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The effect of an instructional unit of electronic music on the musical achievement of students in college basic musicianship and music theory classes
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The effect of an instructional unit of electronic music on the musical achievement of students in college basic musicianship and music theory classes
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THE EFFECT OF AN INSTRUCTIONAL UNIT OF ELECTRONIC MUSIC ON THE MUSICAL ACHIEVEMENT OF STUDENTS IN COLLEGE BASIC MUSICIANSHIP AND MUSIC THEORY CLASSES by Lester Eugene Lehr A Dissertation Presented to the FACULTY OF THE SCHOOL OF MUSIC UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF MUSICAL ARTS (Music Education) June 1980 UMI Number: DP29455 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertalion MuMlsMng UMI DP29455 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 DMA FINAL DISSERTATION APPROVAL This dissertation, written by L EST ER EU G EN E L E H ........................... under the supervision of.î?ÎS..Guidance Committee, and approved by all its members, has been presented to and accepted by the Executive Com mittee of the School of Music, in partial fulfillment of the requirement for the degree of DOCTOR OF MUSICAL ARTS M u sic E d ucation with major in. Deaty^chool of M u s i^ ^ Date 'AN CE CO ITT; Gu: chairman ‘ W Date 1 M/5-6 5 Mus 208 TABLE OF CONTENTS Page LIST OF TABLES................................... .. . iv LIST OF FIGURES..................................... V Chapter I. INTRODUCTION .................................... 1 Purpose of the Study......................... 2 Statement of the Problem ..................... 2 Need for the Study ......................... 3 Questions to Be Answered ..................... 4 Definitions of Terms ......................... 5 Assumptions .................................. 6 Delimitations ................................ 6 Limitations of the Study ..................... 6 Review of Related Literature ................. 7 Organization of the Remainder of the Study . . 10 II. METHOD OF RESEARCH.............. 11 Research Design .............................. 11 Population............ 12 Identification of Variables .... 14 Testing and Instrumentation ................. 15 Procedure.................................... 16 Data Collection and Recording............... 19 III. ANALYSIS OF DATA ................... 20 Original Status of Groups ................... 20 Regression on Melodic Elements and Idioms Achievement (AJMAT) — Hypothesis 1 ........... 21 Regression on Harmonic Elements and Idioms Achievement (AMAT)— Hypothesis 2 ..... . 23 Regression on Rhythmic Elements and Idioms Achievement (AMAT)— Hypothesis 3 ..... . 23 Regression on Notational Skills Achievement (ODMTB)— Hypothesis 4 25 Regression on Aural Skills Achievement (ODMTB) — Hypothesis 5 ..................... 25 ii Chapter Page Regression on ODMTB Posttest Scores-— Hypothesis 6 . . ............ 27 Regression on AMAT Posttest Scores— Hypothesis 6 .... ..................... 27 Supplemental D a t a .............. 29 Summary of Findings......................... 32 Discussion of Findings ................. 32 V. SUMMARY, CONCLUSIONS, RECOMMENDATIONS AND IMPLICATIONS ............................ 35 Summary...................................... 35 Conclusions.............. 36 Recommendations . 37 Implications for Music Education ............. 38 BIBLIOGRAPHY 4 0 APPENDIXES A. ALIFERIS MUSIC ACHIEVEMENT TEST ANALYSIS .... 44 B. OHIO STATE DIAGNOSTIC MUSIC TEST BATTERY DATA . 47 C. VARIABLE LABELS .......................... 49 D. ALIFERIS MUSIC ACHIEVEMENT TEST, STUDENT DATA S H E E T ......................... 51 E. CHART OF STUDENT PERFORMANCE EXPERIENCE .... 53 F. ELECTRONIC MUSIC UNIT LECTURE OUTLINE AND GUIDE 55 111 LIST OF TABLES Table Page 1. Dependent Variable, CAP 1, AMAT Subtest I and II Scores................ . 22 2. Dependent Variable, CAP 2, AMAT Subtest III and IV Scores..................... 24 3. Dependent Variable, CAP 3, AMAT Subtest V and VI Scores.................................... 24 4. Dependent Variable, COP 1, ODMTB Subtest I, III, and V Scores............................ 26 5. Dependent Variable, COP 2, ODMTB Subtest II, IV, and VI Scores........................... 2 6 6. Dependent Variable, V17, ODMTB Posttest Score Totals ................................ 28 7. Dependent Variable, V34, AMAT Posttest Score Totals........................................ 2 8 8. Comparison of Positions of Variables on Seven Stepwise Regressions ......................... 30 9. Summary Table Matrix of Twelve Variables .... 31 IV LIST OF FIGURES Page Figure 11 Research Design 18 Research Method CHAPTER I INTRODUCTION Music theory is considered an essential element in the total curriculum of music education at the college level. Introductory courses of basic musicianship and music theory are particularly crucial to the development of musical con cepts and aural discrimination skills. However, since the Seminar on Comprehensive Musician ship in 1965 (Fitzgerald, 1965), the content and emphasis of these courses have been questioned and reevaluated by music educators. Among several recommendations made at the Seminar, relationships between music theory and contemporary music were given special consideration. The Seminar recommended that concepts of contemporary thought and practice be included in the music theory curric ulum and pedagogy. Seminar groups discussed interrelation ships among core subjects such as music theory and history, making those similarities more apparent and more directly related to performance and ear training skills. The partic ipants also discussed the manner in which courses could be modified to more effectively prepare students and teachers to understand and perform contemporary music and to define comprehensive musicianship within these considerations and recommendations. Purpose of the Study The purpose of the study was to investigate the effect of an instructional unit on the principles of electronic music and aural electronic music dictation on melodic, har monic, rhythmic, and notational skills of students in com munity college basic musicianship and music theory classes. The specific purposes of the study were (1) to deter mine the effect of presentation of a unit on the principles of electronic music synthesis on conceptual understanding of music theory, and (2) to determine the effect of use of an electronic unit synthesizer for music dictation on me lodic, harmonic, and rhythmic auditory discrimination skills of students. Statement of the Problem The problem presented in this research study is to de termine the effect of a unit of electronic music synthesis on the musical achievement of students enrolled in basic musicianship and music theory classes at the college level. The development of a unit of electronic music synthesis for introduction into these classes was stimulated by the activities and recommendations of the seminars and work shops on comprehensive musicianship. Interrelationships fundamental to both music theory and contemporary music had to be identified first. The task then was to determine in what way basic musicianship and music theory courses could be modified to accommodate the material selected. Following the recommendations of the Seminar, two con ditions were incorporated into the design of the unit. First, knowledge in these areas should be directly related to performance skills and to ear training. Second, the courses should prepare students and teachers to understand and teach contemporary music. Need for the Study There were three principal reasons for conducting the study. First, there