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Theology as a basis for golden section analysis: a model of construction for Johann Sebastian Bach's St. John Passion

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THEOLOGY AS THE BASIS FOR GOLDEN SECTION ANALYSIS:
A MODEL OF CONSTRUCTION FOR
JOHANN SEBASTIAN BACH’S ST. JOHN PASSION

by

John S. St. Marie

A Dissertation Presented to the
FACULTY OF THE USC THORNTON SCHOOL OF MUSIC
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF MUSICAL ARTS
(CHORAL MUSIC)

December 2012

Copyright 2012 John S. St. Marie
ii

…These are written that you may believe….
John 20:31 (RSV)

iii

ACKNOWLEDGMENTS

I owe a debt of gratitude to many people for supporting me in this process.
First and foremost to my amazing parents, Teal and Blaze St. Marie, for their
boundless love and unconditional support of me in all of my endeavors.
To the Rev. Heidi Hester for providing the Lutheran perspective for my chapter
on theology and for a safe haven to write in the company of a supportive friend. To Dr.
Laura Harrison for opening her home with a view where I spent many hours trying to get
my ideas from thoughts to words on paper and especially for tolerating my obsessive
need for numerical confirmation by counting all 2031 measures of the St. John Passion –
many times. I would like to express my deep gratitude to Suellen Rowe for going the
extra mile to read and offer editing suggestions – especially for her formatting expertise
and time. Also, to Tino Aceves for providing the correct format for the phonetic
spellings and to numerous other dear friends, especially Ken Faulkner, who offered
words of encouragement and moral support. Also, to the congregations of Shepherd of
the Hills Lutheran Church (Whittier, California) and Irvine United Congregational
Church (Irvine, California) who were faithful supporters during both my academic
studies and my writing process.
And finally to the members of my dissertation committee, Dr. Nick Strimple, Dr.
Jo-Michael Scheibe and Dr. Christian Grases, for your encouragement and enthusiasm
for my topic. Dr. Strimple, thank you for posing the question which started this
incredible journey:
“Why is the break in the St. John Passion so early in the composition?”
iv

TABLE OF CONTENTS

Epigraph ................................................................................................................... ii

Acknowledgments ................................................................................................. iii

List of Tables .......................................................................................................... vi

List of Figures ........................................................................................................ vii

Abbreviations ....................................................................................................... viii

Abstract ................................................................................................................... ix

Chapter One – Introduction ..................................................................................... 1

Chapter Two – The Golden Section: The History of Phi and its Application
in Music ........................................................................................... 8
History of Phi .................................................................................................... 9
Fibonacci and his Rabbits ................................................................................ 11
Phi in Nature, Art and Music ........................................................................... 15
Greater Phi Φ /faɪ/ and Lesser phi φ /fi/ ......................................................... 20
phi Applied to Music ....................................................................................... 23

Chapter Three – Bach’s History: From Arnstadt to Leipzig and the
St. John Passion ............................................................................. 26
Bach in Arnstadt .............................................................................................. 28
Bach’s Exposure to Divine Proportion Principles: A Theory ......................... 28
Bach in Mühlhausen and Weimar ................................................................... 32
Bach in Cöthen ................................................................................................ 34
Bach in Leipzig ................................................................................................ 35
A Brief History of Passion Music .................................................................... 37
Seventeenth Century: Stylistic Changes .......................................................... 38
The Oratorio Takes Root in Germany ............................................................. 39
Passion Oratorio vs. Oratorio Passion ............................................................. 40
Passion Music in Leipzig ................................................................................. 42

Chapter Four – Lutheranism: Influence of Theology on the St. John Passion ..... 47
Bach References Luther’s Writings ................................................................. 48
Martin Luther ................................................................................................... 50
Theologia Crusis vs. Theologia Gloriae ......................................................... 52
Phi Proportions in Biblical Verse .................................................................... 55
Standardized Biblical Versification ................................................................. 56
John 19:30 ........................................................................................................ 59
v

Revelation of Phi Proportion: Biblical Verse of the Passion Narrative .......... 62
Rationale for the Insertion of Matthew Texts .................................................. 64
Phi Reveals a Biblical Textual Bridge: Uniting John and Matthew ................ 66

Chapter Five – Analysis of the St. John Passion: A New Paradigm of Phi
Application .................................................................................... 68
Standard Phi Application in the Literature ...................................................... 70
Analytical Construct 1 – Music Rationale ....................................................... 72
Analytical Construct 2 – Biblical Text Rationale ............................................ 75
Analytical Construct 3 – Music and Biblical Text Rationale .......................... 79
Analytical Construct 4 – Extended Biblical Text Rationale ............................ 82
Textual Bridge 2.0 ..................................................................................... 83
Number Symbolism: A Theory ....................................................................... 88

Chapter Six – Conclusion ...................................................................................... 94

Bibliography ........................................................................................................ 100

Appendices
Appendix A – English Translation of the St. John Passion .......................... 102
Appendix B – Contiguous Numbering of Measures in the
St. John Passion ........................................................................... 115
Appendix C – Outline of Tonal Centers and Performing Forces
for Bach’s St. John Passion ......................................................... 118
Appendix D – Identification of Biblical and Non-Biblical Texts
Organized by Movement as Found in Bach’s St. John Passion .. 122

vi

LIST OF TABLES

Table 1: Synopsis of Alfred Dürr’s Research Outlining the Recreation
of the Four Versions of the St. John Passion from
Extant Manuscripts and the Differences between Them ....... 43

Table 2: Textual Bridge: Biblical Texts Set in Movement 12
of the St. John Passion .......................................................... 77

vii

LIST OF FIGURES

Figure 1: Piano Keyboard Octave .............................................................. 12

Figure 2: Leonardo da Vinci’s Head Sketch .............................................. 13

Figure 3: Leonardo da Vinci’s Vitruvian Man Drawing ............................ 13

Figure 4: Seed-Packing Pattern of a Sunflower ......................................... 16

Figure 5: Geometric Shapes with Golden Proportions: Golden
Rectangle, Pentagram, and Golden Triangle ......................... 17

Figure 6: Linear Illustration of Phi Proportion .......................................... 21

Figure 7: Analytical Construct 1 ................................................................ 73

Figure 8: Analytical Construct 2 ................................................................ 79

Figure 9: Analytical Construct 3 ................................................................ 80

Figure 10: Analytical Construct 4 ................................................................ 87

viii

ABBREVIATIONS

BCE Before the Common Era
c. Circa
CE Common Era
FN Fibonacci Number
GS Golden Section
KJV King James Version (of the Bible)
Matt. The Gospel According to St. Matthew (book in the Bible)
phi
inv
Inverse of phi
RSV Revised Standard Version (of the Bible)
ix

ABSTRACT

The St. John Passion (BWV 245) is a monumental work by Johann Sebastian
Bach in the genre of the oratorio Passion. While significant scholarship on this work
exists, including Bach’s use of Divine Proportion or Golden Section principles in his
compositions, this paper expands the research by setting forth original theories on how
Bach structured the St. John Passion. Bach’s interest in numerology, attention to musical
structure, and use of Divine Proportion or Golden Section principles in his compositions
are well documented and accepted by scholars. This multi-movement work is analyzed
within this paper in terms of phi proportion, showing that phi application by Bach was
driven by a theological premise, thereby revealing a formal structure in the St. John
Passion that has been unexplored in the scholarship to date.
In determining why Bach may have utilized an unorthodox application of Golden
Proportion in this specific piece of music, it was hypothesized that a Lutheran theological
precept may have been utilized to create the dimensions explaining the atypical, early
break of the St. John Passion. Bach, a consummate church musician, would have put
much thought into the creation of his Passion music; scrutinizing the biblical text as he
conceptualized his musical setting and giving great care to constructing a work that was
theologically sound and relevant to the tradition of the Leipzig churches he was serving.
This paper explores the theological understandings of a Lutheran Germany in the
eighteenth-century, the history of the Golden Section, and the influence both had on Bach
in his composition of the St. John Passion. Based upon both textual and musical
considerations, four logical points of departure for the calculation of Golden Section are
x

analyzed in order to demonstrate the plausibility of a theology-informed application of
Golden Proportion and that it was such theological thinking that provided the
dimensional scaffolding for the structuring of Bach’s masterwork, the St. John Passion.

1

CHAPTER ONE

Introduction
The St. John Passion (BWV 245) is a monumental work by Johann Sebastian
Bach in the genre of the oratorio Passion. While significant scholarship on this work
exists, this paper expands the research by setting forth original theories on how Bach
structured the St. John Passion. Bach’s interest in numerology, attention to musical
structure, and use of Divine Proportion or Golden Section principles in his compositions,
are well documented and accepted by scholars. This multi-movement work is analyzed
within this paper in terms of Phi proportion, showing that phi
inv
application by Bach was
driven by a theological premise, thereby revealing a formal structure in the St. John
Passion that has been unexplored in the scholarship to date.
1

The genesis of this investigation stemmed from a discussion about the abnormal
length of Part I in relation to Part II of Bach’s St. John Passion. In addressing this
question, the writer first observed that the break between the two parts happened
approximately at the one-third point of the work, immediately bringing to mind the
Golden Section. With this vague approximation, a hypothesis was formulated that the
division may have been conceived with Phi in mind but applied in its inverse expression.
In subsequent review of the literature, no study was found that analyzed the entirety of
the St. John Passion for Phi proportion, though one dissertation analyzed the first

1
The terms Phi (Greater Phi or Φ = 1.618…) and phi (Lesser phi or φ = 0.618…), refer to
different numerical representations of the Golden Proportion, while phi
inv
(φ
inv
= 0.382…) refers to a
specific application of this proportion. Phi is used within this paper to denote a general expression of the
proportion while phi and phi
inv
refer to more specific applications as applied in music. The differences are
explained in Chapter Two and, from that point forward, these terms are used according to their specific
numerical applications.
2

movement to determine if its da capo form contained this proportion. Researchers
applying Golden Section principles to musical constructs have followed a traditional
pattern of analysis; i.e., calculating the proportional dimension on small compositions or
individual movements, generally less than 200 measures in total. Additionally, Phi
calculation was limited to a linear application whereby the work or movement was
considered in its entirety from first measure to last. The hypothesis of this paper is that
Bach may have structured this multi-movement work, the St. John Passion, utilizing a
theological interpretation of the biblical text as a starting point for calculating the Golden
Section. In determining why Bach may have utilized such an unorthodox approach in
applying Phi proportions in this specific piece of music, it was hypothesized that a
Lutheran theological precept may have been utilized with its application resulting in the
atypical division of the Passion narrative and early break between Part I and Part II
observed in the dimensions of the St. John Passion.
The theological hypothesis stems from Martin Luther’s theology of the cross,
which identifies Christ’s death as the beginning of Christian redemption and life.
Because of this hypothesis, the application of Golden Section principles in this paper will
be calculated from the place in the Passion narrative where Jesus’s death occurs.
Because this event happens near the end of the Passion story, Bach is precluded from
calculating Phi in its typical manner. Therefore, this author hypothesizes that Bach
calculated the Golden Section backward from Jesus’s death, employing a unique
application of Phi to his multi-movement work. This concept of an inverse Phi creating a
3

formal structure in a composition is unique in the scholarship to date. Further research in
this area could yield substantive scholarship about Golden Section analysis of music.
After Bach’s death, a large portion of his personal library was catalogued; its
contents listed several volumes of Luther’s writings. Scholarship has revealed that these
volumes were highly prized by Bach.
2
One of the keystones of Martin Luther’s theology
is that redemption (grace) is rooted in Christ’s sacrifice. Because the presentation of a
Passion during Holy Week was one of the most important and solemn services of the
Lutheran Church in Leipzig, Bach, a consummate church musician in his first year of
service there, would have put much thought into the structure and theological soundness
of the St. John Passion. It is logical that Bach would have scrutinized the biblical text as
he conceptualized his musical setting. Therefore, it is prudent to perform an in-depth
analysis of the text and its theological implications in order to understand Bach’s careful
construction of this masterpiece.
In Bach’s personal copy of the Calov Bible Commentary (Vol. 3/V, column 947),
he underlined two crucial elements in the Gospel of John concerning the most significant
moment in the Passion story, John 19:30: “…[Jesus] said, ‘it is finished’ and he bowed
his head and gave up his spirit.” Concerning this text, Luther wrote, “Christ’s suffering is
the fulfillment of Scripture and the accomplishment of the redemption of the human
race.”
3
Established as a central theological point, underlined by Bach in a valued book

2
Robin A. Leaver, ed., J.S. Bach and Scripture: Glosses from the Calov Bible Commentary (St.
Louis: Concordia, 1985), 24.

3
Ibid., 130.
4

from his library, John 19:30 was selected for this study as the textual point of departure
for the phi
inv
application.
An initial investigation found that John 19:30 is the 70
th
verse of John’s Passion
narrative.
4
Because Phi is a mathematical function, the writer utilized the number of
verses, 70, and multiplied this number by the inverse of phi or phi
inv
(0.382…) resulting
in the rounded product, 27, or the 27
th
verse of John’s account of the Passion story:
70 x 0.382 = 26.74
Interestingly, John 18:27 is the final biblical text set by Bach in Part I of the St. John
Passion. This result suggests that the original hypothesis regarding the abnormal division
of Parts I and II is plausible. Such empirical evidence suggests that phi
inv
is a judicious
method of calculating the Golden Section of this multi-movement work and warrants
further investigation.
The central hypothesis of this study is that Bach utilized the Golden Proportion in
a manner that was shaped by theological principles to provide structure to the St. John
Passion and that this dictum affected the manner of Phi application so that the proportion
existed in an inverse, linear procedure. The basis for calculating phi
inv
in this manner is
rooted in Bach’s analysis of the biblical scripture and his understanding of Lutheran
theology acts as the key to decode this unique application of Golden Section. The initial
calculation employed by Bach had to be conceived prior to the compositional process so
that it informed the musical construct. The theological significance of John 19:30, the

4
John 19:30 (RSV). The Passion story in the Gospel according to St. John includes Chapters 18
and 19. Chapter 18 contains 40 verses and the verse where Jesus gives up his spirit occurs in verse 30 of
Chapter 19; i.e., Jesus’s death occurs in the 70
th
verse of the Passion story.
5

70
th
verse of the Passion story where Jesus’s death occurs, compelled Bach to select this
verse as a point of origin for the mathematical, proportional calculation of phi
inv
. More
than this, Bach capitalized upon numerological revelations inherent in the scripture to
develop a framework for the structure of his oratorio Passion.
To understand the process Bach used when applying Phi proportion to his
compositions, this research begins by noting the origin and history of Phi, how it is
calculated, and where it is observed in nature, architecture, and in music. The
significance of the Fibonacci number sequence and its relation to the calculation of the
Golden Section is provided to orient the reader in Phi application to music. Furthermore,
a foundation for Phi mathematical calculation is presented so that the subsequent
exposition of phi
inv
application upon the St. John Passion is more easily understood.

Relevant biographical information of Bach’s life is also highlighted due to its
importance in understanding his role and duties as Cantor in Leipzig, which shaped the
composer’s approach to his work in preparation for its first performance on Good Friday
in 1724 at the St. Nicolas’ Church. Moreover, a brief historical view of Bach’s
knowledge and application of Phi has been traced to create a foundation for interpretation
and analysis of this special proportion in his compositional process. The writer expands
the scholarship of Golden Section analysis by showing that Phi can be applied to a multi-
movement work; in this case, a complex method derived from theological precepts that
dictate an atypical application of Phi. The scholarship is sparse in addressing Divine
Proportion analysis as applied to large-scale, multi-movement musical structures. No
such research is published with regard to Bach’s masterpiece, the St. John Passion. A
6

brief history of the oratorio Passion genre and its typical construction serves as a baseline
for the analysis of Bach’s St. John Passion.
The theological climate of early eighteenth-century Germany, especially
surrounding Martin Luther’s theology, is essential to this research. Understanding the
Lutheran viewpoint, as it was understood and applied by Bach, sheds light on the
composer’s compositional process in the fulfillment of his role as Cantor in Leipzig.
Considering that Bach was firmly rooted in the theology of Martin Luther and possessed
a penchant for embedding theological beliefs into his musical compositions, it is logical
to assume that a great deal of theological forethought went into the construction of the St.
John Passion. The musical execution of a theological principle is the justification for the
atypical division between Part I and Part II. Moreover, this theology became organically
woven into the very fabric of the St. John Passion so that it acted as a foundational
framework for musical construction. Bach’s genius for musical construction is
universally accepted and scholarship exploring embedded number symbolism in his
compositions is profound. This research explores new avenues of analysis in order to
reveal Bach’s theological onus for creating complex, multi-faceted structures when
conceiving the structural scaffolding of his musical compositions.
A brief discussion regarding the transmission of the St. John Passion and its four
versions highlights the reasons for the selection of Version IV for this analysis. By
establishing that this version was true to Bach’s original compositional intention, it paves
the way for an accurate and purposeful application of phi
inv
to the musical structure of
Version IV. Taking into account both textual and musical considerations, four logical
7

points of departure for the calculation of phi
inv
were selected for this analysis. It was
hypothesized that one or more of these analytical constructs would reveal how Bach may
have conceptualized and organized his work. The analysis demonstrates the plausibility
of a theology-informed application of Golden Proportion that is revealed in the structure
of Bach’s masterwork, the St. John Passion.
Bach exhibited tremendous dedication in fulfilling his duties as a church
musician. His proven proclivity for numbers and mastery of musical structure is well
documented. By combining profound theological insight and expert command of
composition, it is shown in this study that Bach demonstrated great skill in composing the
St. John Passion by embedding it with Divine Proportion. While such a compositional
process is hidden from the listener, it fulfills a pious intention inscribed in many of
Bach’s compositions: Soli Deo gloria – Glory to God alone.
8

CHAPTER TWO
The Golden Section:
The History of Phi and its Application in Music

Analysis of music in terms of Golden Section can be a complex task if Phi is
applied atypically and the analyst does not have documentation from the composer about
his process or access to the composer in order to gain insight about the construction of the
work. This chapter will give the reader a foundational working knowledge of Phi
proportion, its history, and its presence in works of nature, art, and music in order that a
later exposition of Golden Section analysis may be applied to Bach’s St. John Passion.
Beauty, symmetry, and balance are desired qualities that are observed and
reflected in nature, art, and science. The human eye is subconsciously drawn to
aesthetically-pleasing characteristics that exhibit inexplicable equilibrium between the
component elements of tension and relief. Such mysterious phenomena can be observed
in objects that are manmade and those that exist in nature, from the arts to the sciences: in
paintings, in leaf and seed arrangements, in the unique lattices of crystal formations, in
the proportions observed in human and animal physical forms as well as in their
microbiology. The human mind is subconsciously stimulated by the innate sense of
beauty and balance present in such elements.
A fundamental mathematical proportion is often present in objects deemed
beautiful or pleasing. While this proportion has been expressed in nature since the
beginning of time, and in the relatively short time span encompassed by human
expression in art and construction, it has only been explained by mathematical theory
developed over the past 400 years. The observed proportional construct was found to be
9

an irrational number, like , derived from a series of calculations based upon a special
sequence of numbers. This special proportion is now identified by the term Phi and the
observance of its special qualities in numerical terms, as expressed in nature and art, can
now be averaged to reveal the numerical quantitative equivalent of 1.618….
Phi proportion remains a most extraordinary phenomenon observed by mankind
and reproduced in his art, architecture, and music; applied first through intuitive
processes then by methodological application. Contemplating why the human brain has a
preference to this natural proportion is not the purpose of this chapter, but it serves to
remind the reader that the calculation of Phi in any art or science can only be done if this
proportion is desired, understood, and applied purposefully by the artist. Therefore, this
chapter will give a broad overview of this special proportion.
History of Phi
The earliest evidence of mathematical awareness of this special proportion dates
from the sixth century BCE. It was at this time that Pythagoras, a Greek philosopher,
traveled to Egypt and Babylonia to study with the local priests in order to learn their
mathematical mysteries. After 20 or more years of study, he returned to Italy and
established a school of philosophy based on numerology. While Pythagoras left no
writings about this special proportion, Plato described the Pythagorean philosophy in
several of his own books. A definition from Plato’s writings, however, is difficult to
discern because the mathematical revelations were vague; it is believed that he probably
intended to obscure the details in order to preserve the secrets of his brotherhood.
According to Charles Madden in Fib and Phi in Music: The Golden Proportion in
€
2
10

Musical Form, Herz-Fischler surmised that the mathematics to calculate and reproduce
the proportion were developed by many contributors over several centuries and “did not
reach their final form until the time of Euclid, some 300 years after Pythagoras.”
1

This special proportional construct is identified in the literature by many names
including Divine Proportion, Golden Section, Golden Proportion, Golden Ratio, and Phi.
Ancient and modern philosophers and mathematicians have explored the unique
properties of this special proportion. Plato (427-347 BCE) proposed a geometric puzzle
to entice the reader to discover the ratio by making a cut in a line so that “the [ratio of
the] whole to the longer equals [the ratio of] the longer to the shorter.”
2
Plato utilizes the
line because he realized that the answer in mathematical terms was an irrational number
that could not be expressed as a simple fraction.
3
The first clear definition of the
proportional relationship of Plato’s line is found in the writings of Euclid (c. 325-265
BCE) where the division of a line is explained in terms of the “cut [creating segments that
reside] in extreme and mean ratio.”
4

Interestingly, the earliest evidence of man’s use of this proportion predates the
first treatises that discuss it. The study of the architecture of two pyramids on the Giza
plateau in Egypt (c. 2500 BCE) has revealed that Golden Proportion was present in their
design and execution. Scholars doubt that mathematical knowledge of the era could

1
Charles Madden, Fib and Phi in Music: The Golden Proportion in Musical Form (Salt Lake
City: High Art Press, 2005), 5.

2
Scott Olsen, The Golden Section: Nature’s Greatest Secret (New York: Walker, 2006), 6.

3
Ibid.

4
Ibid., 2.
11

explain the construction of the pyramids in terms of purposeful employment of the
proportion; nevertheless, the measuring techniques employed by the builders resulted in a
design that embodies the correct ratio. Mark Lehner showed in his research that certain
aspects of these pyramids express Golden Proportion within a 0.06% margin of error.
5

The Parthenon, by Phidias (490-430 BCE), is thought by many to have been constructed
utilizing the Golden Ratio as well. The subsequent designation of this special
proportional ratio as Phi can be traced to the twentieth century American mathematician,
Mark Barr, who employed the Greek letter, Phi - (Φ) or (φ), derived from the first letter
of Phidias’ name, to represent the ratio in his equations. It should be noted that
controversy exists among researchers as to whether the Parthenon actually displays Phi
proportions; time and weather have obscured some of the structural detail necessary for
definitively proving the inclusion of the proportion as a basis for its design.
Fibonacci and his Rabbits
In his book Liber abaci (1202 CE), Leonardo Pisano Bogollo (c. 1170 – c. 1250)
later known as Fibonacci, proposed a mathematical puzzle that provided a key for later
mathematicians to understand the Golden Proportion. Fibonacci’s teachings gained great
attention in Europe because he introduced the Arabic numbering system to the continent.
Using the reproductive process of a pair of rabbits, Fibonacci developed a model whereby
a series of numbers was revealed based upon how quickly a pair of rabbits could multiply

5
Mark Lehner, The Complete Pyramids: Solving the Ancient Mysteries (London: Thames and
Hudson, 1997), 17.

12

given specific parameters.
6
Beginning with a single pair, each successive generation
could be calculated by adding the total number of progeny pairs to the previously existing
pairs. The model resulted in a series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21… with the
property of the series being expressed in such a way that the successive number in the
series was determined by adding the two numbers immediately preceding. For example:
0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, etc.
Numbers from the Fibonacci sequence are rooted in the very fabric of musical
language. For example, diatonic Western music is based upon an 8-note scale (including
the octave) comprised of 13 chromatic notes. The major scale contains 5 whole- steps
and 2 half steps. Numbers of the Fibonacci sequence are also expressed in the very
construction of the piano keyboard as observed in the following figure.
5 black notes
2 black notes 3 black notes

8 white notes
13 chromatic notes span a complete octave
Figure 1: Piano Keyboard Octave

Fibonacci numbers also appear in the modern scale and in pure harmonic intervals like
the octave (2:1), the fifth (3:2), major sixths (5:3) and minor sixths (8:5).

