, (whom may it please to have
mercy upon us) a Historie which is well agreeing to a Churchyard. And secondly,
they may signifie to them, which are skilled in Naturall Philosophy, all the
principal and necessary operations of the Maistery. These Hieroglyphicke figures
shall serve as two wayes to leade unto the heavenly life: the first and most open
sense, teaching the sacred Mysteries of our salutation; (as I will shew heereafter)
the other teaching every man, that hath any small understanding in the Stone, the
lineary way of the worke; which being perfected by any one, the change of evill
into good, takes away from him the roote of all sinne…
33

The large-scale structure of the Exposition of the Hieroglyphicall Figures itself invites this dual
interpretation—Christian and alchemical—by its division into two parts to this end: “Of the
Theologicall Interpretations, which may be given to these Hieroglyphickes” and then “The

31
Flamel, 22–23.
32
Dixon, xix.
33
Flamel, Exposition of the Heiroglyphicall Figures, 34–35.
228
interpretations Philosophicall, according to the Maistery of Hermes.”
34
Throughout, this
Christian message remains front-and-center: even practical alchemical information involving
transmutational features such as colors and temperature come in a “fervent tone of medieval
Catholic piety,” designed for a “revivalist” seventeenth-century readership.
35
Theologically, the
text contains both medieval and progressive seventeenth-century characteristics. While making
the “traditional” medieval allegorical simile between Christ and the Philosophers’ Stone—and of
distillation as a form of Christian death and resurrection—the author also often refers to the
Stone as a “king,” more typical of post-Reformation treatises handling the filius philosophorum
(Christ-lapis, or Christ as the Stone).
36
The author also often refers to Classical myths, more
frequently cited in alchemical tracts during and after the Renaissance.
37

As I showed in chapter 2, by the seventeenth century Flamel’s explicit Christ-Stone
allegory already had a history of at least 400 years. Drawing from the Codicillus of Ramon Lull,
later works like the Rosarium philosophorum (1550) feature imagery of the “resurrected” Stone
reimagined as a victorious Christ emerging from his tomb.
38
In chapter 6 of Flamel’s Exposition
of the Hieroglyphicall Figures, the author discusses the Stone’s Trinitarian “immortal tripartite
nature”—“triple in name but one in essence”—that brings harmony to the alchemical trinity of

34
In this way, though not actually medieval, it resembles medieval approaches to alchemy in
its claiming both practical and philosophical usefulness (like “sister disciplines” medicine and
pharmacy). See Dixon, xix–xx.
35
Dixon, xix.
36
Dixon, xix–xx. This same “king” as allegorical embodiment of the Stone appears in several
other seventeenth-century alchemical emblem books discussed elsewhere in this dissertation:
Lambsprinck, De lapide philosophica libellus (Frankfurt, 1625); Michael Maier, Atalanta
fugiens (Oppenheim, 1618) and Johann Daniel Mylius, Philosophia reformata (Frankfurt, 1622).
37
Dixon, xx.
38
See C. G. Jung, “The Lapis-Christ Parallel” in Psychology and Alchemy (New York,
1968), 345–431.
229
body, spirit, and soul.
39
Flamel’s associated illustration equates this trinitarian nature with not
just Christ’s resurrection, but with the Last Judgment, depicting three previously deceased
Christians resuscitated on Judgment Day, standing before Christ the Judge and two music-
making angels, whose lute and bagpipe were likely meant to represent the “soul” and “body,”
respectively, now brought into eternal union.
40

In chapter 2, I noted that Martin Luther used a similar metaphor to link alchemy with
descriptions of the End Times in Revelation: that in the process of chemical distillation, one sees
the faithful (vapors) become separated from the unfaithful (dregs), and for this reason that
alchemy is a Christian pursuit, “by reason of the noble and beautiful likeness which it hath with
the resurrection of the Dead on the Day of Judgment.”
41
According to its introduction, Flamel’s
treatise aims to unite a specifically Christian-alchemical approach with Arabic and cabbalistic
wisdom. This is important, in revealing its post-Renaissance thought; but it is also precisely these
avenues of wisdom that late-seventeenth-century Rosicrucians sought to unite in pursuit of
eternal wisdom and divine unification.
42
The Exposition of the Hieroglyphicall Figures, then, is
part of a longer pre-Rosicrucian tradition of merging Christian, Arabic, and cabalistic
knowledge, at first drawing directly from Johannes Reuchlin’s De arte cabbalistica (Hagenau,
1517) and Pico della Mirandola’s “Apologia tredecim Quaestionum” (included in the 1557
Opera published in Venice), then appearing in imagery from major seventeenth-century alchemy
treatises such as Heinrich Khunrath’s Amphitheatrum sapientiae aeternae (1602), Steffan

39
London, Wellcome Institute for the History of Medicine Library, Wellcome MS 2456, fol.
332.
40
See Emanuel Winternitz, Musical Instruments and Their Symbolism in Western Art
(London, 1967) and Dixon, xxxix.
41
Dixon, “Introduction,” xxxix. See also Nummedal, “Alchemy and Religion in Christian
Europe.”
42
See chapter 4.
230
Michelspacher’s Cabala of 1616, and Michael Maier’s Arcana arcanissima of 1614. These
treatises, like Flamel’s Exposition, explicitly state their goal of fusing Western and Eastern
wisdom, toward humanity’s greater good; it is precisely this impulse that forms the Jacob Böhme
school of Rosicrucian thought.
43
If Buxtehude, his circle of friends, or his patrons knew any of
these authors or works, these characteristics would have been familiar, recognizable as part of
the same intellectual and spiritual lineage.
For all of the reasons already presented, Flamel’s Exposition of the Hieroglyphicall
Figures is certainly a product of the seventeenth century, no earlier. While it claims to be a
medieval treatise, no version of text or illustrations from before the seventeenth century exist, its
first appearance being the Paris edition of 1612 (printed by Arnauld de la Chevaliere), with the
English edition of 1624 being a literal translation from the French. As Le livre des figures
Hierogliphiques de Nicolas Flamel, it was first released as a set with two other treatises, Le
Secret Livre of Artephius (which Eirenaeus Orandus kept in the 1624 English edition) and Le
Vray Livre de la Pierre Philosophale du doctor Synesius (later replaced by The Epistle of John
Pontanus).
44
While these circumstances of course point to its inauthenticity as a medieval source,
I believe that they strengthen the chances that Buxtehude had some contact with Flamel’s text. It
would seem, after all, that it was engineered for a specifically seventeenth-century audience, and
it was indeed immensely popular in the years immediately following its early seventeenth-
century “discovery”: after two different 1612 French editions, and the subsequent English
translation of 1624, more French editions based on the original emerged in 1659, 1660, and
1682, with a German translation in 1669, this reprinted in 1673. It was also included in William

43
Dixon, “Introduction,” xxi.
44
Dixon, xli.
231
Salmon’s illustrated Bibliothèque des philosophes chimiques dated 1672-78, and another English
translation appeared in editions of Salmon’s Medicina practica in 1691, 1692, and 1707.
45

Thanks to these, Flamel gained enough of a following in the seventeenth century that other tracts
were “discovered” as well, including Le Sommaire Philosophique, Le Desir Desiré, Le Grand
Eclairissement de la Pierre Philosophale, Le Livre des Laveures, Le Breviaire and La Musique
Chimique. Other treatises attributed to Flamel were published in Borel’s La Bibliotheca chimica
(1654); the Musaeum hermeticum reformatum et amplificatum (1677-78 and 1749); Aurifontina
chymica (1680); and Manget, Bibliotheca chemica curiosa (1702).
46

The intended audiences for these treatises—while seemingly not so concerned about
authenticity—were extremely knowledgeable about actual medieval and Renaissance science.
This was largely thanks to a widespread seventeenth-century drive to compile ancient and
medieval alchemical texts into collections, most notably the Theatrum chemicum (1602), with
continuous volumes appearing in 1613, 1622, 1659 and 1661. Nicolas Barnaud also printed De
occulta philosophia (1601), featuring many of the texts also found in the Theatrum. Thus, works
of less contestable authenticity by authors such as George Ripley, Roger Bacon, Thomas Norton,
and Ramon Lull were probably better known in the seventeenth century than they had ever been,
and on a much broader scale.
47

Like the awareness of numerology exhibited in the Rosicrucian manifestos, the
Exposition of the Hieroglyphicall Figures is also by all metrics “Rosicrucian,” even without
directly claiming to be. Numerologically, the author embeds references to seemingly significant
numbers throughout the work—and as such, hints at but never actually confirms any meanings

45
Dixon xlii.
46
Most historians believe these to be spurious as well. See Dixon, xliii.
47
Dixon, “Introduction,” xix.
232
the reader might suspect. Of all of these numbers—as in many of the musical works this
dissertation treats—three, seven, and twenty-one (7 x 3) appear frequently. Flamel claims to have
decorated three chapels and refurbished seven churches with the wealth he amassed from his
exactly three successful transmutations. Canches dies after seven days’ illness. Abraham’s book
contains exactly seven hieroglyphs spread over twenty-one folios, and Flamel worked on the
problem of transmutation for a total of twenty-one years.
48

From an alchemical standpoint, these numbers probably refer to the threefold alchemical
“trinities” of sun, moon, and Mercury; body, spirit, and soul; and animal, mineral, and vegetable,
with seven—in addition to any Christian traditions equating both Christ and the Virgin with the
number seven’s “holiness”—standing for the seven planets and their seven corresponding metals.
Beyond these inner details, the larger organization of the Exposition of the Hieroglyphicall
Figures into two sections (Christian and Philosophical) itself structurally mirrors the Hermetic
precept of duality and opposition, the harmonization of which through learned transmutation
enacts eternal peace and enlightenment.
49

One of the most striking instances of this three-seven-twenty-one emphasis in the
Exposition—the serpent-related hieroglyphs themselves—leads us to the symbolic core of
Buxtehude’s textual imagery and numerically-charged musical setting. In Flamel’s introduction,
the three hieroglyphic images he first mentions finding in the Book of Abraham occur each
seventh page: “the first seventh,” “the second seventh,” and “the last seventh,” another
conspicuous merging of three and sevens. The author describes the first image as “a Virgin, and
Serpents swallowing her up.”
50
This is a common seventeenth-century alchemical trope, which

48
Flamel, Exposition of the Heiroglyphicall Figures, 4–38.
49
Dixon, xxvi–xxvii.
50
Flamel, Exposition of the Heiroglyphicall Figures, 7.
233
also appears as the final emblem (Figure 7.7) in Maier’s Atalanta fugiens. But interestingly, this
image is not found in any illustrated versions of Flamel’s text—rather, it is always replaced with
an image of two serpents devouring each other on a rod (Figure 7.8), meant instead to symbolize
Mercury’s caduceus.
51

Figure 7.7. Michael Maier, Emblem L, “The Dragon kills the woman, and she kills it, and
together they bathe in the blood,” from Atalanta fugiens (1617).

51
The virgin-serpent image never actually shown is still a common alchemical image, likely
originating in the Turba Philosophorum (ca. 900 C.E.) and most famously appearing in Atalanta
fugiens (1617). In both cases, it signifies the joint death and redemptive unification of the pure
virgin and poisonous dragon, as allegory for the joint death, decomposition, and eventual
redemptive rebirth of the opposite elemental forces in the birth of the Stone. For more
information about the image’s print history, see Dixon, xxviii.
234

Figure 7.8. After Flamel, “a Rod and Serpents swallowing it up,” illustration 1 based on
Flamel’s Exposition, taken from William Salmon’s edition of the Hieroglyphicall Figures, in
Bibliothèque des philosophes chimiques (1672).

The next image, on the “second seventh” page of Abraham’s book is “a Crosse where a Serpent
was crucified” (Figure 7.9). This image probably symbolizes putrefaction (or sometimes,
literally, “crucifixion”) necessary for the eventual “resurrection” of the Stone into its final state
of eternal medicinal purity.
52
But most importantly, it reinforces three central symbolic
relationships also present within the text to Sicut Moses exaltavit serpentem in deserto: the
Christ-Stone connection as exemplars of redemptive death, the union between the Old and New
Testaments contained in the “elevation” of Moses’s brazen serpent in Numbers, and both of
these references joined with ancient Gnostic roots of the image of a serpent-wrapped rod as

52
It could also refer to the more general “fixing” of volatile spirits. See Dixon, xxviii.
235
specifically medicinal.
53
In chapter 6 of the Exposition, the author leans most strongly into the
“putrefaction” reading, in his explanation of the cemetery tympanum.
54

Figure 7.9. After Flamel, “a Cross where a Serpent was crucified,” illustration 2 based on
Flamel’s Exposition, taken from William Salmon’s edition of the Hieroglyphicall Figures, in
Bibliothèque des philosophes chimiques (1672).

The final plate depicts a “Desert (or Wilderness),” in which there also exists a “fount,”
55
with a
multiplicity of serpents, presumably having “sprung” from the redemptive death of crucifixion
(Figure 7.10).

53
C. G. Jung, Psychology and Alchemy, trans. R. F. C. Hull, Complete Digital Edition, vol.
12, The Collected Works of C. G. Jung (Princeton, New Jersey: Princeton University Press,
1968), 517.
54
Dixon, “Introduction,” xxviii.
55
See chapter 6.
236

Figure 7.10. After Flamel, “Deserts, or Wildernesses...a number of Serpents, which ran up and
down here and there,” illustration 3 based on Flamel’s Exposition, taken from William
Salmon’s edition of the Hieroglyphicall Figures, in Bibliothèque des philosophes chimiques
(1672).

Thus, Flamel’s Exposition of the Hieroglyphicall Figures focuses this dissertation’s
larger discussion in three crucial respects: its tremendous popularity meant wide dissemination
across Europe; it expressly seeks literary connections between Hermetic thought and Christian
doctrine, while incorporating cabalistic ideas taken up by German Rosicrucian movements in the
late-seventeenth century; and finally, it relates foundationally to the same emblem-book tradition
with confirmed ties to several of Buxtehude’s texts discussed elsewhere in this study.
56
Flamel’s
treatise was designed for the same learned—and pious—audience as these other examples. It
may well have sat on whichever bookshelf in Buxtehude’s midst held Cor Iesu amanti sacrvm
and Michael Maier’s Atalanta fugiens.

56
Gero, “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude,” 236–
41.
237
To this last point about library contents: another argument for Buxtehude’s contact with
Flamel’s Exposition of the Hieroglyphicall Figures is its title, which directly acknowledges a
connection to the wildly popular emblem-book tradition. By mentioning “Hieroglyphicall
Figures,” the author recalls the text credited as the first printed emblem book, the Hieroglyphica
of Horapollo of 1505. Significantly, considering Hermetic claims to Alexandrian wisdom, it
purports to aid in deciphering ancient Egyptian hieroglyphics, and its wild popularity cemented
the typical emblem-book form of “allegorical emblem - Latin verse - moral motto” that all
alchemical emblem books of the seventeenth century assume. The fashion for emblem books
peaked in the seventeenth century, attracting a wide popular reading audience; for alchemy in
particular, Flamel’s Exposition of the Hieroglyphicall Figures served as an early model for
Michael Maier’s now even more famous Atalanta fugiens and Mylius’ Philosophia reformata.
57

Finally, if Buxtehude did indeed know this text, he carried its “thrice-seven” design,
along with its Christianized-Hermetic spiritual message of cyclic renewal via redemptive death,
into Sicut Moses exaltavit serpentem in deserto by way of number and proportion, as I will show.
Buxtehude also makes audible the text’s “eternal life” message, from which this mystical
numerology springs, through pervasive canon within each otherwise distinct compositional
section. But to set the word “aeternam” (eternal, everlasting), Buxtehude begins with canon
(Example 7.3)—with the main motive also tracing a quasi-circuitous path—but for the final
iterations of the text and this motive, ultimately stacks this motive in fauxbourdon-like
homophony (Example 7.4). This joins canonic connotations of musical eternity
58
with
fauxbourdon’s associations with sweetness and marital union—whether in this case between man

57
Dixon, xxi–xxii.
58
As a compositional “seed” reproducing in abundance. See chapter 3.
238
and God or mercury and sulphur, whose “wedding” in the alchemical flask yields “eternal life”
in the Philosophers’ Stone.
59

Example 7.3. Buxtehude, Sicut Moses, mm. 141-50, canonic imitation.

Example 7.4. Buxtehude, Sicut Moses, mm. 197-206, quasi-fauxbourdon.