was a need to explore and identify the relationships of contemporary music and technique and tra ditional music theory. Since electronic music synthesis is a prominent aspect of contemporary music, the identifica tion of common elements between electronic music and music theory could contribute essential knowledge and skills for improved understanding and performance of contemporary music. According to Leonhard and House (1972) , this infor mation might also provide, at an initial stage of instruc tion, a more comprehensive perception of tonal structure, harmonic relationships, and musical concepts. Second, there was a need to incorporate modern tech nology and equipment in current music theory courses thereby encouraging involvement through understanding and perform- ance of contemporary music. As a result of the increased proliferation of electronic music equipment and its acorn- panying technology, use of this equipment could partially fulfill the needs of comprehensive musicianship. Electronic music synthesis could contribute an important new source of methodology and philosophy for music theory. Third, a study was needed to obtain and evaluate in formation on the effect of electronic music synthesis on musical achievement of students in music theory classes. Each variable of auditory and notation skills should be analyzed individually and collectively in a research set ting. From this information, further decisions concerning the content and direction of music theory with regard to electronic music can be made. Questions to Be Answered This research study provides information and data on the following questions : 1. Will presentation of a unit on the principles of electronic music synthesis effect students' musical achieve ment in their study of basic musicianship and music theory? 2. Will the use of an electronic music synthesizer for music dictation affect students' auditory discrimination? To answer these questions, the following null hypothe ses were posed: 1. There will be no differences in total skill scores between control and experimental groups as measured by pre~ 4 and posttests. 2. There will be no difference in notational skill scores between control and experimental groups as measured by pre- and posttests. 3. There will be no difference in auditory discrimi nation skill scores between control and experimental groups as measured by pre- and posttests. 4. There will be no difference in melodic element scores between control and experimental groups as measured by pre- and posttests. 5. There will be no difference in harmonic element scores between control and experimental groups as measured by pre- and posttests. 6. There will be no difference in rhythmic element scores between control and experimental groups as measured by pre- and*posttests. Definitions of Terms Basic musicianship— course title for the introductory class of music theory. Electronic music unit— the principles of electronic music and acoustics prepared for presentation to experimen tal groups in this study. Music synthesizer--an electronic instrument for the production and replication of sounds through the controlled combination of elements (Beaver, 1968). Music background— the non-musical technical knowledge 5 of music acquired from experience (Reimer, 1970). Music experience— the condition of performance on a musical instrument. Assumptions Several assumptions are necessary prerequisites to the study. 1. The test instruments selected for use in this study are valid and reliable for the purposes of the study. 2. The multiple regression method and data analysis procedures are appropriate to this study. Delimitations The study was limited to students enrolled at American River College in two basic musicianship classes (Music 2) and two music theory classes (Music 3A) during the Fall semester, 1978. The total sample size (n) was 72 students. Limitations of the Study Since no standardized tests exist which incorporate electronic music synthesis as a constituent part within a music theory context, the results of the study are subject to the reliability and validity of the tests of music achievement and statistical methods used. Data regarding reliability and validity are contained in Appendix A and Appendix B. Review of Related Literature A search and review was made of literature available through ERIC, DATRIX, and Psychological Abstracts. No re search studies were found which directly involved the use of electronic music synthesis in the teaching of music the ory; hence, articles and studies related to the general topic are reported here. A dissertation by Gatwood (1960) was the first to sug gest the use of electronic tone oscillators, tape recorders, electronic metronomes, and public address systems as aids in teaching music to large groups of students in public schools. Recht (1962) supported the position, but the electronic instruments employed in the study are primitive when compared to the modular electronic synthesizers and equipment now available. In 1965, the Seminar on Comprehensive Musicianship at Northwestern University recommended that training in the practice of composition was a necessary element in the de velopment of comprehensive musicianship (Fitzgerald, 1965). At that time, recommendations were also made to include concepts of contemporary thought and practice in music the ory curriculum and pedagogy for both teachers and students. In Music in General Education (1965), Ernst and Gary expressed a need for an understanding of the principles of acoustics and electronic music synthesis. Little attention had been given to any type of electronic music until the 7 November, 196 8, issue of the Music Educators Journal. Its purpose was dedicated solely to ". . . explore possible ways and means by which we music educators may be more ef fective, seek new dimensions for our profession." Since then, articles by music educators, composers, and musicians have appeared in increasing numbers on the nature and effect of electronic music in the classroom. The Greenwich Board of Education (Schmidt, 1968) and the Julia B. Masterson School in Philadelphia (Hagemann, 196 8) represent two projects which establish precedent for the utilization of electronic music in the curriculum. The Central Atlantic Regional Education Laboratory (CAREL) pro gram directed by Biasini and Pognowski (1969) is an example of a similar attempt to further develop a music curriculum for children. The purpose of the electronic music labora tory was to provide a vehicle for creative expression. Four objectives of the CAREL project were (1) to develop aural sensitivity, (2) to develop musical concepts, (3) to enhance skills development, and (4) to establish positive attitudes toward music. Knuth (1969) conducted an experiment to determine the effectiveness of electronic pianos through achievement testing. She affirmed the position that music educators must make use of modern technology in developing new learn ing theories and utilizing new facilities and equipment. The behavioral objectives cited in the study involved con- 8 cepts, performance, singing, notation, sight-singing, and aural perception. A study by Ihrke (1972) of 276 member schools of the National Association of Schools of Music reported that new electronic music technology was being limited to its own area in the curriculum. The investigator stated that music educators must inevitably seek and design a training ra tionale which incorporates electronic music and electronic music synthesis concepts and procedures. Only one research study (Wiliman, 1972) was identified that directly investigated the effectiveness of electronic music instructional materials in the classroom. It con tained a