6
The parameters were: Each mature pair produces two offspring, one male, and one female in a
two-month cycle. Maturity of the new pairs occurs when they are two months old. The two-month
reproductive cycle included fertilization and gestation in the first month and offspring rearing during the
second month.
13

The earliest known treatise devoted to this special proportion is credited to Luca
Pacioli (1445-1517 CE) in his Divina Proportione. It was in this three-volume work,
illustrated by Leonardo Da Vinci (1452-1519 CE), that Pacioli discussed sectio aurea, or
what we now term the Golden Section.
7
Da Vinci’s sketches utilized the precise
proportional methods to demonstrate Pacioli’s theories and this collaboration can be
credited with expanding interest in the usage of Golden Section proportions in art.
8

According to Madden, in Fib and Phi in Music, Pacioli’s treatise was widely discussed
among contemporary artists of all kinds though it was “probably plagiarized from Piero
della Francesca.”
9
Nonetheless, Pacioli’s enthusiasm for the subject greatly influenced
the arts community with Leonardo da Vinci sketches factoring prominently in
demonstrations of Pacioli’s De Divina Proportione, such as seen in Figure 2.

Figure 2:
Leonardo da Vinci’s Head Sketch
10

Figure 3:
Leonardo da Vinci’s Vitruvian Man
11

7
Olsen, Golden Section, 2. According to Olsen, the first published use of this phrase, sectio
aurea, occurs in Martin Ohm’s 1835 Pure Elementary Mathematics.

8
Herbert Edwin Huntley, The Divine Proportion: A Study in Mathematical Beauty (New York:
Dover, 1970), 25.

9
Madden, Fib and Phi, 10.

10
Luca Pacioli, De Divina Proportione, (Milan: c. 1497), University of Oklahoma Online
Galleries, accessed October 9, 2012, http://hos.ou.edu/galleries/15thCentury/Pacioli/1509
/Pacioli-1509-pl-1-face-image/. Image courtesy History of Science Collections, University of Oklahoma
Libraries, reproduced by permission.
14

The Vitruvian Man in Figure 3, also drawn by Leonardo da Vinci, is another well-known
illustration of Divine Proportion.
The Fibonacci series was studied, in a limited set, in the seventeenth and
eighteenth centuries by Johannes Kepler (1571-1630 CE) and Robert Simson (1687-1768
CE), respectively, who wanted to express mathematically how the series related to the
Golden Proportion. Their investigations determined that, if the quotients calculated from
adjacent numbers in the Fibonacci’s series were averaged, the result provided a number
that was representative of Golden Proportion with some degree of accuracy, though the
number was irrational. In other words, by dividing any number of the sequential series
by the preceding number in the series, an average value can be interpolated. For
example, given this limited set of the Fibonacci sequence, (2, 3, 5, 8, 13, 21, 34, 55, 89),
the calculation can thus be expressed:
89÷55 = 1.6181…
55÷34 = 1.6176…
34÷21 = 1.6190…
21÷13 = 1.6153…
13÷8 = 1.6250
8÷5 = 1.6000
5÷3 = 1.6666…
3÷2 = 1.5000

The average of the quotients above is 1.6077….
12
Assisted today by computers, modern
mathematicians can calculate this average upon an enormous sampling of adjacent

11
“Vitruvian Man: The Proportions of the Human Figure,” accessed October 9, 2012,
http://www.davincilife.com/vitruvianman.html.

12
The numbers 0 and 1 are not included in this small sampling because they contain unique
mathematical properties that falsely skew the resultant average (i.e., The Zero Property of Multiplication
and the Multiplicative Identity). Steve Conrad and Dan Flegler, “Whole Numbers and Their Basic
Properties,” Math League, accessed September 26, 2012, www.mathleague.com/index.php?option=com
15

Fibonacci numbers resulting in a mean value of the Golden Section, a value expressed by
the number 1.6180339887….
Phi in Nature, Art and Music
One of the original scientists to discover how the Fibonacci sequence related to
the Divine Proportion was Johannes Kepler (1571-1630). Kepler, in his monograph of
1611 entitled “Strena seu de Nive Sexangula,” discovered the Fibonacci sequence
apparently without knowledge of Fibonacci’s research. Attempting to explain the
recurrence of proportions in self-replicating natural phenomena, Kepler realized that the
ratios present between the adjacent number of the series were similar and, if averaged,
would approach the irrational number representing the Divine Proportion. Kepler later
used this sequence and its unique properties to develop a theory of the harmonies and
motions of the planets based upon the Divine Proportion. These theories were rooted in
Kepler’s desire to show the hand of God in creation and to reconcile his theological
beliefs with his scientific knowledge.
After putting forth his explanation of the motion and distances of planets from the
sun, Kepler later applied the same principles to a musical model in order to validate a
system of just-intonation in regards to musical consonance and dissonance. Kepler’s
mathematical proofs regarding music were assimilated by Andreas Werckmeister whose
writings espoused the use of Divine Proportion in music composition. According to
Tushaar Power, Werckmeister’s theories on the use of Divine Proportion in music were
foundational reading for Johann Gottfried Walther and, by extension, Johann Sebastian

_content&view=article&id=67:wholenumbers&catid=31:general.
16

Bach as they contemplated the use and implementation of the Divine Proportion in
musical composition.
13
Kepler’s scientific explorations, while religiously motivated,
resulted in both his excommunication from the Lutheran church, and in his mother being
placed on trial for heresy.
Charles Bonnet, in 1754, coined the term phyllotaxis to describe the presence of
proportional phenomena observed in the plant world (from the Greek phullon “leaf” and
taxis “arrangement”) and, in 1837, the Bravais brothers discovered the crystal lattice and
the ideal divergence angle of phyllotaxis to be 137.5º, which is equal to 360º divided by
Φ
2
. Only this precise angle proves to be ideal to allow the perfect packing of seeds in a
sunflower plant.
14

Figure 4: Seed-Packing Pattern of a Sunflower
15

The Divine Proportion is also present in several, special, geometric shapes such as the
golden rectangle, the pentagram, and the golden triangle.

13
Tushaar Power, “J. S. Bach and the Divine Proportion” (PhD diss., Duke University, 2001),
ProQuest (Document ID # 908115250), 25.

14
Olsen, Golden Section, 12.
15
William Emeny, “The Fibonacci Sequence in Nature,” October 7, 2010, accessed September 30,
2012, http://www.greatmathsteachingideas.com/tag/golden-ratio/. Article gives photo credit of sunflower
image to “lucapost via Flickr.”

17

Figure 5: Geometric Shapes with Golden Proportions:
Golden Rectangle (top), Pentagram (left two), and Golden Triangle (right two)
16

In The Golden Section: Nature’s Greatest Secret, Scott Olsen describes the construction
of a golden rectangle:
Starting with a square, an arc centered on the midpoint of its base swung down
from its upper corner easily produces a large golden rectangle. Importantly, the
small rectangle which we have added to the square is also a golden rectangle.
Continuing with this technique creates a pair of these smaller rectangles.
Conversely, removing a square from a golden rectangle leaves a smaller golden
rectangle, and this process can be continued indefinitely to produce a golden
spiral.
17

The dimensions of the golden rectangle can be observed in the written record
dating back to circa 1445 BCE in the Bible. The construction of the Ark of the Covenant,
which carried the remnants of the Ten Commandments, is described in the book of
Exodus, chapter 25, verses 8-11: “God commanded Moses to have the Israelites build

16
Mark Freitag, “Phi: That Golden Number,” accessed September 26, 2012, http://jwilson.coe.uga
.edu/emt669/student.folders/frietag.mark/homepage/goldenratio/goldenratio.html.
17
Olsen, Golden Section, 8.
18

Him a sanctuary so that He might dwell among them, and specified its dimensions to be
2.5 cubits long by 1.5 cubits wide by 1.5 cubits high.” These measurements reveal a
rectangle in Phi proportion. Considering the scriptures say that God commanded the
vessel to be overlaid with gold, inside and out, the Ark could be literally viewed as a
golden rectangle. One can understand why this proportion became known as the Divine
Proportion since God specified its dimensions.
As stated earlier, this special proportion exists in nature and has been utilized by
humans in architecture, art, and music. Human brains are hardwired to observe and seek
out order, and in observing this natural proportion, human brains are able to process this
construction and thus find a sense of order. This perceived order is often translated as
pleasing, and, naturally, as creative processes are undertaken in art or music, this
proportion is translated through the medium to the observer. With awareness of the
mathematical properties of the Golden Section, one can easily calculate which objects of
art or nature exhibit this proportion. When artists in their respective mediums apply
accurate Golden Section proportions, the resulting painting, musical composition, or
architecture demonstrates intentional planning and purposeful use of Phi into the creative
process.
In art and architecture, fixed measuring units exist that make determining the
existence of Phi proportion in an intact object conclusive. However, application to a
music composition varies because the analyst has choices in the selection of the unit of
measurement. When identifying whether a composer has applied Phi proportion in the
construction of his composition, the selected unit of measurement applied must be
19

carefully discerned before calculation of the Golden Section can be considered accurate
and intentionally used by the composer. Music is an art that has complex components
that defy measurement by simple tools such as a ruler or a stopwatch. For example, the
simple question of the length of a composition can be measured in multiple ways. In
terms of time, music is comprised of a series of rhythmic, melodic, or harmonic events
that unfold in a way that is unique to each performance due to such variables as artistic
interpretation or acoustical setting. Some composers have utilized time as a unit to
identify where the Golden Section lies, but the accuracy in each performance can be
skewed due to human error in executing tempo and because of interpretative tendencies.
A more reliable measurement unit for the calculation of the Golden Section can be
derived from musical components of a composition. Utilizing the number of measures or
notes provides a more concrete unit of measurement that is less subject to error because
of human interpretation. However, some factors continue to make definitive
mathematical measurement difficult. How is the accuracy of calculation influenced when
a composition is more complex? Music is infinitely variable and may contain multiple
movements, time signatures, or tempo changes. Given such variety in compositional
structure, the application of a mathematical function, such as the Golden Section, to
music is difficult. Analysts must exercise good judgment by carefully selecting the unit
of measurement that is the most precise analytical tool for each musical piece. With such
critical discernment, it may be possible to determine meaningful application of the
Golden Section in a composition.
20

Research has shown that two typical units are most often utilized in Golden
Section analysis of music. The first unit utilized in obtaining the raw data for discerning
Phi application is the number of notes; most often used for smaller compositions with
equal note values, such as in Gregorian Chant melodies. The second unit of measurement
for discerning Phi application upon a music piece is the total number of measures. This
unit generates the raw data for analysis and is reserved for larger, more complex
compositions.
In many masterful works of art, Phi proportions are observable and contribute to
an innate harmony and balance that is universally perceived as beautiful. In music, Phi
proportion may not be observable except through detailed analysis; it may or may not be
consciously perceived by, or have an effect upon, the listener. Despite the ambiguity of
Phi’s effect upon a composition, whether it influences a listener’s experience of the work,
composers have purposefully incorporated Phi proportion into their masterpieces. Some
might argue that Phi creates a sense of order for the listener, which may include
observable events such as changes in dynamics, a change or return to a theme, the highest
note in a piece, or a textual component. Such observable events can only be determined
to occur at Phi points through in-depth musical analysis in order to verify if the
composer’s intention to include the Golden Proportion results in an aesthetically-pleasing
composition.
Greater Phi Φ /faɪ/ and Lesser phi φ /fi/
Because proportion in music aims toward balance, one can argue that the presence
of Phi provides structural order to a composition. When analyzing for Golden Section
21

there are two typical applications, Greater Φ and Lesser φ, for which one can solve. In
linear terms, the first application (Greater Φ) assumes a fixed length (a) will act as the
Golden Section point of a longer line; the observer wants to add a length (b) so that Phi
proportion is expressed between (a) and (b) resulting in a line (c) that is longer than the
original line and where (c) exists in Phi proportion to both (a) and (b).
The second application, Lesser φ, assumes a given length (c) will be divided into
two segments, (a) and (b) respectively, that exist in Golden Proportion to each other and
to the original length (c). When someone executes Phi proportion upon the dimensions
of a product, they could apply either application described above depending upon their
working process. These applications are illustrated in the following figure.

Figure 6: Linear Illustration of Phi Proportion
18

An example of the Greater Φ application, where the length is extended, is when a
composer writes 20 measures of music (an A section), and wishes to compose a
contrasting musical section (B section), so that Phi proportion is expressed. To
accomplish this, the composer would perform the following calculation: (20 x 1.618 =
32.36). The product, 32.36, is rounded to 32 measures and represents the total length of
the composition. To find the length of the B section, the composer subtracts the number
of measures in the A section (20 measures) from the total number of measures in the

18
Adapted from Seth T. Miller, “A Little Presentation on the Golden Mean/Phi – for Fun!!!”
(January 4, 2010), accessed September 15, 2012, www.spiritalchemy.com/730/golden-mean-presentation/.
22

work (32 measures), resulting in a B section of 12 measures in length (32 – 20 = 12).
This calculation allows the composer to create a composition expressing Phi proportion.
An example of the Lesser φ application exists when the composer desires to write
a composition whose total length was 32 measures and wishes it to have two contrasting
sections, A and B respectively, that exist in Golden Proportion. The calculation is
modified to solve for the A section dimension [32 x φ (or 0.618) = 19.78]. The product is
rounded to 20 (representing the A section) resulting in a B section that is 12 measures in
length.
The reader may observe that two different numbers representing the Phi
proportion were utilized in the calculations above, 1.618 and 0.618. According to Olsen
Phi contains very unique properties:
Plato realized the answer [to cutting a line in this Phi proportion] is an
irrational number that can be geometrically derived in a line, but cannot be
expressed as a simple fraction. Solving this problem mathematically, and
assuming the mean (longer segment) is 1, we find the greater golden value
of 1.6180339…(for the whole), and the lesser golden value
0.6180339…(for the shorter). We term these Φ “fye” the Greater and φ
“fee” the Lesser respectively. Notice that both their product and their
difference is Unity. Furthermore, the square of the Greater is 2.6180339,
or Φ + 1. Notice also that each is the other’s reciprocal, so that φ is 1/Φ.
19

Because Φ and φ are so unique they are used interchangeably depending upon the
direction of the equation desired. The Greater symbol, Φ = 1.618, is reserved for
obtaining a larger expression of the proportion and the Lesser symbol, φ = 0.618, is
reserved for obtaining a smaller expression of the proportion.

19
Olsen, Golden Section, 6.
23

The application of Phi in this paper utilizes another expression, phi
inv
(or
φ
inv
) to describe the complementary expression of the proportion which is, in effect, no
different than Phi or phi, except that in a linear system it denotes that the start point for
its calculation is toward the end (or the right-hand side) of a given line. The
mathematical proof for this expression can be represented by the following calculation
where N represents the total length of a line:
N x (1 – 0.618) or N x 0.382 = φ
inv
or phi
inv

The equation above represents an inverse linear function.
20

phi Applied to Music
An example of phi application upon a musical example can be seen in the first
movement of the St. John Passion, a 153-measure movement in da capo form. To
calculate whether it displays phi proportion, the analyst applies the following equation:
153 x 0.618 = 94.55. When this product is rounded to the nearest whole number, the
result is 95. Measure 95 is a partial measure consisting of a single quarter note with a
fermata. This measure is observed to be an important structural point in the movement; it
is the concluding cadence of the B section that marks the return to the original A section
at the opening measure of the movement. In other words, the Golden Section is
recognizable by the listener because the next event is a return of familiar musical
material.

20
Other nomenclature exists for this representation of the proportion as exposed in Madden’s Fib
and Phi and revealed in the spiral application of Phi. In a spiral application, whereby Phi is calculated
multiple times upon the same sample, Madden shows that each subsequent calculation of Phi, is, in fact, an
exponential resulting in the nomenclature GS, GS
2
, GS
3
, and so on. This paper chooses to utilize phi
inv
to
bring to the reader’s mind that the calculation is, in effect from right to left rather than the normal left to
right application in a linear system, i.e., expressed in its inverse.
24

Since the discovery of the Golden Section, many composers have intentionally
utilized this proportion in their compositions. Madden’s book, Fib and Phi in Music,
compiles the published research on Golden Section analysis and recalculates the Golden
Section applying a stricter, more standardized criterion in order to carefully determine if
the composers and pieces researched accurately display Golden Section proportion. He
concludes that studied chants from the Liber Usualis show a mild tendency toward
Golden Proportion and he surmises that there may be an innate, rather than purposeful,
urge toward Golden Section in the construction of the melodies.
According to Madden, Golden Section proportion is seen in the Medieval era in
several compositions by Guillaume de Machaut, especially in his virelais and rondeaux,
and in the “Kyrie” of his Messe de Nostre Dame. John Dunstable and Guillaume Dufay
are among the Renaissance composers utilizing Fibonacci numbers and Golden Section in
the construction of several compositions. As described previously, Bach utilized φ
proportion in the first movement of the St. John Passion. Other Baroque composers
shown to have utilized the Golden Section in their compositions are Monteverdi and
Vivaldi. Phi proportions are found throughout the Romantic era in movements of
Mendelsohn symphonies, and in the piano music of Chopin, Brahms, and Schubert.
21

Bartok utilized Golden Section in 26.1% of the 23 pieces analyzed by Madden, Debussy
in 35.7% of 13 pieces, Satie in 54.5% of 11 pieces.
22
Webern, Stravinsky, Sibelius,

21
Madden, Fib and Phi, 247.

22
Ibid., 329.
25

Schoenberg, Prokofieff, Hindemith, and Dallapiccola have all been represented in Golden
Section research as having used the proportion in some of their compositions.
23

According to Madden’s research, Bach utilizes “Phi in at least 14.6 % of the
pieces in The Well-Tempered Clavier, 40% of the fugues in The Art of the Fugue (70% if
an error of one measure is allowed), and to a lesser extent in the Inventions.”
24
It is clear
then that Bach knew of and utilized the Golden Section often in his compositional
process.
The next chapter will explore Bach’s history and show his awareness of Golden
Proportion principles as he gathered knowledge from the writings of Kepler and
Werckmeister and applied that knowledge to his own compositional process.

23
Ibid.
24
Ibid., 147.
26

CHAPTER THREE
Bach’s History:
From Arnstadt to Leipzig and the St. John Passion

This chapter provides relevant biographical information leading up to Bach’s
appointment in Leipzig in 1723 and the first performance of the St. John Passion on
Good Friday in 1724 at St. Nicolas’ Church and concludes this foundational material with
a brief history of Passion music, associated genres, and their typical construction to serve
as a baseline for the analysis of Bach’s St. John Passion.
Johann Sebastian Bach was born March 21, 1685 to Johann Ambrosius and Maria
Elisabeth Bach. Official church documents record his baptism on March 23, 1685 at St.
George’s, the main church in the city of Eisenach, Germany. Descended from a long line
of excellent musicians, it was expected that Sebastian would also study music and
eventually choose it as his vocation. A fine violinist, Ambrosius was director of the
Eisenach town music company and his cousin, Johann Christoph Bach I served as
organist at St. George’s. It is likely that Sebastian’s training in both violin and organ
began at a very early age.
After attending a local German school from age five to seven, Sebastian then
entered St. George’s Latin School. An advanced grasp of written German and Latin, as
well as subjects covered in the sexta (sixth class), warranted Sebastian’s initial placement
in the school’s quinta (fifth class). Here, he held a higher ranking than his brother who
was three years his senior. After the death of his father in 1695, Sebastian went to live
with his eldest brother, Johann Christoph Bach III in the city of Ohrdruf, Germany.
Academic study continued at Ohrdruf’s Lyceum Illustre Gleichense where Sebastian was
27

permitted into the tertia (third class). Extraordinary academic achievement and
placement at or near the top of his classes, earned Sebastian a promotion to the prima
(first class) by the age of fourteen, a full four years younger than the average age of his
classmates. Sebastian’s tuition was paid from the financial support provided by the
wealthy of the city for those less fortunate. In 1700, this funding was lost and, as a result,
he and a friend decided to travel to Lüneburg, Germany to complete their schooling at St.
Michael’s where Sebastian was offered the post of choral scholar. Due to his
extraordinary musical gifts, it would have been easy for Sebastian to obtain an
apprenticeship with a well-established mentor and thus begin his musical career,
following the path that his brothers pursued; however, Sebastian was determined to
complete his schooling and hoped to continue on to university.
Sebastian’s first professional position was not as an organist but as a court
musician in Weimar, Germany, where “the ducal treasury registry lists him as ‘Lackey
Baach,’ indicating that he was hired as a minor court servant.”
1
During his employ in the
court of Weimar, Sebastian was engaged by the city of Arnstadt to examine the city’s
organ for the purpose of inspecting and approving the renovations of this instrument at
the New Church. The skills he obtained during this assignment established him as an
expert in the evaluation of organ construction, a title generally reserved for more
experienced, famous, and well-established organists. Subsequent to his evaluation of the
instrument, Sebastian was invited to perform at the dedication recital of the organ in June
of 1703. This performance may have been a disguised audition for a position as organist.