59
Buxtehude also features extended passages of fauxbourdon in the opening to “Ad Pectus”
(To [Jesus’s] Breast), the fifth section of Membra Jesu Nostri (BuxWV 75).
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
141
Œ Œ
œ
sed
. œ
J
œ
œ
. œ
j
œ #
œ
˙ œ
˙
œ
6
. œ
j
œ #
œ
ha be at
∑
∑
∑
˙
œ
6
œ #
œ
œ
vi tam ae
∑
∑
∑
˙
I
œ
6
œ .
œ
j
œ
ter nam,
∑
∑
∑
œ
˙
I
4
. ˙
Œ Œ
œ
∑
Œ Œ
œ
˙
œ
6
∑
.
œ
J
œ #
œ
Œ Œ
œ
.
œ
J
œ
œ
.
œ
J
œ
œ
∑
œ #
œ
Œ
.
œ
J
œ
œ
œ œ
œ #
˙
I
œ #
∑
Œ Œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
∑
˙
œ #
œ
˙
œ
˙
œ
5
7
˙
I
4
5
Œ Œ
œ
ut
.
˙
. ˙
. ˙
˙
œ
- - - - -
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
151
œ œ
œ
om nis qui
∑
∑
∑
˙
œ
œ œ
œ
cre dit, qui
∑
∑
∑
.
˙
5 6
. œ
J
œ
œ
cre dit in
∑
∑
∑
˙
6
œ
6
˙ œ
e um,
∑
∑
∑
˙
œ
6
Œ ˙
non,
∑
∑
∑
˙
œ
6
Œ
œ #
œ
non, non
∑
∑
∑
. ˙
I
5 6
. œ #
j
œ #
œ
pe re at,
Œ Œ œ
Œ Œ
œ
Œ Œ œ
˙
I
œ
6
∑
Œ
œ #
œ
Œ
œ
œ
Œ
œ
œ
Œ
œ
œ
5
∑
. œ #
j
œ #
œ
.
œ
j
œ
œ #
˙ œ
.
˙
I
Œ
œ
œ
non, non
∑
∑
∑
. ˙ #
6
- - - - - -
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
161
.
œ
J
œ
œ
pe re at
Œ Œ
œ
Œ Œ œ
Œ Œ
œ
.
˙
∑
Œ
œ
œ
Œ
.
œ
j
œ #
Œ
œ
œ
Œ
œ
4
œ
I
Œ Œ
œ
sed
.
œ
J
œ
œ
.
œ
j
œ #
œ
˙ œ
.
˙
.
œ
J
œ
œ
ha be at
∑
∑
∑
.
˙
œ
œ
œ
vi tam ae
∑
∑
∑
œ
œ
œ
6
œ
. œ
J
œ
ter nam,
∑
∑
∑
œ
œ
3 4
œ
.
˙
Œ Œ
œ
∑
Œ Œ
œ
˙
œ
6
∑
.
œ
J
œ
œ
Œ Œ
œ
. œ
J
œ
œ
. œ
J
œ
œ
∑
œ
œ
Œ
.
œ
j
œ
œ
˙
œ
˙
œ
5
6
- - - - - - -
8 Sicut Moses exaltavit serpentem in deserto ita
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
197
Œ Œ
œ
sed
.
˙
.
˙
.
˙
.
˙
.
œ
j
œ
œ
ha be at
∑
∑
∑
. ˙
5
6
œ
œ
Œ
vi tam,
Œ Œ
œ
Œ Œ
œ
Œ Œ
œ
˙
œ
6
∑
. œ
J
œ
œ
.
œ
J
œ
œ
. œ
J
œ
œ
. œ
6
J
œ
6
œ
6
Œ Œ
œ
sed
œ
œ
Œ
œ
œ
Œ
œ œ Œ
˙
œ
6
.
œ
J
œ
œ
ha be at
∑
∑
∑
.
˙
6 7 \
œ
œ
Œ
vi tam,
Œ Œ
œ
Œ Œ
œ
Œ Œ
œ
˙
œ
6
∑
. œ
J
œ
œ
.
œ
J
œ
œ
. œ
J
œ
œ
. œ
6
J
œ
6
œ
6
Œ Œ
œ
sed
œ
œ
Œ
œ
œ
Œ
œ œ Œ
˙
œ
6
.
œ
J
œ
œ
ha be at
∑
∑
∑
˙
œ
- - - - - - - -
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
c
c
c
c
c
S
Vln1
Vln2
Vdg
BC
207
œ
œ
œ
vi tam ae
∑
∑
∑
œ
œ
œ
œ
. œ
J
œ
ter nam.
∑
∑
∑
œ
5
7
œ
4
œ
3
.
˙
Œ Œ
œ
Œ Œ
œ
Œ Œ œ
.
˙
.
˙
.
œ
J
œ
œ
. œ
J
œ
œ
.
˙
.
˙
∑
œ
œ
œ
œ
œ
œ
˙
œ
˙
I
4
2
œ
6
∑
œ
. œ
J
œ
œ
.
œ
J
œ
œ
˙
œ
˙
3 4
∑
.
˙
U
.
˙
U
. ˙
U
.
˙
U
Œ
œ œ œ œ œ
œ
œ
A men, a men a
∑
∑
∑
œ
œ
œ
œ
œ
œ
7
œ
4
œ
3
- - - - - -
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
215
œ œ
Œ Ó
men,
Œ
œ œ œ œ œ
œ
œ
Œ
œ œ œ œ œ
œ
œ
Œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
6
œ
œ
4
œ
3
Œ
œ œ œ œ . œ
œ #
a men, a men, a men,
œ œ
Œ Ó
œ œ
Œ Ó
œ œ Œ Ó
œ
œ
œ
œ
œ
6
œ
œ
7
œ
I
œ œ
Œ Ó
a men,
Œ
œ œ œ œ œ
œ
œ
Œ
œ œ œ œ œ
œ
œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
4
œ
I
Œ
œ œ œ œ œ
œ
œ
a men, a men, a
œ œ
Œ Ó
œ œ
Œ Ó
œ œ
Œ Ó
œ
œ
œ
œ
œ
œ
œ
4
œ
I
œ œ
Œ Ó
men,
Œ
œ œ œ
œ . œ
œ
Œ
œ œ œ œ
.
œ
œ
‰
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
6
œ
œ
œ
œ
4
œ
3
- - - - - - - -
10 Sicut Moses exaltavit serpentem in deserto ita
239
So far, I have outlined the following numerical design in Sicut Moses exaltavit serpentem
in deserto: two lines of text divided into four, reimagined as combinations of threes, fours, and
sevens, presented in interlocking key-and-meter palindromes, all to set a textual story not just of
Jesus, but of the cyclic sublimation and distillation of a crucified serpent in the alchemical flask.
The final operation to unite these symbols takes us—in fittingly circular fashion—back to
ostinato basses, but first to numerical theology.
Every major structure in Sicut Moses exaltavit serpentem in deserto is a figurate number,
and these are the same figurate numbers that structure the ostinato psalm settings (Figure 7.11).
In Sicut Moses, the sixty-four and eighty-one-measure interior sections are both squares, while
the Sonata and “Amen” sections are both squares, each subdivided into a smaller square and
triangle. The moments of alchemical operations, however, are both stars: the serpent’s
“exaltation” section is a thirty-seven-measure star, and the resulting “eternal life” a chiastic
seventy-three-measure star.

Figure 7.11. Sicut Moses: Map of keys, meter, section lengths, and embedded figurate numbers.

240

This “Moses” and “Eternal Life” digit opposition between thirty-seven and seventy-three also
forms meta-triangles and squares as the third and fourth star-numbers in the natural sequence, to
compound their other extraordinary properties outlined in previous analysis chapters.
60

But it is a potent combination of numerical symbol and ostinato pattern that ultimately
join this work with the alchemical-numerical imagery permeating Buxtehude’s fully ostinato
compositions. Through motivic borrowing, Buxtehude’s thirty-seven-measure serpent
“exaltation” section recalls Herr, wenn ich nur Dich hab’ (BuxWV 38), and with it, its divine-
unification connotations of “Squaring the Circle.”
61
The Düben Collection archivists estimate
these works to date from the same three years around 1680. In addition to an identical figurate-
number vocabulary that, in shared star numbers between these compositions, connects
“elevation” to “eternal life,” Sicut Moses contains an extended cameo appearance of the Herr
wenn ich nur Dich hab’ bass pattern (Example 7.5):

Example 7.5. Buxtehude, Herr, wenn ich nur Dich hab’ (BuxWV 38), ostinato bass (top); Sicut
Moses, mm. 52-54, ostinato bass (bottom).

60
See chapter 4 for further explanation. See chapters 5–6 for examples of these numbers in
Buxtehude’s compositional practice.
61
See chapter 5.
241
This immediately follows the text “Just as Moses raised up the serpent in the desert,” at the
precise moment, in performance, when a listener “witnesses” this physical elevation in their
mind’s eye (Example 7.6):

242

Example 7.6. Buxtehude, Sicut Moses, mm. 51-63, internal ostinato quotation from Herr, wenn
ich nur Dich hab’ (BuxWV 38).

For the first three turns of the ground, a one-note embellishment raises the number of
notes to seven (twenty-one notes total), but in its final iteration, the grounds are identical. This
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
51
œ
œ .
œ
œ
œ œ
pen tem in de ser to
∑
∑
∑
œ
5
6
œ
˙
∑
≈
œ
œ
œ
œ
≈
œ
œ
œ
œ
Œ ≈
œ
œ
œ
j
œ
‰ ≈
œ
œ
œ
Œ œ
œ
≈
œ
œ
œ
˙
˙
6
∑
≈
œ
œ
œ
œ
≈
œ
œ
œ
œ
J
œ
‰ ≈
œ
œ
œ
J
œ
‰ ≈
œ
œ
œ
œ
≈œ
œ
œ
œ
≈
œ
œ
œ
˙
˙
6
∑
≈
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
œ
. œ
j
œ
œ
œ
˙
- - -
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
S
Vln1
Vln2
Vdg
BC
55
∑
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
j
œ
‰
œ
œ
œ
œ
j
œ
‰ ≈
œ
œ #
œ
œ œ œ œ
œ œ œœ
œ
œ
˙
˙
6
∑
≈
œ
œ #
œ
.
œ
œ
œ
œ
œ
œ
œ
œ
œ n
œ
œ
≈
œ
œ
œ
œ
œ
œ
œ
œœ
œ
œ
œ œ œœ
œ
œ
œ œ œ œ
˙
6 7 \
˙
6
∑
œ
œ
œ
œ
œ œœ
œ
œ
œ
J
œ ‰ ≈
œ
œ
œ
œ
œ
.
œ
œ
œœ
œ
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
˙
I I
4
7
∑
œ
œ
œ
œ
J
œ
‰
œ
œ
œ
œ
J
œ
‰
J
œ
‰
œ
œ
œ
œ
J
œ
‰
œ
œ
œ
œ
œ
œ œ œ
œ œ œ œ
˙
˙
6
&
&
&
?
?
#
#
#
#
#
#
#
#
#
#
4
3
4
3
4
3
4
3
4
3
S
Vln1
Vln2
Vdg
BC
59
∑
œ
œ
œ
œ
j
œ #
‰
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ œ œ
œ œ œ œ
˙
6 7 \
˙
∑
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
J
œ ‰ ≈
œ
œ
œœ
œ
œ
œ
œ
œ
œ
œ œ
œ œ
œ œ œ œ
œ
œ
˙
3 3 4
∑
œ œ
œ
œ
‰
œ
œ #
œ
œ
‰
œ
œ
œ
‰
œ
œ
œ
œ
œ œ
œ œ
œ œ
œ
œ
6
œ
6 7 \
œ
6
∑
‰
œ
œ
.
œ
œ
˙
U
œ ‰
œ
œ
˙
U
œ œ
œ œ
˙
U
œ
5
6
œ
3 4
˙
U
˙ ˙
i ta,
∑
∑
∑
w
i
Adagio
-
4 Sicut Moses exaltavit serpentem in deserto ita
243
yields a “perfect” twenty-eight bass notes.
62
And the non-bass notes in this section are 280, a
union of this numerus perfectus and the “circle” number ten. With careful geometrical
maneuvering, Buxtehude thereby unites the Old and New Testaments through the Passion, and
joins this symbolism with Hermes, alchemy, and mathematical theology, through “eternal”
ostinato quotation. This readjusts the work’s focal point away from Moses and humanity and
onto the very act of “alchemical” exaltation itself. Whether the product of understanding this
crucifixion to be of Jesus, a serpent, or both, Buxtehude’s twenty-eight-note “perfect” bass
pattern provides dramatic underscoring to cyclic renewal, equally evident to the ear as it is
central to the compositions’ mathematical scaffolding.

7.3 – Conclusion
Meaningful intersections between numbers and theology in Buxtehude’s craft ultimately
necessitate reform not only of our concept of his personal compositional process, but of
numerology’s importance in the larger seventeenth-century intellectual environment that fostered
it. Moreover, the appearance of specifically Rosicrucian textual and numerical tropes in his
music provides a new bridge between alchemy, Christianity, and counterpoint that complicates
the longstanding scholarly discussion of his possible Pietist influences. My goal in chapter 2, in
mapping intersections between seventeenth-century thought about number, alchemy, and
Christianity, was to recontextualize the Rosicrucian movement in the scope of exoteric
intellectual history. If today (outside or inside of academia) we conceptually lump
Rosicrucianism in with cults and a version of “occult” philosophy tinged with post-
Enlightenment notions of occultism as satanic, then this deserves reassessment. Likewise, if the

62
Twenty-eight is the second numerus perfectus. See chapter 4.
244
circumstances of Rosicrucianism’s appearance in 1980s Bach numerological scholarship were
not the best, then this should not reflect poorly on actual seventeenth-century Rosicrucianism in
present and future musicological scholarship. As my investigation has demonstrated, the
philosophies behind the initial Rosicrucian impulse and its aftermath were about social reform,
not Esotericism, and fundamentally Christian, if “supra-confessional” as such. Any post-
Enlightenment anxieties about Paracelsian medicine and alchemy as worthy or unworthy
scientific pursuits, or as Christian or heretical, relate neither to Rosicrucianism’s roots nor its
“furore” as an international phenomenon in the mid-seventeenth century. The fact that
Rosicrucianism did not become a single, unified and therefore “real” organization did not hinder
its appeal and subsequent reach; quite the opposite, its intentional open-endedness only enhanced
its possibility for adoption and interpretation by anyone looking for social reform informed by
intensified spiritual experience.
Therein lies a warrant for reading Buxtehude’s use of number in his ostinato-bass
compositions as potentially Rosicrucian, beyond just mathematically or biblically driven. Both in
written claims and in actual practice, the Rosicrucian brotherhood only existed in largely
unorganized fashion: according to the manifestos, those who were called to join were already
members, and none of the original founding authors ever publicly responded to the hundreds of
potential followers begging for them to reveal themselves, so that the Brotherhood could
cohesively form and carry out its mission as a unified entity. Thus, the “brotherhood” shown in
Voorhout’s painting could have been Rosicrucian, without any “official” identifying features
beyond the dedication. But if they now need any such identifying features to confirm suspicions,
they have indeed left abundant clues, from the “brotherly” dedication and psalm-texted
alchemical canon in Voorhout’s painting, to Buxtehude’s laudatory poems for Theile, Reincken,
245
and Werckmeister, praising their musical and Christian wisdom “from earth to heaven.” Because
of Rosicrucianism’s intentionally elusive nature,
63
one cannot find a linear evidentiary path
between Buxtehude and Rosicrucianism; rather, Rosicrucianism, alchemy, and numerology all
exist as an interrelated web of discursive meaning.
64
This project’s biographical investigation
confirms Buxtehude’s ties to alchemy, number, astronomy, and likely contact with the esoteric
texts upon which Rosicrucianism was founded. In addition to Theile’s alchemy-infused
contrapuntal treatises and studies, even the subject and title of his first public opera are rife with
Rosicrucian undertones, while Reincken’s Hortus Musicus contains a wealth of its own number
symbolism. Theile’s “Harmonischer Baum” from the Musicalisches Kunstbuch—and especially
its text about a wedding—would suggest Theile’s knowledge of the union of mercury and
sulpher as specifically a “chemical wedding.” Considering the Rosicrucian “furore” and the vast
number of texts it left to readers later in the century, it would be surprising if Theile, with his
knowledge of alchemical texts, did not also know that this was the title and subject of the last
Rosicrucian manifesto. All of these factors considered, including Voorhout’s image of
Buxtehude and Reincken as “brothers,” some iteration of Rosicrucianism, whether or not filtered
through the later Jacob Böhme school or directly from the first manifestos, would have made a
convenient platform for their alchemical interests and all musical expressions thereof.

63
Marcia Keith Scuchard, “Leibniz, Benzelius, and the Kabbalistic Roots of Swedish
Illuminism,” in Leibniz, Mysticism and Religion, ed. Allison P. Coudert, Richard H. Popkin, and
Gordon M. Weiner, vol. 158, International Archives of the History of Ideas (Dordrecht; Boston;
London: Kluwer Academic Publishers, 2013), 84.
64
For this reason, scholars like Christopher McIntosh often describe Rosicrucianism is an
“egrigore”: a dynamic magnet or “rolling stone.” For arguments for and against this
understanding of Rosicrucianism, see Tobias Churton, The Invisible History of the Rosicrucians:
The World’s Most Mysterious Secret Society (Rochester, Vermont: Inner Traditions, 2009), 273.
246
These and other works by Theile and Reincken deserve a numerical and textual
reinvestigation, in light of the Rosicrucian and alchemical ripples of thought my study of
Buxtehude’s ostinato psalm settings reveals. Throughout these works, I have demonstrated
Buxtehude’s compositional reliance on the same figurate triangle and square numbers that, when
brought into harmony with geometrical circularity, symbolize the union of heaven and earth, and
of body, spirit, and soul in a seventeenth-century Rosicrucian worldview. That these numerical
tropes (including emphasis on “unity,” three, four, seven, fourteen, and thirty-seven) appear
specifically alongside texts concerning eternity and divine unification, and with their own layers
of possible alchemical double-meanings, lends credence to the idea that Buxtehude at least knew
about Rosicrucian print sources. Considering the close textual similarities between his chosen
psalm texts, plus the unusual Old-Testament Sicut Moses exaltavit serpentem in deserto, and the
Rosicrucian manuscript in Hamburg, alchemical references to “aqua vitae,” and the “Flamel”
serpent-related treatise, would suggest direct contact with these Rosicrucian print sources. Any
one of Theile’s twenty-four benefactors for his stile antico masses could have owned these
treatises and devotional manuals. These were likely the same wealthy patrons Buxtehude
approached for funding for his Abendmusik activities.
65
If any of these esoteric-counterpoint
enthusiasts introduced Buxtehude to the Cor Iesu amanti sacrum, then they easily could have
owned these Rosicrucian sources as well. The fact that Buxtehude never held a job that required
him to write vocal music, meaning that his textual choices were always separate from his actual
job, supports the idea that his textual sources could have come from channels of this sort.

* * *

65
Snyder, Dieterich Buxtehude: Organist in Lübeck, 61–65.
247

Seventeenth-century mathematics experienced, for the first time, intersections between infinitary
and analytic techniques—nearly all of which found strong theological grounding, according to
contemporary treatises.
66
But this theology, like that of Buxtehude’s friends, does not ignore the
esoteric—Leibniz was as engaged with metaphysics and the Christian cabala as with inventing
calculus, while Newton, independently also inventing calculus, spilled more ink over alchemy
than over optics and physics combined.
67
These scientists, with the aim of learning about God
and nature, as a by-product discovered how to quantify infinity, while Buxtehude was using
numbers to express in music, with scientific precision, the concept of eternity in a numerically
ordered heaven.
These numerical mechanisms alone teach us about Buxtehude’s compositional process,
which strives to mirror the order of the cosmos, in structure and proportion. By examining these
cosmological ideals, his friends who forwarded them, and the numerical remnants they left in
work, we piece together a more complete image of Buxtehude the man. Ultimately, his
numerical mechanisms tell us something important about his compositional priorities. These
numerically intricate pieces are also aurally beautiful—and yet, we must concede that Buxtehude
did not necessarily construct his entire Harmonia for mortal ears.
68
It is through Buxtehude’s

66
Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth
Century, 65.
67
Allison P. Coudert, Leibniz and the Kabbalah (Dordrecht: Kluwer Academic Publishers,
1995).
68
In contrast to some other contemporaries who also used numbers in their compositional
processes, for instance (I suspect) Heinrich Biber, I do not necessarily think Buxtehude designed
most of the numerical features in this dissertation to be readily observable by the uninitiated.
While undertaking this project I have imagined Buxtehude many times, though, excitedly
showing Theile or Reincken his “Squaring the Circle” in Herr, wenn ich nur Dich hab’, or
evidence of his having worked as many star numbers as humanly possible into Quemadmodum
248
numerical structures, rather than their earthly sonic result, that he, like Fludd, strings a
monochord through the cosmos from man to his ultimate audience. The glorious sounds he left
us rest just atop an even more profound harmony he entrusted, in the words of his life motto,
“Non homnibus, sed Deo”—not to men, but to God.

desiderat cervus—at least as gleefully as I have shared with colleagues and advisors these
numerical discoveries.

249
BIBLIOGRAPHY

Primary Sources

Agrippa, Heinrich Cornelius. De Occulta Philosophia. Cologne, 1533.

[Andreae, Johann Valentin]. Chymische Hochzeit Christiani Rosencreutz anno 1459. Strasbourg:
Zetzner, 1616.

———. “The Chemical Wedding of Christian Rosenkreuz.” In Rosicrucian Trilogy: The Three
Original Rosicrucian Publications in New Modern Translation, translated by Joscelyn
Godwin, 61–181. Newburyport, Massachussetts: Weiser Books, 2016.