presentation of historical facts, terms, and re cordings to fifth and eighth grade students. The results and conclusions of the research study provided significant evidence supporting the introduction of electronic music information in the classroom. A project by Robert DeWe11 (1973) established a rela tionship between measurement and rhythm in the intermediate grades. With a tape recorder and a reel of prerecorded tape, students learned about and performed rhythmic nota tion through the principles of measuring time in an elec tronic music idiom. The most recent study by Halfner (1973) presented de tails of an experimental course for the study of acoustics at Hampshire College, outlining the basic techniques for utilizing computers arid synthesizers, the latter being employed to translate formula into sounds and to create opportunities for broad experimentation in music theory, perception, and composition. This course emphasized the fundamental relationship of acoustics and the principles of electronic music synthesis. Evidence and experience ob tained from the course contributed additional information in the Halfner study by relating directly to the cognitive and performance skills required of music theory students. The interdisciplinary efforts of Olson (196 7) , Roederer (1974), and Erickson (1975) are cited for reference since they involve interrelated efforts with music, physics, and psychoacoustics. Organization of the Remainder of the Study The remaining chapters of this study are organized as follows : Chapter II contains a discussion of the methodology used in the study, including the statistical procedures. Chapter III is a presentation of the data and their analyses. The findings, conclusions drawn from the study, and recommendations for further study comprise Chapter IV. 10 CHAPTER II METHOD OF RESEARCH A presentation and explanation of the research design, population, materials used, and procedures followed to ob tain and analyze data on the effect of the use of the prin ciples of electronic music in the teaching of music theory are contained in this chapter. Research Design The nonrandomized control group pretest-posttest de sign selected for this research study (Isaac, 1974) is illustrated in Figure 1. NONRANDOMIZED CONTROL GROUP PRETEST-POSTTEST DESIGN Pretest Electronic Unit Posttest Experimental Group X X X Control Group X X Figure 1. Research Design The use of a multiple regression method was considered appropriate and acceptable for the analysis due to the interrelatedness of the variables. This procedure enabled 11 the investigator to study the amounts of change attributable to other variables as well. A correlation matrix of all entered variables was provided by the computer's statisti cal procedure. Population The population used in this study consisted of 72 stu dents enrolled at American River College, a two-year commu nity college, during the Fall semester, 1978. Two Music 2 (Basic Musicianship) classes and two Music 3A (Music Theory) classes were selected for the research study. Two of the three Music 2 classes taught by the inves tigator were arbitrarily designated as the experimental group and the control group. The Music 2 class is a general introduction to music theory and is designed for students with limited or no musical experience or background. Al though some music majors and music minors enroll in Music 2, most students enroll because of a counselor's advice or individual preference. Two classes of Music 3A, taught by another music in structor, were arbitrarily selected as an experimental and a control group. In contrast to Music 2, Music 3A is pri marily intended for music majors or minors who have prior musical experience and performance skills. The Aliferis Music Achievement Test (AMAT) contains a questionnaire which elicits information from the students relative to their musical background prior to their enroll- 12 ment in class. A review of the questionnaires revealed that the prior musical experience of all four groups was approximately the same, ranging from one semester to seven years. Information relative to the academic achivement of the students prior to enrollment in the classes was not available; therefore, no conclusions can be drawn about whether or not the academic achievement varied from one group to another. One basic musicianship class, identified as the exper imental group, met two days a week for one hour and fifteen minutes. The classroom contained a forty square foot area, housing the electronic music laboratory. The basic musi cianship control class also met two days a week for the same block of time, but it met in a different classroom without access to the electronic equipment. Two music theory classes met at 8:00 and 9:00 A.M. re spectively for fifty minutes five days a week. The earlier section was arbitrarily designated the control group and the other became the experimental group. In so doing, the earlier section had less opportunity for exposure to the electronic music equipment. Of the 53 students originally enrolled in the basic musicianship classes, 32 completed both pre- and posttests. In the music theory classes, 46 students took the pretest, and 40 completed the posttest. The total number of students completing pre- and posttesting represents the sample size 13 (n=72) used in the study. Identification of Variables The following dependent and independent variables were identified as those pertinent to the questions posed by the study. Since multiple regression analysis is a method of studying the influence of two or more independent variables on a dependent variable, certain independent variables were chosen for use in the method with the experimental variable because of their presumed importance (Kerlinger and Ped- hauzer, 1973). All variables, with their respective labels used in the computer statistical procedure, are found in Appendix C. The independent or predictor variables considered most essential to the study included : 1. Experimental, Control (Coded 1, 2) 2. Instructor (Coded 1, 2) 3. Instrumental Background (Coded Yes, No) 4. Musical Background (Coded Yes, No) 5. Quiz following Electronic Unit (Continuous) 6. Sex (Coded 1, 2) The dependent variables included the following subset or set score totals for the Aliferis Music Achievement Test (AMAT) and the Ohio State Diagnostic Music Test Battery (ODMTB): 1. AMAT total score 2. ODMTB total score 14 3. AMAT Melodic Subset total score 4. AMAT Harmonic Subset total score 5. AMAT Rhythmic Subset total score 6. ODMTB Parts I, III, V total score 7. ODMTB Parts II, IV, VI total score Testing and Instrumentation The primary instrument used for testing in the study was the college entrance level Aliferis Music Achievement Test (AMAT). A prerecorded tape of the test material was purchased from the publishers for presentation of test items. Where the AMAT is exclusively auditory-visual dis crimination, the Ohio State Diagnostic Music Test Battery (ODMTB) contains sections of aural identification and nota tional skills items which test a contrasting group of tasks. Because additional background information was desired, the ODMTB General Information Test (GIT) scores were included in the testing. The purpose of this test was to provide additional data in the pretesting to account for variations in the population. The AMAT provides a measure of the critical associa tion of auditory-visual stimuli of melody, harmony, and rhythm that represents the musician's ability to correlate sound with notation and notation with sound. Appendix A provides supporting evidence of the predictive validity of the test. Data obtained show substantial correlations be tween various music and academic courses at