1
Christoph Wolff, Johann Sebastian Bach: The Learned Musician (New York: W.W. Norton,
2001), 68.
28

Bach in Arnstadt
Subsequently, Sebastian resigned from the Weimar court and accepted a generous
offer from the town council of Arnstadt for the organist position at New Church.
2
Duties
of this new position were relatively light, providing Sebastian, for the first time,
unfettered access to a fine instrument with which to experiment and hone his craft. The
instrument utilized Andreas Werckmeister’s new “well-tempered” tuning system for
which Bach’s famous collection of preludes and fugues was later to be named. “The
advanced temperament in which Bach’s organ was tuned allowed him to chart a daring
harmonic course and to explore advanced chord progressions for which there were no
precedents whatsoever.”
3

In Arnstadt, Sebastian was also expected to act as choirmaster, but his impatience
with the mediocre talent and impetuousness of the choirboys, many of whom were older
than Sebastian, caused him to eventually refuse this duty because it was not in his
contract. He continued to have difficulties with the church’s council and was
reprimanded in the summer of 1705 for a street fight he instigated with a bassoonist.
That October, Bach requested leave for four weeks in order to travel to Lübeck, Germany
to attend a famous concert series organized by Dietrich Buxtehude (1637-1707).
Bach’s Exposure to Divine Proportion Principles:
A Theory
According to Tushaar Power’s dissertation, “J. S. Bach and the Divine
Proportion,” Bach’s initial exposure to the theories and principles of Golden Section

2
Karl Geiringer, Johann Sebastian Bach: The Culmination of an Era (New York: Oxford
University Press, 1966), 73.

3
Ibid., 101.
29

application most likely occurred between 1705 and 1707. Because no surviving letters or
treatises in Bach’s own handwriting exist to provide insight into what he knew about
Golden Section and when he knew it, Power concentrates on two main areas of research
to establish a timeline. The first area, primary sources, includes Bach’s manuscripts,
while the second area explores the writings and libraries of those in Bach’s small circle.
Power’s dissertation categorizes evidence as internal and external whereby internal
evidence “consists of the proportions themselves as found in Bach’s music” and external
evidence “consists of material drawn from the literature of which Bach may have been
aware, and from the writings of his contemporaries and students, and members of his
circle.”
4
The internal evidence was gained through an analysis of a compendium of da
capo movements in Bach’s choral compositions present in the Neue Bach-Ausgabe in
order to identify which of them expressed Golden Section proportion. Power adopted a
margin of error of ± 3.1% for Golden Section proportion. His results show that the
earliest surviving choral movement written in da capo form displaying Golden Section
proportion was composed c.1713; a cantata written for the name day of Duke Christian of
Saxe-Weissenfels, BWV 208 Was mir behagt, ist nur die muntre Jagd. Power observes
that the da capo aria is comprised of consecutive sections that have measure lengths
utilizing the sequence of the Fibonacci numbers 13, 21, 34, and 55.
5
In this case, the

4
Power, “Bach and Divine Proportion,” 18.

5
Da capo form is comprised of two written out sections, A and B respectively, followed by a
repeat of the A section whereby the conclusion of the movement is indicated by a fermata or fine marking.
In this da capo aria, the B section is 13 measures, the A section is 21 measures, the combined total of the A
and B sections is 34 measures, and the full length of the work is 55 measures (A + B + A). Hence, the Phi
approximations expressed by this Fibonacci sequence are: 55÷34=1.618, 34÷21=1.619, and 21÷13=1.615.

30

proportion is exact in its reproduction of the Fibonacci sequence and its inherent
approximation of Phi expressed in spiral form. In the body of his dissertation, Power
briefly analyzes two multi-movement applications in terms of Golden Section. The bulk
of the literature exploring Golden Section proportions in Bach’s compositions analyzes
single movements or small works. Power’s multi-movement application of Golden
Section is of particular probative value to the thesis of this paper.
Power mainly relies on external evidence to arrive at his theory that Bach was
exposed to the Golden Section principles of music construction between 1705 and 1707.
According to Power, the close relationship between Bach and his cousin, Johann
Gottfried Walther, is the likely source of exchange of knowledge regarding Golden
Section principles. Walther’s library contained the collected works of Andreas
Werckmeister, a significant champion of the Natural Order or Divine Proportion.
Walther even traveled to study for several months under Werckmeister, returning in the
spring of 1705. It is assumed, because of his close relationship with Bach, that Walther
shared the music and knowledge he attained during this trip with Sebastian. Walther
returned with a large sampling of compositions by the renowned Dietrich Buxtehude, a
respected musician with deep connections to Werckmeister who “contributed two
laudatory acrostics to Werckmeister’s Harmonologia Music in 1702.”
6
Barely five
months after Walther’s return from studying with Werckmeister, in October of 1705,
Bach made his famous journey to Lübeck to see Buxtehude’s concert series. The young

6
Power, “Bach and Divine Proportion,” 23.
31

Sebastian was so enthralled that he did not return to Arnstadt until mid-January of 1706;
his 4-week sojourn evolved into an unauthorized 4-month sabbatical.
The lack of internal evidence coinciding with Bach’s exposure in Power’s study is
primarily due to the limited scope of the analysis. Power limited his analysis to choral
compositions in da capo form and BWV 208 was the first choral work wherein Bach
utilized this modern type of aria. Furthermore, Bach’s compositional output in the choral
genre is limited between 1705 and 1713 as the bulk of his choral writing lies later in his
career during his tenure in Leipzig. While Power primarily focused on choral works in
da capo form in his dissertation, Madden’s survey of the research on Golden Section, in
Fib and Phi in Music, contains non-vocal works, such as the Passacaglia for Organ,
BWV 582 (c. 1706-13), in which Madden showed that Bach applied very accurate
Golden Section proportion. Other early Bach compositions may exist that display Golden
Proportion, but the bulk of Bach’s compositions remain unanalyzed for Golden Section
proportion in its typical application, especially in the more abstract applications as
explored in this paper, both in terms of the theological onus for application and analysis
across a multi-movement composition. Future research may confirm the presence of
Golden Section proportion in early Bach compositions that more closely coincide with
the period between 1705 and 1707; the time period that Power suggests was Bach’s initial
exposure to Golden Section principles.
During his service in Arnstadt, Sebastian’s known compositional output for choir
was relatively small and few autographs survive from this era. Partly, this was due to his
refusal to work with what he thought was a substandard choir resulting in more
32

compositions written for the organ or keyboard. Evidence suggests that he composed a
few cantatas near the end of his Arnstadt period, including BWV 150 - Nach dir, Herr,
verlanget mich and BWV 106 – Gottes Zeit ist die allerbeste Zeit. These cantatas may
have been intended for audition elsewhere, performance in nearby courts, or for the
occasional performance in the New Church for services, concerts, weddings, or funerals
when Sebastian could bring in outside forces.
7

Bach in Mühlhausen and Weimar
Constant frustration with the quality of his musicians and the officials in Arnstadt
caused Sebastian to look for a new, more lucrative position, which he secured late in
1707 in the city of Mühlhausen, Germany, at St. Blasius. The Mühlhausen church
program had a prestigious history of great organists and music, though in Sebastian’s
mind it was somewhat antiquated. He set out to reform the music to coincide with and
reflect the new trends being employed throughout Germany. According to his obituary,
“he undertook a journey to Weymar [sic], had the opportunity to be heard by the reigning
Duke, and was offered the post of Chamber and Court Organist in Weymar, of which
post he immediately took possession.”
8
The position as organist in the ducal court of
Wilhelm Ernst in Weimar, which he accepted in 1708, offered almost twice the salary of
St. Blasius’. Sebastian found the opportunity to work with a large and varied array of
professional musicians very attractive. Weimar was well suited to provide the creative
compositional opportunity for religious music for which Sebastian was longing. During

7
Wolff, Bach: Learned Musician, 100.

8
Hans T. David, Arthur Mendel, and Christoph Wolff, eds., The New Bach Reader: A Life of
Johann Sebastian Bach in Letter and Documents (New York: W.W. Norton, 1998), 300.

33

his service in Weimar, Sebastian deepened his relationship with his cousin, Johann
Gottfried Walther, who served as the town organist. “Their common interest in Italian
music formed a strong bond, and there was a friendly competition between them in the
arrangement of Italian concertos for keyboard instruments. According to Walther, Bach
presented him with no less than 200 compositions, partly his own and partly Böhm’s and
Buxtehude’s.”
9

Bach enjoyed great successes in his musical accomplishments and experienced
advancement in his career at Weimar. He cultivated positive relationships with Walther
and with the reigning duke’s nephew, Prince Ernst August who studied clavier with
Sebastian. However, “Ernst August was not what one would call a lovable character;
contemporary reports make him appear a highly eccentric man, whose actions sometimes
bordered on insanity.”
10
Bach’s close relationship with and loyalty to Ernst August
ultimately led to conflict in his relationship with Wilhelm Ernst, the reigning sovereign.
Wilhelm Ernst had a tenuous and strained relationship with Ernst August. At one point,
he forbade the court servants to enter his nephew’s castle and threatened them with a 10
thaler fine and imprisonment. “Bach’s sense of justice and his independent spirit made
him pay no heed to so unreasonable an order. Indeed, on Duke Ernst August’s birthday
he performed a cantata with musicians from the nearby court of Weissenfels, and handed
the Duke a birthday poem bound in green taffeta, for which he was handsomely
rewarded. Naturally the elder Duke’s ire was roused and he soon found a way to punish

9
Geiringer, Bach: Culmination of an Era, 36.

10
Ibid., 38.
34

his concertmaster.”
11
In 1716, when the Kapellmeister died, Wilhelm Ernst appointed
another of his court musicians to the post, which disappointed and humiliated Sebastian.
Sebastian responded by discontinuing composing cantatas and beginning to seek alternate
employment.
Bach in Cöthen
In 1717, Sebastian took charge of an excellent group of seventeen musicians in
the Cöthen court. “A great part of Bach’s output in these years is lost; but what has been
preserved – compositions like the six Brandenburg Concertos – reflect [sic] the
exuberance of an artist discovering new means of expression, and the peace of mind of
the composer who had found real understanding and appreciation in his new patron.”
12

In Cöthen, Sebastian avoided taking sides in the religious debates between the
Calvinists and the Lutherans. The majority of the people were followers of Calvin;
indeed, Sebastian’s patron, though more liberal, was a Calvinist. Sebastian enrolled his
children in the Lutheran school and took membership in the local Lutheran church, but
maintained a reserved outward expression of his beliefs.
Sebastian experienced the loss of his beloved wife, Barbara, in 1720, which drove
him to find consolation through rededicating himself to his composition. “Such creative
activities helped to heal the wound inflicted by Barbara’s death…remarrying after a very
short lapse of time was the custom in his family, and it proves Bach’s deep attachment to
Barbara that he waited from June 1720 to December 1721 before marrying” a talented

11
Ibid., 39.

12
Ibid., 44.
35

young soprano, Anna Magdalena, in the employ of the Cöthen court.
13
Shortly after his
marriage to Anna, the musical climate of the court at Cöthen dramatically changed when
Prince Leopold’s new bride resented the close relationship Bach had with the prince, and
began removing music from the center of the Prince’s activities. Bach felt neglected and
more or less superfluous.
Bach in Leipzig
When the famed Leipzig Cantor, Johann Kuhnau, died in 1722, Sebastian applied
for the position despite having reservations about the nature of the prestigious post. From
his visit with Kuhnau in 1717, Bach had discerned that the duties were much more labor
intensive and required negotiating within a politically-complex hierarchy. In his previous
appointments, he reported and was responsible to a single patron or a small body of
officials. The position in Leipzig required him to answer to almost two dozen superiors
from the school, church, and local government. “To be dependent on these different
governing bodies, which, as might be imagined, would not always live in perfect
harmony, did not seem too pleasant a prospect for any man, least of all for one who had
so little of the touch of the diplomat. There was also the matter of social rank, to which
Sebastian found it somewhat strange (as he admitted to his old friend, Erdmann) to climb
down the ladder.”
14

The position of Thomas Cantor had initially been offered to Georg Telemann,
who utilized the offer to improve his financial situation at his current position in

13
Ibid., 50.

14
Ibid., 54.
36

Hamburg. After this embarrassment, the Leipzig council favored another candidate,
Christoph Graupner, over Sebastian because Graupner’s university education seemed
much more attractive and erudite. They had secretly offered him the post before hearing
Bach’s acclaimed audition. After Sebastian’s brilliant audition, Graupner informed the
Leipzig council that his patron refused to discharge him from service. The council
immediately offered Bach the position with the stipulation that he must attain proper
documentation of his honorable discharge from the service of Prince Leopold and submit
to Latin proficiency and theological examination in order to be declared fit for the office
of Thomas Cantor; a post reserved for the most important musician in Leipzig who was
responsible for overseeing all service music, especially for Vespers and feast days, for the
four principal churches.
Sebastian was formally installed on May 31, 1723 as the Thomas Cantor in
Leipzig, Germany and charged into his new compositional duties with vigor. In his
first year of service, Bach set a grand tone for high feast music presenting his
Magnificat in Eb and Cantata No. 63 on Christmas day in 1723. However, his first large-
scale choral work was reserved for the most holy week of the liturgical calendar.
On Good Friday in 1724, Bach premiered his St. John Passion at St. Nicholas
Church. In the style of an oratorio Passion, this triduum work demonstrated Bach’s
theological depth and compositional innovation; such a monumental work probably was
intended to impress the town council members who were initially suspect of his
education and traditional compositional style. Passion music has a long history in
presenting a biblical text from one of the four Gospels specific to the events just prior to
37

and following the death of Jesus. The history of Passion music puts into context Bach’s
selection of the oratorio Passion genre when setting his St. John Passion.
A Brief History of Passion Music
The first record of a performance of the Passion dates back to the fourth century
in a report by the pilgrim Egeria who visited Jerusalem and described the services of
Holy Week. By the fifth century, Pope Leo the Great decreed that the St. Matthew
Passion should be read at the Mass on Palm Sunday and on Wednesday of Holy Week
while the St. John Passion should be read on Good Friday. Two hundred years later, the
St. Luke Passion replaced that of the St. Matthew Passion on Wednesday of Holy Week
and by the tenth century, the custom was to sing the St. Mark Passion on Tuesday of
Holy Week.
15
The oldest surviving music manuscripts indicate that the Passion was
chanted by a single person and “the earliest definite distribution of the parts of the
Passion lesson among several people is to be found in the Gros livre of the Dominicans
dating from 1254…The first indication of a choral (monophonic) presentation of the
turba is found in the manuscript PL-WRu I-F459, written in 1348.”
16
Polyphonic
treatments of the Passion did not emerge until the middle of the fifteenth century when
settings were typically written for three voice parts in motet style.
The development of more elaborate Passion compositions, with expanded
polyphonic writing, began in the middle of the fifteenth century in England and are often

15
Kurt von Fischer and Werner Braun, "Passion," Grove Music Online, Oxford Music Online,
accessed September 8, 2012, http://www.oxfordmusiconline.com.libproxy
.usc.edu/subscriber/article/grove/music/40090.

16
Ibid.

38

referred to as dramatic Passions. In this genre, the words of the Evangelist are set
monophonically while the turba choruses and words of Jesus are treated polyphonically,
albeit in a simple, perhaps reverent style. There is often an addition of non-biblical texts
to the Passion story in the form of musical movements entitled exordium
17
(introduction)
and conclusio
18
(conclusion). Such additional movements presented composers with
more freedom in their polyphonic treatment and the dramatic Passion is well represented
among composers of many nationalities including Lassus, Vittoria, and Byrd.
Passion music was adopted in Germany in the mid-sixteenth century, but its
development was greatly influenced by Martin Luther (1483-1546) and his reformation
movement. The work of Johann Walter, Luther’s principal musical advisor, provides a
setting of the Passion text with an austere approach; a choral declaration reproducing the
natural rhythms of speech so that the texts could be clearly understood by the worshipers.
This may have been to uplift Luther’s desire to make worship understandable and
accessible to the people. It certainly created a direct contrast to the long melismas on a
single syllable present in the chanting utilized in the Catholic tradition.
19

Seventeenth Century: Stylistic Changes
At the turn of the seventeenth century, influenced by the humanist leanings of the
Florentine Camerata, a significant change in music style occurred. Intending to recreate

17
A typical text for the musical setting of the exordium might simply announce which Passion was
set. For example, “This is the Passion of our Lord, Jesus Christ, according to St. Luke.”

18
It became a common practice to conclude a Passion work with a chorale or series of chorales
that are prayerful in nature and lead the congregation to consider or reflect on the profundity of the Passion
story.

19
Basil Smallman, The Background of Passion Music: J. S. Bach and his predecessors (London:
SCM Press, 1957), 24.
39

the lost music of ancient Greece, this group of musicians, poets, and philosophers
developed a musical style rooted in the natural rhythms of poetry and speech. The
interpretation of this speech-like, musical declaration resulted in a single melodic line
with a two-fold benefit: the text was clear to the listener; and, it adequately portrayed the
broad range of expressivity required to capture the intention, emotion, and meaning of the
libretto. The simplicity of this monodic style, recitativo, was intended to be accompanied
by a basso continuo, a written instrumental bass line over which a player or players
improvised, or realized, a chordal accompaniment. Recitative served to move the action
forward in a dramatic, declamatory style while the aria and arioso transmitted the more
reflective, expressive commentary.
Initially reserved for secular music, the operatic style soon found its way into
sacred music composition. Biblical texts were easily adapted and set in the operatic style
due to the preexisting drama inherent in the stories; and thus, the modern oratorio genre
was born. While the Florentine Camerata introduced the monodic style, it was Claudio
Monteverdi who, with his presentation of the opera, Orfeo (1607), ignited the new
musical trend. His treatment of the foundational components birthed the operatic style
that permeated the continent. The oratorio developed on an almost parallel course to the
secular operatic genre and the long-standing narrative of Passion music began to
transform.
The Oratorio Takes Root in Germany
Heinrich Schütz (1585-1672), having firmly grasped the Italian style in his
Venetian studies with Giovanni Gabrieli and Claudio Monteverdi, is credited with
40

transmitting the oratorio genre to his German homeland. By 1623, Schütz composed one
of the first German oratorios, the History of the Resurrection of Jesus Christ. “In the
preface to [his opera, Dafne, of 1627], Schütz noted that the ‘stylo recitativo’ was ‘almost
unknown in Germany at present.’”
20
Near the end of his compositional career, Schütz
produced three simple liturgical settings of the Passion story “which are unequaled in
dramatic expression by any save those of Bach.”
21
Schütz’s operatic writing influenced a
change in the composers of Northern Germany with the abandonment of the plainsong
narration of the dramatic Passion in favor of the operatic style. Many German composers
embraced the new model and, as a result, a full infusion of recitative, instrumental
accompaniment, lyrical movements, and symphonias were introduced into the Passion
genre. By the late seventeenth and early eighteenth centuries, German Passion music had
successfully embraced the oratorio style, though not without opposition from many
leaders of the church. Longstanding tradition and Lutheran piety caused those church
leaders to look unfavorably upon the inclusion of non-biblical texts, the introduction of
instruments, and instrumental movements into either High Feast or weekly church
services. Nonetheless, the grander, large-form genres of Passion music developed into
the new genres of the Passion oratorio and the oratorio Passion.
Passion Oratorio vs. Oratorio Passion
The Passion oratorio genre is a large-scale, dramatic work meant for performance
outside of church services. The form lends itself to dramatic presentation with the use of

20
Von Fischer and Braun, "Passion."

21
Smallman, Background of Passion Music, 30.
41

a prepared libretto that takes great liberty with the biblical narrative. The introduction of
symphonias created musical asides intended to increase or release tension to create a
satisfying performance. While the biblical narrative served as an inspiration for the
dramatic work, it is paraphrased generously to achieve a sense of cohesive, poetic
storytelling. The compositional elements of recitative and aria, both with instrumental
accompaniment, become excellent vessels for creating and unfolding the action of the
narrative. The recitative and turba choruses loosely follow the biblical text while the aria
becomes the vehicle for commentary used either to elicit an emotional response or as a
reflective tool that enhances the storyline; a powerful musical device that serves to
heighten the emotional response of the listener. In addition, the Passion oratorio genre
embraces the chorale, in some compositions even creating a string of chorales at the end
of a section or of the work that serves as a conclusion. The chorale is a poetic text that
comments upon the action and may have served to generate audience participation in the
dramatic presentation.
22

The oratorio Passion is a large-scale choral work that returns Passion music to the
sacred setting of the church service. It utilizes the forms like symphonia, recitative, and
aria that are borrowed from the operatic genre, but what distinguishes this genre from
other Passion music of the era is the restoration of and integrity in presenting the biblical
text. Though this textual restoration impacts formal construction, because so much
recitative must be written to accommodate the vast role of the Evangelist, the genre

22
See Elwyn A. Wienandt, Choral Music of the Church (New York: Free Press, 1965) for an
argument against congregational participation in the singing of Bach chorales. For an argument in favor of
congregational singing of chorales in Bach’s Passion compositions, see Smallman, Background of Passion
Music, 38, 75-81.

42

capitalizes on the stylistic advances thereby preserving a dramatic presentation of the
Passion story. While commentary texts are retained, these are restricted to the aria,
arioso, and chorale. Great care is given to the placement and position of the commentary
so that these texts do not detract from the biblical narrative. Such treatment preserves the
solemnity associated with presenting the Passion story in the church service, yet,
enhances the experience of the listener by providing a contemporary voice that helps to
organically unfold the drama. In later oratorio Passions, “purely instrumental movements
tend to disappear; the meditative element is then supplied entirely by vocal arias, duets,
and choruses, and by congregational chorales.”
23

Passion Music in Leipzig
Bach’s selection of this genre for his first large-scale choral work in Leipzig was
risky because of the political and religious climate. There was little precedent for the
presentation of large-scale Passion music for Good Friday in this region of Germany
because of the influence of Pietism “which constituted a grave menace to Lutheran
church music.”
24
In fact, the only recorded performance of a large-scale Passion was
under the direction of Johann Kuhnau, Bach’s immediate predecessor, in 1721.
At Leipzig, the traditional Passion setting, in which the narrative and utterances
by individual characters were delivered in unaccompanied plainsong and the
crowd sayings by a choir singing simple chordal responses, had been presented
without interruption for nearly two centuries until 1721, when Kuhnau, yielding
to the pressure of contemporary opinion, had produced an Oratorio version of St.
Mark’s account…which was probably written partly as a sop for the Leipzig
intelligentsia and partly as an attempt to show via media between the simplicity of
the traditional settings and the lurid excesses of the Hamburg Opera style. But

23
Ibid., 37.

24
Ibid., 16.
43

doubtless even this well-mannered breach with tradition aroused considerable
opposition from the conservative and Pietist elements in Leipzig.
25

Though there may have been some sentiment by a few members of the council to seek
out a cantor fluent in the new style, the regional atmosphere and the consensus of the
religious and political thinking in Leipzig certainly veered toward the conservative. The
grand scale of Bach’s Good Friday offering of his St. John Passion must certainly have
ruffled a few feathers or at least raised a few eyebrows with its scale and magnitude.
“The citizens of Leipzig, in particular, whether of conservative or progressive
inclinations, must have been singularly unprepared for so great an advance in musical and
religious thought.”
26
Reactions to the work may have prompted Bach to make significant
revisions for its presentation the following year. In fact, over the course of his extensive
tenure in Leipzig, the St. John Passion was altered for various reasons resulting in four
versions whose differences are outlined in the following table.
Table 1. Synopsis of Alfred Dürr’s Research Outlining the Recreation of the Four
Versions of the St. John Passion from Extant Manuscripts and the Differences between
Them.
Version Description
Version I
(1724)
This version does not survive as a completed manuscript and
reconstruction relies upon recovered performance parts from the
choral ripieno, violin 1, violin 2, and continuo.