[Anonymous]. Confessio Fraternitatis. Kassel, 1615.

———. “Confessio Fraternitatis, 1615.” In Rosicrucian Trilogy: The Three Original
Rosicrucian Publications in New Modern Translation, translated by Joscelyn Godwin,
41–52. Newburyport, Massachussetts: Weiser Books, 2016.

———. “Einfältig ABC-Büchlein Der Rosenkreuzer.” Manuscript. Staats- und
Universitätsbibliothek Hamburg, ca 1700. Codex in scrinio 21. Paper.
http://resolver.sub.uni-hamburg.de/goobi/HANSh1310. Accessed June 18, 2022.

———. “Fama Fraternitatis, 1614.” In Rosicrucian Trilogy: The Three Original Rosicrucian
Publications in New Modern Translation, translated by Christopher McIntosh and Donate
Pahnke McIntosh, 15–32. Newburyport, Massachussetts: Weiser Books, 2016.

———. Fama Fraternitatis, oder Entdeckung der Bruderschafft deß löblichen Ordens deß
Rosen Creutzes/ Beneben der Confession Oder Bekantnuß derselben Fraternitet/ an alle
Gelehrte und Haüpter in Europa geschrieben. Kassel, 1614.

Arndt, Johann. Vier Bücher vom wahren Christentum. Magdeburg: Johann Franken, 1610.

Ashmole, Elias, ed. Theatrum Chemicum Britannicum. London: J. Grismond, 1652.

Bartolus, Abraham. Musica Mathematica. Leipzig: H. Grossen, 1612.

Baryphonus, Heinrich. Pleiades musicae. Halberstadt: Jakob Arnold Kote, 1615.

Bernhard, Christoph. “Tractatus compositionis augmentatus.” In Die Kompositionslehre
Heinrich Schützens in der Fassung seines Schülers Christoph Bernhard, edited by Joseph
Müller-Blattau, 2nd ed., 40–121. Kassel: Bärenreiter, 1963.

250
———. “Tractatus Compositionis Augmentatus.” In The Treatises of Christoph Bernhard,
translated by Walter Hilse, 3:31–196. Music Forum. New York: Columbia University
Press, 1973.

Boethius. Fundamentals of Music. Edited by Claude V. Palisca. Translated by Calvin M. Bower.
New Haven: Yale University Press, 1989.

Brocardo, Jacopo. Mystica et Prophetica Libri Geneseos Interpretatio. Bremen: Theodor
Gluichstein, 1585.

Bruno, Giordano. De innumerabilibus, immense, et infigurabili. Frankfurt: Johann Wechel, Peter
Fischer, 1591.

Cramer, Daniel. Emblemata Sacra. Frankfurt: Lucae Jenissi, 1624.

Crüger, Johann. Praecepta Musicae Practicae Figuralis. Berlin: Johann Kall, 1625.

———. Synopsis Musica. [Berlin]: Johann Kall, 1630.

Dee, John. Monas Hieroglyphica. Antwerp: Willem Silvius, 1564.

Descartes, René. Discourse on Method, Optics, Geometry, and Meteorology. Translated by Paul
J. Olscamp. Indianapolis; Cambridge: Hackett Publishing Company, 2001.

———. The Philosophical Writings of Descartes. Translated by John Cottingham, Robert
Stoothoff, and Dugald Murdoch. Vol. 1. Cambridge: Cambridge University Press, 1985.

Faulhaber, Johann. Academia Algebrae. Darinnen Die Miraculossische Inventiones/ Zu Den
Höchsten Cossen Weiters Continuiert Und Profitiert Werden. Dergleichen Zwar Vor 15.
Jahren Den Gelehrten Auff Allen Universiteten in Gantzem Europa Proponiert, Darauff
Continuiert, Auch Allen Mathematicis Inn Der Gantzen Weiten Welt Dediciert, Aber
Bißhero/ Noch Nie so Hoch/ Biß Auff Die Regulierte/ Zensicubiccubic Coß/ Durch Offnen
Truck Publiciert Worden. Welcher Vorgesetzet Ein Kurtz Bedencken/ Was Einer Für
Authores Nach Ordnung Gebrauchen Solle/ Welcher Die Coß Fruchtbarlich/ Bald/ Auch
Fundamentaliter Lehrnen Und Ergreiffen Will. Augsburg: Johann Ulrich Schönigk, 1631.

———. Fama Siderea Nova. Ulm, 1618.

———. Miracula Arithmetica. Zu der Continuation seines arithmetischen Wegweisers gehörig.
Augsburg: David Franck, 1622.

Flamel, Nicholas. Nicholas Flammel, His Exposition of the Hieroglyphicall Figures Which He
Caused to Bee Painted Vpon an Arch in St. Innocents Church-Yard, in Paris. Together
with the Secret Booke of Artephius, and the Epistle of Iohn Pontanus: Concerning Both
the Theoricke and the Practicke of the Philosophers Stone. Faithfully, and (as the
Maiesty of the Thing Requireth) Religiously Done into English Out of the French and
251
Latine Copies. by Eirenæus Orandus, Qui Est, Vera Veris Enodans... London: Thomas
Snodham for Thomas Walkley, 1624.

Fludd, Robert. Historia Utriusque Cosmi, Tractatus I. Oppenheim: Theodore de Bry, 1617.

Franckenberg, Abraham von. Raphael oder Artzt-Engel. Amsterdam, 1676.

Gerhard, Johann. Erklärung der Historien des Leidens unnd Sterbens unsers Herrn Christi Jesu
nach den vier Evangelisten Also angestellet daß wir dadurch zur Erkenntnis der Liebe
Christi erwecket warden unnd am innerlichen Menschen seliglich zunehmen mögen. Jena,
1611.

Godwin, Joscelyn, Christopher McIntosh, and Donate Pahnke, trans. Rosicrucian Trilogy: The
Three Founding Documents in New Modern Translation. Newburyport, Massachussetts:
Weiser Books, 2016.

Gumpelzhaimer, Adam. Compendium Musicae. Augsburg: Ud. Schönig, 1632.

Harsdörfer, Georg Philipp, and Daniel Schwenter. Deliciae Physico-Mathematicae oder
Mathematische und Philosophische Erquickstunden [1636-1653]. Reprint. Vol. I–III.
Nürnburg and Frankfurt am Main: Keip Verlag, 1991.

Kepler, Johannes. De Nive Sexangula. Frankfurt: Godfrey Tampach, 1611.

———. Harmonices Mundi. Lincii Austriae: Johannes Plancus, 1619.

———. Mysterium cosmographicum. Tübingen, 1596.

Khunrath, Heinrich. Amphitheatrum Sapientiae Aeternae Solius Verae: Christiano-Kabalisticum,
Divino-Magicum, Nec Non Physico-Chymicum, Tertriunum, Catholicon. Hanau:
Guilielmus Antonius, 1609.

———. Magnesia Catholica Philosophorum. Magdeburg: Johan Botcher, 1599.

Kircher, Athanasius. “Musurgia Universalis [Rome: Francesco Corbelletti, 1650].” Hildesheim:
Georg Olm, 1970.

Lambspring, Johannes. “[Alchemistisches Lehrgedicht],” 1556. Ms P 2177. Zentralbibliothek
Zürich. https://doi.org/10.7891/e-manuscripta-6275.

Lange, Johann Christian. Theologia Christiana In Numeris. Das ist: Sonderbahre Darstellung,
wie Die Fürnehmsten Haupt-Stücke Christlicher Gottes-Gelehrtheit...in dem Denario
der...Pythagorischen Tafel, oder in den Grund-Zahlen aller Zahlen von 1 bis
10...fürgebildet und enthalten sind. Franckfurt; Leipzig, 1702.
http://resolver.staatsbibliothek-berlin.de/SBB0001CCF300000000.

252
Leibniz, G.W. Philosophical Writings. Edited by G. H. R. Parkinson. London: J. M. Dent &
Sons, 1988.

Luther, Martin. Lectures on Genesis: Chapters 1-5. Edited by Jaroslav Pelikan. Translated by
George V. Schick. Vol. 1. Luther’s Works. St. Louis: Concordia Publishing House, 1958.

———. Reading the Psalms with Luther [Summarien über die Psalment (1532)]. Translated by
Bruce A. Cameron. St. Louis: Concordia Publishing House, 2007.

Maier, Michael. Arcana Arcanissima, Hoc Est Hieroglyphica Aegyptio-Graeca. London, 1614.

———. Atalanta Fugiens, hoc est, Emblemata nova de secretis naturae chymica, accommodate
partim oculis et intellectui, figuris cupro incises, adjectisque sententiis, Epigrammatis et
notis, partim auribus et recreationi animi plus minus 50 Fugis musicalibus trium Vocum,
quarum duae ad unum simplicem melodiam distichis canendis peraptam,
correspondeant, non absque, singulari jucunditate videnda, legenda, meditanda,
intelligenda, dijudicanda, canenda et audienda. Oppenheim: Johann Theodor de Bry,
1617.

———. Cantilenae Intellectuales, in Triadas 9. Distinctae, de Phoenice Redivivo, Hoc Est,
Medicinarum Omnium Pretiosissima. Rostock: Mauritius Saxon, 1622.

———. De Circulo Physico, Quadrato: Hoc est, AURO, Eiusque virtute medicinali, sub duro
cortice instar nuclei latente; An et qualis inde petenda sit, Tractatus haud inutilis.
Oppenheim: Lucas Jennis, 1616.

———. “Subtilis Allegoria Super Secreta Chymiae.” In Museum Hermeticum Reformatum et
Amplificatum, 701–40. Frankfurt am Main: Sande, 1678.

———. Symbola Aureae Mensae Duodecim Nationum. Frankfurt am Main: Lucas Jennis, 1617.

Mattheson, Johann. Criticae Musicae Tomus Secundus. Hamburg, 1725.

———. Das Beschützte Orchestre. Hamburg: B. Schillers Witwe, 1717.

———. Das Forschende Orchestre. Hamburg: B. Schillers Witwe, 1721.

———. Das neu-eröffnete Orchestre. Hamburg: B. Schillers Witwe, 1713.

———. Der vollkommene Capellmeister. Hamburg: Christian Herold, 1739.

———. Grundlage einer Ehren-Pforte. Hamburg, 1740.

Mylius, Johann. Philosophia reformata. Frankfurt: Lucas Jennis, 1622.

253
North, Roger. Roger North on Music. Edited by John Wilson. London: Novello, 1959.
Philosophia Maturata: An Exact Piece of Philosophy Containing the Practick and Operatives
Part Thereof in Gaining the Philosophers Stone. Lancelot Colson, London: G.
Sawbridge, 1662.

[Remmelin, Johannes]. Mysterium Arithmeticum, 1615.

Ripley, Sir George. “Emblematicall Scrowle.” Ashm. Roll 53A.1530. Bodleian Library, n.d.

Ruland, Martin. Lexicon Alchemiae Sive Dictionarium Alchemisticum. Frankfurt am Main:
Zachariae Palthenii, 1612.

Staden, Sigmund Theophil (Gottlieb). Rudimentum Musicum. Nürnberg, 1636.

Studion, Simon. “Naometria.” [Württemberg], 1604. MS. Cod. Theol. et phil. qt. 23a-b.
Stuttgart, Württembergische Landesbibliothek. http://digital.wlb-
stuttgart.de/purl/bsz411974165.

Trismosin, Salomon. Splendor Solis (1582). Reprint. London: Kegan Paul, Trench and Trubner,
1920.

Valentine, Basil. Révelation des mystères des teintures essentielles des sept métaux. Paris: La
veufve I. de Senlecque, 1668.

Vaughan, Thomas, trans. The Fame and Confession of the Fraternity of R: C:, Commonly, of the
Rosie Cross. With a Praeface Annexed Thereto, and a Short Declaration of Their
Physicall Work. London: Giles Calvert, 1652.

Waite, A. E., ed. Hermetic Museum (1678). 1893 Edition. Vol. 1. York Beach, Maine: Samuel
Weiser, 1991.

Walther, Johann Gottfried. Briefe. Edited by Klaus Beckmann and Hans-Joachim Schulze.
Leipzig: VEB, 1987.

———. Musicalisches Lexicon. Leipzig: Wolffgang Deer, 1732.

Werckmeister, Andreas. Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe. Translated by Dietrich Bartel. Contextual Bach Studies. Lanham:
Lexington Books, 2017.

———. Harmonologia Musica, Oder Kurtze Anleitung Zur Musicalischen Composition.
Quedlinburg: Theodor Philipp Calvisius, 1702.

———. Hypomnemata Musica. Quedlinburg: Theodor Philipp Calvisius, 1697.

254
———. Musicae Mathematicae Hodegus Curiosus, Oder Richtiger Musicalischer Weg-Weiser.
Quedlinburg: Theodor Philipp Calvisius, 1686.

———. Musicalische Paradoxal-Discourse. Quedlinburg: Theodor Philipp Calvisius, 1707.

———. Musicalische Temperatur [Quedlinburg, 1691]. Edited by Rudolf Rasch. Utrecht:
Diapason Press, 1983.

Wierix, Anton II. Cor Iesu amanti sacrvm. [Antwerp], ca. 1585/6.

Secondary Sources

Abraham, Lyndy. A Dictionary of Alchemical Imagery. Cambridge: Cambridge University Press,
1998.

Ackert, Stephen Francis. “Numerical Structures in the Organ Works of Dietrich Buxtehude.”
DMA diss., University of Wisconsin, 1979.

Aiton, E. J., A. M. Duncan, and J. V. Field. “Preface and Introduction.” In The Harmony of the
World by Johannes Kepler, vii–xxxviii. Philadelphia: American Philosophical Society,
1997.

Åkerman, Susanna. Rose Cross over the Baltic: The Spread of Rosicrucianism in Northern
Europe. Leiden: E. J. Brill, 1998.

Apatow, Robert. “The Tetraktys: The Cosmic Paradigm of the Ancient Pythagoreans.” Parabola
24, no. 3 (1999): 38–43.

Armstrong, Arthur Hilary. “Dualism: Platonic, Gnostic, and Christian.” In Neoplatonism and
Gnosticism, edited by Richard T. Wallis, 33–54. Albany: State University of New York
Press, 1992.

Asztalos, Monika. “The Faculty of Theology.” In A History of the University in Europe, edited
by Hilde de Ridder-Symoens, 409–41. Cambridge University Press, 1991.
https://doi.org/10.1017/CBO9780511599507.016.

Atlas, Allan W. “Gematria, Marriage Number, and Golden Sections in Dufay’s ‘Resvellies
Vous.’” Acta Musicological 59 (1987): 111–26.

Bach-Nielsen, Carsten. “The Role of the Lutheran Church in Denmark.” Kirchliche
Zeitgeschichte 25, no. 2 (2012): 293–310.

Baker, Nancy, and Thomas Christensen. Aesthetics and the Art of Musical Composition in the
Age of the German Enlightenment. Cambridge: Cambridge University Press, 1995.
255

Bakker, Pieter. Andreas Werckmeister: The Historical Positioning of His Writings. Translated by
Pleuke Boyce. Schraard: Kunst en Wetenschap, 2015.
https://www.academia.edu/12304029/Andreas_Werckmeister_the_Historical_Positioning
_of_his_Writings.

———. Modern Numbers in Ancient Music: Andreas Werckmeister as a Source. Translated by
Pleuke Boyce. Schraard: Kunst en Wetenschap, 2015.
http://www.pieterbakker.eu/ancient.pdf.

———. Modern Numbers: Source References in the Numerical Research of Bach’s Musical
Structures. Translated by Pleuke Boyce. Schraard: Kunst en Wetenschap, 2015.
https://www.academia.edu/15734670/Modern_Numbers_Source_References_in_the_Nu
merical_Research_of_Bachs_Musical_Structures.

———. Postmodern Numbers: Ruth Tatlow on Proportions in the Written Music of J. S. Bach.
Translated by Pleuke Boyce. Schraard: Kunst en Wetenschap, 2015.
http://www.huygens-fokker.org/docs/Tatlow.pdf.

Baldwin, M. “Alchemy and the Society of Jesus in the Seventeenth Century: Strange
Bedfellows?” Ambix 40, no. 2 (1993): 41–64.

Barry, Kieren. The Greek Qabalah: Alphabetic Mysticism and Numerology in the Ancient World.
York Beach, Maine: Samuel Weiser, Inc, 1999.

Bartel, Dietrich. “Andreas Werckmeister’s Final Tuning: The Path to Equal Temperament.”
Early Music 43 (2015): 503–12.

———. “Introduction to the Musicalische Paradoxal-Discourse.” In Andreas Werckmeister’s
Musicalische Paradoxal-Discourse: A Well-Tempered Universe, 3–48. Lanham:
Lexington Books, 2017.

———. Musica Poetica: Musical-Rhetorical Figures in German Baroque Music. Lincoln:
University of Nebraska Press, 1997.

———. “Preface.” In Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe, xiii–xv. Lanham: Lexington Books, 2017.

Beach, David W. Aspects of Unity in J. S. Bach’s Partitas and Suites. Rochester: University of
Rochester Press, 2005.

Beery, Janet L. “Formulating Figurate Numbers.” BSHM Bulletin: Journal of the British Society
for the History of Mathematics 24, no. 2 (2009): 78–91.
https://doi.org/10.1080/17498430902820879.

256
Berg, Clemens G. van den. “Dissecting Jesus: The Spiritual Role of the Senses in Buxtehude’s
Cantata Cycle Membra Jesu Nostri (1680).” Junctions: Graduate Journal for the
Humanities 3, no. 1 (2018): 30–44.

Berger, Harry. “Fictions of the Pose: Facing the Gaze of Early Modern Portraiture.”
Representations 46 (1994): 87–120.

Bettels, Christian. “Form und Funktion kontrapunktischer Kompositionstechniken in den
deutschsprachigen Vokalwerken Dieterich Buxtehudes.” In Buxtehude jenseits der Orgel.
Akademie für Alte Musik – Hochschule für Künste Bremen, edited by Michael Zywietz,
23–42. Graz: Akademische Druck- und Verlags-Anstalt, 2008.

Bilak, Donna. “Alchemy and the End Times: Revelations from the Laboratory and Library of
John Allin, Puritan Alchemist (1623–1683).” Ambix 60, no. 4 (2013): 390–414.
https://doi.org/10.1179/0002698013Z.00000000040.

Bindon, Peter. “The Hermetic Museum, 1625.” Rosicrucian Digest 1 (2011): 54–56.

Blankenburg, Walter. “Die Symmetrieform in Bachs Werkem und ihre Bedeutung.” Bach-
Jahrbuch 38 (50 1949): 24–39.

Board, Ryan Andrew. “Buxtehude’s Membra Jesu Nostri: A Study in Baroque Affections and
Rhetoric.” DMA diss., University of Missouri-Kansas City, 2006.

Bolzoni, Lina. “The Memory Theatre of Giulio Camillo: Alchemy, Rhetoric, and Deification in
the Renaissance.” In Lux in Tenebris: The Visual and the Symbolic in Western
Esotericism, edited by Peter J. Forshaw, 66–80. Leiden: Brill, 2017.