one, two, and _____________________________________________________________15 four-year institutions. Reliability coefficients available with the AMAT in cluded in Appendix A illustrate another reason for its selection in this study. Intercorrelations between part and total scores presented in Appendix A provide data for entering freshmen and afford comparisons with the sample population of this study. The ODMTB, Elements of Music Theory Section I— Form II, and the GIT were included in the study to reveal potential correlations between closely related skills. The length and content of the latter test sought to measure and evalu ate a subject's experience and exposure to general music information, names, dates, and compositions. The AMAT student data sheet and a chart categorizing the students based on that response are found in Appendix D and Appendix E respectively. Multiple correlations (R) of Music Placement Tests I, II, and III and the Ohio State Psychological Examinations, along with other variables, support the validity and relia bility of the test instrument. Data are included in Appendix B. Procedure In the absence of identified research involving the use of synthesizers, the investigator had to develop an in structional unit integrating the principles of electronic music and acoustics. The students were given instruction 16 and demonstration on unit materials by using an ARP Odyssey and Moog 15 electronic music synthesizers. The synthesizers replaced the piano in all experimental groups for music dictation and sight-singing. The piano was used for dicta tion and sight-singing in all control groups. Students enrolled in two basic musicianship classes and two music theory classes at American River College for the Fall semester, 1978, were arbitrarily selected as the population for this study. The first class meeting of both basic musicianship classes and several minutes of the second meeting were taken for clerical and administrative duties, test instructions, course objectives, grading, attendance, and class procedure. The remainder of the second meeting was used for the admin istration of the AMAT. Two subsequent class meetings, one for the GIT and one for the ODMTB, were used to complete the pre te s ting. Similarly, class procedure and administration were discussed in the first two class meetings of the music the ory classes. The testing began at the third class session with the AMAT, followed by the ODMTB in identical order. This completed all pretesting. Instructions for testing contained in the Aliferis Manual were followed as recommended, and a prerecorded tape accompanying the test material was used, thereby insuring uniformity for each presentation. Similarly, the informa- 17 -H O in o CM •H I —I -H -H -H "r4 O •rH -H ü -P •pH *H O o ü -H -H W : s : r—I •H ro ro iH 18 tion and instructions prefacing each section of the ODMTB were followed. A key of aural test items with one example exercise was prepared for piano from a sample test for Part II, IV, and VI of the ODMTB. The research design and course plan is shown in Figure 2. The electronic music unit representing the treatment effect was then presented to experimental classes. Data Collection and Recording Pre- and posttest responses of the AMAT and the ODMTB were collected on scanner sheets. In addition, sex, in structor, general music information background, and musical performance background were coded and included for analysis in the data of the experiment. Pretest criteria to determine coding of students' gen eral music and performance background were established. A score of 70 percent was arbitrarily selected on the ODMTB GIT as the measure to determine the coding of students as having or not having sufficient general musical information background. Similarly, musical performance background was assessed from the questionnaire of the AMAT. Four years or more of immediate prior experience was arbitrarily chosen to be the point at which students were dichotomously as signed to groups of experience and non-experience. 19 CHAPTER III ANALYSIS OF DATA Data were collected for each student from all pre- and posttests described in Chapter II and analyzed using a mul tiple regression program. A mean and standard deviation table for each variable for the seventy-two cases, correla tion coefficient table of all variables, stepwise regression for each dependent variable, and a summary table for each dependent variable were made. Stepwise multiple regression analyses were used to determine the optimum predictor sets. Regressions were obtained to test each statistical hypothe sis. The results are presented in the initial portion of the chapter followed by an evaluation of the regression for each hypothesis. A statement of the findings concludes the chapter. Original Status of Groups A pretest-score, correlations-coefficient matrix of each subtest for the AMAT, ODMTB/ and AMAT-ODMTB was made. The resulting data were then analyzed to determine the ex istence of significant intercorrelations between subtests. No individual or consistent patterns of coefficients were found to exist. It was then deemed appropriate to combine 20 similar subtests in response to the hypotheses posed for examination in the multiple regression procedure. From the AMAT questionnaire form, information of students' sex and extent of previous instrumental experience was obtained and is included in Appendix E. Instructor, experimental/control, instrumental expe rience , musical background, and post electronic unit quiz scores represent the independent variables of the first computer run. The dependent variables were the AMAT and ODMTB posttest total scores, subtest totals CAP 1, CAP 2, and CAP 3 for the AMAT, and subtest totals COP 1 and COP 2 for the ODMTB. Regression on Melodic Elements and Idioms Achievement (AMAT)— Hypothesis 1 Musical achievement as exemplified by the recognition of melodic elements and idioms subtests of the AMAT were combined to form a dependent variable. Independent predic tor variables of instructor, instrumental experience, musi cal background, experimental effect, and post-unit quiz were entered into the regression program to test the hy pothesis . The results of the regression are summarized in Table 1. No amount of change was accounted for by the experimen tal variable. An F value of 2.51 was required for signifi cance at the .05 level with 4 and 67 degrees of freedom. Since the F value achieved was less than required, the null 21 TABLE 1 DEPENDENT VARIABLE, CAP 1, AMAT SUBTEST I AND II SCORES variable Multiple ^ Square Vl Instructor 0.45 0.20 0.20 V19 Instrumental Background 0.50 0.25 0.06 V35 Quiz 0.51 0.26 0.06 V2 Experimental Effect 0.51 0.26 0.00 V20 Musical Background 0.51 0.26 0.00 22 hypothesis of no difference was not rejected for the re gression of the AMAT represented as CAP 1. Regression on Harmonic Elements and Idioms Achievement (AMAT)— Hypothesis 2 Combining harmonic elements and idioms subtests of the AMAT represented the next regression procedure. Identical predictor variables were used for the dependent variable, CAP 2. Table 2 contains the results of the regression. The amount of change contributed by the independent variable, V2, is insignificant. With 4 and 67 degrees of freedom, the F value achieved was 0.02. An 2 value of 2.51 was required at the .05 level for significance. As the F value achieved was less than required, the null hypothesis of no difference was not rejected for CAP 2. Regression on Rhythmic Elements and Idioms Achievement (AMAT)--Hypothesis 3 The rhythmic subtests of elements and idioms together, CAP 3, represent the next regression procedure. The same predictor variables were used with the new dependent vari