25
Ibid., 17.

26
Ibid., 18.
44

Version Description
Version II
(1725)
Survives virtually complete, though the parts for the transverse
flutes, oboes, and viola for movement 1 are missing. Alfred Dürr
summarizes the multiple changes Bach made between Version I
and Version II as follows:
Movement 1 was replaced by 1
II
, ‘O Mensch, bewein dein
Sünde groß’
Movement 11
+
, “Himmel reiße, Welt erbebe’ was newly
inserted after movement 11.
Movement 13 was replaced by 13
II
, ‘Zerschmettert mich, ihr
Felsen und ihr Hügel’.
Movements 19-20 were replaced by 19
II
, “ach windet euch
nicht so, geplagte Seelen.’
Movement 33
I
(3 bars) was replaced by movement 33
II
(7
Bars). This was to accommodate the addition of two verses
from Matt. 27:51-2.
Movement 40 was replaced by 40
II
, ‘Christe, du Lamm
Gottes.’
Version III
(c.1730)
This version consists of two main changes: 1) all of the changes
made in Version II were removed; and, 2) all of the texts
included from the Gospel of Matthew were excised resulting in
the following alterations:
Movement 12c was shortened by 7 measures.
Movement 13
III
replaced previous versions.
Movement 33
III
, a sinfonia that is no longer extant, replaced
Movements 33-5.
The removal of the Matthew texts was presumably in response to
an order by the Leipzig council.
Version IV
(c.1749)
For all intents and purposes, Version IV is a return to Version I
with minor changes and improvements.
Note: This table is a summary of the main differences between the four versions of the St. John Passion.
For a more thorough accounting, see Alfred Dürr, Johann Sebastian Bach’s St. John Passion: Genesis,
Transmission, and Meaning, trans. Alfred Clayton (New York: Oxford University Press, 2002), 3-10.
45

This paper utilizes the critical edition printed by Bärenreiter, which is based upon
Version IV (c. 1749) of the St. John Passion. This version is considered the latest form
of the work and is transmitted in original parts and stems from the later years of Bach’s
life. Version IV, for all intents and purposes, returns to the original form of the work that
was first performed in 1724 with some musical and textual improvements or alterations
made by Bach. Beginning in the late 1730’s Bach set out to replace the original score of
Version I, now lost, but only completed the first 10 movements before he abandoned the
project for unknown reasons. Arthur Mendel hypothesizes that Bach planned to present
the work during Holy Week in 1739 and began preparation of a new score but
discontinued his work in response to a conflict with the Leipzig Council.
27
Toward the
end of his life, Bach supervised a copyist’s completion of the score though his
examination of the work was in varying degrees of detail. Dürr submits, “Some
movements were carefully revised, though the majority were either checked superficially
or not at all.”
28

During his twenty-seven year tenure as Thomas Cantor, Sebastian persevered
through countless difficulties with the undisciplined schoolboys, with the town council
policies and restrictions, and with loss of wages when he was bypassed for the
appointment as the University’s director of the “New Service.” Despite these
disappointments, Sebastian’s compositional output and creativity flourished during his
time in Leipzig. Responsible for planning and implementing music for the four main

27
Alfred Dürr, Johann Sebastian Bach’s St. John Passion: Genesis, Transmission, and Meaning,
trans. Alfred Clayton (New York: Oxford University Press, 2002), 11.

28
Ibid.
46

churches, it was imperative he possess significant Lutheran theological understanding in
order to fulfill his duties as cantor.
The literature exploring Bach’s sacred music is vast, but there is a general
consensus that his church music represents a pinnacle of ingenuity reflecting
compositional mastery of the Baroque style. His religiosity has been examined by
scholars, and some believe his faith may have wavered or been nonexistent; nevertheless,
Bach’s grasp of theological concepts, as executed in his church music, demonstrated
exceptional skill and mastery in their application of Lutheran ideals.
29
The next chapter
will explore how Bach may have intentionally applied theology into the fabric of his
compositional structure. The writer will demonstrate that Bach, aware of Werckmeister’s
writings that espoused the application of the Natural Order or Divine Proportion in
music construction, utilized a theological precept to reproduce this proportion in his St.
John Passion.

29
See Robin A. Leaver’s article, “J.S. Bach’s Faith and Christian Commitment,” The Expository
Times, no. 96 (March 1985): 168, for a discussion of history’s view of Bach’s religiosity.
47

CHAPTER FOUR
Lutheranism:
Influence of Theology on the St. John Passion

Chapter Four explores the theological roots of Lutheranism and their importance
to the construction of Bach’s St. John Passion. It provides a brief history of Martin
Luther’s life and the main theological philosophies that influenced Bach’s education and
informed his compositions for the church. Such exposition lays a foundation for Bach’s
unorthodox application of the Golden Proportion in the St. John Passion. This chapter
also analyzes Phi proportions inherent in the standardized biblical verse as filtered
through one of Luther’s main theological beliefs, which sets the groundwork for the phi
inv

analysis upon the music and text of Bach’s St. John Passion that follows in Chapter Five.
Considering that Bach was firmly rooted in the theology of Luther and excelled at
compositional construction, it is not difficult to imagine that he possessed an ingenious
ability to embed theological beliefs into his musical compositions. Therefore, it is logical
to examine whether theological forethought was woven into the St. John Passion. The
writer’s hypothesis explores the theory that a theological principle was employed in the
construction of the St. John Passion; theology provided a framework for the
compositional process that affected the proportions between Part I and Part II, which
resulted in an atypical division.
Bach’s knowledge and application of Lutheran principles are crucial to
understanding the primary role he held as Cantor in the Leipzig, Germany church during
the early eighteenth century. A cantor’s role was to provide music that supported and
enhanced the theology and tradition central to the church’s mission, as well as to instruct
48

the parishioners about the church’s theology and traditions. Bach’s dedication to his
craft, whether ascribed to his personal belief or to the fulfillment of his duties, required a
profound knowledge of Luther’s theological writings and their implications. An
informed composer might utilize musical affect and text to incorporate theological
principles into his musical work, while an extraordinary composer, like Bach, takes it a
step further by infusing the music with theology so deeply as to make it a foundation for
the structure of the work. This structure may not be apparent to a listener and is
concealed in such a manner that an analysis, using traditional methods of score
examination, may not reveal it. In order to understand the concealed scaffolding of the
St. John Passion, a working knowledge of Luther’s theology and its deeply rooted
implications are necessary.
Bach grew up in a devoutly Lutheran tradition and his family, possessing an
impressive musical pedigree, served with distinction for generations in the church. Both
Bach’s academic and musical studies were rooted in the Lutheran church. Even when he
was serving in a non-Lutheran post in Weimar, Germany, he and his family attended a
Lutheran church.
Bach References Luther’s Writings
As a Cantor in Leipzig, his duties required that he had a working knowledge of
Lutheran theology. After Bach’s death, a list of his theological library was compiled
49

which revealed that Bach owned a large collection of Luther’s theological writings,
including the following
1
:
[ 1. ] Calovii Schrifften. 3. Bände
[ 2. ] Lutheri O 7. Bände
[ 3. ] Idem. Liber 8. Bände
[ 4. ] Ej. Tischreden
[ 5. ] Ej. Examen Conc. Trid.
[ 6. ] Ej. Comment. Über den Psalm 3ter Theil
[ 7. ] Ej. Hauss Postille
[ 8. ] Mülleri Schluss Kette

In all, twenty-one volumes of Luther’s writings were found in the inventory of Bach’s
library, not including Luther’s smaller works or octavos. The Calovii Schrifften listed
above are often incorrectly referred to as a “Bible,” and more frequently, as “Bach’s
Bible,” but the title page provides a more accurate description:
The German Bible of Dr. Martin Luther with the addition of the exposition to be
found in Luther’s writings, so that…everywhere the real literal understanding, and
to a considerable extent also salutary application, of Holy Scripture, especially
together with the inspiring words of that man of God [that is, Luther], is presented
by Dr. Abraham Calov.
2

Thus, this set of volumes is a collection of Luther’s commentaries organized by scripture
verses.
This set of three books was rediscovered in the United States in 1934 and Robin
Leaver’s thorough investigation of them revealed that Bach used these resources on a
regular basis. Contained in them are underlined passages, copious notes in the margins,
and even corrections of misprints, written in Bach’s hand. One carefully underlined

1
It should be noted that Ej. Examen Conc. Trid. was not written by Luther but by Martin
Schemnitz and was a compilation of apologetic works concerning the Council of Trent. For a more
detailed account of the library contents, see Leaver, J. S. Bach and Scripture, 24.

2
Ibid., 22.

50

section is Luther’s commentary on a portion of the St. John Passion narrative. This
suggests that Bach was keenly interested in Luther’s interpretation of the specific biblical
passage. The commentary is in reference to the words, “it is finished”
3
-- the biblical
phrase which forms the locus of this author’s argument that the organizational structure
of Bach’s St. John Passion was determined by theological principle. To fully understand
this theological principle, it is necessary to more closely examine Luther’s theology in
order to gain direct insight into how this was referenced by Bach.
Martin Luther
Martin Luther (1483-1546) was an educated man who attended Latin schools in
Mansfeld, Magdeburg, and Eisenach, Germany, from an early age. Luther’s education as
a law student and Augustinian monk contributed to his great passion for the study of
philosophy, which he utilized to develop logical, theological principles that helped chart a
new course for many Christians. Luther dedicated his life to the development of an
interpretation of faith based on scripture, leading to a reformed branch of Christianity.
It was never Luther’s intention to separate from the Roman Catholic Church;
instead, he wanted to encourage congregants to cultivate a more meaningful, personal
relationship with God. Initially, Luther set out to influence such changes within the
Roman Catholic tradition and he lobbied to reform some of the practices and traditions
which he perceived as abuses imposed by the political leaders of the church. Luther’s
outspoken passion for church reform caused him to be accused of heresy in 1520 and he

3
John 19:30 (RSV).
51

was eventually excommunicated from the Roman Catholic Church at the Diet of Worms
of 1521. Following this ruling, Luther went into hiding to avoid execution.
The period of his exile shaped his ministry at Wittenberg, and his translation of
the Bible into German influenced many German congregations to implement reforms. It
was during this time that Luther’s study and devotions solidified and became the basis of
a reformed church. The scholarly writings emanating from this time of his seclusion
addressed issues of the reform movement and elevated Luther as the leader to whom most
reformers deferred in matters regarding the changing atmosphere of church ritual and
practice. With the invention of the Gutenberg press, Luther’s theology spread quickly
across Germany. Most of Luther’s theological works, including his German translation
of the Bible from Greek and Latin, were published during his lifetime.
Luther’s study and interpretation of scripture were driven by his personal struggle
to reconcile the righteousness of God with the sinfulness of humanity. To bridge this
gap, Luther relied upon the Christological passages in the canon that focused upon
Christ’s sacrifice as the act of grace that atones for humanity’s sins; a gospel of free grace
and justification through faith alone attainable solely through the death and resurrection
of Jesus Christ. In Luther’s estimation, the Gospel of John, the Epistles of Paul, and the
First Letter of John held the greatest significance in the revelation of grace; these became
the pillars of his developing theology.
4

4
Carl E. Braaten, Principles of Lutheran Theology, 2d ed. (Philadelphia: Fortress Press, 2007), 2.
52

Theologia Crusis vs. Theologia Gloriae
One of the cornerstones of Luther’s theology became known as theologia crusis,
or the theology of the cross, developed out of a dispute regarding the means and process
of salvation. Medieval theologians adhered to the dogma of theologia gloriae or the
theology of glory. This line of reasoning stemmed from an understanding that salvation
was based upon cooperation between humanity and God; the accumulation of good works
done by, and for, the recipient deemed them worthy of receiving God’s grace.
5
Luther’s
philosophical approach found this line of thinking faulty because it was developed
utilizing isolated biblical texts. Such narrow focus, Luther argued, was dangerous when
developing doctrine. The “Heidelberg Disputation” of 1518, which was held at a meeting
of the Augustinian order when Luther was a delegate, argued against the theology of
glory and deemed that God’s revelation and gift of salvation is only achieved through
Christ’s death on the cross. Jesus’s sacrifice is the only event that reconciles creation to
God, and through this act, humanity’s sins are atoned and grace is received. A result of
Luther’s theology of the cross was a new understanding of the role and importance of
“good works.” A Christian is compelled to do good works in response to, and out of
gratitude for, God’s gift of grace, thereby negating the theology of glory. Luther’s
doctrine places the focus on God’s salvific work and not mankind’s.
This theology provides the framework for Luther as it employs the cross of Christ
as the focal point and fulcrum for understanding not only scripture but also the life of a

5
Eric W. Gritsch and Robert W. Jenson, Lutheranism: The Theological Movement and Its
Confessional Writings (Philadelphia: Fortress Press, 1976), 47-8.
53

Christian.
6
Luther wrote, “It is impossible for a person not to be puffed up by his good
works unless he has first been deflated and destroyed by suffering and evil until he knows
that he is worthless and that his works are not his but God’s.”
7
This understanding
developed from his own struggle with feelings of unworthiness in reconciling himself to
God. He wrote, “Fall down and pray for grace and place your hope in Christ in whom is
our salvation, life, and resurrection…. The law humbles, grace exalts. The law effects
fear and wrath, grace effects hope and mercy.”
8

As Luther’s own theology continued to mature, he constantly pointed students and
those who read his writings back to the cross of Christ as the starting point of salvation.
Bach’s understanding of the importance of Christ’s act as the defining moment of
Christian reconciliation comes directly from Luther. The fact that Bach underlined
Luther’s writings in his Calov Bible Commentary in reference to John 19:30,32,34 is
significant.
9
Robin Leaver sheds some light on the meaning of Luther’s discourse:
Objective and subjective realities meet in the cross of Christ. On the one hand
there is the objective reality of the death of Christ, and on the other, the subjective
reality of faith by which the believer makes the sacrifice of the cross his own. In
the cross, there is the objective demonstration of the grace of God, which needs to
be received subjectively and experienced in the life of the individual Christian.
So Luther’s theme here is that although the death of Christ was once-and-for-all,
its significance needs to be applied daily in Christian faith and life. At the heart
of the message is the grace of God, which gives to the believer the assurance of

6
Robert Kolb, “Luther on the Theology of the Cross,” Lutheran Quarterly 16 (Winter 2002): 444.

7
Timothy E. Lull, ed., Martin Luther’s Basic Theological Writings (Minneapolis: Fortress Press,
1989), 44.

8
Ibid., 42.

9
Leaver, J. S. Bach and Scripture, 129.
54

forgiveness of sin. It is significant, indeed, that it is these words emphasizing the
grace of God in the shed blood of the Savior that [Bach] underlined here.
10

This sacrifice sums up the core of Lutheranism; it is the beginning of one’s new
life, reconciled to God. Therefore, in Bach’s writing of the St. John Passion, he infuses
this literal theological premise into the music. He utilizes the death of Christ as the
starting point of construction.
As discussed in Chapters Two and Three, Phi, or the Natural Order, is viewed as
an expression of God’s perfect creation. Its incorporation into the canvas of the
respective arts was considered by many to be an act of piety and reverence. Because
music of the church was intended to invoke and enlighten the listener, its construction
was thoughtful and purposeful. It is shown that by 1705, Bach studied proportionally-
based architectonics as a structural tool for composition and utilized this tool as early as
1706.
11
It is not such a leap, therefore, to investigate whether he utilized Phi in the
construction of the St. John Passion in 1724 and that he began his calculation from the
theologically significant text, “It is finished.”
12
Utilizing this moment in the Passion
story to apply Phi to the musical composition, Bach not only reveals his theological
underpinnings, but reinforces the belief that death, usually viewed as the ultimate ending,
actually serves as both the literal and theological beginning.

10
Ibid., 135.

11
Power, “Bach and Divine Proportion,” 67.

12
John 19:30 (RSV).
55

Phi Proportions in Biblical Verse
The calculation of Phi requires the reader to approach the music and the Bible
from a numerical standpoint, as Phi is a mathematical function. Its application requires a
starting point for calculation, and, in some manner, the music and the biblical texts must
be viewed in such a way that clear and consistent start and end points can be identified
within these sources. Consider a straight line with two points ( ); one is
identified as a starting point and the other, an endpoint. The distance between these two
points can be measured and the length determined. Depending upon the available tools
or the user’s preference, line length could be expressed in a multitude of measuring units
such as inches, centimeters, millimeters, or even miles. With the length established, Phi
can then be applied and a consistent result, no matter the measuring unit, is achieved.
In simple terms, music is similar to the mathematical line because it contains clear
starting and ending points. The units for measurement in music are varied according to
the analyst’s preference; the total number of measures or number of beats is often utilized
in the calculation of Phi in music. It should be noted that music notation is more
complex and has more subjective rules than those observed in the mathematical arena;
not all measures are created equally and beats can be subjective depending upon tempo
and complexity inherent in certain time signatures.
When looking at a biblical text from a mathematical standpoint to determine
reasonable start and end points, the reader is presented with multiple complexities that
require a brief historical perspective. Because the text has been translated and transcribed
into many languages, typical units of measurement used for the application of Phi are
56

rather subjective. The number of words or sentences, for example, can vary greatly from
one version to the next making the calculation unreliable. Since consistency of
measurement is required in order to calculate Phi accurately, a brief discussion is
necessary regarding the standardization of the biblical verses and how this meets the
measurement criterion.
Standardized Biblical Versification
The history of written biblical texts begins with the Jewish Scriptures, attributed to
Moses in the early 1400’s BCE, which were recorded on leather scrolls and tablets. In
approximately 450 BCE, councils of rabbis codified the first five books of what would
later become the Bible, and other Jewish Scriptures and organized them by topic,
including the Torah (Law), the Nebiim (Prophets), and the Ketubim (Writings); these are
collectively referred as Tanakh. These writings were considered as the inspired and
sacred authority of God, a concept often referred to as Elohim. Though Jewish Scriptures
were hand-copied, they were extremely accurate. Scribes developed a phenomenal
system of intricate and ritualistic methods for counting letters, words, and paragraphs to
insure against errors because a single copy error required the immediate destruction of
the entire scroll.
13

When Christianity began, Jewish scriptural texts remained foundational for the new
religion and their content was maintained in the Bible with some additions and is referred
to as the Old Testament. The Christian Church began recording its history in
approximately 50 CE. Over the next century, the church compiled new texts consisting

13
For a more detailed account of Jewish scriptural history and its written transmission, see Henry
H. Halley, Halley's Bible Handbook, 25th ed. (Michigan: Zondervan, 2000).
57

of four literary types: Gospels, History, Letters (Epistles), and Apocalyptic writings. This
collection in the Bible is referred to as the New Testament. As the Christian Church
grew and its organizational structure solidified, the need for the dissemination and
copying of these writings was apparent. The early church leaders therefore drew upon
the traditions they had inherited from the Jewish scribes so that accuracy in reproduction
of these writings was maintained.
14

Prior to determining how the written biblical text can be utilized in Phi calculation,
a brief discussion of the state of its structure and standardization during Luther’s
reformation era, Bach’s era, and modern times is necessary. Codification of biblical texts
had existed in a common form since the thirteenth century. The biblical narrative is
delineated by content into Hebrew scripture and Greek scripture (i.e., Old Testament and
New Testament, respectively), books, chapters, and verses. Even though its texts have
been translated into multiple languages over many centuries, this structure remains
constant.
During Luther’s Reformation in the sixteenth century, the final development in the
biblical organization was the division of chapter content into numbered verses. While
Luther did not use verses in his hand-written German translation of 1522, this system was
developed in response to Luther’s concerns about scriptural accuracy in the printing press
reproduction of the Bible. The potential for errors arising in the type setting process
during mass reproduction of the Bible necessitated accuracy for any false text could lead

14
For a detailed account of Christian biblical history and its written transmission, see F.F. Bruce,
The New Testament Documents: Are They Reliable? 5
th
ed. (Downers Grove, Illinois: InterVarsity Press,
1960), 21-8.
58

to a false doctrine. To defend against any attempt to falsify his teachings or
interpretations, “Luther invented a trademark with the warning 'This sign is a guarantee
that books bearing it have passed through my hands'.”
15
Under Luther’s watchful eye,
the organization and content of the Bible was carefully scrutinized, and the 1545 edition
of the German Bible received his final approval. After his death, numerous editors
wanted to add additional safeguards to ensure each reprint was accurate; however,
Christoph Walther wished to remain authentic to Luther’s original authoritative style and
text. He would not permit the addition of verse numbers into the chapters, as Luther had
not numbered them himself.
16
The French printer Estieene in his Greek-Latin New
Testament adopted versification in 1551. Within the same decade, the system of
versification spread widely, influenced by the adoption of this system in the Geneva
Bibles of 1559. This innovative system has remained in place since its standardization in
1586.
17
Therefore, the ordering and versification of the biblical texts that Bach used
remain consistent with the translations of today’s Bible.
Establishing the consistency of biblical verse is critical in recreating the tools for
calculating Phi used by Bach for a modern analysis. While the delineation of the biblical
text structure into book, chapter, and verse can be quantified for utilization in a
mathematical equation, the most practical of these units of measurement is the verse, and
therefore is the unit of measurement that will form the basis of this hypothesis.

15
M.H. Black, The Cambridge History of the Bible, Vol. 3, The West from the Reformation to the
Present Day, Chapter XII: The Printed Bible, ed. S. L. Greenslade (Cambridge: Cambridge University
Press, 1969), 433.

16
Ibid., 434.

17
Ibid., 442-5.
59

John 19:30
As revealed earlier in this chapter, the crucial verse of the Passion story is John
19:30, “When Jesus had received the vinegar, he said, ‘It is finished’; and he bowed his
head and gave up his spirit.”
18
This action is the cornerstone of Luther’s theology of the
cross because it identifies the fundamental reason to believe. For Luther and for Bach,
this salvific act solidifies redemption for all. Bach, in his personal copy of the Calov
Bible Commentary (Vol. 3/V, column 947), identifies the importance of this Lutheran
viewpoint by underlining Luther’s commentary regarding this verse, “that Christ’s
suffering is the fulfillment of Scripture and the accomplishment of the redemption of the
human race.”
19
While this action appears in all four gospels, the foundation of Luther’s
discourse on the theology of the cross relies heavily upon his interpretation of the Gospel
of John. This gospel focuses more on Jesus’s divinity and provides a clearer pedagogical
focus regarding man’s salvation through Christ.
20
Luther recognizes Jesus’s death as the
act that provides hope for man’s salvation. Therefore, Jesus’s death is the beginning of
the Christian believer’s reconciliation to God. Bach recognizes this pivotal point in
Luther’s theology and transforms it into a literal basis for conceiving the musical
structure of his St. John Passion by applying the Divine Proportion in an atypical
manner.