Borthwick, E. K. “The Riddle of the Tortoise and the Lyre.” Music & Letters 51, no. 4 (1970):
373–87.

Brach, Jean-Pierre. “Mathematical Esotericism.” In The Cambridge Handbook of Western
Mysticism and Esotericism, edited by Glenn Alexander Magee, 405–16. Cambridge:
Cambridge University Press, 2016.

———. “Mystical Arithmetic in the Renaissance: From Biblical Hermeneutics to a
Philosophical Tool.” In Mathematicians and Their Gods: Interactions between
Mathematics and Religious Beliefs, edited by Snezana Lawrence and Mark McCartney,
105–20. Oxford: Oxford University Press, 2015.

———. “Numbers Are Meant for Counting, Right?” In Hermes Explains: Thirty Questions
about Western Esotericism, edited by Marco Pasi, Peter J. Forshaw, and Wouter J.
Hanegraaff, 47–53. Amsterdam: Amsterdam University Press, 2019.

Brann, N. “Alchemy and Melancholy in Medieval and Renaissance Thought: A Query into the
Mythical Basis of Their Relationship.” Ambix 32, no. 3 (1985): 127–48.
257

Braun, Werner. Die Musiktheorie des 16. und 17. Jahrhunderts in Deutschland. Band 2:
Deutsche Musiktheorie von Calvisius bis Mattheson. Darmstadt: Wissenschaftliche
Buchgesellschaft, 1994.

Brooke, Maxey. “Fibonacci Numbers: Their History Through 1900.” The Fibonacci Quarterly 2,
no. 2 (April 1964): 149–54.

Buelow, George J. “Hamburg Opera during Buxtehude’s Lifetime: The Works of Johann
Wolfgang Frank.” In Church, Stage, and Studio, edited by Paul Walker, 138–40. Ann
Arbor: UMI, 1990.

———. “Symposium on Seventeenth-Century Music Theory: Germany.” Journal of Music
Theory 16 (1972): 36–49.

Burnett, Charles. “Music and Magnetism, from Abu Ma’shar to Kircher.” In Music and
Esotericism, edited by Laurence Wuidar, 9:13–22. Aries: Texts and Studies in Western
Esotericism. Leiden and Boston: Brill, 2010.

Burtenshaw, Leonard John. “The Stylistic Influences on the Principal Basso Ostinato Organ
Works of Dietrich Buxtehude.” PhD diss., University of Sidney, 1978.

Butler, Christopher. “Numerological Thought.” In Silent Poetry: Essays in Numerological
Analysis, edited by Alastair Fowler, 1–31. London: Routledge & K. Paul, 1970.

Butler, Gregory. “Rhetorical Personification of the Dead in 17th Century German Funeral
Music.” Journal of Musicology 9, no. 2 (1991): 186–213.

Butt, John. Music Education and the Art of Performance in the German Baroque. Cambridge:
Cambridge University Press, 1994.

———. “Review of Bach and the Riddle of the Number Alphabet.” Music & Letters 73, no. 1
(February 1992): 105–7. https://doi.org/10.1093/ml/73.1.105.

———. “The Contents, Layout and Style of Instruction Books.” In Music Education and the Art
of Performance in the German Baroque, 52–67. Cambridge Musical Texts and
Monographs. Cambridge: Cambridge University Press, 1994.
https://doi.org/10.1017/CBO9780511597312.004.

Chafe, Eric. Analyzing Bach Cantatas. New York: Oxford University Press, 2000.

Christensen, Thomas. “Bach among the Theorists.” In Bach Perspectives 3, edited by Michael
Marissen, 23–46. Lincoln: University of Nebraska Press, 1998.

Churton, Tobias. The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret
Society. Rochester, Vermont: Inner Traditions, 2009.
258

Collins, Denis Brian. “Canon in Music Theory from c. 1550 to c. 1800.” PhD diss., Stanford
University, 1992.

Cooper, Jeffrey. “The Seven Planets in Bach, Buxtehude, and a Dresden Ballet of 1678.” DMA
diss., University of Houston, 2017.

Copenhaver, Brian P. “Number, Shape, and Meaning in Pico’s Christian Cabala: The Upright
Tsade, the Closed Mem, and the Gaping Jaws of Azazel.” In Natural Particulars: Nature
and the Disciplines in Renaissance Europe, edited by Anthony Grafton and Nancy
Siraisi, 25–76. Cambridge, MA: MIT Press, 1999.

Corry, Leo. A Brief History of Numbers. Oxford: Oxford University Press, 2015.
http://ebookcentral.proquest.com/lib/socal/detail.action?docID=2084891.

Coudert, Allison P. Alchemy: The Philosopher’s Stone. London: Wildwood House, 1980.

———. Leibniz and the Kabbalah. Dordrecht: Kluwer Academic Publishers, 1995.

———. “Spiritual Alchemy.” In Dictionary of Gnosis and Western Esotericism, edited by W. J.
Hanegraaff, 46–47. Leiden: Brill, 2005.

Cox, David. “Buxtehude and His Passion Music.” The Musical Times 112, no. 1537 (1971):
232–34. https://doi.org/10.2307/956401.

Cramer, Craig. “Form and Registration in Buxtehude’s Ciacona in C Minor.” In Dietrich
Buxtehude and Samuel Scheidt: An Anniversary Tribute. The Proceedings of the
International Buxtehude / Scheidt Festival and Conference at the University of
Saskatchewan, November 1987, edited by Isabelle Mills and Walter Kreyszig, 79–90.
Saskatoon: University of Saskatchewan Printing Services, 1988.

Crippa, Davide. The Impossibility of Squaring the Circle in the 17th Century: A Debate Among
Gregory, Huygens, and Leibniz. Cham, Switzerland: Birkhäuser (Springer Nature
Switzerland AG), 2019.

Cunningham, Lawrence S. “Nearer to God: Demystifying Mysticism.” Commonweal, September
26, 2011. https://www.commonwealmagazine.org/nearer-god.

Currie, Randolph N. “A Neglected Guide to Bach’s Use of Number Symbolism.” Bach 5, no. 1–
4 (1974): 23–32; 36; 3–12; 3–8.

———. “Cyclic Unity in Bach’s ‘Sechs Chorale’: A New Look at the ‘Schüblers,’ Part I.” Bach
4, no. 1 (1973): 26–38.

259
———. “Cyclic Unity in Bach’s ‘Sechs Chorale’: A New Look at the ‘Schüblers,’ Part II.” Bach
4, no. 2 (1973): 25–39.

Dahlhaus, Carl. “‘Einleitung’ and ‘Kritischer Bericht.’” In Johann Theiles Musicalisches
Kunstbuch, 1:vii–ix; 132–39. Denkmäler norddeutscher Musik. Kassel: Bärenreiter,
1965.

———. “Zur Geschichte der Permutationsfuge.” Bach Jahrbuch 46 (1959): 95–110.

Dear, P. “Jesuit Mathematical Science and the Reconstruction of Experience in the Early
Seventeenth Century.” Studies in History and Philosophy of Science 18, no. 2 (1987):
133–75.

Defant, Christine. Instrumentale Sonderformen in Norddeutschland - Eine Studie zu den
Auswirkungen eines Theologenstreites auf Werke der Organisten Weckmann, Reincken
und Buxtehude. Vol. 41. Europäische Hochschulschriften 36. Frankfurt a. M, Bern, New
York, Paris: P. Lang, 1990.

———. “Johann Adam Reinckens ‘Hortus Musicus’ - Versuch einer Deutung als Metapher für
die hochbarocke Musikauffassung in Deutschland.” Die Musikforschung 42 (1989): 128–
48.

Dehnhard, Walther. “Kritik der Zahlensymbolischen Deutung im Werk Johann Sebastian
Bachs.” In Kongreßbericht Stuttgart 1985. Kassel; Basel: Bärenreiter, 1985.

Del Centina, Andrea. “Pascal’s Mystic Hexagram, and a Conjectural Restoration of His Lost
Treatise on Conic Sections.” Archive for History of Exact Sciences 74 (2020): 469–521.

DeVun, Leah. Prophecy, Alchemy, and the End of Time: John of Rupescissa in the Late Middle
Ages. New York: Columbia University Press, 2009.

Dickreiter, Michael. Der Musiktheoretiker Johannes Kepler. Berne: Francke Verlag, 1973.

Dickson, Donald R. “Johann Valentin Andreae’s Utopian Brotherhoods.” Renaissance Quarterly
49, no. 4 (1996): 760–802.

Dietz, Feike. “Linking the Dutch Market to Its German Counterpart: The Case of Johannes
Boekholt and a Newly Discovered 1661 Edition of Levendige Herts-Theologie.” In
Illustrated Religious Texts in the North of Europe, 1500-1800, edited by Feike Dietz,
Adam Morton, Lien Roggen, Els Stronks, and Marc Van Vaeck, 237–56. Farnham:
Ashgate, 2014.

Dixon, Laurinda S. “Introduction.” In Nicolas Flamel: His Exposition of the Hieroglyphicall
Figures (1624), 2:xiii–Iviii. English Renaissance Hermeticism. New York: Garland Pub.,
1994.

260
Dobbs, Benjamin M. “A Seventeenth-Century Musiklehrbuch in Context: Heinrich Baryphonus
and Heinrich Grimm’s Pleiades Musicae.” PhD diss., University of North Texas, 2015.

Dodds, Michael R. “Columbus’s Egg: Andreas Werckmeister’s Teachings on Contrapuntal
Improvisation in Harmonologia Musica (1702).” Journal of Seventeenth-Century Music
12, no. 1 (2006). https://sscm-jscm.org/v12no1.html.

Duparcq, Jean-Jacques. “Contribution à l’étude des proportions numériques dans l’œuvre de Jean
Sebastien Bach.” Revue Musicale, 1977, 301–2.

———. “L’Art de Fugue, un ‘problème algébrique.’” Positions Luthériennes 33 (1985): 69–85.

Eckerson, Sara. “On Buxtehude’s Quemadmodum Desiderat Cervus.” FORMA DE VIDA:
Revista Do Programa Em Teoria Da Literatura Da Universidade de Lisboa, A ARTE
ALEGRE #5, 13 (May 2018): (online). https://formadevida.org/seckersonfdv13.

Elders, Willem. “A New Case of Number Symbolism in Josquin?” Early Music 37, no. 1 (2009):
21–26.

———. “Introduction.” In Symbolic Scores: Studies in the Music of the Renaissance, 1–16.
Leiden and New York: E. J. Brill, 1994.

———. “The Number Seven as Signifier of Symbolism in the Sacred Music of the
Renaissance.” Sacred Music 146, no. 2 (Summer 2019): 7–27.

Elferen, Isabella van. “Mystical Love in Seventeenth- and Eighteenth-Century Lutheran Poetry
and Theology.” In Mystical Love in the German Baroque: Theology, Poetry, Music, 151–
224. Lanham, MD: The Scarecrow Press, 2009.

———. “‘Recht bitter und doch süße’: Textual and Musical Expression of Mystical Love in
German Baroque Meditations of Christ’s Passion.” Bach 35, no. 1 (2004): 1–28.

———. “Spiritual and Mystical Love in Seventeenth-Century Vocal Music.” In Mystical Love in
the German Baroque: Theology, Poetry, Music, 225–63. Lanham, MD: The Scarecrow
Press, 2009.

Eschenbach, Gunilla. “Dietrich Buxtehudes Membra Jesu Nostri im Kontext lutherischer Mystik-
Rezeption.” Kirchenmusikalisches Jahrbuch 88 (2004): 41–54.

Evans, Brian. The Development of Mathematics Throughout the Centuries: A Brief History in a
Cultural Context. Somerset: John Wiley & Sons, Incorporated, 2014.

Faivre, Antoine. Access to Western Esotericism. Albany: State University of New York, 1994.

———. “Mystische Alchemie und geistige Hermeneutik.” In Correspondences in Man and
World, 323–60. Leiden: Eranos Yearbook; E. J. Brill, 1973.
261

Faivre, Antoine, and Karen-Claire Voss. “Western Esotericism and the Science of Religions.”
Numen 42 (1995): 48–77.

Falk, Myron. “Seventeenth-Century Contrapuntal Theory in Germany.” PhD diss., University of
Rochester, 1965.

Federico, P. J. Descartes on Polyhedra: A Study of the De Solidorum Elementis. Edited by G. J.
Toomer. Vol. 4. Sources in the History of Mathematics and Physical Sciences. New
York; Heidelberg; Berlin: Springer-Verlag, 1982.

Felbick, Lutz. Lorenz Christoph Mizler de Kolof: Schüler Bachs und pythagorischer Apostel der
Wolffischen Philosophie. Hildesheim: Olms, 2012.

Fideler, David. Jesus Christ, Sun of God: Ancient Cosmology and Early Christian Symbolism.
Wheaton, IL: Quest Books, 1993.

Findlen, Paula. Athanasius Kircher: The Last Man Who Knew Everything. New York; London:
Routledge, 2004.

Fitger, Malin. “The Tetractys and the Hebdomad: Blavatsky’s Sacred Geometry.”
Correspondences 8, no. 1 (2020): 73–115.

Forshaw, Peter J. “Cabala Chymica or Chemia Cabalistica—Early Modern Alchemists and
Cabala.” Ambix 60, no. 4 (2013): 361–89.
https://doi.org/10.1179/0002698013Z.00000000039.

———. “Isn’t Alchemy a Spiritual Tradition?” In Hermes Explains: Thirty Questions about
Western Esotericism, edited by Wouter J. Hanegraaff and Peter J. Forshaw, 105–12.
Amsterdam: Amsterdam University Press, 2019.

———. “Oratorium–Auditorium–Laboratorium: Early Modern Improvisations on Cabala,
Music, and Alchemy.” ARIES - Journal for the Study of Western Esotericism 10, no. 2
(2010): 169–95. https://doi.org/10.1163/156798910X520584.

Funkhouser, Sara. “Heinrich Isaac and Number Symbolism: An Exegesis of Commemorative
Motets Dedicated to Lorenzo de’ Medici and Maximilian I.” DMA diss., University of
Missouri, 1981.

Gauger, Ronald Raymond. “Ostinato Techniques in Chaconnes and Passacaglias of Pachelbel,
Buxtehude and J.S. Bach.” PhD diss., University of Wisconsin, 1974.

Geck, Martin. Die Vokalmusik Dietrich Buxtehudes und der fruḧe Pietismus. Kassel: Bar ̈ enreiter,
1965.

262
Gentzke, Joshua Levi Ian. “Imagining the Image of God: Corporeal Envisioning in the
Theosophy of Jacob Böhme.” In Lux in Tenebris: The Visual and the Symbolic in
Western Esotericism, edited by Peter J. Forshaw, 103–29. Leiden: Brill, 2017.

Gero, Olga. “Text and Visual Image in the Sacred Vocal Works of Dieterich Buxtehude.” Early
Music 46, no. 2 (2018): 235–49.

Ghyka, Matila. The Geometry of Art and Life. New York: Dover, 1977.

Gilly, Carlos. Cimelia Rhodostaurotica. Amsterdam: BPH, 1995.

Gingerich, Owen. “Kepler and His Trinitarian Cosmology.” In Mathematicians and Their Gods:
Interactions between Mathematics and Religious Beliefs, edited by Snezana Lawrence
and Mark McCartney, 77–88. Oxford: Oxford University Press, 2015.

Glasmeier, Michael. “Körperteile – zu Dietrich Buxtehudes Membra Jesu Nostri.” In Buxtehude
jenseits der Orgel. Akademie für Alte Musik – Hochschule für Künste Bremen, edited by
Michael Zywietz, 43–56. Graz: Akademische Druck- und Verlags-Anstalt, 2008.

Gleixner, Ulrike. “Pietists and Gender. Self-Modeling and Agency.” In A Companion to German
Pietism, 1660-1800, edited by Douglas H. Shantz, 55:423–71. Brill’s Companions to the
Christian Tradition. Leiden and Boston: Brill, 2015.

Godwin, Joscelyn. “A Context for Michael Maier’s ‘Atalanta Fugiens’ (1617).” The Hermetic
Journal, 1985, 4–10.

———. Athanasius Kircher’s Theatre of the World: The Life and Works of the Last Man to
Search for Universal Knowledge. Rochester, Vermont: Inner Traditions, 2009.

———. “Esoteric Theories of Color.” In Lux in Tenebris: The Visual and the Symbolic in
Western Esotericism, edited by Peter J. Forshaw, 447–76. Leiden: Brill, 2017.

———. “Introduction to The Chemical Wedding of Christian Rosenkreuz.” In Rosicrucian
Trilogy: The Three Original Rosicrucian Publications in New Modern Translation, 55–
60. Weiser Books, 2016.

———. “Introduction to the Confessio Fraternitatis.” In Rosicrucian Trilogy: The Three
Original Rosicrucian Publications in New Modern Translation, 35–40. Newburyport,
Massachussetts: Weiser Books, 2016.

———. Music, Mysticism and Magic: A Sourcebook. London; New York: Routledge & Kegan
Paul, 1986.

———. Robert Fludd: Hermetic Philosopher and Surveyor of Two Worlds. London: Thames
and Hudson, 1979.

263
———, ed. The Harmony of the Spheres: A Sourcebook of the Pythagorean Tradition in Music.
Rochester, Vermont: Inner Traditions International, 1993.

Gorham, Geoffrey. “God and the Natural World in the Seventeenth Century: Space, Time, and
Causality.” Philosophy Compass 4, no. 5 (2009): 859–72. https://doi.org/10.1111/j.1747-
9991.2009.00233.x.

Gouk, Penelope. “Music and the Sciences.” In The Cambridge History of Seventeenth-Century
Music, edited by Tim Carter and John Butt, 132–57. Cambridge: Cambridge University
Press, 2005. https://doi.org/10.1017/CHOL9780521792738.007.

———. “Transforming Matter, Refining the Spirit: Alchemy, Music and Experimental
Philosophy around 1600.” European Review 21, no. 2 (2013): 146–57.
https://doi.org/10.1017/S1062798712000324.

Grapenthin, Ulf. “Beziehungen zwischen Frontispiz und Werkaufbau in Johann Adam Reinckens
Hortus Musicus von 1688.” In Proceedings of the Weckmann Symposium: Göteborg, 30
August - 3 September 1991, 199–210. Göteborg: Göteborg, Dept. of Musicology, 1993.

———. “Buxtehude Im Neuen Licht. Ein Beitrag Zur Ikonographie Des Komponisten.”
Concerto 25 (February 2008): 38–41.

———. “Die »beyden damahls extraordinair berühmten Organisten, Herren Reincken und
Buxtehuden« und ihr gelehrter Freund Johann Theile.” Buxtehude-Studien: Im Auftrag
der Internationalen Dieterich-Buxtehude-Gesellschaft (IDBG) 4 (2021): 11–32.

Gregory, Andrew. “The Pythagoreans: Number and Numerology.” In Mathematicians and Their
Gods: Interactions between Mathematics and Religious Beliefs, edited by Snezana
Lawrence and Mark McCartney, 21–50. Oxford: Oxford University Press, 2015.