able . A summary of independent variable values is presented in Table 3. The independent variable, experimental effect, again accounted for any of the variance in the regression. The stepwise regression produced an F value of 1 with 5 and 6 6 degrees of freedom. The F value required was 2.36 at the .05 level. Since the F value obtained was far less 23 TABLE 2 DEPENDENT VARIABLE, CAP 2, AMAT SUBTEST III AND IV SCORES variable Multiple ^ Square ^ S e VI Instructor 0.23 0.05 0.05 V2 0 Musical Background 0.26 0.07 0.02 V19 Instrumental Background 0.27 0.0 7 0.00 V2 Experimental Effect 0.27 0.07 0.00 TABLE 3 DEPENDENT VARIABLE, CAP 3, AMAT SUBTEST V AND VI SCORES variable Multiple ^ Square ^h^nge Vl Instructor 0.51 0.26 0.26 V19 Instrumental Background 0.59 0.35 0.0 8 V2 0 Musical Background 0.60 0.36 0.01 V35 Quiz 0.60 0.36 0.00 V2 Experimental Effect 0.60 0.36 0.00 than the value required for statistical signficance at the .05 level, the null hypothesis was not rejected. Regression on Notational Skills Achievement ( .0DMTB) — Hypothesis 4 Subtests I, III, and V of the ODMTB comprise the nota tional skills variable designated as COP 1. This was the next dependent variable with the same group of predictor variables. A summary of the results is found in Table 4. Although the amount of change is very slight, the variance contrib uted, 0.01 is not of sufficient magnitude to be recognized. On step five of the regression, an F value of 1.44 was achieved with 5 and 66 degrees of freedom. However, this is still less than the 2.36 required to gain significance at the .05 level. As such, the fourth null hypothesis of no significance was not rejected. Regression on Aural Skills Achievement (ODMTB) — - Hypothesis 5 Interval, scale, and triad recognition sections, sub tests II, IV, and VI respectively, are combined to repre sent the dependent variable COP 2. The initial predictor group was employed as before. The results of the regres sion are found in Table 5. Although a change of 0*01 occurred with the experimen tal effect variable, this amount contributes little variance to the total for the dependent variable. An F value of 25 TABLE 4 DEPENDENT VARIABLE, COP 1, ODMTB III, AND V SCORES SUBTEST I, Variable Multiple R R Square RSQ Change VI9 Instrumental Background 0.49 0.24 0.24 VI Instructor 0.58 0.33 0.09 V20 Musical Background 0.61 0.37 0.04 V2 Experimental Effect 0.62 0.38 0.01 V35 Quiz 0.62 0.39 0.01 TABLE 5 DEPENDENT VARIABLE, COP 2, ODMTB IV, AND VI SCORES SUBTEST II, Variable Multiple R R Square RSQ Change V19 Instrumental Background 0.44 0.19 0.19 VI Instructor 0.50 0.25 0.05 V20 Musical Background 0.51 0.26 0.02 V35 Quiz 0.5 3 0.2 8 0.02 V2 Experimental Effect 0.54 0.29 0.01 26 2.36 is required to be significant with 5 and 66 degrees of freedom at the .05 level. Since the F value achieved was 1.00, the value was far less than required at the .05 level. The null hypothesis of no difference was not rejected. Regression on ODMTB Posttest Scores— Hypothesis 6 A stepwise regression using the ODMTB posttest total, V17, as the dependent variable was conducted. Table 6 contains a summary of the results of the regression. The experimental variable contributed only 0.01 percent of the change of the total accountable variance. The largest change is noted in the instrumental background in the amount of 0.19. For the ODMTB posttest total score, the null hy pothesis of no difference was not rejected. Regression on AMAT Posttest Scores— Hypothesis 6 The AMAT posttest total, V34, was then entered as the next dependent variable. A summary of the regression is found in Table 7. In this case, the experimental variable was not included in the computations because of collinearity with previously entered variables. Hence, the null hypoth esis of no difference was also not rejected. Only four variables of interest are included in Table 7. The largest change of 0.29 is found in the variable representing the instructor. 27 TABLE 6 DEPENDENT VARIABLE, V17, ODMTB POSTTEST SCORE TOTALS Variable Multiple ^ square RSQ R ^ Change VI9 Instrumental Background 0.55 0.30 0.30 Vl Instructor 0.63 0.40 0.10 V20 Musical Background 0.66 0.43 0.03 V2 Experimental Effect 0.67 0.45 0.01 TABLE 7 DEPENDENT VARIABLE, V34, AMAT POSTTEST SCORE TOTALS Variable Muli^ple ^ Square RSQ R ^ Change Vl Instructor 0.51 0.26 0.26 Vl9 Instrumental Background 0.59 0.35 0.10 V20 Musical Background 0.60 0.36 0.01 V35 Quiz 0.60 0.36 0.00 28 Supplemental Data Similar subtests were combined to form subtest cluster totals. In the AMAT, there are two tests each for melody, harmony, and rhythm. The ODMTB contained three tests of notational skills and three tests of auditory discrimina tion skills. These were dependent variables in separate multiple regressions. Extremely low correlations resulted between the sub test clusters and the experimental variable. The highest correlations of 0.16 (COP 1) and,0.15 (COP 2) were found between the ODMTB subtest clusters and the experimental variable. All correlations between the AMAT subtest clus ters and the experimental variable were below 0.10. With these additional regressions, comparisons and evaluations were made of the important independent vari ables : experimental effect, instrumental background, musi cal background, and instructor. The inconsistent pattern of these variables with the experimental variable is illus trated in Table 8. The highest position as identified by the lowest number was associated with the ODMTB posttest cluster, COP 1-V19. Data resulting from a multiple regression analysis employing all thirty-nine variables are found in Table 9. Twelve select variables were chosen for illustration in the matrix for purposes of comparison with former regressions. No significant values were found. 29 CO o ro CO CN CO 00 H o CN rH -H CO M CM in I —I CO M M in CD rH -H I —I •rH •rH H H O CM CM 30 CM r ~ i n O 0 0 CM en en o 0 0 O o P 4 ro r H co ro UO o CM uo o O u O o o 0 1 O o o o o o o r H rH lD < x > rH en 0 0 o o en 0 0 o O C L t r H en â– M ’ 'd * ro ro 1 —1 p uo O o O O o 0 1 o O o O o o 1 —1 o ro r H co in o en ro 00 en o 00 00 Pj in o in r~ CM LfO rH o < O O o o 0 1 o o o o O 1 —1 o o (M rO 1 —1 s j i 00 CM ro en H p es en o A CM o CM r H CM < X > o K) p (H M CM O O o O O 1 O O O P H O o O 1 —1 in ro ro O O r H o CM 00 o en A O « s t * ro ro en CM o UO uo ro " d * U1 C H U o O o O O o O rH O o o o kl 1 9 KO â– M ’ CM 00 rO O 1 —1 en ro o en H in 1 —! o CM â– M ’ CM CM O CM o CM ro o cd ro > O o O o O O rH o o o O o > pq 1 —! \Û en O ro o ro en CM m o m ro O CM <n vD p uo ro M H > o o o O 1 o rH O o o o o o § in ro o o en 00 o CM .o 00 00 O O uo o co CM ro CM TT ' d ' ro CM H O > o O o 0 1 1 —1 o O o o O O O Dû X { —1 00 in O VO CM 00 00 UO en â– d ’ ry* en ro o m O ' d * « d * TT ro r H « d * ' d ' ' d * l - H rH Eh Eh > O 1 0 1 0 1 rH 0 1 0 1 O 1 0 1 o 1 0 1 Q 1 0 1 m co o m o p TT 1 —1 o W rH o in in uo CM ' d * CM UO en 00 rH > o o rH 0 1 o . o O o O O o o Eh en o 00 00 ro r' ' d ' ro rH 00 vo uo (M o O r H o O o o o O O rH rH >H > o 1 —1 O 0 1 O o O 1 o O o O o g o en en uo rH VD uo ro rH UO r H o o ro â– UO r H ' d * CM UO « d * ro D > c / ] 1 —1 eô o O 1 O o O o â– o O o o Td c 0 1 —1 o - P ( d H 1 —1 u 4 - ) tn «O « d (U p a -P IH Eh u 0 p IH ( d o EH g W +4 m u 0 W tn +J >1 -rH 1 —1 C D rH Aî C Q g g +J rH « d +J f d ü e u Td O .P ( d f d )4 4 J 4-> 4-> < d â– P o 4-J - P U O D W ü c ô - P N 1 —1 0 g +J e u O e u C Q -H «S â– 5 g < U 6 fl» 1 —1 0 s f f i K n -H f d IH ot )4 H m H u P m +J ( U e h 4 - > • H EH - P H Eh H W JH s W C Q ü î s C X Q a rd O Q H H O H S < Ck < <3 < O O 1 —1 CM ro rH CM r ~ - en o TT uo A Bd & PH 1 —1 CM r H 1 —! CM ro ro < < < q q I 31 î> ï> > >. > !