18
John 19:30 (RSV).

19
Leaver, J.S. Bach and Scripture, 130.

20
Jaroslav Jan Pelikan, introduction to Luther’s Works, Vol. 24, Sermons on the Gospel of St.
John, Chapters 14-16, by Martin Luther, ed. Jaroslav Jan Pelikan (St. Louis: Concordia, 1961), ix.
60

The Passion story from the Gospel of John is comprised of Chapters 18 and 19; a total
of 82 biblical verses with the salvific act of Jesus’s death happening in the 70
th
verse. If
this verse is viewed as the beginning, then several questions become apparent, including:
1) How does the analyst overcome the linear nature of a narrative or a composition
when the starting point occurs any place other than the first measure or verse?
2) If an atypical starting point divides the narrative/composition and two parts are
created, what portion should be considered for analysis?
3) Should the unanalyzed portion be discarded? If not, then how can it be
incorporated?
All good questions, and they must be reconciled as they relate to the St. John Passion in
order for this particular piece of music to exist within typical approaches to analysis.
The first question is reconciling an atypical starting point within the confines of a
musical or narrative system whose rules are set. In the St. John Passion, a theological
principle indicates an alternative starting point, though the resulting structure of the
narrative/music is not altered in any way. The starting point is simply conceptual and
was utilized as a basis for constructing the main scaffolding upon which the musical
process was carried out; no musical rules were broken to accommodate the
conceptualization of the composition. In terms of narrative, this remains intact despite
minor additions and subtractions to the text. Bach’s projection of the theological
interpretation is cleverly overlaid on the narrative to emphasize certain ideals without
subverting or compromising the integrity and intention of the Passion story. In fact, such
dimensionality augments the analytical arguments put forth in this paper.
61

Concerning the second question above, the division of the narrative at John 19:30
creates two unequal parts. The contents of the larger, first part, is the core of the passion
narrative. The smaller, second part, directs the reader to consider how scripture was
fulfilled by Jesus’s sacrifice, and provides a detailed account of the events of his burial.
Theologically, everything after Jesus gives up his spirit is a justification for his sacrifice
and sets the scene for the Resurrection Story, while the larger portion of the narrative
encompasses the events up to and including the death of Jesus. It is this final act which
forms the core of Luther’s theology of the cross focusing on man’s reconciliation to God
through Jesus. Two compelling reasons for analyzing the first part of the division exist:
1) it is larger, and 2) it is the core of the passion narrative.
The third question posed about discarding the smaller portion during analysis is
rendered moot if analysis of the composition as a whole is executed. Such an analysis of
the whole composition is included in Chapter Five. Therefore, analysis of the larger
portion of the biblical narrative revealed by the phi calculation will be examined in this
section.
The bulk of the Passion story resides in verses 1 through 70, with verse 70 being
the pivotal theological point, Jesus’s death, acting as both an ending to the action of the
narrative and a theological beginning. With verse 70 being the dividing point of the
narrative, it makes sense to focus on the larger portion when calculating phi. If verse 70
is used as the beginning, then the inverse linear function is required for calculation. As
explained in Chapter 2 of Power’s, J. S. Bach and the Divine Proportion, Bach applied
62

Phi in at least three archetypal forms.
21
Each of these archetypes considers the
application of the Golden Section based upon the whole of the musical work. Because
Power’s archetypes rely upon a linear concept of music, start and end points are
definitive and the calculation of phi is unambiguous. The principles of the archetypes
remain applicable to this research though the method is altered in the analysis of the St.
John Passion to accommodate the infusion of a theological precept. Considering only the
music of the St. John Passion does not reveal strict phi proportions. How then does Bach
incorporate Phi proportions into this work? The answer lies in analyzing the scriptures
for phi proportions with the Lutheran interpretation of Jesus’s death as the beginning.
Revelation of Phi Proportion:
Biblical Verse of the Passion Narrative

Jesus relinquished his spirit in the 70
th
verse of the passion narrative; this atypical
starting point breaks the narrative into two unequal parts (1-70 and 71-82 respectively)
with the larger comprising the bulk of the narrative. This larger segment contains 70
units (verses) and the Golden Section can be calculated with the equation:
70 x 0.618 = 43.26, which is rounded to 43
This calculation assumes a forward linear process so that 43 is the expression of phi when
the beginning point is 1. If, however, the starting point is 70, an inverse equation can be
expressed as follows:
70 x 0.382 = 26.74, which is rounded to 27
The reader will notice that the Golden Section and its inverse as calculated in each
equation remains proportional and their lengths are complementary [70-43=27 and 70-

21
See Chapter Three for a more detailed discussion of Power’s, “Bach and Divine Proportion.”
63

27=43]. The fact that verse 70 is identified in Luther’s theology of the cross and acts as a
starting point makes a compelling argument for phi
inv
to be favored over phi. Indeed,
when looking at the music of Bach’s St. John Passion, one finds that the 27
th
verse of the
narrative, John 18:27, “Peter again denied it and immediately the cock crowed,” plays a
very important role in both Luther’s theology and in the textual choices Bach makes to
conclude Part I. Therefore, it is prudent to explore Luther’s view of Peter’s denial and its
importance in the Passion story. Specifically, how its pairing with Jesus’s sacrifice might
be a key to understanding mankind’s reconciliation with God.
For Luther, Peter’s act of denial holds great significance because Peter’s
sinfulness is an archetype of humanity’s sinfulness. It is through Peter’s reconciliation
that Luther ultimately finds hope for himself and for all believers. Consider Luther’s
own writings on the matter:
Peter, the greatest and best apostle, falls more shamefully than the other apostles
and yet is restored. If I were able to paint a portrait of Peter, I would inscribe
everywhere, on each hair of this head, the words “forgiveness of sins,” because he
is an example of this article of the forgiveness of sins. And this is how the
evangelists depict him. For no other part of the entire Passion account is
described with so many words as is the fall of Peter. Everything that befell Christ
is indicated by the evangelists in a few words, and then they move on. But they
hack away at Peter so shamefully that they cannot find enough words to describe
his fall, and this is especially true of St. John. It is as if he were saying, ‘This is
the fruit and benefit of Christ’s suffering; in it you have forgiveness of
sins’…Thus the fruit and power of Christ’s sufferings is to recall that there is
forgiveness of sins, so that everyone may know that Christ’s kingdom is nothing
other than forgiveness of sins. And this comfort has been set here against the
most grievous of sins—despair. If Peter did not stand there as an example,
saying, ‘I, too, have sinned,’ then we would all have to abandon hope and fall into
despair amid our sins…Thus, no matter how great a sinner you may be, look at
Peter. You will not find any sin to equal his, except for obduracy and
presumption, which is a sin unto death [1 John 5:16]. Thus this example is
beneficial both to me and to Peter, who would otherwise have become altogether
too arrogant. When we hear that Peter denied Christ and swore on pain of his
64

salvation that he did not know this man, this is a sermon for us. For God has dealt
with us, too, in this way.
22

It is significant that the Golden Section analysis of the biblical texts reveals a connection
between Peter’s denial and Jesus’s death. The relationship between humanity
(represented by Peter) and God (in Jesus’s act of sacrifice) has long been the focus of
theological discourse. Golden Section analysis of the biblical text reveals a significant
pairing explored in theological doctrine and identified as a cornerstone of reconciliation
theology. Should the pairing revealed by Golden Section analysis of scripture also be
executed by Bach in his setting of the St. John Passion, then it would show that, at the
least, Bach utilized Golden Section calculation in the compositional process to preserve
the innate Golden Section proportion present in the biblical narrative. More likely, the
act of preserving this Golden Section proportion might represent, for Bach, a great act of
piety which comments upon his theological insight if it were purposefully woven into the
construction of this massive composition.
Rationale for the Insertion of Matthew Texts
In order to show that this was Bach’s intention, some anomalies in the biblical
texts of the St. John Passion must be addressed. On two occasions in the St. John
Passion, Bach inserts texts taken from the Gospel of Matthew. These additions occur at
the death of Christ and at Peter’s denial, the two main loci of the Golden Section analysis
exposed above. In both instances, the added Matthew texts provide expanded accounts of
these significant, Passion story events.

22
Martin Luther, Luther’s Works. Vol 69, Sermons on the Gospel of St. John, Chapters 17-20, ed.
Christopher Boyd Brown (St. Louis: Concordia, 2009), 186-7.
65

The reader may recall that the actual calculation of phi
inv
on the 70
th
verse of
John’s passion narrative resulted in the product 26.74, [70 x 0.382 = 26.74]. In Golden
Section application to music, the number is rounded. If the product were maintained
exactly, a numerical coincidence present in the biblical narrative is revealed. This
number, applied to the Gospel of Matthew, reveals a parallel account of Peter’s denial.
Matthew 26:74 states, “Then he began to invoke a curse on himself and to swear, ‘I do
not know the man.’ And immediately the cock crowed.” The verses from the narratives
of both gospels conclude with these italicized words. Bach utilizes this shared text as a
pivot point between the gospels to extend the biblical narrative in the libretto of his St.
John Passion by including Matthew 26:75, “And Peter remembered the saying of Jesus,
… And he went out and wept bitterly.” The additional text provides Bach the
opportunity to capitalize on Matthew’s more emotional account of Peter’s denial, thereby
including Peter’s remorse and, by extension, humanity’s.
The second interpolated textual insertion in Bach’s St. John Passion occurs at the
death of Jesus in the passion narrative. Bach sets John 19:30, “When Jesus had received
the vinegar, he said, ‘It is finished’: and he bowed his head and gave up his spirit.”
23
At
this point in his libretto, Bach adds two verses from the Gospel of Matthew. This is
accomplished by referencing the parallel verse from Matthew 27:50, “And Jesus cried
again with a loud voice and yielded up his spirit,” and then setting the two subsequent
verses, Matthew 27:51-2, “And behold, the curtain of the temple was torn in two, from
top to bottom: and the earth shook, and the rocks were split; the tombs also were opened,

23
John 19:30 (RSV).
66

and many bodies of the saints who had fallen asleep were raised.”
24
While these verses
follow the death of Jesus in the narrative, the action depicted in them occurs
simultaneously with and because of Jesus’s death. These verses have significant
theological implications and provide powerful symbology for the Lutheran faith. The
temple curtain symbolizes Jewish sacrificial law for the atonement of sins, and its fabric
being torn in two symbolizes that the law is no longer the primary method of receiving
salvation; the law is superseded by Jesus’s sacrifice, which becomes the only necessary
act for salvation. As noted by R. Alan Culpepper, “The role of Jesus is bound up with the
human condition apart from God. Jesus provides a solution to the human condition;
therefore, how one understands that condition determines in large measure how Jesus’
[sic] role will be understood.”
25
A central tenet of the Lutheran faith is that Jesus’s
sacrifice reconciles the believer to God who graciously grants salvation. By inserting
Matthew 27:51-2 into the libretto of his St. John Passion, Bach asserts his Lutheran
theological roots and extends the length of the passion narrative from 70 verses to a total
of 72 verses. I believe that this addition of text serves another purpose for Bach that is
revealed only by phi
inv
calculation.
Phi Reveals a Biblical Textual Bridge:
Uniting John and Matthew
As shown earlier, the phi
inv
calculation on 70 verses revealed the product of
26.74. Bach utilized this number as a textual pivot to transition his libretto from the
Gospel of John to the Gospel of Matthew. The addition of two verses from Matthew to

24
Matthew 27:50-2 (RSV).

25
R. Alan Culpepper, The Gospel and Letters of John (Nashville: Abingdon Press, 1998), 89.
67

the 70 existing verses from John’s account extends the total number of verses to the point
of Jesus’s death in Bach’s passion narrative to 72. When the phi
inv
calculation, 72 x
0.382 is performed, the resultant product is 27.50. The meaning of this number is
initially veiled, but knowing Bach’s numerical awareness and affinity, it seems logical to
explore the significance of 27.50. In fact, if the analyst assumes that 27.50 also refers to
the Gospel of Matthew, an amazing and profound result of Bach’s numerical play is
disclosed. Matthew 27:50 states, “And Jesus cried again with a loud voice and yielded
up his spirit.” The importance of this text is self-evident in that it parallels John 19:30,
the foundational theological event explored earlier in this chapter, which serves as both
an ending point and a beginning point conceptually for the application of phi
inv
principles
to the compositional structure.
Such analysis of Bach’s St. John Passion reveals a cyclical reference found only
through this type of analysis, and points to confirmation of Bach’s in-depth
constructional methods; he begins with Jesus’s death in John 19:30 and concludes, by
numerical reference, with Jesus’s death in Matthew 27:50; a perfect set of bookends
revealing the depth of Bach’s theological understanding and how this may have affected
his compositional process. With the exposition of the theological foundation and how
Golden Section analysis may have been applied to the biblical text of the Passion story,
similar principles can now be explored in the music of Bach’s St. John Passion.

68

CHAPTER FIVE

Analysis of the St. John Passion:
A New Paradigm of Phi Application

It is the premise of this paper that Bach generated a musical model which applies
Golden Section in its inverse expression (phi
inv
or φ
inv
) to the St. John Passion based upon
a theological principle rooted in Lutheran theology: Jesus’s death on the cross is the act
which begins mankind’s reconciliation to God.
1
Because of this belief, Bach viewed the
death of Jesus in the Passion story as a starting point for determining the dimensions and
structure of his composition. With this original hypothesis, the writer formulated a
methodology of applying Golden Section analysis in its inverse expression in order to
explain the placement of the division between Part I and Part II in the St. John Passion.
As discussed in Chapter Two, a line divided at the Lesser Golden Section results
in two segments that remain in phi proportion to the original line, as well as in relation to
each other.
2
To calculate the phi point in music, the total number of measures or beats,
N, is multiplied by 0.618 and the resultant number indicates where, on the line, the

1
The writer will maintain the nomenclature of phi
inv
(0.382) when discussing the applications
relevant to this paper’s hypothesis because of either a theological principle or a strictly musical dimension
present in the St. John Passion where Part I is smaller than Part II. It should be noted that Madden, in his
book Fib and Phi, developed useful nomenclature to represent the φ points specific to spiral application
(GS
1
=0.618, GS
2
=0.382, GS
3
=0.236, GS
4
=0.146, etc.). Madden’s system is represented by a series of
equations in which the first calculation of φ is [N x (0.618) = GS
1
]. The second calculation in the spiral is
[N x (GS
1
x 0.618) = 0.382 (or GS
2
)]; the third [N x (GS
2
x 0.618) = 0.236 (or GS
3
)]; the fourth [N x (GS
3
x
0.618) = 0.146 (or GS
4
)]; etc. The reader might note that the product of Madden’s second calculation, GS
2
,
in spiral phi is 0.382, which is identical to the writer’s preferred nomenclature φ
inv
or phi
inv
. The primary
purpose of both nomenclatures is to establish a distinction between theological application principles of
phi
inv
and the series of Phi applications known as the spiral.

2
The reader should recall from Chapter Two the special qualities of this proportion and its
numerical expression. Plato’s description was noted as the segmenting of a line into two unequal parts so
that the two resulting segments are in the same proportion to each other as the longer segment is to the
whole line. The numerical derivation of Phi (≈ 1.618…) is an irrational number derived from averaging
consecutive numbers in a series of Fibonacci numbers.
69

Golden Section lies (N x 0.618 = φ

or phi). Similarly, the inverse of Lesser Golden
Section is calculated by taking the complement of 0.618 (mathematically expressed as 1.0
- 0.618 = 0.382). Therefore the mathematical formula to calculate the phi
inv
is expressed
by the following equation:
N x (1 – 0.618) or N x 0.382 = φ
inv
or phi
inv

Four points of departure for the application of phi
inv
to the St. John Passion were
selected for analysis based upon either musical or theological principles. These four
analytical constructs expose the plausibility of phi
inv
application to the work as
hypothesized by the writer. Of the four analytical constructs identified, three of these
analyze the St. John Passion from a theological standpoint. The theologically-based
constructs use as their point of departure for calculating phi
inv
the moment of Jesus’s
death; more specifically, the measure or movement where this text is transmitted in the
St. John Passion. These three theologically-based constructs reference the groundwork
laid in Chapter Four whereby the salvific event acts as the beginning of mankind’s
redemption, and, in so doing, lays the groundwork for the theological onus that may have
influenced Bach’s construction of the St. John Passion. Analytical Construct 1 uses a
purely musical, linear point of departure; the concluding measure of the work. This
original research demonstrates that the calculation of phi
inv
is an important analytical tool,
employed in piety by Bach, to demonstrate a theological principle thereby creating a new
foundation for musical analysis.
70

Standard Phi Application in the Literature
Before presenting the four analytical constructs, a brief discussion about how Phi
has been applied in other researchers’ music analyses is in order. In almost all cases
found by this writer, the Golden Section analysis in music is limited to a single movement
or small work; the length of which is generally less than 200 measures in total. The
incidence of Phi calculation upon multi-movement or single movement compositions
with significantly increased measures is rare in research. In fact, only one dissertation
even broached the topic of a multi-movement application of Phi. While multi-movement
application of Phi was not the primary focus of Tushaar Power’s dissertation, J. S. Bach
and the Divine Proportion, he did touch on a multi-movement analysis in two Bach
compositions that he believed contained Golden Proportion. The first multi-movement
work he analyzed for Phi proportion was the Prelude and Fugue (BWV 552) from Bach’s
Clavierübung III
3
:
The Prelude and Fugue…provides [sic] an example where two movements
display a proportional relationship of a major Golden section. The prelude
is 205 measures long and the Fugue is 117 measures long…an
approximation to Phi becomes evident: 322 ÷ 205 = 1.571. This is a less
accurate approximation to Phi than the two other examples presented thus
far, but falls within the tolerances of ± 3.1% of Phi (i.e., 1.568 to 1.668)
adopted in this study…Thus the pair of movements here exhibit [sic] a
proportional relationship which approximates, albeit coarsely, to the
Golden Section.
4

3
Power, “Bach and Divine Proportion,” 95. It should be noted that Tushaar Power’s dissertation
was a specific study on Phi proportion in the da capo arias of J. S. Bach. It is unclear how this reference to
the Prelude and Fugue applies to his research. His identification does support the case for looking at a
multi-movement treatment of Phi.

4
Ibid., 97.
71

The second multi-movement Phi analysis that Power puts forth pertains to three
sequential movements taken from the Bach cantata, BWV 120a. His research on this
work indicated that Bach parodied two of his previously existing compositions and
utilized these as movements for a new cantata composed for a wedding. Power
concludes that the near exact dimensions of the existing movements were provided
symmetry by the insertion of a newly composed recitative movement between them
whose dimensions created a form that displayed the “major and minor Golden Sections
combined.”
5
In summarizing these two isolated cases of multi-movement application of
Phi proportions, Power states,
One can at this juncture differentiate that the composer approached the
proportional organization of a piece of music in two distinctly separate
ways. The first way is evident in the Chromatic Fantasy discussed above,
and is an approach where the composer conceived of a whole, and then
apportioned its internal form. The second approach is that [sic] evident in
BWV 120a, where one can see that the elements between which
proportions exist were conceived sequentially, so that each element was
conceived in relation to each other. Although the entire form exhibits
proportional architecture, one must note that the limits of the whole were
not first set and then apportioned.
6

Since Bach’s first musings into using Golden Section in 1707, it is plausible that
his skill in applying Phi proportion may have progressed from single-movement to multi-
movement models so that, by 1724, he was able to execute a grand application of phi
inv

for his setting of the St. John Passion. The following analytical constructs will apply
theological and musical reasoning as a basis for phi
inv
application to the St. John Passion
to determine if Divine Proportion was one of the tools utilized by Bach to create a

5
Ibid., 125.

6
Ibid., 126.
72

structural scaffolding for the work. Such analysis may provide insight into the role that
theology played in Bach’s structural conception and execution in order to foster a deeper
understanding of his compositional process.
Analytical Construct 1
Music Rationale

This analytical construct applies a typical approach for applying phi to musical
compositions in that it considers the entire work as the basis for calculation of the Golden
Section. Because the dimensional relationship between Part I and Part II of the St. John
Passion is skewed, the break between the sections lies closer to the beginning of the work. A
typical phi application multiplies the total number of measures by 0.618 to reveal the Golden
Section, or GS. Such a calculation results in an uneven division of the work whereby the first
part is larger than the second in a typical application. However, this is not the case in Bach’s
St. John Passion as Part I possesses significantly fewer measures than Part II. As discussed
in Chapter Four, a strong theological rationale for the death of Jesus being viewed as a
starting point in Christian salvation may have prompted Bach to apply the Golden Section in
its inverse expression, phi
inv
. Due to the linear nature of music, this research is solving for
the inverse expression of phi in order to accommodate the theological reasoning for Bach’s
structuring the work; i.e., the conclusion is the point of departure. This inverse application of
phi results in a smaller first section followed by a larger second section; as is found in the
dimensions of Part I and Part II of the St. John Passion.
Solving for phi
inv
in a typical musical composition, an analyst utilizes the total
number of measures of the work to be analyzed; in the case of the St. John Passion, the
73

total number of measures is 2031. When phi
inv
is calculated using the total number of
measures,
2031 x 0.382 = 775.84
the result is the 776
th
measure of the work; specifically, measure 21 in movement 16, or
the 38
th
measure of Part II. The following figure shows this analysis:

Figure 7: Analytical Construct 1
Considering that this application was performed upon a large number of measures, it is
necessary to determine if 38 measures is an acceptable distance from the intended target
(i.e., margin of error), which would be the first measure of Part II. If the distance lies
within an acceptable margin of error, the researcher could reasonably conclude that
Analytical Construct 1 was an accurate hypothesis showing that Bach employed phi
inv
to
determine the dimensions of Part I and Part II of his St. John Passion so that the break
was indicated by a Golden Section calculation.
Scientific method dictates a result be accurate in order for it to be considered
significant. To determine if 38 measures is a reasonable margin of error, a mathematical
equation can be performed to determine the degree of precision that the phi
inv
calculation
expressed:
38 ÷ 2031 = 0.0187
74

or a 1.87% margin of error. Research applying Phi proportions to musical structure
shows a variance of accepted margins of error ranging from 0.1% to 10%; the smaller
margin of error represents an extraordinarily accurate Phi representation while the larger
number indicates a loose concept of Phi application, if at all. According to standards
employed by Charles Madden, a margin of error of 0.1% is needed to show conclusively
that the composer employed Golden Section in the compositional process. “If analysts
work within this tighter framework, they can discover who has used GS or FN rigorously
or knowingly, and who has not.”
7
While Analytical Construct 1 reveals a 1.87% margin
of error, its proximal result is impressive considering the massive size of the work. It is
important to observe that a majority of available research on Golden Section analysis in
music displays a high margin of error and authors have claimed the proportion exists in
their research when a degree of error is found to be between ±3% and ±10%. In
comparison to most research on Phi or phi proportion performed in music analysis, a
1.87% margin of error might have recently been considered an impressive, even a
definitive result. Considering the size and scope of the St. John Passion, and the sparse
research on multi-movement application of Golden Section in music, it may be that this
margin of error points strongly to the use of phi
inv
proportion in this Bach masterpiece;
however, adhering to the more narrowly defined acceptable margin of error of 0.1%
presented in Madden’s research, this result is not considered definitive. At best, one
could say that it simply points toward a “good” possibility that the work was conceived
with phi
inv
as a structural marker to indicate the place of division between Parts I and II.