Griffel, Margaret Ross. “Erschaffene, gefallene, und wieder aufgerichtete Mensch, Der (Adam
und Eva).” In Operas in German: A Dictionary. Vol. 1. Lanham: Rowman & Littlefield,
2018.

Grześkowiak, Radosław, and Paul Hulsenboom. “Emblems from the Heart: The Reception of the
‘Cor Iesu Amanti Sacrum’ Engravings Series in Polish and Netherlandish 17th-Century
Manuscripts.” Werkwinkel 10 (2015): 131–54.

Hanegraaff, Wouter J. Esotericism and the Academy: Rejected Knowledge in Western Culture.
New York: Cambridge University Press, 2012.

———. Western Esotericism: A Guide for the Perplexed. Bloomsbury Academic. Guides for the
Perplexed. London and New York, 2013.

264
Harmsen, Theodor. “The Mind’s Eye: Images of Creation and Revelation in Mystical Theology
and Theosophy.” In Lux in Tenebris: The Visual and the Symbolic in Western
Esotericism, edited by Peter J. Forshaw, 152–78. Leiden: Brill, 2017.

Harrison, Carol. “Augustine and the Art of Music.” In Resonant Witness: Conversations Between
Music and Theology, edited by Jeremy Begbie and Steve Guthrie, 27–45. Grand Rapids:
Eerdmans Publishing Co., 2011.

Hasler, Johann F. W. “Performative and Multimedia Aspects of Late-Renaissance Meditative
Alchemy: The Case of Michael Maier’s Atalanta Fugiens (1617).” Revista de Estudios
Sociales 39 (April 2011): 135–44.

Hedesan, Georgiana D. “Reproducing the Tree of Life: Radical Prolongation of Life and Biblical
Interpretation in Seventeenth-Century Medical Alchemy.” Ambix 60, no. 4 (2013): 341–
60. https://doi.org/10.1179/0002698013Z.00000000038.

Henninger, S. K. Touches of Sweet Harmony: Pythagorean Cosmology and Renaissance Poetics.
Second, Expanded Edition. San Marino, CA: Angelico Press, 2013.

Herz-Fischler, Roger. A Mathematical History of the Golden Number. Toronto; New York:
Wilfrid-Laurier University Press; Dover Reprints, 1987.

Hicks, Andrew. “Pythagoras and Pythagoreanism in Late Antiquity and the Middle Ages.” In A
History of Pythagoreanism, edited by Carl A. Huffman, 416–34. Cambridge: Cambridge
University Press, 2014. https://doi.org/10.1017/CBO9781139028172.021.

Hinlicky, Paul R. Paths Not Taken: Fates of Theology from Luther Through Leibniz. Grand
Rapids, Michigan: William B. Eerdmans Publishing, 2009.

Hobart, Michael E. The Great Rift: Literacy, Numeracy, and the Religion-Science Divide.
Cambridge, MA: Harvard University Press, 2018.

Hopper, Vincent. Medieval Number Symbolism. New York: Columbia University Press, 1938.

Horsten, Leon. “Absolute Infinity in Class Theory and in Theology.” In Objectivity, Realism,
and Proof : FilMat Studies in the Philosophy of Mathematics, edited by Francesca
Boccuni and Andrea Sereni, 103–22. Boston Studies in the Philosophy and History of
Science. Cham: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-
319-31644-4_7.

Hösch, Wolfgang. “Motivische Integration, Proportion und Zahlensymbolik in Johann Sebastian
Bachs Magnificat.” Musik und Kirche 46, no. 6 (1976): 265–69.

Houten, Kees van, and Marinus Kasbergen. Bach en het getal. Zutphen: De Walburg Pers, 1985.

265
Humphreys, David. The Esoteric Structure of Bach’s Clavierübung III. Cardiff: University
College Cardiff, 1983.

Huntley, H.E. The Divine Proportion. New York: Dover, 1970.

Iliffe, Bob. “Newton, God, and the Mathematics of the Two Books.” In Mathematicians and
Their Gods: Interactions between Mathematics and Religious Beliefs, edited by Snezana
Lawrence and Mark McCartney, 121–44. Oxford: Oxford University Press, 2015.

Ilnitchi, Gabriela. “‘Musica Mundana’: Aristotelian Natural Philosophy and Ptolemaic
Astronomy.” Early Music History 21 (2002): 37–74.

Irwin, Joyce L. Foretastes of Heaven in Lutheran Church Music Tradition: Johann Mattheson
and Christoph Raupach on Music in Time and Eternity. Lanham, MD: Rowman &
Littlefield, 2015.

———. “German Pietists and Church Music in the Baroque Age.” Church History 54, no. 1
(1985): 29–40.

———. Neither Voice nor Heart Alone: German Lutheran Theology of Music in the Age of the
Baroque. New York: P. Lang, 1993.

———. “‘So Faith Comes from What Is Heard’: The Relationship between Music and God’s
Word in the First Two Centuries of German Lutheranism.” In Personal Witness:
Conversations between Music and Theology, edited by Jeremy Begbie and Steven
Guthrie, 66–82. Grand Rapids, Michigan: Eerdmans Publishing Co., 2011.

Jaacks, Gisela. “Wer ist Wer? und weitere Rätsel. Zur Diskussion um das sogenannte
Buxtehude-Bild von Johannes Voorhout.” In Buxtehude jenseits der Orgel. Akademie für
Alte Musik – Hochschule für Künste Bremen, edited by Michael Zywietz, 57–68. Graz:
Akademische Druck- und Verlags-Anstalt, 2008.

Jarman, Carol. “Buxtehude’s Ciacona in C Minor and the Nicene Creed.” The Musical Times
146 (2005): 58–69.

Jensen, Niels Martin. “Buxtehudes vokale und instrumentale Ensemblemusik.” In 800 Jahre
Musik in Lübeck. Dokumentation zum Lübecker Musikfest 1982, edited by Arnfried Edler,
Werner Neugebauer, and Heinrich W. Schwab, 21:53–62. Veröffentlichung. Lübeck: Der
Senat der Hansestadt Lübeck, Amt für Kulture, 1983.

Jones, Matthew L. “Descartes’s Geometry as Spiritual Exercise.” Critical Inquiry 28, no. 1
(October 2001): 40–71. https://doi.org/10.1086/449032.

———. The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the
Cultivation of Virtue. Chicago, UNITED STATES: University of Chicago Press, 2006.
http://ebookcentral.proquest.com/lib/socal/detail.action?docID=408535.
266

Jung, C. G. Psychology and Alchemy. Translated by R. F. C. Hull. Complete Digital Edition.
Vol. 12. The Collected Works of C. G. Jung. Princeton, New Jersey: Princeton University
Press, 1968.

Kahn, Charles H. Pythagoras and the Pythagoreans: A Brief History. Indianapolis: Hackett,
2001.

Kalvesmaki, Joel. “Formation of the Early Christian Theology of Arithmetic: Number
Symbolism in the Late Second and Early Third Century.” PhD diss., Catholic University
of America, 2006.

———. The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity.
Washington, DC; Cambridge, MA and London: Center for Hellenic Studies, Trustees for
Harvard University; Harvard University Press, 2013.

Kaplan, David L. “Stylistic Tendences in the String Sonatas of Dietrich Buxtehude.” In Dietrich
Buxtehude and Samuel Scheidt: An Anniversary Tribute: The Proceedings of the
International Buxtehude / Scheidt Festival and Conference at the University of
Saskatchewan, November 1987, edited by Isabelle Mills and Walter Kreyszig, 91–105.
Saskatoon: University of Saskatchewan Printing Services, 1988.

Karstädt, Georg. “Richtiges und Zweifelhaftes im Leben und Werk Dietrich Buxtehudes.” Musik
und Kirche 49 (1979): 163–70.

Kee, Piet. “Astronomy in Buxtehude’s Passacaglia: Measure and Number in Ostinato Works.”
The Diapason 75 (1984): 27–33.

———. Number and Symbolism in the Passacaglia and Ciacona: A Forgotten and Hidden
Dimension. United Kingdom: John Loosemore Center Buckfastleigh, 1988.

———. “The Secrets of Bach’s Passacaglia.” The Diapason, 1983-07; 1983-08; 1983-09 1983,
10–12; 4–6; 11–13; 10–12.

Kellner, Herbert Anton. “Diskussion: Welches Zahlenalphabet benütze der Thomaskantor
Kuhnau?” Die Musikforschung 33 (1980): 124–25.

———. “Kepler, Bach and Gauss.” Bach 25, no. 1 (1994): 45–46.

———. “The Mathematical Architecture of Bach’s Goldberg Variations.” English Harpsichord
Magazine 2, no. 8 (1981): 183–89.

———. “Was Bach a Mathematician?” English Harpsichord Magazine 2, no. 2 (1978): 32–36.

Kevorkian, Tanya. “Pietists and Music.” In A Companion to German Pietism, 1660-1800, edited
by Douglas H. Shantz, 55:171–200. Leiden and Boston: Brill, 2015.
267

Kim, Youn Ju. “Dieterich Buxtehude’s Membra Jesu Nostri: An Historical Overview, Analysis
and Conducting Guide.” DMA diss., Arizona State University, 2012. (UMI 3503836).

Kler, Herman de. “Johannes Voorhout und seine 'Häusliche Musikszene’.” Ars Organi 56
(2008): 192.

Knobloch, Eberhard. “Mathematics and the Divine: Athanasius Kircher.” In Mathematics and
the Divine: A Historical Study, edited by T. Koetsier and L. Bergmans, 333–46.
Amsterdam: Elsevier, 2005.

Koopman, Ton. “Aufführungspraxis in der Musik Dietrich Buxtehudes.” In “Ein fürtrefflicher
Componist und Organist zu Lübeck”: Dietrich Buxtehude (1637-1707). Im Auftrag des
Museums für Kunst und Kulturgeschichte (Die Lübecker Museen) und der Bibliothek der
Hansestadt Lübeck, edited by Dorothea Schröder, 101–8. Lübeck: Dräger, 2007.

Krummacher, Friedhelm. “Parodie, Umtextierung und Bearbeitung in der Kirchenmusik vor
Bach.” Svensk tidskrift för musikforskning 53 (1971): 23–48.

Labuschagne, Caspar J. “On the Structural Use of Numbers as a Composition Technique: [Ps 79;
Deut 3:1-17].” Journal of Northwest Semitic Languages 12 (1984): 87–99.

Lawrence, Snezana. “Capital G for Geometry: Masonic Lore and the History of Geometry.” In
Mathematicians and Their Gods: Interactions between Mathematics and Religious
Beliefs, edited by Snezana Lawrence and Mark McCartney, 167–90. Oxford: Oxford
University Press, 2015.

Leaver, Robin A. “Number Associations in the Structure of Bach’s Credo, BWV 232.” Bach 7,
no. 3 (1976): 17–24.

Lehmann, Hartmut. “Buxtehude und der frühe Pietismus.” In Dietrich Buxtehude und die
europäische Musik seiner Zeit. Bericht über das Lübecker Symposion 1987, edited by
Arnfried Edler and Friedhelm Krummacher, 67–76. Kassel: Bärenreiter, 1990.

Lennon, Thomas M. “The Leibnizean Picture of Descartes.” In Nature Mathematized, edited by
W.R. Shea, I:215–26. Dordrecht; Boston: Springer, 1983.

Lester, Joel. Between Modes and Keys: German Theory 1592-1802. Stuyvesant, NY: Pendragon
Press, 1989.

Linden, S. J. “Mystical Alchemy and Eschatology in Seventeenth Century Religious Poetry.”
Pacific Coast Philology 19 (1984): 79–88.

Linfield, Eva. “Dietrich Buxtehude’s Sonatas: A Historical and Analytical Study.” PhD diss.,
Brandeis University, 1984.

268
———. “The Viol Consort in Buxtehude’s Vocal Music: Historical Context and Affective
Meaning.” In Church, State, and Studio: Music and Its Contexts in 17th-Century
Germany, edited by Paul Walker, 163–92. Ann Arbor, Michigan: UMI Research Press,
1990.

Lodder, Jerry. “Construction of the Figurate Numbers.” Number Theory 4 (2017): 30.

Lohmann, Heinz. “Bemerkungen zur Zahlensymbolik in der Klavier-Übung III von Johann
Sebastian Bach.” Kirchemusiker 25, no. 2 (1974): 55–58.

Mackey, Elizabeth. “The Sacred Music of Johann Theile.” PhD diss., University of Michigan,
1968.

Mancosu, Paolo. Philosophy of Mathematics and Mathematical Practice in the Seventeenth
Century. New York; Oxford: Oxford University Press, 1996.

March, Lionel. “Palladio, Pythagoreanism and Renaissance Mathematics.” Nexus Network
Journal 10, no. 2 (2008): 227–44.

Marshall, Robert L. The Compositional Process of J.S. Bach: A Study of the Autograph Scores of
the Vocal Works. 2 vols. Princeton University Press, 1972.

Masson, Cynthea. “Queer Copulation and the Pursuit of Divine Conjunction in Two Middle
English Alchemical Poems.” In Intersections of Sexuality and the Divine in Medieval
Culture: The Word Made Flesh, edited by Susannah Chewning, 37–48. Florence, United
Kingdom: Taylor & Francis Group, 2005.
http://ebookcentral.proquest.com/lib/socal/detail.action?docID=4817660.

Matter, E. Ann. “Buxtehude and Pietism? A Reappraisal.” The American Organist 21 (1987):
81–83.

McClean, Adam. “Introduction and Commentary.” In The Chemical Wedding of Christian
Rosenkreutz, translated by Joscelyn Godwin, 7–11; 107–58. Magnum Opus Hermetic
Sourceworks 18. Boston: Phanes Press, 1991.

McGrath, Alister E. Luther’s Theology of the Cross: Martin Luther’s Theological Breakthrough.
Oxford: Basil Blackwell, 1985.

McGuire, J. E. “Space, Geometrical Objects and Infinity: Newton and Descartes on Extension.”
In Nature Mathematized, edited by W. R. Shea, I:69–112. Dordrecht; Boston: Springer,
1983.

McIntosh, Christopher. “Introduction to the Fama Fraternitatis.” In Rosicrucian Trilogy: The
Three Original Rosicrucian Publications in New Modern Translation, 3–14.
Newburyport, Massachussetts: Weiser Books, 2016.

269
———. The Rosicrucians: The History, Mythology and Rituals of an Esoteric Order.
Newburyport, Massachussetts: Weiser Books, 1997.

Meinl, C. “Alchemie und Musik.” In Der Alchemie in der Europaischen Kultur- und
Wissenschaftgeschichte, 16th Wolfenbüttler Symposium, Herzog August Bibliothek, 201–
27. Wiesbaden: O. Harrass, 1984.

Melamed, Yitzhak Y., ed. “Eternity in Early Modern Philosophy.” In Eternity: A History. Oxford
Philosophical Concepts Series. New York, New York: Oxford University Press, 2016.

Merzbach, Uta C., and Carl B. Boyer. A History of Mathematics. Third Edition. Hoboken, New
Jersey: John Wiley & Sons, Inc., 2011.

Meyer, Ulrich. “Zum Problem der Zahlen in Johann Sebastians Werk.” Musik und Kirche 49
(1979): 58–71.

Mies, Paul. “Zur Frage des Mathematischen bei J. S. Bach.” Bach-Jahrbuch 36 (1939): 43–49.

Milka, A. P. “Warum ended die ‘Fuga a 3 Soggetti’ BWV 1080/19 in Takt 239?” BJ 100 (2014):
11–26.

Moore, A. W. The Infinite. Repr. The Problems of Philosophy. London: Routledge, 1995.

Morelli, Nicolò. “Petrarch’s Deer in Rerum Vulgarium Fragmenta 190 and the Visio Beatifica.”
Italian Studies 76, no. 3 (2021): 237–53.
https://doi.org/10.1080/00751634.2021.1936799.

Newman, W. “Prophecy and Alchemy: The Origin of Eirenaeus Philalethes.” Ambix 37, no. 3
(1990): 97–115.

Norden, Hugo. “Proportions and the Composer.” The Fibonacci Quarterly 10, no. 3 (April
1972): 319–24.

———. “Proportions in Music.” The Fibonacci Quarterly 2, no. 3 (October 1964): 219–20.

North, J. D. “Finite and Otherwise: Aristotle and Some Seventeenth Century Views.” In Nature
Mathematized, edited by W. R. Shea, I:113–48. Dordrecht; Boston: Springer, 1983.

North, John. “The Quadrivium.” In A History of the University in Europe, edited by Hilde de
Ridder-Symoens, 337–59. Cambridge University Press, 1991.
https://www.cambridge.org/core/product/identifier/CBO9780511599507A138/type/book
_part.

Nowak, Adolf. “Die ‘numeri judiciales’ des Augustinus und ihre musiktheoretische Bedeutung.”
Archiv für Musikwissenschaft 32 (1975): 196–207.

270
Nummedal, Tara. “Alchemy and Religion in Christian Europe.” Ambix 60, no. 4 (2013): 311–22.
https://doi.org/10.1179/0002698013Z.00000000036.

———. Anna Zieglerin and the Lion’s Blood: Alchemy and End Times in Reformation Germany.
Haney Foundation Series. Philadelphia: University of Pennsylvania Press, 2019.

———. “Corruption, Generation, and the Problem of Menstrua in Early Modern Alchemy.”
edited by Eleanor Decamp and Bonnie Lander Johnson, 111–22. Studies in European
Literature and Thought, 1400-1700. Philadelphia: University of Pennsylvania Press,
2018. https://doi.org/10.9783/9780812295092-008.

———. “Words and Works in the History of Alchemy.” Isis 102, no. 2 (2011): 330–37.
https://doi.org/10.1086/660142.

Nummedal, Tara, and Donna Bilak, eds. Furnace and Fugue: A Digital Edition of Michael
Maier’s “Atalanta Fugiens” (1618) with Scholarly Commentary. Charlottesville:
University of Virginia Press, 2020. https://doi.org/10.26300/bdp.ff.

Oh, Jihye. “Number Symbolism in J.S. Bach’s Keyboard Music.” DMA diss., Claremont
Graduate University, 2016.

O’Meara, Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity. New
York: Oxford University Press, 1989.

Palisca, Claude V. “Applications of Mathematic and Geometry in Galilei’s Dialogo of 1581.” In
Music and Mathematics in Late Medieval and Early Modern Europe, edited by Philippe
Vendrix, 235–51. Turnhout, Belgium: Brepols Publishers, 2008.

Peck, Russel A. “Number as Cosmic Language.” In Essays in the Numerical Criticism of
Medieval Literature, edited by Caroline D. Eckhardt, 15–64. London: Associated
University Presses, 1980.

Pedoe, Dan. Geometry and the Liberal Arts. New York: St. Martin’s, 1976.

Pesic, Peter. “Earthly Music and Cosmic Harmony: Johannes Kepler’s Interest in Practical
Music, Especially Orlando Di Lasso.” Journal of Seventeenth-Century Music 11, no. 1
(2005). http://sscm-jscm.org/v11/no1/pesic.html.

Peterson, Mark A. Galileo’s Muse: Renaissance Mathematics and the Arts. Cambridge, MA:
Harvard University Press, 2011.
http://ebookcentral.proquest.com/lib/socal/detail.action?docID=3300993.