> o o O V V Summary of Findings In the instance of each hypothesis, the null hypothe sis was not rejected. The F scores found in each instance of stepwise regression for all hypotheses were below that required for significance at the .05 level. An analysis of the data indicates that music performance background, musi cal information background, and instructor are stronger predictors or contributors to musical achievement when com pared with the experimental effect. Several multiple regressions were obtained for addi tional analysis using a variety of independent variables. The amount of change noted between regressions was negli gible. The highest correlations obtained were between sub tests and total test scores, whereas the remaining coeffi cients were low. The post quiz variable and each of the variables included in Table 9 resulted in consistently low correlation values. Discussion of Findings Variables of instructor, instrumental background, musi cal background, and sex were included with pretest-posttest subtest scores, cluster scores, and the post-electronic unit quiz score in a multiple regression. There were no significant levels of correlations among important vari ables. There are several possible reasons why the test data produced these results. Although the AMAT and ODMTB measured important charac- ^2 teristics of aural discrimination and conceptual knowledge learned in music theory, there was no specific analysis other than the electronic music quiz which tested the stu dent's knowledge of the interrelatedness of acoustics, electronic music synthesis, and music theory. Nor was there any specific test or subtest of timbre identification or discrimination. Therefore, test instruments should be devised and included which will contribute another dimen sion to the research. It was noted in several instances, that students requested that the timbre being used on the synthesizer at that moment for dictation be changed so that the tone quality could be more•pleasant and perceptible. The limited manner in which the synthesizer was util ized may be another factor. Students were not instructed or allowed to use the synthesizer individually. The syn thesizer was used for demonstration of scales, chords, and materials of music notation and theory. The exclusive use of synthesizer may contribute significant results. Obser vations were made by both instructors that students were keenly interested in the operation and function of the synthesizer. These observations suggest that test results might have been substantially improved had each student been allowed to operate the synthesizer equipment and indi vidually apply the knowledge and information presented in the electronic music unit. Also, if some modification were made in the materials 33 contained in the unit on electronic music and the inter relatedness of subject areas, or the timing of its presen tation in the course, the results might have been different. 34 CHAPTER IV SUMMARY, CONCLUSIONS, RECOMMENDATIONS AND IMPLICATIONS Summary Purpose The purpose of this study was to investigate the effect of a unit comprising principles of electronic music and electronic music dictation on musical achievement of stu dents in first-semester college basic musicianship and music theory classes. The investigator's primary concern was achievement of melodic, harmonic, rhythmic, and notational skills competence. Students in control groups received in struction of the regular course materials with music dicta tion given on piano. In contrast, the experimental groups received a unit on the principles of electronic music, acoustics, and music dictation, employing ARP Odyssey and Moog 15 electronic music synthesizers. Questions to Be Answered Answers to the following questions were sought: 1. Would the presentation of a unit on the principles of electronic music synthesis effect achievement of students in the study of basic musicianship and 35 music theory? 2. Would the use of electronic music synthesizers for music dictation affect music achievement pertain ing to auditory discrimination competence? Conclusions Within the assumptions and limitations of the study and based on the findings cited in Chapter III, the follow ing conclusions are presented. Question 1. Conceptual Understanding and Achievement of Skills In the test of aural skills of intervals, scales, and triads discrimination of the ODMTB, the null hypothesis of no difference was not rejected. The results' for the nota tional skills achievement of the ODMTB also confirmed the null hypothesis of no difference. In reference to aural discrimination of melody, harmony, and rhythm as tested by the AMAT, the null hypothesis was not rejected. Therefore, it was concluded that there was no significant improvement of conceptual understanding as represented by notational skills or aural discrimination as evidenced by music dictation. Question 2. Electronic Music Synthesis Non-significant correlation coefficient values were found for the experimental effect in contributing to a 36 change in musical achievement represented by the total scores of the tests employed. The use of electronic music Synthesizer in context of the two courses of basic musician ship and music theory contributed no significant changes in music skills achievement. Thus, the conclusion was drawn that the presentation of a unit on the principles of elec tronic music and acoustics had no effect on a student's general music achievement. Recommendations As a result of this investigation, the following rec ommendations for further study are presented: 1. Data indicate that no significant achievement was gained by students in aural or notational skills with the knowledge of electronic music synthesis or electronic music dictation as presented in this study. Modifications of existing music theory curricula to include a unit of this nature should be seriously questioned. 2. Based on a review of the literature, not only was there no research identified in the areas of this study, but it also appeared to the investigator that there is a paucity of research in the teach ing of auditory discrimination skills. While the results of this study indicate that no significant musical achievement resulted in this research study, music educators should engage in and report 37 research on comparative methods of music education pertaining to music theory in order that improve ments in instruction can be documented. These areas might include the content and approach of textbooks, the techniques of dictation for audi tory discrimination skills, and the interdiscipli nary studies of music, physics, and psychoacoustics cited previously which give evidence of new direc tions for investigation. 3. A study should be conducted to identify those qualities of timbre produced by electronic music synthesizers which produce optimum student achieve ment in auditory discrimination skills, facili tating and enhancing both the instruction and learning of these complex skills. Implications for Music Education The following implications are based on the findings of the study and the observations of the investigator dur ing the course of the experiment: 1. The testimony of music educators, of composers, and of personal experience confirms the value of electronic music synthesis as an interesting, stimulating, and creative medium for students. Music teachers must make every effort to utilize contemporary technology to acquaint students with contemporary music and its potential. 38 2. A study or project should be initiated to identify the tasks considered essential in music theory courses. All information and data available in research studies pertinent to those areas should be obtained, analyzed, and published. Where no research presently exists, research studies should be initiated. 