7
FN refers to Fibonacci Number. Madden, Fib and Phi, 25.
75

Analytical Construct 2
Biblical Text Rationale

This analytical construct transfers the application of phi
inv
from the linear process
most typically applied in music analysis, to one based upon theological precepts laid out
in Chapter Four. A selected point of departure for the calculation of phi
inv
relies on the
theological interpretation of Jesus’s death as a beginning for the believer rather than a
conclusion to a narrative; the theological implications which held such deep significance
that it becomes the onus for Bach’s atypical application of phi
inv
. The point of departure
for the calculation is not the final measure of the composition, but rather, an internal
measure where Jesus’s death in the Passion narrative occurs. This moment in the biblical
narrative occurs at the conclusion of John 19:30, “When Jesus had received the vinegar,
he said, ‘It is finished’; and he bowed his head and gave up his spirit.”
8
Bach breaks up
this verse and sets them in two movements, movement 29 and 31 respectively. The first
half, “When Jesus had received the vinegar, he said, ‘It is finished’;” is set in the
Evangelist’s recitative of movement 29. This is followed by a commentary text by Bach
in the form of an alto aria in movement 30; then Bach completes the John 19:30 verse in
a two-measure recitative stated by the Evangelist in movement 31, “and he bowed his
head and gave up his spirit.”
Bach’s choice to split this verse into two movements separated by a commentary
aria is unusual. Even more unusual, and perhaps unsettling, is the musical effect that
movement 30, “Es ist vollbracht” (it is finished) has upon the listener. The movement
begins with a plaintively mournful melody of a solo viola di gamba accompanied by a

8
John 19:30 (RSV).
76

continuo which is joined by the singer pleading for comfort; as a commentary on this part
of the Passion narrative, the A section is extraordinarily reflective of the emotions elicited
from the biblical text. However, the B section erupts into a triumphant, melismatic
outburst that is almost shocking in its effect, “With might the hero of Judah triumphs and
ends the strife.”
9
Perhaps, it is a foreshadowing of the Easter triumph, Bach’s way of
assuring the listener that death and mourning are not the end of the story. The aria
concludes with a sudden return to the mournful theme of the viola di gamba with two
repetitions of, “it is finished,” by the alto soloist; it is as though the eruption had never
occurred.
Following this commentary, the biblical narrative resumes with a sparse, two-
measure recitative completing the text from John 19:30, “and he bowed his head and
gave up his spirit.” The fact that this short, partial verse is separated from the rest of the
narrative is significant. Traditionally, in the presentation of a Passion text in a Good
Friday service, silence is observed after this text is presented. If this moment, measure
1571 of the St. John Passion, was utilized by Bach as a starting point for phi
inv

application, one would expect the Golden Section to reveal the break between Part I and
Part II of Bach’s St. John Passion. Applying this theory, the phi
inv
calculation is
expressed mathematically as:
1571 x 0.382 = 600.122.
The 600
th
measure of the work falls in measure 8 of movement 12a; or 138 measures
before the break between Part I and Part II of the St. John Passion. Certainly, if the

9
Dürr, Bach’s St. John Passion, 165.
77

application of phi
inv
were intended to reveal the break, this is poorly conceived as the
margin of error is 6.79%, calculated as follows:
138 ÷ 2031 = 0.0679 x 100 = 6.79%
This percentage is far from the 0.1% margin of error that was adopted for this study from
Madden. However the analyst observed that the text revealed in measure 600 fell in the
middle of movement 12 which is the movement where Bach sets the final biblical text of
Part I of the St. John Passion, the denial of Peter.
10

Table 2. Textual Bridge: Biblical Texts Set in Movement 12 of the St. John Passion
Movement Biblical Texts
12
a

John, Chapter 18
24
Now Annas had sent him bound unto Caiaphas the high
priest.
25
And Simon Peter stood and warmed himself. They said
therefore unto him,
12
b
Art not thou also one of his disciples?
12
c
He denied it and said, I am not.
26
One of the servants of the high priest, being his kinsman
whose ear Peter had cut off, saith, Did not I see thee in the
garden with him?
27
Peter then denied again: and immediately the cock crew.
Matthew, Chapter 26
74
…and immediately the cock crew.
75
And Peter remembered the word of Jesus…And he went out
and wept bitterly.
Note: Biblical texts taken from the King James Version.

As discussed in Chapter Four, the pairing of Jesus’s death and Peter’s denial has been
a focus of theological discourse and a cornerstone of reconciliation theology.

10
Movement 12 is comprised of three conjoined movements identified as 12
a
, 12
b
, and 12
c
,
respectively. The three movements comprise 38 measures of music and set strictly biblical texts as
performed by the Evangelist, the crowd, Peter, and a servant.

78

Furthermore, it was shown that a phi
inv
proportion existed in the biblical text of St. John’s
account whereupon the death of Jesus occurred in the 70
th
verse of the Passion narrative.
When phi
inv
was calculated upon this number,
70 x 0.382 = 26.74
the product was rounded to indicate the 27
th
verse of chapter 18 in John’s Passion
narrative, “Peter then denied again: and immediately the cock crew.” It was observed
that it was at this point in the biblical narrative of the Passion where Bach inserted a verse
from the Matthew Passion narrative, Matthew 26:75. Recalling that the product from the
phi
inv
calculated on the 70 verses of John’s Passion account revealed 26.74, the writer
found the identical text “and immediately the cock crew” in Matthew 26:74. Perhaps this
textual bridge provided a means for Bach to include the next verse from Matthew’s
account, Matt 26:75. Furthermore, it seems plausible that Bach may even have attempted
to maintain the phi
inv
proportion present in the biblical text. The question then became,
did Bach maintain this proportion in his musical setting of the St. John Passion? Because
of this reasoning, the author expanded the analysis from the original theory to include this
possibility: perhaps the placement of the break between Part I and Part II was not the aim
of Bach’s use of phi
inv
proportion. If not the break, then did Bach intend to reproduce
this textual phenomenon in his musical depiction so that the proportion existed exactly in
the music as it did in the biblical verses? If this were the case, then the textual bridge
“and immediately the cock crew” may have been the aim of the composer’s proportional
construction. So, how far from this text does this analytical construct fall? Consider the
following pictorial representation:
79

Figure 8: Analytical Construct 2
The reader may notice that the biblical text in movement 12 contains this textual bridge.
11

If Bach’s aim were to reproduce phi
inv
proportion in terms of the textual bridge, then this
Golden Section point falls just 23 measures prior to the measure where the identified
bridge occurs resulting in a 1.0% margin of error; a close approximation of phi
inv

proportion.
12
Analytical Construct 2 does not point to a definitive application of phi
inv

proportion by Bach because it does not meet Madden’s standard of 0.1% margin of error.
Analytical Construct 3
Music and Biblical Text Rationale

The starting point for calculating phi
inv
in this construct, as in Analytical
Construct 2, relies on identifying where the death of Jesus occurs in the body of the St.
John Passion. While the previous construct departed from a biblical text, it is practical to
consider all of the texts Bach utilized to create the work including those that are
commentary in nature. For this reason, movement 35 is considered a possible point of
departure for the calculation of phi
inv
. It is comprised of a commentary text compiled by

11
See Table 2 where the duplicated texts are bolded.

12
Margin of error calculated using the following equation: 20 ÷ 1571 = 0.01. The number 20
represents the number of measures away from the bridge text and 1571 is the measure determined to be the
departure for phi
inv
calculation. The product is multiplied by 100 to convert to a percentage of 1.0%.
80

Bach that is loosely modeled on Barthold Heinrich Brockes’ libretto.
13
The aria
concludes with the text, “Thy Jesus is dead!” and the movement concludes in measure
1759.
14
When phi
inv
is calculated from this starting point,
1759 x 0.382 = 671.94
the Golden Section falls in measure 672 of the work, or measure 42 of movement 13.
This movement is also a commentary text that was probably authored by Bach and
inspired by the first verse of a poem by Christian Weise (1642-1708), “Weeping Peter.”
15

The indicated Golden Section point falls 66 measures away from the structural break
between Part I and Part II. The margin of error is determined to be 3.75%.
16
Consider
the following pictorial representation:

Figure 9: Analytical Construct 3
Thus, one can conclude that this analytical construct possesses a weaker, more suspect
application of phi
inv
when compared to the previous scenarios and does not meet
Madden’s standard of 0.1% margin of error.

13
Dürr, Bach’s St. John Passion, 47.

14
Ibid., 167.

15
Ibid., 42.

16
The calculation to determine the margin of error for Analytical Construct 3 in relation to the
break between Part I and Part II is: 66 ÷ 1759 = 0.0375 x 100 = 3.75%.
81

However, when scrutinizing other elements of the relationship between these two
movements, interesting theological implications are exposed. Simple examination shows
that movement 35 and movement 13 have the distinction of being the final arias of Part II
and Part I, respectively. The fact that calculating phi
inv
from a non-biblical, commentary
text/aria, movement 35, reflecting upon the death of Jesus, produces a Golden Section
point referring to a non-biblical commentary text/aria, movement 13, reflecting upon
Peter’s denial, is poignant. As discussed earlier, Bach masterfully crafted a textual
bridge to fuse the John and Matthew accounts thereby using the more emotional
concluding text from Matt. 26:75, “And he went out and wept bitterly.”
17
Movement 13
is the aria that Bach interpolates as he reflects upon the added text of Matt. 26:75. In a
sense, the phi
inv
calculation is highlighting a musical form, the aria. Both texts were
chosen by Bach to reflect on the Passion story. Such selected texts provide some insight
into the dedication of the composer to his church duties and perhaps shed light on Bach’s
own religious beliefs. Both arias are passionate musical reflections that personalize the
Passion story for the listener.
Movement 35: Dissolve, my heart, in floods of tears | In honor of the highest! |
Tell to the world and to heaven your sorrow, | Thy Jesus is dead!
18

Movement 13: Ah, my soul | Where dost thou wish to go, | Where shall I turn for
succor? | Shall I stay, | Or should I wish | Hill and mountain to o’erwhelm me? |
In the world there is no counsel, | And in the heart | There stand the pains | Of my
transgression, | For the servant hath denied his master.
19

17
Matt. 26:75 (RSV).

18
Dürr, Bach’s St. John Passion, 167.

19
Ibid., 145.
82

When looking at the texts in this construct, a type of call and response is exposed. In
movement 35, the soprano concludes the aria declaiming, “Thy Jesus is dead!” and, in the
GS
2
of movement 13, the tenor responds, “Where shall I turn for succor?” This scenario
may yield significant insight into theological and personal aspects of Bach’s St. John
Passion.
Returning to the argument proposed in Analytical Construct 2 where the textual
bridge was identified as the possible target of the phi
inv
point, Analytical Construct 3
reveals that the Golden Section point falls 52 measures away from the textual bridge
resulting in a margin of error of 2.96%.
20
While the textual bridge calculation is slightly
better than the 3.75% margin of error found in relation to the structural break, it too
produces a weak phi
inv
proportion, resulting in an interpretation that neither scenario for
this construct can definitively point to Bach’s intentional application of Golden Section in
the St. John Passion.
Analytical Construct 4
Extended Biblical Text Rationale

As in the previous two analytical constructs, the determination of the starting
point for this construct uses a theological premise to identify the starting point for a phi
inv

calculation. In the previous constructs, both musical and textual rationales were more
concrete. Analytical Construct 1 conformed to a typical application of Golden Section on
musical composition wherein the final measure, 2031, of the St. John Passion was
selected as starting point for calculation. Analytical Constructs 2 and 3 relied upon the

20
The calculation to determine the margin of error for Analytical Construct 3 in relation to the
textual bridge is: 52 ÷ 1759 = 0.0375 x 100 = 2.96%.
83

theological precept that Jesus’s death was the beginning of mankind’s salvation and so
therefore the biblical narrative text identifying the moment of Jesus’s death was
interpreted as the starting point for the calculation of phi
inv
. The identification of Jesus’s
death as the starting point in the Passion narrative remains the objective for Analytical
Construct 4. However, the determination of this point of departure, in this construct,
requires a more in-depth theological understanding rooted in the theology of the cross as
was discussed in Chapter Four.
Textual Bridge 2.0
In Bach’s structuring of the St. John Passion, there exists an extended narrative
surrounding Jesus’s death. In St. John’s account Jesus “gave up the ghost” in John 19:30
and the story continues with the preparation for Jesus’s burial.
21
Instead of proceeding to
the burial scene texts in John 19:31, Bach chooses to extend the death scene by adding
two verses from the St. Matthew account of the Passion story. The parallel verse to John
19:30 is Matt. 27:50 “…yielded up the ghost.” Here, Bach inserts the two subsequent
verses, Matt. 27:51-52, into his libretto:
Matthew 27
50
…yielded up the ghost.
51
And, behold, the veil of the temple was rent in twain from the top to the
bottom; and the earth did quake, and the rocks rent;
52
And the graves were opened; and many bodies of the saints which slept
arose

This additional text from Matthew details a series of acts that occur simultaneously with
the moment when Jesus gives up his spirit; such acts are not present in John’s account.
According to Luther’s theology of the cross, Matthew’s extended account symbolizes that

21
John 19:30 (KJV); Matt. 27:50-2 (KJV).
84

the law is no longer necessary to gain God’s favor and that Christ’s death becomes the
only needed act for salvation. According to Dr. Robert Smith’s commentary and
interpretation of Matt. 27:51-2, the acts that occur in tandem with Jesus’s death change
the focus of eschatology for his followers:
So far in the course of Jesus’ [sic] passion, God has been silent and either
distant or inactive. But at the precise moment of Jesus’ [sic] dying, God
sends powerful signals of divine approval upon the crucified. God does
indeed ‘desire’ him. Matthew tells how the curtain of the temple was torn
or split. This was most likely the curtain between the Holy Place and the
Holy of Holies rather than the curtain at the entrance, and its tearing at this
precise moment signifies its end and the opening of a fresh approach to the
throne of grace through the crucified. Not the curtain in the temple, not
sacrifices and rituals, not the priests and their leadership but the crucified
and resurrected one will save God’s people from their sins.

Furthermore, the earth shook and the rocks split. The earthquake signals
the great exchange: as Jesus dies, the dead revive. Tombs were opened,
and many bodies of the saints who had fallen asleep, many holy people of
old, were raised from death. Jesus’ [sic] death is the great consummation
of the promises of God, and the rising of ancient holy ones celebrates that
fact. But his death is inseparable from his resurrection, and so the vivified
saints enter the holy city, but only after he quits his own tomb on the third
day....

Matthew’s intention, of course, is to declare that in the earth-shattering
moment of Jesus’ [sic] death-and-resurrection, considered as a single
complex event, God touches the universe with creative hands here at the
end of ages as at the beginning and the old world with its old patterns and
institutions starts to crack apart and the new world begins to emerge from
the dust and ashes of the old. And a new community of old saints and new
believers emerges in that hour.
22

In the original exposition of the justification for calculating phi
inv
upon the biblical text
alone, it was determined that in the Gospel of John, the death of Jesus occurs in the 70
th

verse of the Passion narrative. Extending the Passion narrative, to incorporate the

22
Robert H. Smith, Matthew: Augsburg Commentary on the New Testament (Minneapolis:
Augsburg), 1989.
85

understanding that the events of Matt. 27:51-2 occur simultaneously with Jesus’s death,
increases the number of verses in Bach’s extended Passion narrative by two, so that the
total number of verses, from the beginning of the Passion narrative to Jesus’s death, is 72.
Recalculating phi
inv
on the adjusted number of verses present in Bach’s biblical narrative
yields another numerical sleight of hand that, many scholars argue, would be attractive to
Bach:
72 x 0.382 = 27.50
The resulting product appears to be a direct reference, numerically, to Matthew 27:50:
“Jesus, when he had cried again with a loud voice, yielded up the ghost.”
23
It is highly
significant that this numerical manipulation comes full circle. The initiation point for the
calculation of phi
inv
,
John 19
30
“When Jesus therefore had received the vinegar, he said, It is finished: and
he bowed his head, and gave up the ghost.”

reveals the parallel text from the Gospel of Matthew,
Matthew 27
50
Jesus, when he had cried again with a loud voice, yielded up the ghost.
24

For the second time, a textual bridge is used to pave the way for Bach to include
additional Matthew verses.
This additional text set by Bach is in recitative style and sung by the Evangelist in
movement 33; the conclusion of which is measure 1623. When movement 33 is utilized
as the starting point for the calculation of phi
inv
, the resulting equation reveals the 620
th

23
Matt. 27:50 (KJV).
24
John 19:30 (KJV); Matt. 27:50 (KJV) (emphasis mine).
86

measure of the St. John Passion placing the Golden Section at measure 6 of movement
12
c
.
1623 x 0.382 = 619.99
This Golden Section point falls 118 measures from the break resulting in a 7% margin of
error if the target of phi
inv
was, indeed, the break between Part I and Part II.
25
A margin
of error this large makes the hypothesis that the break was the intended target very
unlikely. In fact, this result is the least accurate of all the analytical constructs presented
thus far. What then does Golden Section analysis reveal?
The reader should recall that movement 12 is the final biblical text set in Part I,
the denial of Peter, and contains the textual bridge that Bach utilizes to transition his
libretto from the Gospel of John to the Gospel of Matthew.
26
More specifically,
movement 12
c
is a 16-measure recitative where Bach locates the textual bridge where
text is shared between John 18:27 “Peter then denied again: and immediately the cock
crew” and Matt 26:74, “Then began he to curse and to swear, saying, I know not the
man. And immediately the cock crew.”
27
In fact, the final beat of measure six is the
exact measure where Bach begins the text of John 18:27. From the discussions
previously exposed in Chapter Four as well as in Analytical Construct 2, the reader may
recall an incredible, dual reference occurs when phi
inv
is calculated on the 70 biblical

25
The calculated margin of error for this deviation from the break is: 118 ÷ 1623 = 0.7 x 100 =
7%.

26
See Table 2 - Textual Bridge: Biblical Texts Set in Movement 12 of the St. John Passion for the
texts of movement 12.

27
John 18:27 (KJV); Matt. 26:74 (KJV) (emphasis mine).
87

verses of the Passion story in the Gospel of John; the product, 26.74, can be used to
access parallel texts from the Passion accounts of John and of Matthew. From this one
product, two incredible biblical references emerge that are inherently and mathematically
present in the Bible:
1) The product, 26.74, is rounded to 27. This can be seen as a reference to the
27
th
verse of the Passion narrative, or John 18:27.

2) The exact product, 26.74, references a verse in the Gospel of Matthew: Matt.
26:74.
28

These two verses conclude with an identical text, “and immediately the cock crew.” This
parallel text was utilized by Bach to extend John’s Passion account to include Matthew’s
more dramatic and human account of Peter’s denial where Peter goes out and weeps
bitterly. Recall that the calculation of phi
inv
from the start point in measure 1623 resulted
in a Golden Section that fell in measure 620 of the St. John Passion. This is the exact
measure where the text bridge is presented. Consider the following pictorial
representation:

Figure 10: Analytical Construct 4

28
There are 70 total verses from the beginning of John’s Passion narrative to the death of Jesus in
John 19:30. The calculation for phi
inv
is: 70 x 0.382 = 26.74, which is rounded to 27. The 27
th
verse of
John’s Passion narrative is John 18:27.
88

The fact that Analytical Construct 4 reveals the exact measure of the textual bridge is
amazing by itself, however, when a phi
inv
analysis of movement 12c alone is performed,
another amazing mathematical improbability is revealed:
16 measures x 0.382 = 6.11
The rounded product indicates that measure 6 is the Golden Section of the movement. So
not only does this measure serve as the Golden Section of the movement but,
simultaneously as the Golden Section for Analytical Construct 4 where phi
inv
is
calculated from measure 1623, which is the concluding measure of movement 33, where
Bach inserted two additional texts from the Gospel of Matthew, Matt. 27:51-2. The fact
that this measure serves as the Golden Section for both calculations above is an
irrefutable indicator that the textual bridge holds great significance for Bach in terms of
its role in expressing Phi proportion in the structural design of Bach’s St. John Passion.
Because both phi
inv
calculations above fall exactly on the opening measure of the textual
bridge in measure 6, there is no margin of error; it is exact.
Number Symbolism: A Theory
In the mid to late twentieth century, there was a significant body of scholarly
writing published that explored the use of number symbolism in Bach’s musical
compositions. It is difficult to know what the composer intended and what the analyst
can state with certainty. Several more recent books and articles have been more critical
about these types of interpretations.
29
As Rebecca Lloyd states, “any reasonably
mathematically aware scholar will know that, given enough data, it is possible to find

29
See Ruth Tatlow’s book, Bach and the Riddle of the Number Alphabet (New York: Cambridge
University Press), for a source of recent scholarship criticizing work on the number alphabet theory.
89

almost any desired ‘significant’ pattern.”
30
However, it is widely accepted that Bach
employed extra-musical compositional tools such as organizing the letters of his last
name to create the B-A-C-H melodic motive.
There is some consensus that certain numbers play an important role in Bach’s
compositions, and precedence exists for the widespread number symbolism that was
influential in Lutheran Orthodoxy in the seventeenth and eighteenth centuries.
There is indeed documentary evidence…which illustrates that number
symbolism did indeed have currency in Lutheran Orthodoxy, and it is
discussed in the texts of which Bach would have been aware. Yet, this
Lutheran theory of number symbolism is strictly limited, and is biblically
rooted.
31

Unlike symbolism or cabalistic references which depend upon perception
and recognition to realize fully their potential or intended effect, Bach’s
proportional schemes are conceptual and not referential. If the Divine
Order is present in the conception of a composition’s form and
dimensions, then it need hardly have its origins or inner workings
advertised to the mundane world in order to realize its ultimate goal: to be
recognized by Him as an act of Piety, and in effect, a musical offering.
32

One of the easiest numerological applications for a composer to employ is found
in the dimension of the composition. Because the composer can freely choose the length
of a movement or composition in terms of measures or beats, it would be a simple matter
for the composer to utilize this number to represent something extra-musical. Number
symbolism of this type requires less interpretation by an analyst than an elaborate code or
system by which some revelation is uncovered. Given such a simple numerological
system, the need for elaborate interpretation is diminished; one need only find what the

30
Rebecca Lloyd, “Bach: Luther’s Musical Prophet?” Current Musicology, no. 83 (Spring 2007):
21.
31
Power, “Bach and Divine Proportion,” 15-16.

32
Ibid., 205.
90

number is referencing to uncover the meaning. In the course of this paper, analysis for
the Golden Section based upon theological principles showed that Bach maintained
proportions in his St. John Passion that paralleled the internal proportions in the biblical
text of the Passion narrative.
In Analytical Construct 1, it was shown that the Golden Section calculation
resulted in a chapter and verse product that was utilized as a textual bridge. It does not
seem conjectural, after this epiphany, to assume that Bach may have selected the number
of measures in the St. John Passion in order to reference biblical texts by their chapter
and verse; i.e., the standardized biblical versification can be used as a cipher to decode
this simple number symbolism. With this idea in mind, the writer looked at the starting
points of the four analytical constructs to see if this type of numerical symbolism might
be present. The total number of measures Bach composed in the St. John Passion is
2031.
33
Using biblical versification as the cipher, the resulting number is 20:31. Three of
the four gospels have possible corresponding texts:
34

Matthew 20
31
The crowd rebuked them, telling them to be silent; but they cried out the
more, “Lord, have mercy on us, Son of David!”
Luke 20
31
and the third took her, and likewise all seven left no children and died.
John 20
31
but these are written that you may believe that Jesus is the Christ, the Son of
God, and that believing you may have life in his name.”

Since the composition is a setting of the Passion according to St. John, the most likely
versified reference would be this gospel. And, as discussed earlier, many of the

33
Analytical Construct 1 where phi
inv
was calculated based upon musical considerations that
determined the starting point.