Petzoldt, Martin. “Passionspredigt und Passionsmusik der Bachzeit.” In Johann Sebastian Bach:
Matthäus-Passion, edited by Ulrich Prinz, 50–75. Kassel: Bärenreiter, 1990.

271
Pfanku, Kristin. “Ancient Magic: A Survey of the Technical Hermetica.” Rosicrucian Digest 1
(2011): 46–53.

Phelps, Ruth. The Universe of Numbers. San Jose, CA: Rosicrucian Order, AMORC, 2015.

Piorko, Megan. “Chymical Collections: Seventeenth Century Textual Transmutations in the
Work of Arthur Dee.” PhD diss., Georgia State University, 2020.

Power, Tushaar. “J. S. Bach and the Divine Proportion.” PhD diss., Duke University, 2001.

———. “The Proportional Design of J.S. Bach’s Two Italian Cantatas.” Musical Praxis 1, no. 2
(1994): 35–44.

Prinke, Rafal T. “Lampado Trado: From the Fama Fraternitatis to the Golden Dawn.” The
Hermetic Journal 30 (1985): 5–14.

Rashed, Rashid. Classical Mathematics from Al-Khwārizmī to Descartes. Translated by Michael
H. Shank. London and New York: Routledge, 2015.

Rathey, Markus. “Buxtehude and the Dance of Death: The Chorale Partita Auf Meinen Lieben
Gott (BuxWV 179) and the Ars Moriendi in the Seventeenth Century.” Early Music
History 29 (2010): 161–88.

Reis, Helmut. Der goldene Schnitt. Bonn: Verlag für Musikwissenschaft, 1990.

Riedweg, Christoph. Pythagoras: His Life, Teaching and Influence. Translated by Steven
Rendall. Ithaca, NY: Cornell University Press, 2005.

Rivera, Benito V. German Music Theory in the Early 17th Century: The Treatises of Johannes
Lippius. Ann Arbor: UMI Research Press, 1974.

Roob, Alexander. Alchemy and Mysticism. Translated by Shaun Whiteside. Köln: Taschen, 2016.

Roth, Marjorie A. “Prophecy, Harmony, and the Alchemical Transformation of the Soul: The
Key to Lasso’s Chromatic Sibyls.” In Music and Esotericism, edited by Laurence
Wuidar, 9:45–76. Aries: Texts and Studies in Western Esotericism. Leiden and Boston:
Brill, 2010.

Rumsey, David. “Bach and Numerology: ‘Dry Mathematical Stuff’?” Literature & Aesthetics 7
(1997): 143–65.

Sambursky, Shmuel. “On the Origin and Significance of the Term Gematria.” Journal of Jewish
Studies 29 (Spring 1978): 35–38.

Sargent, Emily Jo. “The Sacred Heart: Christian Symbolism.” In The Heart, edited by James
Peto, 102–14. New Haven: Yale University Press, 2007.
272

Schenkman, Walter. “Tatlow’s Bach and Bach’s Signatures in the Goldberg Variations.” Bach:
The Journal of the Riemenschneider Bach Institute 34, no. 2 (2003): 63–106.

Schering, Arnold. “Bach und das Symbol: insbesondere die Symbolik seines Kanons.” BJ 22; 25
(1928 1925): 40–63; 119–37.

———. “Geschichtliches Zur Ars Inveniendi in Der Musik.” Jahrbuch Der Musikbibliothek
Peters 32 (1925): 25–34.

Schillinger, Joseph. The Mathematical Basis of the Arts. New York: The Philosophical Library,
1948.

Schmidt-Biggermann, Wilhelm. “Der Streit zwischen Kosmologie und Harmonie zwischen
Robert Fludd und Johannes Kepler.” In Buxtehude jenseits der Orgel. Akademie für Alte
Musik – Hochschule für Künste Bremen, edited by Michael Zywietz, 119–50. Graz:
Akademische Druck- und Verlags-Anstalt, 2008.

Schneider, Ivo. “Between Rosicrucians and Cabbala - Johannes Faulhaber’s Mathematics of
Biblical Numbers.” In Mathematics and the Divine: A Historical Study, edited by T.
Koetsier and L. Bergmans, 313–30. Amsterdam: Elsevier, 2005.

———. “Textbooks of German Reckoningmasters in the Early 17th Century.” Journal of the
Cultural History of Mathematics 2 (1992): 47–52.

Schneider, Matthias. “Ein ‘Kleines Harmonisches Labyrinth’: Buxtehudes Orgelmusik und ihre
Stimmungen.” In Orgelbau, Orgelmusik und Organisten des Ostseeraums im 17. und 19.
Jahrhundert, edited by Matthias Schneider, 55–70. Frankfurt: Lang, 2006.

Schneider, Walter. “‘‘Diese Schrift muss von Innen heraus und von Aussen hinein verstanden
werden’: Die Lehren der Rosenkreuzer aus dem 16. und 17. Jahrhundert und ihre
Publikationsgeschichte.” Rosenkreuzer Lehrtafeln 4 (2007): 2–12.

Schnoor, Arndt. “Ein Unbekanntes Porträt von Johann Theile (1645/46-1724).” In Dieterich
Buxtehude: Text - Kontext - Rezeption, edited by Wolfgang Sandberger and Volker
Scherliess, 33–34. Kassel; New York: Bar ̈ enreiter, 2011.

Schöttler, Tobias. “From Causes to Relations: The Emergence of a Non-Aristotelian Concept of
Geometrical Proof out of the Quaestio de Certitudine Mathematicarum.” Society and
Politics 6, no. 2 (2012): 29–47.

Schrader, Dorothy V. “The Arithmetic of Medieval Universities.” In The European
Mathematical Awakening: A Journey Through the History of Mathematics from 1000 to
1800, edited by Frank J. Swetz, 14–25. Mineola, New York: Dover Publications, Inc.,
2013.

273
Schuler, R. M. “Some Spiritual Alchemies of Seventeenth-Century England.” Journal of the
History of Ideas 41, no. 2 (1980): 293–318.

Schwab, Heinrich W. “Johannes Voorhouts Gemälde ‘Häusliche Musikszene’ (1674). Zum
Problem der Identifikation Dietrich Buxtehudes.” In Musikvidenskabelige Kompositioner.
Festkrift Til Niels Krabbe, 1941-3. Oktober-2006 Kopenhagen, 55–73. København: Det
Kongelige Bibliotek i kommission hos Museum Tusculanum Forlag, 2006.

———. “Wenn “Brüder einträchtig beieinander wohnen”: Zur bildlichen Darstellung
Buxtehudes auf dem Gemälde von Johannes Voorhout (1674).” In Dieterich Buxtehude:
Text - Kontext - Rezeption, edited by Wolfgang Sandberger and Volker Scherliess, 11–32.
Kassel; New York: Bar ̈ enreiter, 2011.

Scuchard, Marcia Keith. “Leibniz, Benzelius, and the Kabbalistic Roots of Swedish Illuminism.”
In Leibniz, Mysticism and Religion, edited by Allison P. Coudert, Richard H. Popkin, and
Gordon M. Weiner, 158:84–106. International Archives of the History of Ideas.
Dordrecht; Boston; London: Kluwer Academic Publishers, 2013.

Shackelford, Jole. “Paracelsianism and the Orthodox Lutheran Rejection of Vital Philosophy in
Early Seventeenth-Century Denmark.” Early Science and Medicine 8, no. 3 (2003): 210–
52.

———. “Paracelsianism in Denmark and Norway in the 16th and 17th Centuries.” PhD diss.,
University of Wisconsin, 1989. UMI 8914538.

———. “Rosicrucianism, Lutheran Orthodoxy, and the Rejection of Paracelsianism in Early
Seventeenth-Century Denmark.” Bulletin of the History of Medicine 70, no. 2 (1996):
181–204.

Shane, David. “Figurate Numbers: A Historical Survey of an Ancient Mathematics.” Monarch
Review 5 (2018): 10–29.

Shantz, Douglas H. An Introduction to German Pietism: Protestant Renewal at the Dawn of
Modern Europe. Baltimore: Johns Hopkins University Press, 2013.

Shaposhnikov, Vladislav. “Theological Underpinnings of the Modern Philosophy of
Mathematics.” Studies in Logic, Grammar and Rhetoric 44, no. 57 (2016): 31–54.
https://doi.org/10.1515/slgr-2016-0009.

Shay, Edmund. “New Insights into Bach’s Orgelbüchlein, Part 1.” The Diapason, April 1985,
12–13.

———. “New Insights into Bach’s Orgelbüchlein, Part 2.” The Diapason, May 1985, 12–13.

———. “The Schübler Chorales & The Numbers Game.” The Diapason, September 1999, 16–
17.
274

Shea, William R. “Descartes and the Rosicrucian Enlightenment.” In Metaphysics and the
Philosophy of Science in the 17th and 18th Centuries, edited by R. S. Woolhouse, 73–99.
Dordrecht: Kluwer Academic Publishers, 1988.

Shepherd, Alan. Let’s Calculate Bach: Applying Information Theory and Statistics to Numbers in
Music. Quantitative Methods in the Humanities and Social Sciences. Cham, Switzerland:
Springer, 2021.

Sheppard, H. J. “The Redemption Theme and Hellenistic Alchemy.” Ambix 7 (1959): 42–46.

Silbiger, Alexander. “Passacaglia and Ciaccona: Genre Pairing and Ambiguity from Frescobaldi
to Couperin.” Journal of Seventeenth-Century Music 2, no. 1 (1996). http://sscm-
jscm.org/v2/no1/silbiger.html.

Simons, Shelbie. “Dialog and Dualism: A Study of Lutheran Theology Applied to Selected
Buxtehude Vocal Cantatas.” DMA diss., University of Oklahoma, 2006.

Smend, Friedrich. J. S. Bach bei seinem Namen Gerufen. Kassel; Basel: Bärenreiter, 1950.

———. Johann Sebastian Bach: Kirchenkantaten. Berlin: Christlicher Zeitschriftenverlag, 1950.

Smoley, Richard. “From Lead to Gold: Hermes and Alchemy.” Rosicrucian Digest 1 (2011): 12–
20.

Snyder, Kerala J. “Buxtehude’s Organ Music: Drama without Words.” The Musical Times 120
(1979): 517–21.

———. Dieterich Buxtehude: Organist in Lübeck. 2nd ed. Rochester, NY: University of
Rochester Press, 2/2007.

———. “Dietrich Buxtehude’s Studies in Learned Counterpoint.” Journal of the American
Musicological Society 33 (1980): 544–64.

———. “Oratorio on Five Afternoons: From Lübeck Abendmusiken to Bach’s Christmas
Oratorio.” In J. S. Bach and the Oratorio Tradition: Bach Perspectives 8, edited by
Daniel R. Melamed, 69–95. Urbana: University of Illinois Press, 2011.

———. “Soloists and Capella in the Vocal Music of Buxtehude.” In Dietrich Buxtehude and
Samuel Scheidt: An Anniversary Tribute. The Proceedings of the International Buxtehude
/ Scheidt Festival and Conference at the University of Saskatchewan, November 1987,
edited by Isabelle Mills and Walter Kreyszig, 195–99. Saskatoon: University of
Saskatchewan Printing Services, 1988.

275
———. “Tradition with Variations: Chorale Settings per Omnes versus by Buxtehude and
Bach.” In Music and Theology: Essays in Honor of Robin A. Leaver on His Sixty-Fifth
Birthday, edited by Daniel Zager, 31–50. Lanham, MD: The Scarecrow Press, 2006.

Son, Se. “Figures of Musica Poetica in the Passacaglias of Dieterich Buxtehude and J. S. Bach.”
DMA diss., University of Cincinnati, 2012. UMI 3554392.

Speerstra, Joel. “Musica Poetica and Figural Notation.” In Bach and the Pedal Clavichord: An
Organist’s Guide, 114–29. New York: University of Rochester Press, 2004.

Sponheuer, Bernd. “Das Phantastische und das Geordnete. Zu Buxtehudes Orgelciaconnen.”
Musica 41 (1987): 495–502.

———. “Phantastik und Kalkül. Bemerkungen zu den Ostinato-Kompositionen in der
Orgelmusik Dietrich Buxtehudes.” In Dietrich Buxtehude und die europäische Musik
seiner Zeit. Bericht über das Lübecker Symposion 1987, edited by Arnfried Edler and
Friedhelm Krummacher, 289–309. Kassel: Bärenreiter, 1990.

St. Marie, John S. “Theology as the Basis for Golden Section Analysis: A Model of Construction
for Johann Sebastian Bach’s “St. John Passion".” DMA diss., University of Southern
California, 2012. UMI 3551558.

Stillwell, John. Elements of Mathematics: From Euclid to Gödel. Princeton, New Jersey:
Princeton University Press, 2016.

Strohm, Reinhard. “De plus En plus: Numbers, Binchois, and Ockeghem.” In Citation and
Authority in Medieval and Renaissance Musical Culture: Learning from the Learned,
edited by Suzannah Clark and Elizabeth Eva Leach, 4:160–73. Studies in Medieval and
Renaissance Music. Woodbridge: The Boydell Press, 2005.

Struik, D. J. “Simon Steven and the Decimal Fractions.” In The European Mathematical
Awakening: A Journey Through the History of Mathematics from 1000 to 1800, 96–101.
Mineola, New York: Dover Publications, Inc., 2013.

Swetz, Frank J. “Leibniz, the Yijing , and the Religious Conversion of the Chinese.”
Mathematics Magazine 76, no. 4 (October 2003): 276–91.
https://doi.org/10.1080/0025570X.2003.11953194.

———. “Perspective: The European Mathematical Awakening.” In The European Mathematical
Awakening: A Journey Through the History of Mathematics from 1000 to 1800, edited by
Frank J. Swetz, 1–3. Mineola, New York: Dover Publications, Inc., 2013.

Szulakowska, Ursula. “Geometry and Astrology in Late Medieval and Early Renaissance
Alchemy.” In The Alchemy of Light: Geometry and Optics in Late Renaissance
Alchemical Illustration, 10:13–27. Symbola Et Emblemata. Leiden: Brill, 2000.

276
Tapp, Christian. “Infinity in Mathematics and Theology.” Theology and Science 9 (2011): 91–
100. https://doi.org/10.1080/14746700.2011.547009.

Tatlow, Ruth. Bach and the Riddle of the Number Alphabet. Cambridge: Cambridge University
Press, 1991.

———. Bach’s Numbers: Compositional Proportion and Significance. Cambridge: Cambridge
University Press, 2015.

———. “Collections, Bars and Numbers: Analytical Coincidence or Bach’s Design?”
Understanding Bach 2 (2007): 37–58.

———. “Parallel Proportions, Numerical Structures and Harmonie in Bach’s Autograph Score.”
In Exploring Bach’s B-Minor Mass, edited by Yo Tomita, Robin A. Leaver, and Jan
Smazcny, 142–62. Cambridge: Cambridge University Press, 2013.

———. “Text, the Number Alphabet and Numerical Ordering in Bach’s Church Cantatas.” In
Bach’s 1. Leipziger Kantatenjahrgang, 3:121–33. Dortmunder Bach-Forschungen.
Dortmund: Klangfargen, 2002.

———. “The Use and Abuse of Fibonacci Numbers and the Golden Section in Musicology
Today.” Understanding Bach 1 (2006): 69–85.

———. “Theoretical Hope: A Vision for the Application of Historically Informed Theory.”
Understanding Bach 8 (2013): 33–60.

———. “Towards a Theory of Bach’s Compositional Style.” In Bach Und Die Stile, 2:19–36.
Dortmunder Bach-Forschungen. Dortmund: Klangfargen, 1999.

———. “When the Theorists Are Silent: Mattheson, Bach and the Development of Historically
Informed Analytical Techniques.” In What Kind of Theory Is Music Theory, edited by P.
Broman, 1:203–16. Stockholm Studies in Musicology. Stockholm: Stockholm University,
2007.

Tilley, Janette. “Meditation and Consolatory Soul-God Dialogues in Seventeenth-Century
Lutheran Germany.” Music & Letters 88 (2007): 436–57.

Tilton, Hereward. The Quest for the Phoenix: Spiritual Alchemy and Rosicrucianism in the Work
of Count Michael Maier (1569-1622). Berlin; New York: Walter de Gruyter, 2003.

———. “The Rosicrucian Manifestos and Early Rosicrucianism.” In The Occult World, edited
by Christopher Partridge, 128–40. New York, New York: Routledge, 2015.

Tomlinson, Gary. Music in Renaissance Magic: Toward a Historiography of Others. Chicago;
London: University of Chicago Press, 1993.

277
Varwig, Bettina. “Metaphors of Time and Modernity in Bach.” The Journal of Musicology 29,
no. 2 (Spring 2012): 154–90.

Vogelsänger, Siegried. “Passacaglia Und Chaconne in Der Orgelmusik. Von Frescobaldi Bis
Bach.” Musik Und Kirche 37 (1967): 14–24.

Vries, Alyke Zwaantina de. “The General Reformation Divini et Humani: The Rosicrucian Call
for Change, Its Sources, and Early Impact.” PhD diss., Radboud University Nijmegen,
2020.

Walker, D. P. Studies in Musical Science in the Late Renaissance. London: The Warburg
Institute, 1978.

Webber, Geoffrey. “Modes and Tones in Buxtehude’s Organ Works.” Early Music 35 (2007):
355–70.

———. Northern German Church Music in the Age of Buxtehude. Oxford: Clarendon Press,
1996.

Wellesz, E. “Music in the Treatises of Greek Gnostics and Alchemists.” Ambix 4 (1951): 145–
58.

Wells, Robin Headlam. “Number Symbolism in the Renaissance Lute Rose.” Early Music 9, no.
1 (January 1981): 32–42.

Werckmeister, Andreas. Andreas Werckmeister’s Musicalische Paradoxal-Discourse: A Well-
Tempered Universe. Translated by Dietrich Bartel. Contextual Bach Studies. Lanham:
Lexington Books, 2017.

Wilkinson, Robert J. “The Poetic Transformation of Christian Cabbala: Gematria between
Divination and Honorific Poetry in the German Lands of the Eighteenth Century.” ARIES
- Journal for the Study of Western Esotericism 20 (July 2020): 173–206.
https://doi.org/10.1163/15700593-02002001.

Willard, Thomas. “Dreams and Symbols in The Chemical Wedding.” In Lux in Tenebris: The
Visual and the Symbolic in Western Esotericism, edited by Peter J. Forshaw, 130–51.
Leiden: Brill, 2017.

Williams, Peter F. “Was Bach an Organ Expert or an Acquisitive Reader of Andreas
Werckmeister?” Journal of the American Musical Instrument Society 11 (1985): 38–54.

Wilson, Robin, and John Fauvel. “The Lull before the Storm: Combinatorics in the
Renaissance.” In Mathematicians and Their Gods: Interactions between Mathematics
and Religious Beliefs, edited by Snezana Lawrence and Mark McCartney, 89–104.
Oxford: Oxford University Press, 2015.