3. Since educational training, equipment, facilities and financial expenditures are required to imple ment electronic music instruction, additional evidence and data from further investigations are essential prerequisites to the contracting of those commitments. In many situations, alterna tive solutions can be found to eliminate or mini mize problems encountered in establishing an electronic music laboratory. 39 40 BIBLIOGRAPHY Beaver, P., & Krause, B. L. Nonesuch guide to electronic music. New York: Electra Corporation, 1968. Biasini, A., & Pognowski, L. Development of a music cur riculum for young children. Washington, D.C.: Cen tral Atlantic Regional Educational Laboratory, 1969. (Datrix No. ED 032 938 24 PS 002204) DeWell, R. Interrupted sound. Music Educators Journal, 1973, ^(3) , 59-61. Erickson, R. Sound structures in music. Berkeley, Calif.: University of California Press, 1975. Ernst, K. D., & Gary, C. L. (Eds.). Music in general edu cation. Washington, D.C.: Music Educators National Conference Publication, 1965. Fitzgerald, R. B. CMP seminar on comprehensive musician ship. Music Educators Journal, 1965 _^(1) , 56-57. Gatwood, R. F. The applications of certain types of elec tronic equipment to the teaching of music. (Doctoral dissertation. New York University, 1969). Disserta tion Abstracts International, 1961, 2JL, 3478-3479. Halfner, E. Computers, synthesizers, and the physics of music. Paper presented at the Conference on Computers in the Undergraduate Curricula, Claremont, California, 1973. (Datrix No. ED 081 206 EM Oil 378) Ihrke, W. R. A study of the present state of electronic music training including computer assisted instruction; A bibliography. Final report. Storrs: Conncecticut University, 19^72. (Datrix No. ED 063 806 24 EM 010 164) Isaac, S., & Michaels, W. B. Handbook in research and evaluation. San Diego, Calif.: Robert R. Knapp, Publisher, 1971. 41 Kerlinger, F. N., & Pedhauser, F. J. Multiple regressions in behavioral research. New York: Holt, Rinehart and Winston, 1973. Knuth, A. M. Integration of the systems approach and electronic technology in learning and teaching music. Report on Federal Project #1309. San Francisco, Calif.: Frederick Burk Foundation for Education, 1969. CDatrix No. ED 031 783 24 EA 002 421) Leonhard, C., & House, R. W. Foundations and principles of music education. 2nd ed. New York: McGraw-Hill Book Company, 197 2. Poland, W. Data supplement for measuring musical behavior and predicting success in the University School of Music. Unpublished paper, Chicago, Illinois, 196 3. TaT Poland, W. Measuring musical behavior and predicting suc cess in the University School of Music. (Ohio State University) Unpublished paper prepared for AERA, annual meeting, Chicago, Illinois, 1963. (b) Recht, M. Electronics as an aid to music education. Music Educators Journal, April 1962, p. 65. Reimer, B. A philosophy of music education. Englewood Cliffs, N.J.: Prentice-Hall, 1970. Roederer, J. Introduction to physics and the psychophysics in music. London: The English Universities Press, Limited, 197 4. Schmidt, L. Project P.E.P. Music Educators Journal, 1968, 3. Wiliman, F. R. A study of attitudes, competencies, and understandings achieved through the medium of elec tronic music in selected upper elementary and junior high school classrooms, (Doctoral dissertation. University of North Dakota, 1972). Dissertation Abstracts International, 1973, 33, 4819A. 42 43 APPENDIX A ALIFERIS MUSIC ACHIEVEMENT TEST ANALYSIS 44 ALIFERIS MUSIC ACHIEVEMENT TEST ANALYSIS Correlations Between AMAT Total Scores and One, Two, and Four-Year Honor Point Ratios (Grade Point Averages) Total Score Correlated with Music Academic All Courses Courses Courses 1-Year H.P.S. .61 .25 .47 2-Year H.P.S. .53 .28 .40 3-Year H.P.S. .66 .32 .56 Correlations Between AMAT Total Scores and Four-Year Honor Point Ratios in Major Subject Areas Major Subject Correlations with Areas Total Score Theory .66 Harmony .40 Music Education .29 Major Instrument .29 Performing Organization .26 AMAT Sections Reliability Estimates Melodic . 84 Harmonic .72 Rhythmic .88 45 Intercorrelations of Part and Total Scores on the AMAT for Entering Freshmen Fall 1950 Test Scores Harmonic Rhythmic Total Melodic .66 .41 .90 Harmonic .32 .81 Rhythmic .88 46 APPENDIX B OHIO STATE DIAGNOSTIC MUSIC TEST BATTERY DATA 47 OHIO STATE DIAGNOSTIC MUSIC TEST BATTERY DATA Multiple Correlation (R) of Music Placement Tests Sections I, II, III and The Ohio State Psychological Examina tion with First Quarter Freshman Music Theory Grades for Freshmen Music Majors entering 1958 (N = 91) = .83. Correlation (r) of predicted First Quarter Freshman Music Theory Grades and actual grades for Freshmen Music Majors entering 1962 (N = 87) = .65. Multiple Correlation (R) of Sex, Music Placement Tests Sections I, II, III and The Ohio State Psychological Examination with Total Grade Point-Hour Ratio at the end of 6 quarters for Freshmen Music Majors entering 1956-1957 (N = 165) = .65. Correlation (r) of predicted and actual 6 Quarter Total Grade Point-Hour Ratio for Freshmen Music Majors entering 1958, 1959, 1960 (N = 252) = .69. Multiple Correlation (R) of Sex, Attendance at special test days. Music Placement Tests Sections I, II, III and The Ohio State Psychological Examination with Total Grade Point-Hour Ratio at the end of 12 quarters for Freshmen Music Majors entering 1954-1955 (N = 153) = .69. Correlation (r) of predicted and actual 12 quarter Total Grade Point-Hour Ratio for Freshmen Music Majors entering 1957-1958 (N = 165) = .68. 48 APPENDIX C VARIABLE LABELS 49 VARIABLE LABELS VI Instructor VI9 Instrumental Background V2 Experimental Effect V20 Musical Background V3 Subject Number V21 AMAT Pretest #1 V4 ODMTB Pretest #1 V22 AMAT Pretest #2 V5 ODMTB Pretest #2 V23 AMAT Pretest #3 V6 ODMTB Pretest #3 V2 4 AMAT Pretest #4 V7 ODMTB Pretest #4 V2S AMAT Pretest #5 V8 ODMTB Pretest #s V26 AMAT Pretest #6 V9 ODMTB Pretest #6 V2 7 AMAT Pretest Total VIO ODMTB Pretest Total V2 8 AMAT Posttest #1 Vil ODMTB Posttest #1 V2 9 AMAT Posttest #2 VI2 ODMTB Posttest #2 V30 AMAT Posttest #3 VI3 ODMTB Posttest #3 V31 AMAT Posttest #4 V14 ODMTB Posttest #4 V32 AMAT Posttest #s VIS ODMTB Posttest #s V33 AMAT Posttest #6 VI6 ODMTB Posttest #6 V34 AMAT Posttest Total VI7 ODMTB Posttest Total V35 Post Electronic Unit Quiz VI8 Sex Compute CAPl = V2 8 + V29 CAP2 = V30 + V31 CAP3 = V32 + V33 COPl = Vil + VI3 + VIS C0P2 = VI2 + V14 + V16 50 APPENDIX D ALIFERIS MUSIC ACHIEVEMENT TEST, STUDENT DATA SHEET 51 5 o o CO C D 35 c f e o 0 • H c r c £ V ) u O Ü C J C •n • H 1 ( w o ^ > > T : t - > e < ~ L - c . ! ; . e >1 CL % fell c Ü lL > . o -C t > 6C . u K • o BC C r t c c c c q o • â– 3 e e s 7 S u o c : B o £* c #4 Cl f e . O U lJ U Cl n o K CL«-( e x: 6 C h uc c E L q o e O c c e l - ( (C 3 3 f a j z z ! 