34
Matt. 20:31 (RSV); Luke 20:31 (RSV); John 20:31 (RSV).
91

theological principles are rooted in the Lutheran understanding of the theology of the
cross. If this interpretation were carried forward to apply to this verse, it would stand
alone as the word on which to build the story of redemption.
Analytical Construct 2 used the concluding measure, 1571 from movement 31, as
the starting point for calculating phi
inv
. Using versification as a cipher reveals no directly
corresponding verse in any of the gospels; however if chapter 15 were the starting point,
and the verses were contiguously counted, the 71
st
verse refers to:
35

Matthew 17
4
And Peter said to Jesus, “Lord, it is well that we are here; if you wish, I will
make three booths here, one for you and one for Moses and one for Elijah.”
Luke 17
8
Will he not rather say to him, ‘prepare supper for me, and gird yourself and
serve me till I eat and drink; and afterward you shall eat and drink’?
John 17
11
And now I am no more in the world, but they are in the world, and I am
coming to thee. Holy Father, keep them in thy name, which thou hast given
me, that they may be one, even as we are one.

Because these results are interpolated due to the lack of a direct reference, it is likely that
these results are unintended. However, it is interesting that the result for the Gospel of
John results in this particular verse.
Analytical Construct 3 calculated phi
inv
from the commentary text that concluded
movement 35, “Your Jesus is dead!” in measure 1759. With the same versification
cipher, no directly corresponding text is revealed. As above, utilizing chapter 17 as the
starting point, the 59
th
biblical verse results in the following verses:
36

35
Matt. 17:4 (RSV); Luke 17:8 (RSV); John 17:11 (RSV).

36
Matt. 18:32 (RSV); Luke 18:22 (RSV); John 18:33 (RSV).
92

Matthew 18
32
Then his lord summoned him and said to him, ‘You wicked servant!

I
forgave you all that debt because you besought me;
Luke 18
22
And when Jesus heard it, he said to him, “One thing you still lack. Sell all
that you have and distribute to the poor, and you will have treasure in heaven;
and come, follow me.”
John 18
33
Pilate entered the praetorium again and called Jesus, and said to him, “are
you the King of the Jews?”

Again, these are interpolated results as there was no correlating verse and it is likely that
these results are unintended.
Analytical Construct 4 yielded an exact phi
inv
proportion pointing to a textual
bridge at the precise location of the Golden Section. This construct used the concluding
measure, 1623, from movement 12
c
of the St. John Passion. Applying the simple cipher
to determine if the concluding measure of this construct was used by Bach to highlight a
biblical verse is as simple as taking 1623 and interpreting it as Chapter 16, verse 23.
With this cipher, three of the four gospels yield the following texts:
37

Matthew 16
23
But he turned and said to Peter, “Get behind me, Satan! You are a
hindrance to me; for you are not on the side of God, but of men.”
Luke 16
23
and in Hades, being in torment, he lifted up his eyes, and saw Abraham
far off and Lazarus in his bosom.
John 16
23
In that day you will ask nothing of me. Truly, truly, I say to you, if you
ask anything of the Father, he will give it to you in my name.

While there are three results, a strong argument exists indicating that the Gospel
of Matthew is the intended target. The point of departure for Analytical Construct 4 is
movement 33. This is where Bach sets two verses from the Gospel of Matthew,

37
Matt. 16:23 (RSV); Luke 16:23 (RSV); John 16:23 (RSV).
93

Matt. 27:51-2. The concluding measure is 1623, a number that Bach had control over in
terms of length of his composition and could have maintained the proportional
relationship with any number of measures. Selecting this particular number suggests that
Bach may have exercised great care to craft a unified Passion where his keen numerical
observations justified the inclusion of Matthew texts into his St. John Passion. Because
of this, it is highly likely that Matthew’s gospel acted as both departure and arrival for
this numerical sleight of hand. This verse is the climax of the particular story being
related in this chapter of the Bible. Jesus revealed that he was to suffer, die, and be
resurrected. Peter, horrified by Jesus’s words, rebuked him saying that this will never
happen to Jesus and Jesus’s reply was recorded in Matt. 16:23. The fact that, again, this
calculation pairs Jesus’s death with a verse consisting of a statement by Peter recalls
Luther’s theology of glory juxtaposing God and humankind in reconciliation.
94

CHAPTER SIX

Conclusion

This paper has explored a complex conceptualization of the musical structures,
predicated upon a theological rationale, as they apply to Bach’s masterwork, the St. John
Passion. Music scholars have employed Golden Section analysis upon many works by
various composers in order to gain insight about their compositional processes through
identifying significant structural components. Many such analyses have been performed
upon compositions by Bach revealing that his use of the Golden Section is frequent and
purposeful. Several considerations set this study apart from others in the related
scholarship. This study applies Golden Section analysis upon a massive, multi-
movement work where most Golden Section studies to date have examined small
compositions or individual movements from larger compositions. Additionally, this
study considered an extra-musical premise to determine how to apply Golden Section to
the composition. These revelations were identified in the libretto to obtain a starting
point for the phi
inv
calculation and resulted in a new archetype of Phi application whereby
an embedded Phi proportion was revealed. This application was shown to be a basis for
structuring the St. John Passion resulting in an atypical break between Part I and Part II
which did not follow the literary structure of the Passion story for the Gospel of John as
was traditionally applied in Bach’s time.
The history of Phi was presented to illuminate the significance of the proportion
as it occurs in nature and so that the reader might understand how this proportion is not
only beautiful, but how the proportion serves an innately functional purpose; e.g., the
95

packing of seeds in a sunflower, the arrangement of leaves on a stem in order to
maximize sun exposure, the orbits of the planets as exposed by Kepler. Moreover, this
study showed that this proportion was naturally and, later, purposefully recreated in art,
science and music. Analysis reveals its fundamental beauty as expressed in musical form
by identifying the purposeful application of this natural phenomenon in music. Power’s
research provided theories for Bach’s knowledge of Divine Proportion application and
many studies have revealed this proportion in his music. However, scholarship is lacking
in Golden Section analysis of Bach’s earlier works which might show how early in his
oeuvre he began to employ Phi proportions.
Working within a politically-charged atmosphere in Leipzig, in terms of the town
council’s opposing desires for musical pietism or modernism, Bach displayed great
innovation while remaining true to the tradition of his musical heritage. As third choice
for the position of Cantor, Bach was compelled to show his theological and
compositional prowess. He unveiled his St. John Passion within a year of his
appointment; its scale and profundity certainly did not ingratiate him to the conservatives
active in the church’s political structure who revered a 200-year tradition of the Passion
presented in plainchant. Bach’s presentation of the St. John narrative in the form of an
oratorio Passion was theologically grounded in Lutheran principles while extraordinarily
musically advanced. Bach’s knowledge, and study, of Lutheran ideals was extensive and,
in his Calov Bible Commentary, he underlined Martin Luther’s own writings surrounding
John 19:30; identifying this as a highly significant salvific moment expounded in the
theology of the cross.
96

While analysts have explored Divine Proportion in music, most analyses have
been limited to small works. This study provides validity for the analysis of more
complex structures that are performed across multi-movement compositions. With the
success of this larger application, it is hoped that more research will be undertaken that
can provide deeper understanding of the composer’s process in terms of both inherent
musical symmetry and structure and extra-musical, embedded information that might
enlighten the understanding of the composer’s work.
1

A theological precept for Bach’s construction of the St. John Passion was proven
to be plausible based upon calculating phi
inv
from four different starting points; one based
upon musical dimension and three upon theological conceptions. While all the analytical
constructs appeared to approach Phi proportion, Analytical Construct 4 revealed an exact
expression in light of the theological premise centered at the death of Jesus in John 19:30.
This passage became the mathematician’s window into a concealed Phi proportion that
was inherent in the scripture; the pairing of Jesus’s death and Peter’s denial. Bach
observed the numerical reference and utilized this as a textual bridge in the libretto of his
St. John Passion merging the shared text – And immediately the cock crew – from the
27
th
verse of John’s Passion narrative and Matt. 26:74. Bach created a second textual
bridge by including parallel verses from Matthew in order to extend John’s account of the
moment of Jesus’s death in the narrative. By doing so, the total number of verses was
extended to 72, thereby creating a full circle with another Phi calculation:

1
Madden, Fib and Phi, 109-50. All of the studied works from the Baroque era compiled by this
author contain less than 200 measures and are limited to the study of individual movements or small,
complete works. In fact, a great number of the works are small enough that they were analyzed by the
number of beats they contain.
97

72 x 0.382 = 27.50
which is a reference to the Gospel of Matthew, “and he yielded up the ghost.”
2

Because the starting points for the analytical constructs were based on a numerical
interpretation of the scripture, a numerological aspect was unearthed whereby
interpreting the concluding measure numbers as scriptural chapter and verse revealed
compelling findings. Based upon the research presented in the analytical constructs of
Chapter Five, it is the opinion of this writer that Bach utilized Phi in the construction of
his St. John Passion in a very calculated and precise methodology. Possessing keen
intellect, a penchant for mathematics and a profound understanding of Lutheran theology,
Bach certainly observed the Phi proportion in the biblical text that connected Jesus’s
death to Peter’s denial. This would have seemed a divine confirmation of Luther’s
interpretation as expressed in his theology of the cross. The odds that a Phi proportion
exists in the biblical narrative and that the textual bridge it reveals exists in the exact
execution of a Phi proportion in a composition of this magnitude would be
astronomically small. By recreating both a numerical and textual Phi proportion in his St.
John Passion, Bach exercised a great act of piety. The concurrence of this proportion is
clearly revealed in the Phi analysis on the biblical text in Chapter Four and in Analytical
Construct 4 of Chapter Five.
The literature written about Bach contains many numerological and theological
studies. Some studies appear to be highly interpretive and their validity has been called
into question. The methodology in this research avoided speculation and interpretation

2
Matt. 27:50 (KJV); John 19:30 (KJV).
98

by adhering to the high standards set forth in Madden’s book, Fib and Phi in Music.
When seeking an explanation for the abnormally early break between Part I and Part II of
the St. John Passion, and being aware of research espousing Bach as a theologian, the
writer began with a hypothesis that the Golden Proportion was executed from a
theological standpoint resulting in the Phi proportion being expressed atypically; i.e., the
work was conceived in reverse with phi
inv
proportion governing the construction.
The writer believes that the break between Part I and Part II of the St. John
Passion was, indeed, dictated by Bach’s extra-musical, theological rationale, evidenced
by his atypical application of Phi proportion. The resulting textual bridge, revealed by
Bach’s phi
inv
application from the death of Jesus in John 19:30, reveals the denial of Peter
– this is the final biblical text presented in Part I. It is followed by a reflective aria on
Peter’s shame and Part I concludes with the traditional chorale prior to the presentation of
the sermon in the context of a Good Friday service.
When the textual bridge was discovered during analysis and the writer observed
that the calculation corresponded directly to the biblical chapter and verse, it was logical
for the writer to explore the numerological aspect present in the concluding measure
numbers of the various constructs. It is hoped that continued research will validate the
findings presented in this paper and that multi-movement works by Bach as well as other
composers will be analyzed to reveal other musical structures exhibiting Phi proportion.
With this new horizon of research possibilities, it is uncertain what will be
uncovered. What is certain, however, is that Bach remains a masterful architect, a
composer who was able to build intricately constructed works of art that are timeless.
99

Bach’s compositions and his compositional process continue to draw intense interest for
scholarly research. This analysis and research was driven by such a fascination which
proves that Bach, in particular his larger compositions like the St. John Passion,
continues to be a source of inspiration to new generations.
Bach is considered by some as “‘the classic Lutheran layman,’ ‘a sign of God,’ …
‘the first great German voice since Luther,’ and, more extravagantly still, ‘Bach, the Fifth
Evangelist.’”
3
The St. John Passion, at least in terms of this research, is seen as Bach’s
ultimate proclamation of his Lutheran heritage; a reiteration of the words found in the
1580 Augsburg Confession of the Evangelical Lutheran Church:
…human beings cannot be justified before God by their own powers,
merits, or works. But they are justified as a gift on account of Christ
through faith when they believe that they are received into grace and that
their sins are forgiven on account of Christ, who by his death made
satisfaction for our sins.
4

Bach ingeniously combined his skill in mathematics, music, and theology to
create a unique Passion narrative that not only lifted up the biblical text but provided a
deep commentary on the human experience of grace. Returning to the verse that remains
the cornerstone of this research, the verse indicated by the number of measures Bach
composed in his St. John Passion, 2031:
John 20:31, “these are written that you may believe.”

Soli Deo gloria.

3
Leaver, J. S. Bach and Scripture, 13.

4
Robert Kolb and Timothy J. Wengert, eds., The Book of Concord: The Confessions of the
Evangelical Lutheran Church (Minneapolis: Fortress Press, 2000), 39-40.
100

BIBLIOGRAPHY

Black, M.H., The Cambridge History of the Bible. Vol. 3, The West from the Reformation
to the Present Day, Chapter XII: The Printed Bible. Edited by S. L. Greenslade.
Cambridge: Cambridge University Press, 1969.

Braaten, Carl E. Principles of Lutheran Theology, 2d ed. Philadelphia: Fortress Press,
2007.

Bruce, F. F. The New Testament Documents: Are They Reliable? 5
th
ed. Downers
Grove, Illinois: InterVarsity Press, 1960.

Culpepper, R. Alan. The Gospel and Letters of John. Nashville: Abingdon Press, 1998.

David, Hans T., Arthur Mendel, and Christoph Wolff, eds. The New Bach Reader: A Life
of Johann Sebastian Bach in Letter and Documents. New York: W.W. Norton, 1998.

Dürr, Alfred. Johann Sebastian Bach’s St. John Passion: Genesis, Transmission, and
Meaning. Translated by Alfred Clayton. New York: Oxford University Press, 2002.

Geiringer, Karl. Johann Sebastian Bach: The Culmination of an Era. New York: Oxford
University Press, 1966.

Gritsch, Eric W. and Robert W. Jenson. Lutheranism: The Theological Movement and Its
Confessional Writings. Philadelphia: Fortress Press, 1976.

Halley, Henry H. Halley's Bible Handbook, 25th ed. Michigan: Zondervan, 2000.

Huntley, Herbert Edwin. The Divine Proportion: A Study in Mathematical Beauty. New
York: Dover, 1970.

Kolb, Robert. “Luther on the Theology of the Cross.” Lutheran Quarterly 16 (Winter
2002): 443-466.

Kolb, Robert and Timothy J. Wengert, eds. The Book of Concord: The Confessions of
the Evangelical Lutheran Church. Minneapolis: Fortress Press, 2000.

Leaver, Robin A., ed. J. S. Bach and Scripture: Glosses from the Calov Bible
Commentary. St. Louis: Concordia, 1985.

Leaver, Robin A., “J.S. Bach’s Faith and Christian Commitment.” The Expository
Times, no. 96 (March 1985): 168-73.

101

Lehner, Mark. The Complete Pyramids: Solving the Ancient Mysteries. London: Thames
and Hudson, 1997.

Lloyd, Rebecca. “Bach: Luther’s Musical Prophet?” Current Musicology, no. 83 (Spring
2007): 5-32.

Lull, Timothy E., ed. Martin Luther’s Basic Theological Writings. Minneapolis:
Fortress Press, 1989.

Luther, Martin. Luther’s Works. Vol. 69, Sermons on the Gospel of St. John, Chapters
17-20. Edited by Christopher Boyd Brown. St. Louis: Concordia, 2009.

Madden, Charles. Fib and Phi in Music: The Golden Proportion in Musical Form. Salt
Lake City: High Art Press, 2005.

Olsen, Scott. The Golden Section: Nature’s Greatest Secret. New York: Walker, 2006.

Pelikan, Jaroslav Jan. Introduction to Luther’s Works. Vol. 24, Sermons on the Gospel
of St. John, Chapters 14-16, by Martin Luther, vi-ix. Edited by Jaroslav Jan Pelikan. St.
Louis: Concordia Publishing House, 1961.

Power, Tushaar. “J. S. Bach and the Divine Proportion.” PhD diss., Duke University,
2001. ProQuest (Document ID # 908115250).

Smallman, Basil. The Background of Passion Music: J. S. Bach and his predecessors.
London: SCM Press, 1957.

Smith, Robert H. Matthew: Augsburg Commentary on the New Testament. Minneapolis:
Augsburg, 1989.

Tatlow, Ruth. Bach and the Riddle of the Number Alphabet. New York: Cambridge
University Press, 1991.

Von Fischer, Kurt and Werner Braun. "Passion." Grove Music Online, Oxford Music
Online, accessed September 8, 2012, http://www.oxfordmusiconline.com.libproxy
.usc.edu/subscriber/article/grove/music/40090.

Wienandt, Elwyn A. Choral Music of the Church. New York: Free Press, 1965.

Wolff, Christoph. Johann Sebastian Bach: The Learned Musician. New York: W.W.
Norton, 2001.
102

Appendix A: English Translation of the St. John Passion
1

Part I
1 Chorus
Lord, thou our Governor, whose renown
Is excellent in all the earth!
Shew us through thy Passion,
That thou, the very Son of God,
In every age,
Even in the greatest lowliness,
Wast glorified!
2
a
Evangelist
Jesus went forth with his disciples over the brook
Cedron, where was a garden, into the which he entered,
And his disciples. And Judas also, which betrayed him,
Knew the place: for Jesus oft-times resorted thither with
his disciples. Judas then, having received a band of men
and officers from the chief priests and Pharisees,
cometh thither with lanterns and torches and weapons.
Jesus therefore, knowing all things that should come
Upon him, went forth, and said unto them,
Jesus
Whom seek ye?
Evangelist
They answer him,
2
b
Chorus
Jesus of Nazareth.
2
c
Evangelist
Jesus saith unto them,
Jesus
I am he.
Evangelist
And Judas also, which betrayed him, stood with them.
As soon then as he had said unto them, I am he, they
Went backward, and fell to the ground. Then asked he them again,
Jesus
Whom seek ye?
Evangelist
And they said,

1
Dürr, Bach’s St. John Passion, 135-77. Italicized words from this translated source represent
biblical texts while non-italicized words are commentary texts compiled by Bach.
103

2
d
Chorus
Jesus of Nazareth.
Evangelist
Jesus answered,
Jesus
I have told you that I am he: if therefore ye seek me, let these go their way:
3 Chorale
O greatest love, o love that’s never-ending,
Which thee hath brought unto this martyr’s path!
I lived with the world in gladness and delight,
And thou must suffer.
4 Evangelist
That the saying might be fulfilled, which he spake,
Of them which thou gavest me have I lost none.
Then Simon Peter having a sword drew it,
and smote the high priest’s servant,
And cut off his right ear.
The servant’s name was Malchus.
Then said Jesus unto Peter,
Jesus
Put up thy sword into the sheath:
the cup which my Father hath given me, shall I not drink it?
5 Chorale
Thy will be done, Lord God, at once
On earth and in heavens’ realm.
Grant us patience in adverse times,
Obedience in love and pain;
Defend and keep all flesh and blood,
Which doth transgress against thy will.
6 Evangelist
Then the band and the captain and officers of the Jews took Jesus, and bound
him. And led him away to Annas first; for he was father in law to Caiaphas,
which was the high priest that same year. Now Caiaphas was he, which gave
counsel to the Jews, that it was expedient that one man should die for the
people.
7 Alto Aria
From the bonds of my sings to unbind me,
My Saviour is being bound.
From all the running sores of vice
Fully to heal me,
He allows himself to be wounded.
8 Evangelist
And Simon Peter followed Jesus,
and so did another disciple:
104

9 Soprano Aria
I follow thee also with steps that are joyful,
And will not leave thee,
My life, my light.
Assist thou the path
And yet do not cease,
Thyself to draw me, to push me, and to entreat!
10 Evangelist
That disciple was known unto the high priest, and went in with Jesus into the
palace of the high priest. But Peter stood at the door without. Then went out
that other disciple, which was known unto the high priest, and spake unto her
that kept the door, and brought in Peter. Then saith the damsel unto Peter,
Ancilla
Art not thou also one of this man’s disciples?
Evangelist
He saith,
Peter
I am not.
Evangelist
And the servants and officers stood there, who had made a fire of coals;
for it was cold: and they warmed themselves: and Peter stood with them,
and warmed himself. The high priest then asked Jesus of his disciples,
and of his doctrine. Jesus answered him,
Jesus
I spake openly to the world; I ever taught in the synagogue, and in the temple,
whither the Jews always resort; and in secret have I said nothing.
Why askest thou me? Ask them which heard me, what I have said unto them:
behold, they know what I said.
Evangelist
And when he had thus spoken, one of the officers
which stood by struck Jesus with the palm of his hand, saying,
Servant
Answerest thou the high priest so?
Evangelist
Jesus answer him,
Jesus
If I have spoken evil, bear witness of the evil:
but if well, why smitest thou me?
105

11 Chorale
What man hath thee thus smitten,
My saviour, and with tortures
So badly bruised and hurt?
For thou art not a sinner,
As we are and our children,
Thou knowest no transgressions.

I, I and my sins,
Which are as numerous as small grains
Of sand found by the sea,
For thee they have brought forth
The sorrow, which o’erwhelms thee,
And the doleful host of torments.
12
a
Evangelist
Now Annas had sent him bound unto Caiaphas the high priest.
And Simon Peter stood and warmed himself.
They said therefore unto him,
12
b
Chorus
Art thou not also one of his disciples?
12
c
Evangelist
He denied it and said,
Peter
I am not.
Evangelist
One of the servants of the high priest,
being his kinsman whose ear Peter had cut off, saith,
Servant
Did not I see thee in the garden with him?
Evangelist
Peter then denied again: and immediately the cock crew.
And Peter remembered the word of Jesus.
And he went out, and wept bitterly.
13 Tenor Aria
Ah, my soul
Where dost thou wish to go,
Where shall I turn for succour?
Shall I stay,
Or should I wish
Hill and mountain to o’erwhelm me?
In the world there is no counsel,
And in the heart
There stand the pains
Of my transgression,
For the servant hath denied his master.
106

14 Chorale
Peter, who doth not think back
And his God denieth,
Who yet at a solemn glance
Bitter tears doth weep.
Jesus, also look on me,
When I resist repentance
When things evil I have done
Stir my inner conscience.

Part II
15 Chorale
Christ, the source of our salvation,
No evil committed,
Who for us was in the night
Like a thief arrested,
Brought up before godless men
And falsely accused,
Derided, mocked and spat upon,
As the scriptures tell us
16
a
Evangelist
Then led they Jesus from Caiaphas unto the hall of judgment:
and it was early; and they themselves went not into the judgment hall,
lest they should be defiled; but that they might eat the Passover.
Pilate then went out unto them, and said,
Pilate
What accusation bring ye against this man?
Evangelist
They answered and said unto him,
16
b
Chorus
If he were not a malefactor, we would not have delivered him up unto thee
16
c
Evangelist
Then said Pilate unto them,
Pilate
Take ye him, and judge him according to your law.
Evangelist
The Jews therefore said unto him,
16
d
Chorus
It is not lawful for us to put any man to death:
107

16
e
Evangelist
That the saying of Jesus might be fulfilled, which he spake, signifying what
death he should die. Then Pilate entered into the judgment hall again, and
called Jesus, and said unto him,
Pilate
Art thou the King of the Jews?
Evangelist
Jesus answered him,
Jesus
Sayest thou this thing of thyself, or did others tell it thee of me?
Evangelist
Pilate answered,
Pilate
Am I a Jew? Thine own nation and the chief priests have delivered thee unto
me: what hast thou done?
Evangelist
Jesus answered,
Jesus
My kingdom is not of this world: if my kingdom were of this world, then
would my servants fight, that I should not be delivered to the Jews: but now is
my kingdom not from hence.
17 Chorale
Ah mighty King, great in all times and ages,
How can I rightly praise this great devotion?
No human heart can yet imagine ever,
What it may give thee.