278
Wolff, Christoph. “Das Hamburger Buxtehude-Bild.” Musik und Kirche 53 (1983): 8–19.

Wollny, Peter. “Imitatio und Aemulatio in der geistlichen Vokalmusik von Dietrich Buxtehude.”
In Dieterich Buxtehude: Text - Kontext - Rezeption, edited by Wolfgang Sandberger and
Volker Scherliess, 89–109. Kassel; New York: Bärenreiter, 2011.

———. Studien zum Stilwandel in der protestantischen Figuralmusik des mittleren 17.
Jahrhunderts. Vol. 5. Forum Mitteldeutsche Barockmusik. Beeskow: Ortus, 2016.

Wollny, Peter, and Stephen Rose. “From Lübeck to Sweden: Thoughts and Observations on the
Buxtehude Sources in the Düben Collection.” Early Music 35, no. 3 (2007): 371–83.

Wurm, Karl. “Ein hermeneutischer Versuch zu D. Buxtehudes Passacaglia in d BuxWV 161 und
zu J. S. Bachs Präludium und Fuge C-Dur BWV 547.” Musik und Kirche 54 (1984): 263–
71.

Yates, Frances A. The Rosicrucian Enlightenment. London: Routledge & Kegan Paul, 1972.

Yearsley, David. Sex, Death, and Minuets. Chicago: University of Chicago Press, 2019.

Yearsley, David Gaynor. “Alchemy and Counterpoint in an Age of Reason.” Journal of the
American Musicological Society 51, no. 2 (1998): 201–43.

———. “Ideologies of Learned Counterpoint in the Northern German Baroque.” PhD diss.,
Stanford University, 1995.

———. “In Buxtehude’s Footsteps.” Early Music 35 (2007): 339–53.

———. “Towards an Allegorical Interpretation of Buxtehude’s Funerary Counterpoints.” Music
& Letters 80 (1999): 183–206.

———. “Vor deinen Thron tret ich and the Art of Dying.” In Bach and the Meanings of
Counterpoint, 1–41. Cambridge: Cambridge University Press, 2002.

Zacher, Gerd. “Vater unser im Himmelreich. Die Proportionen in Bachs Choralvorspiel à 2 Clav.
Et Pedal e Canto fermo in Canone, BWV 682.” Kerchemusiker 43, no. 3 (1992): 81–86.

Zorach, Rebecca. The Passionate Triangle. Chicago; London: University of Chicago Press,
2011.

279
APPENDIX

B
c
c
c
c
Violino 1
Violino 2
Soprano
Basso
Continuo
&
&
&
?
∑
∑
Œ
œ
Œ
œ
Herr, Herr,
˙
˙ #
6
∑
∑
‰
J
œ œ
œ #
˙
wenn ich nur dich
˙
˙
6
∑
∑
œ
‰
j
œ
. œ #
œ
j
œ
J
œ
hab, so frag ich nichts, so
˙
˙
I
∑
∑
.
œ
œ
œ
œ
.
œ
œ
œ
œ
œ #
œ
frag ich nichts nach Him
˙
˙ #
6
∑
∑
. ˙
œ
mel
˙
˙
6
-
&
&
&
?
Vln. 1
Vln. 2
BC
6
∑
∑
Œ
œ
˙
und Er
˙
˙
I
4
Œ
œ
Œ
œ
∑
˙
Ó
den,
˙
˙ #
6
‰
J
œ œ
œ #
˙
Ó Œ
œ
∑
˙
˙
6
.
œ
j
œ
. œ #
œ
j
œ
J
œ
Œ
œ
‰
j
œ
I
œ
I
œ
∑
˙
˙
I
.
œ
œ
œ
œ
. œ
œ
œ #
œ
˙
. œ
j
œ
∑
˙
˙ #
6
.
œ
œ #
.
œ
œ
.
œ
œ
.
œ
œ
.
œ
œ
œ
œ .
œ
œ
œ
œ
∑
˙
˙
6
-
&
&
&
?
Vln. 1
Vln. 2
BC
12
œ
œ #
œ . œ
J
œ
œ
œ
œ
œ
˙
∑
˙
˙
I
4
˙
Ó
˙ Ó
Œ
œ
Œ
œ
Herr, Herr,
˙
˙ #
6
Ó Œ
œ
∑
‰
J
œ œ
œ #
˙
wenn ich nur dich
˙
˙
6
Œ
œ
‰
j
œ # œ
œ
∑
œ
‰
j
œ
. œ #
œ
j
œ
J
œ
hab, so frag ich nichts, so
˙
˙
I
˙
. œ
j
œ
Œ
œ
Œ
œ
.
œ
œ
œ
œ
.
œ
œ
œ
œ
œ #
œ
frag ich nichts nach Him
˙
˙ #
6
-
&
&
&
?
Vln. 1
Vln. 2
BC
17
.
œ
œ #
j
œ
J
œ .
œ
œ
œ
œ
‰
J
œ œ
œ #
˙
œ œ
Œ
œ
mel, Herr,
˙
˙
6
œ
œ
. œ
œ
œ
œ
.
œ #
œ
.
œ
j
œ
. œ #
œ
œ
œ
Œ
œ
‰
j
œ # œ
œ
Herr, wenn ich nur
˙
˙
I
.
œ
œ
œ
œ œ œ
.
œ
œ
œ
œ
. œ
œ
œ # œ
˙
. œ
j
œ
dich hab so
˙
˙ #
6
.
œ
J
œ #
˙
œ
œ œ œ
.
œ
œ #
j
œ
J
œ .
œ
œ
œ
œ
frag ich nichts, so frag ich nichts nach
˙
6 ⧵ 7
˙
œ N
œ
œ .
œ
J
œ
. ˙
œ #
œ
œ
œ
œ
˙
Him mel und Er
˙
˙
I
4
- - -
Herr, wenn ich nur dich hab'
Dieterich Buxtehude
BuxWV 38
Canto solo con 2 violini
© 2022 Malachai Komanoff Bandy. All Rights Reserved.
280

&
&
&
?
Vln. 1
Vln. 2
BC
22
˙ Ó
˙
Ó
˙
Œ
œ
den, wenn
˙
˙ #
6
∑
∑
.
œ
J
œ #
œ œ
œ
œ
mir gleich Leib und Seel ver
˙
6 ⧵ 7
˙
∑
Œ
œ . œ
J
œ #
œ
œ
œ œ œ
œ
schmacht, wenn mir gleich
˙
˙
I
4
Ó Œ
œ
œ œ
œ
œ
œ
œ œ
œ
˙ Ó
Leib
˙
˙ #
6
.
œ
J
œ #
œ œ
œ
œ
œ
œ
œ ˙
∑
˙
˙
6
-
&
&
&
?
Vln. 1
Vln. 2
BC
27
œ
œ
œ . œ
j
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ
œ
.
œ
j
œ #
wenn mir gleich
˙
˙
I
5
4
˙
Ó
˙ Œ
œ
œ œ
œ #
œ
œ
œ
œ
Leib und Seel verschmacht, wenn
˙
˙ #
6
∑
.
œ
J
œ #
œ œ
œ
œ
œ
œ ˙
mir gleich Leib
˙
6 ⧵ 7
˙
Œ
œ . œ
J
œ #
œ
œ
œ œ œ
œ
∑
˙
˙
I
5
4
œ œ
œ
œ
œ
œ œ
œ
œ œ
œ
œ
œ
œ #
œ
∑
˙
˙ #
6
-
&
&
&
?
Vln. 1
Vln. 2
BC
32
œ œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
∑
˙
˙
6
œ
œ ˙ œ
œ
œ œ
œ # œ œ
œ
∑
˙
˙
I
œ
œ
œ
œ
œ #
œ
œ
œ
œ #
œ
œ
œ
œ
œ
˙
‰
œ
œ
œ #
œ
œ
œ
∑
˙
˙ #
6
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
.
œ
J
œ
∑
˙
6 ⧵
˙
i
&
&
&
?
Vln. 1
Vln. 2
BC
36
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ N œ
œ
œ
œ
œ
œ
œ
œ
∑
˙
˙
I
œ
œ
œ
œ #
œ
œ
œ #
œ
œ
œ
œ
œ
œ N
œ
œ
œ
I
œœ
œ
œ
œ
œ #
œ
œ
œ
œ
œ #
œ
œ
œ
œ N
œ
∑
˙
˙ #
6
˙
≈
œ
œ
œ #
œ
œ
œ N
œ
œ
œ
œ
œ #
œ
œ
œ
œ #
œ
œ N
œ
œ
œ
œ
∑
˙
˙
6
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
˙
˙
I
2 Herr, wenn ich nur dich hab
281

&
&
&
?
Vln. 1
Vln. 2
BC
40
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
∑
˙
˙ #
6
œ
œ
œ #
œ
œ
œ
˙
˙
≈
œ
œ N
œ
œ
œ
œ
œ
∑
˙
6 ⧵
5
˙
6
≈
œ N
œ
œ
œ
œ
œ
œ
œ #
.
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œœ . œ
œ
∑
˙
6
˙
I I 4
˙
Ó
˙
Ó
‰
J
œ œ œ œ #
œ . œ
œ
so bist du doch Gott al le
˙
˙ a
6 ⧵ 7
œ
œ #
œ
œ
œ
œ
˙
3 3
Ó
œ
œ
œ
œ
œ
œ
3 3
˙
Ó
zeit,
˙
6 ⧵
˙
6
- -
&
&
&
?
Vln. 1
Vln. 2
BC
45
œ
œ
œ
œ
œ
œ
˙
3 3
œ
œ #
œ
œ
œ
œœ
œ
3 3
∑
˙
˙
˙ Ó
˙
Ó
‰
J
œ œ œ œ #
œ . œ
œ
so bist du doch Gott al le
˙
˙ #
6 ⧵ 7
Ó
œ
œ
œ
œ
œ
œ
3 3
œ
œ #
œ
œ
œ
œ
˙
3 3
˙
Ó
zeit,
˙
6 ⧵
˙
6
˙
œ
œ
œ
œ
œ
œ
3 3
œ
œ
œ
œ
œ
œ
˙ #
3 3
∑
˙
˙
I
˙ Ó
˙
Ó
œ
œ
œ
œ
œ
œ
˙
3 3
mei nes Her zens Trost,
˙
˙ #
6
- - - -
&
&
&
?
Vln. 1
Vln. 2
BC
50
Ó
œ
œ
œ
œ
œ
œ
3 3
Ó
œ
œ
œ
œ
œ
œ
3 3
œ
œ #
œ
œ
œ
œ
˙
3 3
mei nes Her zens Trost,
˙
˙
6
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
3 3 3
3
œ
œ
œ
œ
œ
œ
˙
3 3
Ó
œ
œ
œ
œ #
œ
œ
3 3
mei nes Her zens
˙
˙
I
œ
œ
œ
œ
œ
œ
˙
3 3
Ó
œ
œ
œ
œ #
œ
œ
3 3
j
œ
J
œ œ œ œ #
œ . œ
œ
Trost, so bist du doch Gott al le
˙
˙ a
6 6 ⧵ ⧵ 7
œ
œ
œ
œ
œ
œ #
˙
3 3
˙
œ
œ
œ
œ
œ
œ
3 3
˙
œ
œ
œ
œ
œ
œ
3 3
zeit, mei nes Her zens
˙
˙
6
- - - - - - - -
&
&
&
?
Vln. 1
Vln. 2
BC
54
œ
œ
œ
œ
œ
œ
œ
œ
. œ #
œ
œ
˙
œ
œ
œ
œ
œ
œ
3
3
œ
œ
œ
œ
œ
˙
Trost und mein
˙
6 5
˙
I
˙
‰
œ
œ #
œ
˙ Ó
j
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Heil. Al le lu ia,
˙
˙ #
6
œ
œ
œ #
œ
œ œ
œ
œ
œ
œ
œ
œ
Ó ‰
œ
œ
œ
˙
Ó
˙
˙
6
œ
œ N
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
Œ
œ
œ #
œ
œ
œ
œ
œ
œ
al le lu
˙
6 5
˙
I
- - - - - -
3 Herr, wenn ich nur dich hab
282

&
&
&
?
Vln. 1
Vln. 2
BC
58
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
˙
œ
œ
œ #
œ
˙
Œ
œ
ia, al
˙
˙ #
6
˙
Ó
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ . œ
œ
œ
œ
œ
œ #
œ
œ
œ
J
œ
œ
œ #
œ
le lu ia, al le lu
˙
6 ⧵ 5
˙
Œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
I
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
˙
ia,
˙
˙
I
œ
œ œ
œ
. œ œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œœ
œ
œ
œ œ
Ó ‰
œ
œ #
œ
al le lu
˙
˙ #
6
- - - - - - - - -
&
&
&
?
Vln. 1
Vln. 2
BC
62
. œ
œ
. œ
œ N
. œ
j
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ N
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
ia, al
˙
˙
6
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
I
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
le lu ia,
˙
˙
I
œ
œ
œ #
œ
œ
Œ
œ
œ
œ
œ
œ œ
œ
œ
œ
œ œ
œ
œ #
œ
œ
œ
œ
œ
œ œ
œ
œ
œ #
œ
al le
˙
6 5
˙ #
7
œ
œ
œ #
œ
œ
œ #
œ
œ
œ
œ . œ
œ
˙
Œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
J
œ œ
œ
œ
lu ia, al le lu
˙
6 6 ⧵ 7
˙
6
- - - - - - - - -
&
&
&
?
Vln. 1
Vln. 2
BC
66
. œ
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
˙
œ
œ
œ
œ
œ
œ
œ
œ
˙ #
ia,
˙
˙
I
œ
œ
œ
œ
œ
Œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
Œ œ
œ #
œ
œ
œ
œ
œ #
œ
al le lu
˙
˙ #
5
œ
œ
œ
œ #
œ
œ
œ
.
œ
œ N .
œ
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
˙
Œ ‰ j
œ
ia, al
˙
6 6 ⧵ 3
˙
6
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
‰
J
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ #
j
œ
J
œ
le lu ia, al
˙
˙
I
- - - - - - -
&
&
&
?
Vln. 1
Vln. 2
BC
70
œ
œ
œ œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
œ
œ
le lu ia,
˙
˙ #
6
œ
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
œ #
œ
œ
œ N
œ
œ
œ
œ
œ
‰ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ #
al le lu ia,
˙
˙
6
œ
.
œ
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
œ
œ #
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
al le lu
˙
˙
I I
4
›
U
›
U
›
U
ia.
›
U
- - - - - - - -
4 Herr, wenn ich nur dich hab
283

B
b
b
b
b
c
c
c
c
Violino 1
Violino 2
Tenor
Continuo
&
&
V
?
Œ
œ . œ œœ œ
Œ
œ . œ œœ œ
∑
œ
œ
œ
œ œ
œ
64 Repetatur
œ
. œ
J
œ
œ
œ
œ
œ
. ˙ œ
œ
œ
œ
∑
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
Œ
œ . œ œ œ œ
Quem ad mo dum de
œ
œ
œ
œ œ
œ
∑
∑
. ˙ œ
œ
œ
œ
si
œ
œ
œ
œ
- - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
5
∑
∑
5
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
∑
∑
.
œ œ
œ
œ
œ b
œ
œ
œ
œ .
œ
œ
de rat, de si de rat cer
œ
œ
œ
œ
Œ
œ . œ œœ œ
Œ
œ . œ œœ œ
œ
Œ Ó
vus.
œ
œ
œ
œ œ
œ
œ
. œ
J
œ
œ
œ
œ
œ
. ˙ œ
œ
œ
œ
∑
œ
œ
œ
œ
- - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
9
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
9
∑
œ
œ
œ
œ œ
œ
.
œ œ
œ
œ
œ b
œ
œ
œ
œ .
œ
œ
œ
œ
œ
. œ
œ
œ
œ
œ
œ . œ
œ
Ó Œ
œ
Que
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
. œ œ œ œ
˙
mad mo dum de si
œ
œ
œ
œ œ
œ
∑
∑
œ œ
œ b
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
œ
œ
œ
- - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
13
∑
∑
13
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ œ
œ
Ó Œ
œ
œ
œ
œ
∑
œ
œ N
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
de rat cer
œ
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Ó Œ
œ
œ
œ b
œ
œ
Œ Ó
vus,
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
œ œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
Ó Œ
œ
œ
œ
œ
ad
œ
œ
œ
œ
- - - - - - - - - - -
Chiaccona, Quemadmodum desiderat cervus à 3
Dieterich Buxtehude
BuxWV 92
© 2022 Malachai Komanoff Bandy. All Rights Reserved.
Tenor con due violini
284

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
17
œ
Œ Ó
œ
Œ Ó
17
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
fon
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
tes a qua
œ
œ
œ
œ
Ó
œ œ
Œ
Ó
œ œ
Œ
œ
œ œ
Œ
œ œ
rum, i ta, i ta
œ
œ
œ
œ œ
œ
œ œ
Œ
œ œ
Œ
œ œ
Œ
œ œ
Œ
Œ
œ œ
‰
œ œ
œ
i ta i ta de
œ
œ
œ
œ
∑
∑
.
˙ œ
œ
œ
œ
si
œ
œ
œ
œ œ
œ
- - - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
22
∑
∑
22
œ
œ
œ œ
œ
œ œ
œ
œ œ œ
œ
de rat a ni ma
œ
œ
œ
œ
∑
∑
œ œ
‰
j
œ
œ
‰
j
œ
me a, ad te, ad
œ
œ
œ
œ œ
œ
∑
∑
œ
‰
J
œ
œ
œ
œ
. œ
œ
te, ad te De
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
Œ Ó
us
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
œ
œ
œ
œ
- - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
27
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
œ
27
∑
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
.
œ
œ b .
œ
œ .
œ
œ
n
œ
œ
œ
œ
œ
œ
œ œ
œ
œ œ
œ
œ
œ
Ó Œ ‰
J
œ
si
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
œ œ
‰
j
œ œ œ
≈
œ
œ
œ
ti vit, si ti vit, si
œ
œ
œ
œ œ
œ
Ó Œ ‰ J
œ
Ó Œ ‰
J
œ
œ œ
œ œ
œ
œ
œ
œ
j
œ
‰
ti vit a ni ma me a ad te,
œ
œ
œ
œ
- - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
31
œ œ
‰
J
œ
œ œ
Œ
œ œ
‰ J
œ
œ œ
‰
J
œ b
31
‰
œ
œ
J
œ
‰ ‰
œ
œ
.
œ
œ
ad te De um fon tem
œ
œ
œ
œ œ
œ
‰
J
œ
œ
‰ J
œ
. œ œ
œ
‰
J
œ
œ
œ
. œ œ
œ œ Œ Ó
vi vum,
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
œ
œ
œ
œ
œ
œ
œ
œ
Quan do ve ni
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
am et ap pa
œ
œ
œ
œ
∑
∑
œ œ
‰
œ
œ
œ œ
‰ œ
œ
re bo, ap pa re bo, ap pa
œ
œ
œ
œ œ
œ
- - - - - - - - - - - - -
2
Chiaccona, Quemadmodum desiderat, cervus à 3
285