1 ëè 52 APPENDIX E CHART OF STUDENT PERFORMANCE EXPERIENCE 53 CHART OF STUDENT PERFORMANCE EXPERIENCE Group N Four or More Years Experience No Experience Experimental Mus i c 2 13 5 8 Music 3A 20 11 9 — _ " " " ' Total 33 16 17 Control Music 2 19 4 15 Music 3A 20 13 7 ____- ----- ' " Total 39 17 22 54 APPENDIX F ELECTRONIC MUSIC UNIT LECTURE OUTLINE AND GUIDE 55 ELECTRONIC MUSIC UNIT LECTURE OUTLINE AND GUIDE (Experimental Groups) What are the characteristics of musical sound? a. Sound— vibrations per second, cycles per second, hertz, are technical terms used to describe periodic sound. b. Musical tone— is regular, periodic, repeated patterns depicted as waveforms. c. Noise— is irregular, aperiodic waveform. What are sound waves? a. Variations (alternations) in air pressure like the displace ment of water when a stone or object is dropped in a still pond (111. no. 1). When viewed horizontally, the waves might look like this (111. no. 2). b. When someone sings, speaks, or plays an instrument, similar waves are generated, transmitting the sound through the air to your ear. These sound waves can be (111. no. 3) picked up by a microphone and converted into electrical signals. Each signal or sound has: 1. its own waveshape or waveform which we call quality or timbre ; 2. a vibrating frequency or pitch if it is periodic; 3. if it is something like thunder, surf, wind, certain drums, or a non-repeated pattern, it is called aperiodic. Music is mostly periodic type of waveform. There are four basic, com mon periodic waveforms of a pairticular shape : sine wave— 111. no. 4 b. sawtooth wave— 111. no. 5 c. square wave— 111. No. 6 d. pulse wave— 111. no. 7 pure, flute-like sound bright, full brassy sound a bright, but hollow sound, e.g., clarinet a nasal, reedy sound The quality or timbre of a sound enables the listener to distinguish between it and other tones which have the same pitch and/or loud ness. For example, the difference between an oboe, clarinet, or clarinet and trumpet, or between Carol's or Heather's voice, with 56 each pair being able to produce the same pitch. The volume is also called amplitude and can be seen in the height of the wave (111. no. 8). Changing frequency or amplitude of a wave will not count as a change in its shape, even though some instruments' tone changes slightly in different registers. Why are these important to both music theory and in electronic music? To answer this we must investigate the acoustical properties of sound further. Why do differently shaped waveforms produce different sounds? The main reason is that differently shaped waveforms have different over tones. And, what are overtones? An example and illustration will provide us with a definition. Let's say you are listening to a particular pitch; low A at 110 Hertz (Hz). The acoustic effect produced by a single vibration at this frequency would be describe as a pure sound— one with no harmonics, or overtones. Remember the sine wave Cl11. no. 4). But most natural sounds, musical sounds of the piano, violin and other instruments do not consist of just a simple, single vibration. Virtually all musical instruments produce "complex," composite sounds consisting of the main sound or vibration called the fundamental plus a number of additional sounds of lesser volume or amplitude called overtones or partials or harmonics. 5th Harmonic 4th Harmonic 3rd Harmonic 2nd Harmonic Fundamental 550 Hz 440 330 220 110 Hz The overtones consist of vibrations that are simply multiples of the fundamental frequency, 110, 220, 330, 440, 550, etc. Overtones like these are called harmonics. It is the relationship of the relative amplitudes or volumes of different harmonics that causes the distinguishing features between two or more sounds of the same pitch. Let's see how each of the four basic waveforms differ from each other by their harmonic content and consequently in their timbre or quality of tone (111. no. 9). Note that the square wave is made up of the fundamental frequency plus all ODD numbered harmonics, while (Moog 15) the sawtooth and narrow 57 pulse wave are made up of the fundamental plus ALL harmonics. When you listen to the difference you will hear brighter sound characteristics in the pulse wave. Why? Because of the greater volume or amplitude of the harmonics. The Moog 15 in our lab uses four waveforms. Listen to each: a. sine wave - b. triangle wave - c . sawtooth wave - d. rectangle wave - Certain percussion instruments like gongs, chimes, triangle, and bells produce overtones that are not exact multiples of the fundamental even to the extent that it is virtually impossible to determine the fundamental pitch. Now we can relate the concept of waveform and harmonics together graphically to illustrate the resulting complex waveform (111. no. 10). Fundamental and 2nd harmonic Fundamental and 3rd harmonic Fundamental & 2,3,4,5th har. Fundamental & 3rd & 5th har. From all of this information we can see that complex waveforms can be synthesized or combined by adding together a number of simple waves. This process is called additive synthesis. Incidentally, the term synthesizer is used to describe the electronic instrument which can mechanically create an infinite variety of acoustical sounds or timbres through the process of additive or subtractive synthesis— the process of removing or filtering out certain frequencies. Now that we have established a basic knowledge and framework of the acoustical properties of sound, in particular, musical sounds, we ask how does this relate to music theory and the relationship be tween notes in our musical system? Let's begin with the piano keyboard since it provides us with a visual illustration of pitches for what we call equal tempered tuning. Two things need to be kept in mind : a. The mechanical nature of the piano key and the rather stable condition of the string allow us to hear the same pitch each time we depress the same key. 58 b. We can see the distance between keys being played which also gives us a spacial distance between pitches. First, is the piano timbre a simple or pure waveform or a complex wave form? Yes, complex. Since it is a complex waveform we refer back to the harmonic series to recall the 2nd harmonic or overtone. This gives us what we call an octave or eight tones of white keys apart. Using the alphabet— A through G— letter names are assigned to each white key. For example, A— 440 vibrations per second as a starting pitch, 880 v.p.s. is a multiple of 2 of the lower fre quency. Next, notice that the keys are arranged in a symetrical pattern of white keys with more noticeable black keys in patterns of twos and threes. They are found between notes called "C." Let's diagram the keyboard and assign letter names to each key. OCt CLYC/ It becomes rather obvious that if A has a vibrating frequency of 440 v.p.s. that each other tone or pitch or key must also have a rather specific vibrating frequency in relation to each other. Since there are a total of twelve keys between "C" and "C" one octave above, we can establish by measurement of the number of vibrations that there are approximately 15 to 30 v.p.s. between adjacent keys in this register or octave and thus in the tonal system of tradi tional western music. We must note that there is a proportional increase in the number of vibrations per second between notes as the pitch rises. The interval between two adjacent keys or pitches is designated as a semitone or a half step. Notice that there are two naturally occurring half steps in the system. Consequently between "C" and "D" is called a whole step as it combines by addition the two semitones. Let's sing some intervals of half and whole steps. (Also, ask the class to identify the same intervals after playing them on the keyboard. Draw a keyboard on the blackboard and have the class identify half and whole steps.) In conclusion, you can see that it is possible to measure the distances and relationships between notes or tones in a very exact manner as well as abstractly. I hope that this presentation will be helpful to you in your study of music theory and the understanding of tonal structure. 59 60, 61 62 w D O ' 3 67 mi ^ a % CL :' a/» < g ^ O ' ^ *«# % # ] «4 : = 4 I 1x4 ^ : 14, 2 : : PC) C 14 ___ - £ b c? ^4 _ ; ; 3 4 14 \ ------ 68 su o X CL. 69 mo cm o 03 70
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The effect of an instructional unit of electronic music on the musical achievement of students in college basic musicianship and music theory classes
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