I cannot with my senses reach and utter
With what and how thy mercy to compare.
How can I then thy deeds of loving-kindness,
In work repay thee?
18
a
Evangelist
Pilate therefore said unto him,
Pilate
Art thou a king then?
Evangelist
Jesus answered,
Jesus
Thou sayest that I am a king. To this end was I born, and for this cause came
I into the world, that I should bear witness unto the truth. Every one that is of
the truth heareth my voice.
Evangelist
Pilate saith unto him,

108

Pilate
What is truth?
Evangelist
And when he had said this, he went out again unto the Jews, and saith unto
them,
Pilate
I find in him no fault at all. But ye have a custom, that I should release unto
you one [at the passover]: will ye therefore that I release unto you the King
of the Jews?
Evangelist
Then cried they all again, saying,
18
b
Chorus
Not this man, but Barabbas.
18
c
Evangelist
Now Barabbas was a robber [murderer]. Then Pilate therefore took Jesus,
and scourged him.
19 Bass Arioso
Behold then, o my soul, with timorous pleasure,
With bitter joy and sad and heavy heart,
Thy greatest good in Jesus’ [sic] sufferings,
How on the thorns, the which do pierce him,
Heaven’s primroses flower for thee!
Many a sweet fruit thou canst thus from his sorrow pluck,
Therefore look on him evermore.
20 Tenor Aria
Consider how his back that’s stained with blood,
In all its aspects
Like unto the heavens is,
Where, after the watery billows
Of the deluge of our sings have passed,
The most beautiful of rainbows stands
As symbol of the grace of God!
21
a
Evangelist
And the soldiers plaited a crown of thorns, and put it on his head, and they
put on him a purple robe. And said,
21
b
Chorus
Hail, King of the Jews!
21
c
Evangelist
And they smote him with their hands. Pilate therefore went forth again, and
saith unto them,
Pilate
Behold, I bring him forth to you, that ye may know that I find no fault in him.
Evangelist
Then came Jesus forth, wearing the crown of thorns, and the purple robe.
And Pilate saith unto them,
109

Pilate
Behold the man!
Evangelist
When the chief priests therefore and officers saw him, they cried out, saying,
21
d
Chorus
Crucify him, crucify him.
21
e
Evangelist
Pilate saith unto them,
Pilate
Take ye him, and crucify him: for I find no fault in him.
Evangelist
The Jews answered him,
21
f
Chorus
We have a law, and by our law he ought to die,
because he made himself the Son of God.
21
g
Evangelist
When Pilate therefore heard that saying, he was the more afraid; And went
again into the judgment hall, and saith unto Jesus,
Pilate
Whence art thou?
Evangelist
But Jesus gave him no answer.
Then saith Pilate unto him,
Pilate
Speakest thou not unto me? knowest thou not that I have the power to crucify
thee, and have power to release thee?
Evangelist
Jesus answered,
Jesus
Thou couldest have no power at all against me,
except it were give thee from above:
therefore he that delivered me unto thee hath the greater sin.
Evangelist
And from thenceforth Pilate sought to release him:
22 Chorale
Through this thy prison, Son of God,
To us must freedom come.
Thy dungeon is the throne of grace,
The refuge of the faithful.
And if thou wast not thus in thrall
Our thraldom would eternal be.
23
a
Evangelist
But the Jews cried out, saying,
110

23
b
Chorus
If thou let this man go, thou art not Caesar’s friend:
whosoever maketh himself a king speaketh against Caesar.
23
c
Evangelist
When Pilate therefore heard that saying, he brought Jesus forth, and sat
down in the judgment seat in a place that is called the Pavement, but in
Hebrew, Gabbatha. And it was the preparation of the passover, and about the
sixth hour: and he saith unto the Jews,
Pilate
Behold your King!
Evangelist
But they cried out,
23
d
Chorus
Away with him, away with him, crucify him.
23
e
Evangelist
Pilate saith unto them,
Pilate
Shall I crucify your King?
Evangelist
The chief priests answered,
23
f
Chorus
We have no king but Caesar.
23
g
Evangelist
Then delivered he him therefore unto them to be crucified.
And they took Jesus, and led him away.
And he bearing his cross went forth into a place called the place of a skull,
which is called in the Hebrew Golgotha:
24 Bass Aria
Hasten, ye souls that are tempted,
Leave your dens of torment,
Hasten―where to?―to Golgotha!
Take up the wings of faith,
Flee―where to?―to the hill of the cross,
There where your salvation lies.
25
a
Evangelist
Where they crucified him, and two other with him, on either side one,
and Jesus in the midst. And Pilate wrote a title, and put it on the cross.
And the writing was, JESUS OF NAZARETH THE KING OF THE JEWS.
This title then read many of the Jews: for the place where Jesus was crucified
was nigh to the city: and it was written in Hebrew, and Greek, and Latin.
Then said the chief priests of the Jews to Pilate,
25
b
Chorus
Write not, The King of the Jews; but that he said, I am King of the Jews.
111

25
c
Evangelist
Pilate answered,
Pilate
What I have written I have written.
26 Chorale
In the recesses of my heart
Thy name and cross alone
Gleam at all times and hours,
Wherefore I can rejoice.
Come to me in this image
As comfort in my distress,
How thou, Lord Christ, so gently
Thyself didst bleed to death.
27
a
Evangelist
Then the soldiers, when they had crucified Jesus, took his garments,
and made four parts, to every soldier a part; and also his coat:
now the coat was without seam, woven from the top throughout.
They said therefore among themselves,
27
b
Chorus
Let us not rend it, but cast lots for it, whose it shall be:
27
c
Evangelist
That the scripture might be fulfilled, which saith,
They parted my raiment among them, and for my vesture they did cast lots.
These things therefore the soldiers did.
Now thee stood by the cross of Jesus his mother, and his mother’s sister,
Mary the wife of Cleophas, and Mary Magdalene.
When Jesus therefore saw his mother, and the disciple standing by,
whom he loved, he saith unto his mother,
Jesus
Woman, behold thy son!
Evangelist
Then saith he to the disciple,
Jesus
Behold thy mother!
28 Chorale
He took care of everything,
Even at the last hour,
Of his mother he did think,
And gave her a guardian.
O man, strive for what is right,
Love both God and human kind,
Die thereafter without pain,
And do not be sorrowful.
112

29 Evangelist
And from that hour the disciple took her unto his own home.
After this, Jesus knowing that all things were now accomplished,
that the scripture might be fulfilled, saith,
Jesus
I thirst.
Evangelist
Now there was set a vessel full of vinegar: and they filled a sponge with
vinegar, and put it upon hyssop, and put it to his mouth. When Jesus therefore
had received the vinegar, he said,
Jesus
It is finished.
30 Alto Aria
It is finished!
O comfort for afflicted souls!
The night of mourning
Now doth toll the final hour.
With might the hero of Judah triumphs
And ends the strife.
It is finished!
31 Evangelist
And he bowed his head, and gave up the ghost.
32 Bass Aria
My dearest saviour, may I ask thee
Jesus, thou who was dead,
Now that thou are nailed to the cross
And thyself hast said: it is finished,
Thou livest now forever,
Have I been released from death?
Nowhere in death’s final hour
Shall I turn for succour
Can I through thy pains and death
Heaven now inherit?
Has all the world’s salvation come?
But to thee, who dost redeem me,
O thou dearest lord!
Though nothing thou canst say for pain,
Give me but what is thy due,
Yet dost thou bow thy head
And in silence utter: yes.
More I do not hope for!
33 Evangelist
And, behold, the veil of the temple was rent in twain from the top to the
bottom: and the earth did quake, and the rocks rent; And the graves were
opened; and many bodies of the saints which slept arose.
113

34 Tenor Arioso
My heart, while the whole world
With Jesus’ [sic] sufferings also suffers,
The sun appareled is in mourning,
The veil is rent, the rocks crash down,
The earth doth quake, and graves do open,
Because they see their maker die,
What for thy part canst thou do now?
35 Soprano Aria
Dissolve, my heart, in floods of tears
In honour of the highest!
Tell to the world and to heaven your sorrow,
Thy Jesus is dead!
36 Evangelist
The Jews therefore, because it was the preparation, that the bodies should
not remain upon the cross on the sabbath day (for that sabbath day was an
high day), besought Pilate that their legs might be broken, and that they
might be taken away. Then came the soldiers, and brake the legs of the first,
and of the other which was crucified with him. But when they came to Jesus,
and saw that he was dead already, they brake not his legs: But one of the
soldiers with a spear pierced his side, and forthwith came there out blood
and water. And he that saw it bare record, and his record is true: and he
knoweth that he saith true, that ye might believe. For these things were done,
that the scripture should be fulfilled, A bone of him shall not be broken. And
again another scripture saith, They shall look on him whom they pierced.
37 Chorale
Help us, Christ, the Son of God,
Through thy most bitter pains,
To obey thee always,
To eschew all evil,
Thy death and its cause
Fruitfully to ponder,
And thus, though poor and weak,
To give thankofferings to thee!
38 Evangelist
And after this Joseph of Arimathaea, being a disciple of Jesus, but secretly
for fear of the Jews, besought Pilate that he might take away the body of
Jesus: and Pilate gave him leave. He came therefore, and took the body of
Jesus. And there came also Nicodemus, which at the first came to Jesus by
night, and brought a mixture of myrrh and aloes, about a hundred pound
weight. Then took they the body of Jesus, and wound it in linen clothes with
the spices, as the manner of the Jews is to bury. Now in the place where he
was crucified there was a garden; and in the garden a new sepulcher wherein
was never man yet laid. There laid they Jesus therefore because of the Jews’
preparation day; for the sepulchre was nigh at hand.
114

39 Chorus
Sleep well, ye holy relics,
Which I no longer now bewail,
Sleep well and also bring me sleep!

The grave, which is your destined place
And now no sorrow knows,
Doth open heaven up for me and shuts the gates of hell.
40 Chorale
O Lord, let thy dear angel small
At the last hour translate my soul
To the bosom of Abraham,
The body in its small place of rest
Lie gently without hurt and pain
Resting until judgment day!
And then awake me from the dead,
That with mine eyes I shall see thee
In joy eternal, Son of God,
My saviour and the throne of grace!
Lord Jesus Christ, O hear my cry,
I wish to praise thee eternally!

115

Appendix B: Contiguous Numbering of Measures in the St. John Passion

Movement
Number
Number of
Measures
Starting
Measures
PART I
No. 1 = 153 1
No. 2 = 39
2a 154
2b 171
2c 175
2d 184
2e 188
No. 3 = 11 193
No. 4 = 15 204
No. 5 = 12 219
No. 6 = 11 231
No. 7 = 114 242
No. 8 = 3 356
No. 9 = 164 359
No. 10 = 46 523
No. 11 = 24 569
No. 12 = 38
12a 593
12b 598
Textual Bridge (m. 620) 12c 615
No. 13 = 91 631
No. 14 = 16 722
TOTAL # MEASURES 737
PART II
No. 15 = 17 738
No. 16 = 80
16a 755
16b 765
16c 793
116

Movement
Number
Number of
Measures
Starting
Measures
16d 796.5
16e 813
No. 17 = 22 835
No. 18 = 29
18a 857
18b 876
18c 880
No. 19 = 18 886
No. 20 = 64 904
No. 21 = 106
21a 968
21b 972.5
21c 983.5
21d 996
21e 1019.5
21f 1024
21g 1057
No. 22 = 12 1074
No. 23 = 88
23a 1086
23b 1087.5
23c 1120
23d 1130
23e 1156.5
23f 1160
23g 1164
No. 24 = 191 1174
No. 25 = 32
25a 1365
25b 1382.5
25c 1393.5
No. 26 = 16 1397
No. 27 = 83
117

Movement
Number
Number of
Measures
Starting
Measures
27a 1413
27b 1422
27c 1477
No. 28 = 16 1496
No. 29 = 14 1512
No. 30 = 44 1526
No. 31 = 2 1570
Analytical Construct 2 1571
No. 32 = 45 1572
No. 33 = 7 1617
Analytical Construct 4 1623
No. 34 = 9 1624
No. 35 = 127 1633
Analytical Construct 3 1759
No. 36 = 30 1760
No. 37 = 17 1790
No. 38 = 25 1807
No. 39 = 172 1832
No. 40 = 28 2004
Analytical Construct 1 2031

118

Appendix C: Outline of Tonal Centers and Performing Forces for Bach’s St. John
Passion

NBA Movement Tonal Center Instrumentation Vocal Forces
PART I
1 Herr, unser Herrscher G minor 2 ob, 2 vln, 1
vla, 1 Continuo
Chorus
2a Jesus ging mit seinen
Jüngern
C minor Continuo Evangelist,
Jesus
2b Jesum von Nazareth G minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
2c Jesus spricht zu ihnen G minor Continuo Evangelist,
Jesus
2d Jesum von Nazareth C minor 2 ob, 2 vln, vla,
Continuo
Chorus
2e Jesus antwortete Bb major Continuo Evangelist,
Jesus
3 O große Lieb G minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
4 Auf daß das Wort erfüllet
würde
Bb major Continuo Evangelist,
Jesus
5 Dein Will gescheh, Herr
Gott, zugleich
D minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
6 Die Schar aber und der
Oberhauptmann
F major Continuo Evangelist
7 Von den Stricken meiner
Sünden
D minor 2 ob, Continuo Alto solo
8 Simon Petrus aber
folgete Jesu nach
Bb major Continuo Evangelist
9 Ich folge Bb major 2 fl, Continuo Soprano solo
10 Derselbige Jünger war
dem Hohenpriester
bekannt
G minor Continuo Evangelist,
Maid, Peter,
Jesus,
Attendant
11 Wer hat dich so
geschlagen
A major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
12a Und Hannas sandte ihn
gebunden
A major Continuo Evangelist
12b Bist du nicht seiner
Jünger einer
E major 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
12c Er leugnete aber und
sprach
A major Continuo Evangelist,
Petrus,
Attendant
119

NBA Movement Tonal Center Instrumentation Vocal Forces
13 Ach, mein Sinn F# minor 2 vln, vla,
Continuo
Tenor solo
14 Petrus, der nicht denkt
zurück
F# minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
PART II
15 Christus, de runs selig
macht
E major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
16a Da führeten sie Jesum A major Continuo Evangelist,
Pilate
16b Wäre dieser nicht ein
Übeltäter
D minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
16c Da sprach Pilatus zu
ihnen
D minor Continuo Evangelist,
Pilate
16d Wir durfen niemand töten A minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
16e Auf daß erfüllet würde
das Wort
A minor Continuo Evangelist,
Pilate, Jesus
17 Ach großer König A minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
18a Da sprach Pilatus zu ihm C major Continuo Evangelist,
Pilate
18b Nicht diesen, sondern
Barrabam
D minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
18c Barrabas aber war ein
Mörder
D minor Continuo Evangelist
19 Betrachte, meine Seel Eb major 2vln, 2 vla
d’amore,
Continuo
Bass solo
20 Erwäge, wie sein
blutgefärbter Rücken
C minor 2vln, 2 vla
d’amore,
Continuo
Tenor solo
21a Und die Kriegsknechte
flochten eine Krone
G minor Continuo Evangelist
21b Sei gegrüßet, lieber
Jüdenkönig
Bb major 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
21c Und gaben ihm
Backenstreiche
G minor Continuo Evangelist,
Pilate
21d Kreuzige, kreuzige G minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
21e Pilatus sprach zu ihnen G minor Continuo Evangelist,
Pilate
120

NBA Movement Tonal Center Instrumentation Vocal Forces
21f Wir haben ein Gesetz F major 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
21g Da Pilatus das Wort
hörete
D minor Continuo Evangelist,
Pilate, Jesus
22 Durch dein Gefängnis,
Gottes Sohn
E major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
23a Die Jüden aber schrieen
und sprachen
B major Continuo Evangelist
23b Lässest du diesen los E major 2 fl, 2 ob
d’amore, 2 vln,
vla, Continuo
Chorus
23c Da Pilatus das Wort
hörete
F# minor Continuo Evangelist,
Pilate
23d Weg, weg mit dem B minor 2 fl, ob, ob
d’amore, 2 vln,
vla, Continuo
Chorus
23e Spricht Pilatus zu ihnen B minor Continuo Evangelist,
Pilate
23f Wir haben keinen König B minor 2 fl, ob, ob
d’amore, 2 vln,
vla, Continuo
Chorus
23g Da überantwortete er ihn B minor Continuo Evangelist
24 Eilt, ihr angefochtnen
Seelen
Gminor 2 vln, vla,
Continuo
Bass solo,
Chorus
25a Allda kreuzigten sie ihn Bb minor Continuo Evangelist
25b Schreibe nicht: der Jüden
König
Bb major 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
25c Pilatus antwortet Bb major Continuo Evangelist,
Pilate
26 In meines Herzens
Grunde
Eb major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
27a Die Kriegsknechte aber G minor Continuo Evangelist
27b Lasset uns den nicht
zerteilen
C major 2 fl, ob, ob
d’amore, 2 vln,
vla, Continuo
Chorus
27c Auf daß erfüllet würde
die Schrift
A minor Continuo Evangelist,
Jesus
28 Er nahm alles wohl in
acht
A major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
29 Und von Stund an nahm
sie der Jünger
D major Continuo Evangelist,
Jesus
30 Es ist vollbracht B minor 2 vln, vla, vla da Alto solo
121

NBA Movement Tonal Center Instrumentation Vocal Forces
gamba, Continuo
31 Und neiget das Haupt F# minor Continuo Evangelist
32 Mein teurer Heiland, laß
dich fragen
D major 2 vln, vla,
Continuo
Chorus, Bass
solo
33 Und siehe da, der
Vorhang im Tempel
zerriß
B minor Continuo Evangelist
34 Mein Herz, indem die
ganze Welt
G major 2 fl, 2 ob da
caccia, 2 ob
d’amore, 2 vln,
vla, Continuo
Tenor solo
35 Zerfließe, mein Herze F minor Fl, ob da caccia,
Continuo
Soprano solo
36 Die Jüden aber, dieweil
es der Rüsttag war
C minor Continuo Evangelist
37 O hilf, Christe, Gottes
Sohn
F major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
38 Darnach bat Pilatum
Joseph von Arimathia
Bb minor Continuo Evangelist
39 Ruht wohl, ihr heiligen
Gebeine
C minor 2 fl, 2 ob, 2 vln,
vla, Continuo
Chorus
40 Ach Herr, laß dein lieb
Engelein
Eb major 2 fl, 2 ob, 2 vln,
vla, Continuo
Choral
Note: There are two numbering systems utilized to divide the St. John Passion. The Bach-Werke-
Verzeichnis (BWV: Bach Works Catalogue) is the system that has been used to number Bach’s works and
is used here to separate the movements musically. The Neue Bach-Ausgabe (NBA) refers to the second
complete edition of Bach’s works published by Bärenreiter. The NBA numbers delineate scriptural texts
that have been divided into multiple movements from the Passion story and grouped together. This
numbering is preferred for this study because of its clearer identification of biblical texts which organizes
the presentation of the Passion story.
122

Appendix D: Identification of Biblical and Non-Biblical Texts Organized by Movement
as Found in Bach’s St. John Passion

NBA Source Text
PART I
1 Bach Commentary
2a

John 18: 1-8

Biblical
2b
2c
2d
2e
3 Bach Commentary
4 John 18: 9-11 Biblical
5 Bach Commentary
6 John: 18:12-14 Biblical
7 Bach Commentary
8 John: 18:15 Biblical
9 Bach Commentary
10 John: 18:15b-23 Biblical
11 Bach Commentary
12a
John 18: 24-27. Matthew 26:75

Biblical 12b
12c
13 Bach Commentary
14 Bach Commentary
PART II
15 Bach Commentary
16a

John 18: 28-36

Biblical
16b
16c
16d
16e
17 Bach Commentary
18a
John18:37-19:1

Biblical 18b
18c
19 Bach Commentary
20 Bach Commentary
21a

21b
21c
123

NBA Source Text
21d John: 19:2-12a Biblical
21e
21f
21g
22 Bach Commentary
23 John: 19:12b-17 Biblical
24 Bach Commentary
25 John: 19:18-22 Biblical
26 Bach Commentary
27 John 19:23-27a Biblical
28 Bach Commentary
29 John 19:27b-30a Biblical
30 Bach Commentary
31 John 19:30b Biblical
32 Bach Commentary
33 Matthew 27:51-52 Biblical
34 Bach Commentary
35 Bach Commentary
36 John 19: 31-37 Biblical
37 Bach Commentary
38 John 19:38-42 Biblical
39 Bach Commentary
40 Bach Commentary
Note: When Bach is listed in the source column, this indicates that Bach compiled these commentary texts
to fashion the libretto for his St. John Passion. These commentary texts are comprised of traditional
chorales, original texts authored by Bach or paraphrases modeled upon the poetry of other Passion librettos
including the Brockes libretto which was popular in Germany between 1712 and 1727.

Abstract (if available)

Abstract The St. John Passion (BWV 245) is a monumental work by Johann Sebastian Bach in the genre of the oratorio Passion. While significant scholarship on this work exists, including Bach’s use of Divine Proportion or Golden Section principles in his compositions, this paper expands the research by setting forth original theories on how Bach structured the St. John Passion. Bach’s interest in numerology, attention to musical structure, and use of Divine Proportion or Golden Section principles in his compositions are well documented and accepted by scholars. This multi-movement work is analyzed within this paper in terms of phi proportion, showing that phi application by Bach was driven by a theological premise, thereby revealing a formal structure in the St. John Passion that has been unexplored in the scholarship to date. ❧ In determining why Bach may have utilized an unorthodox application of Golden Proportion in this specific piece of music, it was hypothesized that a Lutheran theological precept may have been utilized to create the dimensions explaining the atypical, early break of the St. John Passion. Bach, a consummate church musician, would have put much thought into the creation of his Passion music

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Asset Metadata

Creator St. Marie, John S. (author)

Core Title Theology as a basis for golden section analysis: a model of construction for Johann Sebastian Bach's St. John Passion

School Thornton School of Music

Degree Doctor of Musical Arts

Degree Program Choral Music

Publication Date 11/09/2012

Defense Date 10/16/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Bach,divine proportion,golden section,OAI-PMH Harvest,Passion,phi,St. John Passion

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Strimple, Nick L. (committee chair), Grases, Cristian F. (committee member), Scheibe, Jo-Michael (committee member)

Creator Email stmariemusic@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-109292

Unique identifier UC11290203

Identifier usctheses-c3-109292 (legacy record id)

Legacy Identifier etd-StMarieJoh-1278.pdf

Dmrecord 109292

Document Type Dissertation

Rights St. Marie, John S.

Type texts

Source 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 a...

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