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
36
∑
∑
36
œ œ œ
œ
œ
œ
œ
œ b
œ
œ œ
.
œ
œ
re bo, ap pa re bo an te fa ci em tu
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ Ó
am,
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
œ
œ
œ
œ
œ œ
Œ Ó
œ œ
Œ Ó
Œ ≈
œ
œ
œ
œ
≈
œ
œ
œ
O
œ
œ
œ
œ œ
œ
∑
∑
œ
≈
œ
œ
œ b
œ
≈
œ
œ
œ
n
œ
œ
œ
œ
- - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
41
∑
∑
41
œ
œ
œ
œ
œ
œ
œ
j
œ
‰ ‰
j
œ
fons, O
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ b
œ
œ . œ
œ
fons vi
œ
œ
œ
œ
∑
∑
j
œ
‰
œ
œ
œ
œ
œ
œ
œ b
œ
ta ve na a qua rum, ve na a
œ
œ
œ
œ œ
œ
Œ
œ
œ b
œ
œ
œ Œ
Ó Œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
qua rum vi ven ti
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
45
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ b
œ
45
œ
Œ Ó
um
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
. œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
Ó Œ
œ
œ œ
quan do
œ
œ
œ
œ
œ
Œ
œ
œ
œ
œ
œ
œ
œ b
œ
œ œ
œœ
œ œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
. œ œ œ
œ
œ œ
ve ni am, quan do,
œ
œ
œ
œ œ
œ
.
œ œœ
œ
œ b
œ
œ
œ
œ
œ
œ
.
œ œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ œ
œ œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
quan do, quan do ve
œ
œ
œ
œ
- - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
49
œ
Œ Ó
œ
Œ Ó
49
. œ œ œ
‰
j
œ œ
œ
œ
œ
œ œ œ
ni am ad a quas dul
œ
œ
œ
œ œ
œ
∑
∑
.
œ œ
œ œ
.
œ œ
œ
œ
œ
ce di nis, dul ce di nis, dul
œ
œ
œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
ce
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
. œ
œ
.
œ œ
œ
œ
di nis
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - - -
3
Chiaccona, Quemadmodum desiderat, cervus à 3
286

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
53
Ó
œ œœ
œ œœ
œ œœ
œ œœ
œ œ
œ
œ œœ
53
œ
œ
Œ Ó
tu a,
œ
œ
œ
œ œ
œ
œ œ
œ
œ œ œ
œ
œ
œ
œ
.
œ
œ
œ œ
œ
œ œ œ œ
œ
œ
.
œ
œ
∑
œ
œ
œ
œ
œ
Œ
œ œ
œ
œ œ œ
œ
Œ Ó
œ œ œ
œ œ œ
œ œ
œ
œ œ œ
si ti o, si ti o, si ti o, si ti o,
œ
œ
œ
œ œ
œ
œ œ
œ
œ œ œ œ
œ
œ
.
œ
œ
œ œ
œ
œ œ œ
œ œ œ
. œ
œ
Œ
œ œ œ
œ
œ
œ
œ . œ
œ
si ti o, Do mi
œ
œ
œ
œ
- - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
57
œ
Œ Ó
œ
Œ Ó
57
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
ne fons vi ta
œ
œ
œ
œ œ
œ
∑
∑
j
œ
‰
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
es, sa ti a
œ
œ
œ
œ
Ó ‰
œ
œ
œ
œ
œ
œ
‰
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ Ó
me,
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ œ
œ
œ
œ
œ
œ
Ó Œ
œ
œ
œ
œ
si ti o,
œ
œ
œ
œ
- - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
61
œ
Œ Ó
œ
Œ Ó
61
. œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
si ti o, si ti o te De um
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œŒ
.
œ
œ
œ
.
œ
œ
œ
3
3
vi vum, si ti o, si ti o,
œ
œ
œ
œ
Œ
œ
˙
Œ
œ
. œ
j
œ
. œ
œ
œ
Œ Ó
3
si ti o,
œ
œ
œ
œ œ
œ
Ó
.
œ
j
œ
œ
˙
œ
∑
œ
œ
œ
œ
œ œ
. œ
j
œ
˙
Œ
œ
Œ
œ
˙
O
œ
œ
œ
œ œ
œ
œ
˙
œ
œ
œ
œ
œ
Ó
.
œ
j
œ
quan
œ
œ
œ
œ
- - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
67
œ
Œ Ó
œ
Œ Ó
67
œ œ œ œ œ œ œ œ œ
œ
œ
do, O quan do ve ni am et ap pa
œ
œ
œ
œ œ
œ
‰
J
œ œ œ œœœœ œ
œ
œ
œ
‰
J
œ
œ œ
œœ
œ
œ
œ
œ
œ
œ
œ œ
Œ ‰
J
œ
œ œ
re bo, O quan do
œ
œ
œ
œ
œ œ
Œ
œœœœœ
œ
œ
œ œ
Œ
œœœœœ
œ
œ
œ œ œ œ œ
œ
œ
œ œ
œ œ œ
ve ni am et ap pa re bo Do mi ne,
œ
œ
œ
œ œ
œ
œ œ
Œ Ó
œ œ Œ Ó
Œ
œ
œ
œ
œ
œ
œ
œ
œ
an te fa ci em tu
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - -
4
Chiaccona, Quemadmodum desiderat, cervus à 3
287

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
71
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Ó
œ
œ
œ
œ
œ
œ
71
œ
Œ Ó
am,
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ . œ
œ
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œœ
œ
œ
œ
œ
œ
œ
œ
≈
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Ó Œ ‰
J
œ
pu
œ
œ
œ
œ
-
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
75
œ
Œ Ó
œ
Œ Ó
75
œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
tas ne vi de bo di em
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ œ
œ œ
≈
œ
œ
œ
il lam, di em in quam ju cun di
œ
œ
œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
ta
œ
œ
œ
œ œ
œ
∑
∑
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
tis et la ti
œ
œ
œ
œ
- - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
79
Œ
œ
œ œ œ
Œ
œ
œ œ œ
79
. œ
œ
j
œ
‰
œ œ œ
ti a di em quam
œ
œ
œ
œ œ
œ
œ œ
.
œ
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
fe cit Do mi
œ
œ
œ
œ
.
˙ œ
. ˙ œ
œ œ œ
œ
œ
œ
œ
œ
œ
œ
œ
nus, ex ul ta
œ
œ
œ
œ œ
œ
.
œ
œ
œ
˙
.
œ
œ
œ
.
œ
J
œ
œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
œ
œ
œ
œ
mus et la te mur in
œ
œ
œ
œ
.
œ
œ
œ
œ
.
œ
œ
œ
œ
œ
Œ ‰
j
œ
œ
œ
œ
œ
Œ Ó
e a,
œ
œ
œ
œ œ
œ
- - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
84
.
œ
œ
œ
œ
.
œ
œ
.
œ
œ
.
œ
œ
œ
œ
.
œ
œ
.
œ
œ
84
Ó Œ
. œ
œ
u bi,
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
œ
œ
Œ Œ
.
œ
œ b
u bi, u bi,
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
u bi, u bi est cer ta, cer ta se
œ
œ
œ
œ
∑
∑
. œ œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
cu ri tas, se cu
œ
œ
œ
œ œ
œ
∑
∑
œ œ ‰
J
œ
œ œ
œ
.
œ
œ
ra, se cu ra tran quil li
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - - -
5
Chiaccona, Quemadmodum desiderat, cervus à 3
288

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
89 œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
89
œ
Œ Ó
tas,
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ .
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ .
œ
œ
∑
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
œ
œ
œ
œ
œ
œ
œ
œ
et tran quil la ju
œ
œ
œ
œ œ
œ
∑
Ó Œ ‰
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
cun di
œ
œ
œ
œ
- - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
93
Œ ‰
J
œ
œ
œ b
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
93
œ
Œ Ó
tas,
œ
œ
œ
œ œ
œ
‰ J
œ .
œ
œ b .
œ œ
œ
œ
œ
‰
J
œ
. œ œ
œ
œ
.
œ
œ
Ó Œ ‰
j
œ
jo
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
œ
œ
œ
œ
œ œ
œ
œ
œ b
œ
œ
œ œ
cun da, jo cun da
œ
œ
œ
œ œ
œ
∑
∑
‰
œ
œ b . œ
œ
J
œ
‰
œ
œ
œ
fe li ci tas, fe lix ae
œ
œ
œ
œ
- - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
97
∑
∑
97
œ œ œ œ
œ œ œ
œ œ œ œ
œ
œ b
œ
œ
ter ni tas, jo cun da fe li ci tas ae ter
œ
œ
œ
œ œ
œ
∑
∑
œ
œ b
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
∑
∑
œ œ
œ
œ
œ
œ œ
‰
œ
œ
na be a ti tu do et
œ
œ
œ
œ œ
œ
∑
∑
.
œ
J
œ b
œ œ
. œ
œ
be a ta Tri ni
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
101
∑
∑
101
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
ta et Tri ni ta
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
œ .
œ
œ
tis u ni
œ
œ
œ
œ
Ó ‰
œ
œ
œ
œ
œ
œ b
‰
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ Œ
œ
tas, et
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
œ
œ
œ œ œ œ
.
œ œ
j
œ
‰
u ni ta tis De i tas,
œ
œ
œ
œ
- - - - - - - - - - - - - - -
6
Chiaccona, Quemadmodum desiderat, cervus à 3
289

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
105
œ
œ œ œ
œ œ
‰
J
œ
œ
Œ ‰
j
œ œ œ
105
‰
j
œ œ œ œ œ œ
et De i ta tis be
œ
œ
œ
œ œ
œ
œ œ
œ œ œ
œ . œ œ
œ œ
‰
J
œ
œ
œ
œ
.
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ .
œ œ
a ta vi si
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ Ó
o
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
Œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
quod est gau
œ
œ
œ
œ
- - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
109
w
œ
œ
˙
109
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œ
œ
.
˙
.
œ
œ
œ
œ
œ
. œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
di um Do mi ni tu
œ
œ
œ
œ
œ
œ
œ œœ
‰
J
œ
œ œœ
œ œ
œ œœ
‰
J
œ
œ œœ
œ
Œ Œ ‰
J
œ
i, O
œ
œ
œ
œ œ
œ
Œ ‰
J
œ œ œ œ
‰
J
œ
Œ ‰
J
œ
œ œ œ Œ
œ œ œ
‰
J
œ
œ œ œ
œ œ œ
gau di um, O gau di um, gau di um,
œ
œ
œ
œ
- - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
113
œ œ œ
‰
J
œ
œ œœ
‰
J
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ œœ
113
œ œ œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
gau di um su
œ
œ
œ
œ œ
œ
œ œœ
‰
J
œ
œœœ
œ
œ œœ
Œ ‰
J
œ
œ œœ
œ œœ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ œ
per gau di
œ
œ
œ
œ
œ
j
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œœ
Œ
œ
œ
œ
œ
œ
œ
œ
j
œ
‰ Œ Ó
um
œ
œ
œ
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
.
œ œ
œ
œ
œ
œ
œ
œ
œ
.
œ
œ
.
œ
œ
Œ ‰
J
œ
œ œ œ
‰
J
œ
O gau di um, O
œ
œ
œ
œ
- - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
117
œ
œ
œ œ œ
œ œ œ
œ œ œ
œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
117
œ œ œ
œ œ œ
œ œ œ
Œ
gau di um, gau di um, gau dium
œ
œ
œ
œ œ
œ
Œ
œ œ œ
œ
œ
œ .
œ
œ
œ œ
‰
J
œ
œ
œ
œ
œ
œ
œ b
œ
œ
œ
œ
œ
œ
œ œ
Œ
su per,
œ
œ
œ
œ
œ
Œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
J
œ
‰
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
su
œ
œ
œ
œ œ
œ
- - - - - - - - - - - - - - -
7
Chiaccona, Quemadmodum desiderat, cervus à 3
290

&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
120
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ .
œ
œ . œ
œ
120
œ
œ
œ
œ
œ
œ
œ
œ
. œ
œ
per, su per gau di
œ
œ
œ
œ
œ
Œ
œ œ œ
œ œ œ
œ
Œ
œ œ œ
œ œ œ
œ
œ œ œ
œ œ œ
œ œ œ
um, gau di um, gau di um, gau di um,
œ
œ
œ
œ œ
œ
œ
œ œ
œ œ œ
œ œ œ œ
œ œ
œ œ œ
œ œ œ
œ œ
œ
œ
œ œ
œ œ œ
œ œ
œ
œ
œ
. œ œ
gau di um vin ces om ne gau di
œ
œ
œ
œ
- - - - - - - - - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
123
œ
Œ Ó
œ
Œ Ó
123
œ œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
œ
um, om
œ
œ
œ
œ œ
œ
∑
∑
œ
œ
œ
œœ
œ
œ
œœ
œ
œ
œ
. œ
œ
ne gau di
œ
œ
œ
œ
œ œœœ œœ
œ œœ
œ œ œ
œ œœœ œœ
œ œœ
œ œ œ
œ
Œ
œ
œ
um, om ne,
œ
œ
œ
œ œ
œ
œ œ œ
œ œ œ
œ œ .
œ
œ
œ œ œ
œ
œ œ œ
.
œ œ
œ
œ
œ œ
œ
œ .
œ œ
om ne gau di
œ
œ
œ
œ
- - - - - - - - - - -
&
&
V
?
b
b
b
b
Vln. 1
Vln. 2
T
BC
127
œ
Œ
œ
Œ
œ
Œ
œ
Œ
127
œ
Œ Ó
um.
œ
œ
œ
œ œ
œ
œ
‰
J
œ
œ
œ
. œ
œ
œ
‰
J
œ
œ
œ
.
œ
œ
∑
œ
œ
œ
œ
œ
Œ
œ
Œ
œ
Œ
œ
Œ
∑
œ
œ
œ
œ œ
œ
œ
Œ ‰
J
œ
.
œ
œ
œ
Œ ‰
J
œ
. œ
œ
∑
œ
œ
œ
œ
œ
Œ Ó
œ
Œ Ó
∑
œ
Œ Ó
8
Chiaccona, Quemadmodum desiderat, cervus à 3

Abstract (if available)

Abstract Despite his reputation as Germany’s preeminent organist-composer of the late seventeenth century, Dieterich Buxtehude (ca. 1637-1707) remains a surprisingly elusive character in the Western musical canon. Few contemporary documents detailing his life survive, only a few of his works can be firmly dated, he published almost nothing relative to his known output—and most manuscripts in his hand were lost by 1750. Consequently, modern scholarship tends to emphasize better-documented peripheral aspects such as his known influence on J. S. Bach. Most historians also assume Buxtehude’s purely Lutheran identification based on his high-profile job as organist, music director, and Werkmeister (accountant) at the most prestigious Lutheran church in Lübeck, a major center of Hanseatic power. Emerging details about Buxtehude’s life, however, complicate exclusively Lutheran impressions of his religious and intellectual proclivities. Most recently, Olga Gero traced the previously unidentified text of Buxtehude’s sacred concerto Fallax mundus to a Flemish Jesuit emblem book. This adds to a growing list of works, including a Pange lingua and a Salve desiderium incorporating Marian texts, appearing strangely un-Lutheran for a composer of his employment and social prominence.

This project offers a new perspective regarding Buxtehude’s mystical-musical interests, by illuminating elements of number symbolism, alchemy, and occult philosophy within his basso ostinato psalm settings: Herr, wenn ich nur Dich hab’ (BuxWV 38), Quemadmodum desiderat cervus (BuxWV 92), and Laudate pueri Dominum (BuxWV 69). Across these pieces, coordination between textual meaning and measure number, note number, and large- and small-scale congruence between them points to a numerically conscious premeditation. This also manifests in geometrical design: major sectional proportions repeatedly align with the Pythagorean ratios 1:2 and 3:4, while “figurate” numbers—especially triangle, square, and the palindromic “star” numbers thirty-seven and seventy-three—form the foundation for Buxtehude’s bass-line patterns and textual division points. These features offer insight into Buxtehude’s compositional process, whose mathematical intricacy surpasses our current understanding and pedagogy of seventeenth-century music. His most elaborate mathematical schemes also accompany texts thematically resonant with seventeenth-century alchemical precepts. This corroborates and deepens questions about known occult fascinations within Buxtehude’s milieu: as David Yearsley has shown, Buxtehude’s close friends practiced counterpoint for philosophical reasons outside of musical composition. Despite post-Enlightenment personal legacies stripped of esoteric elements, their treatises intertwine functional music-theory discourse with alchemical innuendo and compositional puzzles demanding a “gnosis” of counterpoint as potent, transformative magic.

Several studies from the 1980s and early 2000s by Piet Kee and Carol Jarman examine the numerical proportions of individual Buxtehude organ works. However rigorous, concrete meaning of mathematical occurrences remains ambiguous in the absence of associated texts. Relying on a combination of textual and numerical content, my analyses reveal in Buxtehude’s vocal works recurring numerical tropes widely associated with the union of heaven and earth in seventeenth-century alchemy and Rosicrucianism. As the apex of musical-geometrical symbolism, his setting of Psalm 73 “solves,” through compositional dimensions, the infamous impossibility of “Squaring the Circle,” alchemical symbol for divine unification. Ultimately, cognizance of Buxtehude’s musical engagement with number begins to close significant gaps in our current understanding of his thought, Christian identity, and compositional progeny. Recognizing esoteric aspects of Buxtehude’s work as conceptually foundational refocuses his image within exoteric historiography and expands our vocabulary surrounding seventeenth-century German compositional practice.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Musical landscape in Northern Germany in the early seventeenth century: musica poetica and its application in the settings of Komm, Heiliger Geist, Herre Gott by Heinrich Schütz, Johann Hermann S...

Asset Metadata

Creator Bandy, Malachai Komanoff (author)

Core Title Number, structure, and mathematical theology in Dieterich Buxtehude's Basso Ostinato psalm Settings

School Thornton School of Music

Degree Doctor of Philosophy

Degree Program Music (Historical Musicology)

Degree Conferral Date 2022-08

Publication Date 07/26/2022

Defense Date 06/21/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag alchemy,Bach, Johann Sebastian, 1685-1750,Baroque music,basso ostinato,Buxtehude,canon,chaconne,ciaccona,counterpoint,esotericism,figurate number,German Baroque music,ground bass,Hamburg,Herr wenn ich nur dich hab,Khunrath,Laudate pueri,Lubeck,Maier,mathematics,musical symbolism,number symbolism,numerology,OAI-PMH Harvest,occult philosophy,proportion,Pythagorean ratio,Pythagoreanism,Quemadmodum desiderat cervus,Reincken,Rosicrucianism,seventeenth century,Sicut Moses exaltavit serpentem in deserto,squaring the circle,Theile,Walther,Werckmeister

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Gilbert, Adam Knight (committee chair), Bartel, Dietrich (committee member), Brown, Bruce Alan (committee member), Gilbert, Rotem (committee member)

Creator Email malachai.bandy@pomona.edu,mbandy@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC111374348

Unique identifier UC111374348

Legacy Identifier etd-BandyMalac-10986

Document Type Dissertation

Format application/pdf (imt)

Rights Bandy, Malachai Komanoff

Type texts

Source 20220728-usctheses-batch-962 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu