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The effect of different musical timbres on students’ identification of melodic intervals Hinton, Dallas Edward 1982

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THE EFFECT OF DIFFERENT MUSICAL TIMBRES ON STUDENTS' IDENTIFICATION OF MELODIC INTERVALS by DALLAS EDWARD HINTON M. Ed., The U n i v e r s i t y of B r i t i s h Columbia, 1980 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION in THE FACULTY OF GRADUATE STUDIES Department of V i s u a l and Performing A r t s i n Education Music Education Programme We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1982 ©Dallas Edward Hinton, 1982 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a gree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . V i s u a l and Performing Arts sin Education Department o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date A p r i l 10, 1982 i i Supervisor: Dr. John S. Murray ABSTRACT Musical timbre, an a t t r i b u t e of musical tone, i s seldom considered to play an important part in p i t c h i d e n t i f i c a t i o n . C o l l e g e / u n i v e r s i t y music students r o u t i n e l y are given ear t r a i n i n g , i . e . , are taught to i d e n t i f y i n t e r v a l s and chords from d i c t a t i o n , as part of t h e i r regular harmony or theory c l a s s e s . For t h i s e x p l o r a t o r y study f i v e hypotheses were formulated, s t a t i n g that a b i l i t y to i d e n t i f y melodic i n t e r v a l s during music d i c t a t i o n i s not a f f e c t e d by d i f f e r e n c e s i n timbre, the use of f a m i l i a r or u n f a m i l i a r timbres (MAJOR), formal ear t r a i n i n g experience (FETE), or playing/performing experience on an instrument (PPEM), and that there i s no s i g n i f i c a n t i n t e r a c t i o n between PPEM and FETE. Melodic i n t e r v a l s were presented i n random order by s i x instruments: c l a r i n e t , trumpet, piano, v i o l i n , xylophone, and synthesizer (sine waveform). Each instrument played twelve randomly assorted melodic i n t e r v a l s , based on C4 and not exceeding one octave. The independent v a r i a b l e s were MAJOR instrument, FETE, and PPEM. The dependent measures were the scores achieved on an author - w r i t t e n melodic i n t e r v a l d i c t a t i o n t e s t c l o s e l y resembling the " t y p i c a l " ear t r a i n i n g quiz used i n many c o l l e g e / u n i v e r s i t y music theory c l a s s e s . A m u l t i v a r i a t e a n a l y s i s of variance (MANOVA) was used for an a n a l y s i s of PPEM (three l e v e l s ) compared with FETE (three l e v e l s ) . A second MANOVA a n a l y s i s was used f o r MAJOR. Appropriate Scheffe post hoc analyses were c a r r i e d out. I t was found^, that the amount of playing/performing experience a f f e c t e d subjects' scores on the dependent v a r i a b l e s , but only for those subjects with more than ten years of PPEM. The amount of formal ear t r a i n i n g experience a l s o s i g n i f i c a n t l y a f f e c t e d subjects' scores, but there was no c l e a r p a t t e r n d i s c e r n i b l e . Both PPEM and FETE i n t e r a c t e d with the dependent v a r i a b l e s to produce pairwise d i f f e r e n c e s at various l e v e l s of each independent v a r i a b l e . No s i g n i f i c a n t i n t e r a c t i o n between PPEM and FETE was found. There were s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s among the v a r i o u s , l e v e l s .of the declared MAJOR instruments, but no c l e a r pattern was found. I t was concluded that FETE, PPEM, and MAJOR a l l a f f e c t e d subjects' scores on i n t e r v a l s presented with d i f f e r e n t timbres. i v TABLE OF CONTENTS Chapter Page ABSTRACT i i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS i x Chapter 1. DESCRIPTION OF THE STUDY AREA 1 Int r o d u c t i o n to the Problem 1 The Problem 4 D e f i n i t i o n of Terms 5 S t a t i s t i c a l Hypotheses 10 Assumptions, Scope, and L i m i t a t i o n s 11 Chapter 2. REVIEW OF THE LITERATURE 12 Summary 22 C h a p t e r s . METHODOLOGY 25 Population and Sample 25 S e l e c t i o n of I n t e r v a l s and Timbre Sources 27 Preparation of the Test Tape 29 Testing Procedure 31 V S t a t i s t i c a l Design and A n a l y s i s 33 Chapter 4. RESULTS 36 Summary of the Problem 36 S t a t i s t i c a l Re su l t s 37 I n t r o d u c t i o n 37 Tests of Hypothes i s I 38 Tests of Hypothes is I I 43 Tests of Hypothes i s I I I 44 Tests of Hypothes i s IV 48 Tests of Hypothes i s V 48 Chapter 5. CONCLUSIONS 53 I n t r o d u c t i o n 53 Summary of Resu l t s . 54 Conc lus ions 56 Suggestions for Fur ther Study 58 SOURCES CONSULTED 60 Books 60 A r t i c l e s and P e r i o d i c a l s 63 Unpubl i shed M a t e r i a l s 68 Appendix 1. Melodic I n t e r v a l I d e n t i f i c a t i o n - - I n s t r u c t i o n s to Performers 70 Appendix 2. Quest ionnaire and I n t e r v a l Answer Form 73 Appendix 3. L i s t and S p e c i f i c a t i o n s of Equipment used for the . Study 77 Appendix 4. Contents of the Test Tape 79 Appendix 5. I n t e r v a l Randomization Program 81 Appendix 6. Order of I n t e r v a l s as P layed to Subject s 84 v i Appendix 7. Coding Method Used f o r I d e n t i f y i n g Responses . 89 Appendix 8. The Computer Program used for Conversion of Scores 91 Appendix 9. The Computer Program used for Transformation and S t a n d a r d i z a t i o n of Scores 94 Appendix 10. C e l l Means, Variance, and Standard Deviation for PPEM and FETE 100 Appendix 11. C e l l Means, Variance, and Standard Deviation for MAJOR 102 v i i LIST OF TABLES Table Page 1 . 3 X 3 MANOVA DESIGN 35 2. MANOVA SUMMARY TABLE FOR PPEM AND FETE 39 3. SCHEFFE POST HOC COMPARISON OF PPEM LEVELS 39 4. SCHEFFE POST HOC PAIRWISE COMPARISON OF PPEM LEVELS ... 40 5. SCHEFFE POST HOC COMPARISON OF PPEM 41 6. SCHEFFE POST HOC COMPARISON OF FETE 45 7. SCHEFFE POST HOC PAIRWISE COMPARISON OF FETE 46 8. MANOVA SUMMARY TABLE FOR MAJOR 49 9. SCHEFFE POST HOC COMPARISON OF MAJOR LEVELS 49 10. SCHEFFE POST HOC COMPARISON OF MAJOR 50 v i i i v-LIST OF FIGURES Figure Page 1. Rhythmic Pattern used for Melodic I n t e r v a l s 30 2. PPEM Compared With SCORES 42 3. FETE Compared With SCORES 47 4. MAJOR Compared With SCORES 51 5. SCORE Compared With MAJOR 52 i x ACKNOWLEDGEMENTS No p r o j e c t of t h i s type can be s u c c e s s f u l l y completed without a s s i s t a n c e from many people. The author would l i k e to thank a l l the f a c u l t y and students who p a r t i c i p a t e d i n the study and those who a s s i s t e d with various other aspects of i t . In p a r t i c u l a r , the author would l i k e to thank the f o l l o w i n g : Mr. Kevin Barrington-Foote, Dr. Wallace Berry, Dr. R. E..Bruce, Dr. A l l e n E. Clingman, Mr. John Jacyna, Mr. David K i r s c h n e r , Mr. Fred Koch, Miss Kenna Leatherdale, Dr. Seong-Soo Lee, Dr. John Murray, Mr. Hans-Karl P i l t z , Dr. Harold R a t z l a f f , Dr. Todd Rogers, and Mr. Peter S t i g i n g s . S p e c i a l mention must be made of the support o f f e r e d by the author's w i f e , who was an u n f a i l i n g source of strength and encouragement throughout. This study was completed with the f i n a n c i a l a s s i s t a n c e of a research grant from the Educational Research I n s t i t u t e of B r i t i s h Columbia (ERIBC), for which the author i s g r a t e f u l . 1 Chapter 1 DESCRIPTION OF THE STUDY AREA In t r o d u c t i o n to the Problem Ear t r a i n i n g has long been a part of t r a d i t i o n a l c o l l e g e music theory i n s t r u c t i o n . In 1942, Hindemith declared that the i n t e r v a l i s " . . . the basic u n i t of musical i n s t r u c t i o n . " 1 In 1949, he commented that The a b i l i t y , to f o l l o w musical d i c t a t i o n i s not n e c e s s a r i l y an index of the degree or q u a l i t y of musical t a l e n t . . . . On the other hand i t cannot be denied that the complete absence of such a b i l i t y i s at l e a s t an unfavorable i n d i c a t i o n of the st a t e of a musician's knowledge. I t i s ther e f o r e necessary to develop it--whatever i t s amount or q u a l i t y may b e — t o the utmost, j u s t as a l l other p a r t s of h i s g i f t must be developed. 2 Some i n s t i t u t i o n s include ear t r a i n i n g i n the music theory c l a s s e s ; others, however, teach these s k i l l s i n separate c l a s s e s on an i n t e n s i v e b a s i s . 3 Ear t r a i n i n g s k i l l s are often d i v i d e d 1 Paul Hindemith, The C r a f t of Musical Composition, t r a n s . Arthur Mendel (New York: Associated Music P u b l i s h e r s , 1942), Book I , p. 57. 2 Paul Hindemith, Elementary T r a i n i n g for Musicians, 2nd ed. (New York: Associated Music Publ i shers , 1 949) , p~. 181. 3 For example, Be.rklee College of Music, Boston, Mass.; Northeastern U n i v e r s i t y , Boston, Mass.; and J u l l i a r d School of Music, New York. 2 i n t o two d i s t i n c t aspects: v i s u a l ( a c t i v e ) , i . e. s i g h t - s i n g i n g from a w r i t t e n stimulus, and aud i t o r y ( p a s s i v e ) , i . e. a t t a c h i n g a l a b e l or designator to a heard stimulus.' 1 During the e a r l y stages of "passive" t r a i n i n g , students are required to l i s t e n to aud i t o r y s t i m u l i and a t t a c h appropriate l a b e l s , e.g. minor t r i a d , p e r f e c t f i f t h . In more advanced c l a s s e s , students may be required to a t t a c h s e v e r a l l a b e l s i n v o l v i n g musical notation of p i t c h , rhythm, and/or d u r a t i o n . M a t e r i a l may be presented m e l o d i c a l l y . ascending, m e l o d i c a l l y descending, harmonically, or by a combination of these methods. 5 At many i n s t i t u t i o n s , ear t r a i n i n g t r a d i t i o n a l l y has meant l i s t e n i n g to and sin g i n g with the piano as a means to l e a r n i n g i d e n t i f i c a t i o n of melodic and harmonic i n t e r v a l s . Gephardt, however, observed that: Nonpianist students often v e r b a l i z e t h e i r b e l i e f that t h e i r d i c t a t i o n a b i l i t i e s might improve i f the musical m a t e r i a l were presented i n a more f a m i l i a r timbre--that of the instrument on which they themselves perform. In the course of presenting heard m a t e r i a l , students are often observed " f i n g e r i n g , " on a make-believe instrument, the notes of an i n t e r v a l or * Paul J . Vander Gheynst, "The E f f e c t of Timbre on A u d i t o r y - V i s u a l D i s c r i m i n a t i o n " (Ed. D. d i s s e r t a t i o n , U n i v e r s i t y of I l l i n o i s , 1978); Donald L. Gephardt, "The E f f e c t s of D i f f e r e n t F a m i l i a r and U n f a m i l i a r Musical Timbres on Musical Melodic D i c t a t i o n " (Ed.D. d i s s e r t a t i o n , Washington U n i v e r s i t y , M i s s o u r i , 1978). 5 A melodic i n t e r v a l i s one in which the notes are played c o n s e c u t i v e l y ; an harmonic i n t e r v a l i s one i n which the notes are played simultaneously. 3 melodic passage that they are asked to i d e n t i f y . . . . One can s p e c u l a t e that perhaps the student i s t r y i n g to get the " f e e l " k i n e s t h e t i c a l l y of performing the p i t c h e s that he/she i s h e a r i n g . 6 Another f a c t o r which may be o p e r a t i n g i s that of the student's experience of timbre changes w i t h i n the range of a p a r t i c u l a r instrument. The c l a r i n e t , f o r example, has a p a r t i c u l a r l y c h a r a c t e r i s t i c change of timbre i n the t h r o a t r e g i s t e r . A c l a r i n e t i s t may p o s s i b l y be more s e n s i t i v e to such timbre d i f f e r e n c e s than are other musicians. Beyer found that performers are more s e n s i t i v e to p i t c h v a r i a t i o n s produced by t h e i r own instruments, and has t h e o r i z e d that these s u b j e c t s might be ab l e to use timbre as a guide to p i t c h and i n t e r v a l ident i f i c a t i o n . 7 Many textbooks on ear t r a i n i n g ignore the e f f e c t of timbre with statements such as: Any melody possesses at l e a s t three b a s i c c h a r a c t e r i s t i c s : . . . time, . . . p i t c h , . . . [and] timbre. Since t h i s t h i r d c h a r a c t e r i s t i c of melody v a r i e s with the instrument on which a melody i s performed, we s h a l l ignore i t and concern o u r s e l v e s e x c l u s i v e l y with rhythm and p i t c h . 8 In the o p i n i o n of the author, and of many other music educators, i n s u f f i c i e n t a t t e n t i o n has been p a i d to the e f f e c t s of timbre on the p e r c e p t i o n of p i t c h . 6 Gephardt, p. 6. 7 George Heydrick Beyer, "The Determination of P i t c h D i s c r i m i n a t i o n i n High School Students with M u s i c a l T r a i n i n g " (M.A. t h e s i s , C a l i f o r n i a S tate U n i v e r s i t y , 1977). 8 W i l l i a m E. Thomson and R i c h a r d P. Delone, I n t r o d u c t i o n to  Ear T r a i n i n g ( C a l i f o r n i a : Wadsworth P u b l i s h i n g , 1968), p.1. 4 As r e c e n t l y as 1978, Gephardt st a t e d t h a t : Although some current music educators, such as Spohn and T r y t h a l l , discount the importance of the connection between timbre and p i t c h perception, other p s y c h o p h y s i c i s t s and musicians have pointed out that there may be an important r e l a t i o n between the a t t r i b u t e s . 9 Gephardt's statement r e i n f o r c e s the opinion of Roederer: Whereas considerable research has been done on the perception of p i t c h and loudness of pure tones. . . much remains to be done i n the study of the perception of q u a l i t y or timbre of complex t o n e s . 1 0 The Problem In t h i s study, the main area of i n t e r e s t was the e f f e c t of instrumental timbre upon students' a b i l i t y to perceive and describe melodic i n t e r v a l s . This study attempted to explore p o s s i b l e answers to the f o l l o w i n g questions: 1) Do d i f f e r e n c e s i n timbre a f f e c t students' a b i l i t y to i d e n t i f y melodic i n t e r v a l s during d i c t a t i o n ? 2) Does the length of time that students have been t r a i n i n g to i d e n t i f y melodic i n t e r v a l s have a r e l a t i o n s h i p with a p o s s i b l e e f f e c t of f a m i l i a r i t y of timbre, as measured by a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? 3) Does the length of time that students have been p l a y i n g t h e i r declared major instrument have a r e l a t i o n s h i p with a p o s s i b l e e f f e c t of 9 Gephardt, p.86. 1 0 Juan .G. Roederer, I n t r o d u c t i o n to the Physics and  Psychophysics of Music (London: The E n g l i s h U n i v e r s i t i e s Press, 1973), p. 127. 5 f a m i l i a r i t y of timbre, as measured by a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? 1 1 4) Does the use of f a m i l i a r or u n f a m i l i a r timbre sources a f f e c t students' a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? D e f i n i t i o n ' o f Terms Ear t r a i n i n g . For the purposes of t h i s study, the d e f i n i t i o n of ear t r a i n i n g used by Shaw i s accepted: . . . that branch of musical education which attempts to develop a p o s i t i v e awareness i n the mind of the var i o u s phenomena which c o n s t i t u t e the mere m a t e r i a l of music, the c h i e f of which are time and rhythmic r e l a t i o n s h i p s ; p i t c h r e l a t i o n s h i p s , whether simultaneous or in succession; t o n a l i t y and modulation. I t i s concerned with the mind rather than the f i n g e r s , and with terminology and the symbols of no t a t i o n only so far as these r e l a t e to mental conceptions of musical sound. 1 2 Formal Ear T r a i n i n g Experience (FETE). For the purposes of t h i s study, FETE i s defined as the number of months a subject has spent e n r o l l e d i n a u n i v e r s i t y l e v e l theory/harmony course. I t was assumed t h a t , at the i n s t i t u t i o n s being used for t h i s study, an average amount of ear t r a i n i n g i s done during r o u t i n e classroom i n s t r u c t i o n . Music d i c t a t i o n . For the purposes of t h i s study, the 1 1 In t h i s study, the term "instrument" includes the v o i c e . 1 2 Grove's D i c t i o n a r y of Music and Musicians, 5th ed. (1954), s.v. " E a r - t r a i n i n g , " by Harold Watkins Shaw. 6 d e f i n i t i o n of music d i c t a t i o n used by Gephardt and others i s accepted: . . . music d i c t a t i o n i s [a task] which r e q u i r e s the subject to reproduce, i n exact musical n o t a t i o n using the commonly accepted symbols which designate musical p i t c h , . . . the heard' musical m a t e r i a l which i s presented to the s u b j e c t . . . . The term d i c t a t i o n r e f e r s to i t s common denotation by music theory i n s t r u c t o r s . 1 3 Frequency. The p h y s i c a l property, frequency, i s defined by Seashore and others as c y c l e s per second (cps) and i s perceived as p i t c h . 1 * P i t c h . A musical p i t c h i s defined f o r purposes of t h i s study as being any of the frequencies normally used i n the equal tempered sc a l e using a standard tuning reference of A = 440 Hz. Pitc h e s used in t h i s study cover a one octave range from C4 to C5. 1 5 Pure Tone. For purposes of t h i s study, a pure tone i s considered to be a tone that has no harmonics present. Complex Tone. For purposes of t h i s study, a complex tone i s considered to be one that i s produced by a s i n u s o i d a l wave, and 1 3 Gephardt, p. 18. 1 * A f t e r C a r l E. Seashore, The Psychology of Musical Talent (Boston: S i l v e r Burdett, 1919). ' 5 The p i t c h n o tation used i n t h i s study i s that adopted by the American Standards A s s o c i a t i o n i n 1960, as a l t e r e d and used by The I n s t r u m e n t a l i s t and other j o u r n a l s . In t h i s n o t a t i o n , CO i s 16.352 Hz, and i s l o c a t e d four octaves below piano "middle C", designated as C4. 7 has s e v e r a l p a r t i a l s or harmonics forming an i n t e g r a l part of the sound. P a r t i a l . For purposes of t h i s study, a p a r t i a l i s considered to be one of the frequencies, other than the fundamental, present in a tone. A p a r t i a l may or may not have a whole-number r e l a t i o n s h i p to the fundamental; i . e . i t may or may not be a m u l t i p l e of the fundamental. 1 6 Harmonics. For the purposes of t h i s study, the d e f i n i t i o n used by Backus w i l l be used: . . . the c o n s t i t u e n t p a r t i a l s must be r e l a t e d i n a very simple way; t h e i r frequencies must be i n t e g r a l m u l t i p l e s . . . times the fundamental frequency of the v i b r a t i o n . . . . P a r t i a l s r e l a t e d i n t h i s simple way are given a s p e c i a l name: they are c a l l e d harmonics. 1 7 Hertz (Hz). The term "Hertz" i s an i n t e r n a t i o n a l l y used term meaning c y c l e s per second, and i s used as a measure of the frequency of a sound. Cent. The term "cent" i s a measure of p i t c h used for a l t e r a t i o n s of l e s s than a semitone. There are 100 cents in each semitone. Decibel (dB). A d e c i b e l i s a measure of sound pressure l e v e l (SPL), and i s c a l c u l a t e d with the f o l l o w i n g formula: 1 6 A f t e r Arthur Benade, Fundamentals of Musical Acoustics (New York: Oxford U n i v e r s i t y Press, 1976), p. 63. 1 7 John Backus, The A c o u s t i c a l Foundations of Music (New York: W. W. Norton, 1969), pp. 108-109. 8 L = 10 Log I/Io (Equation 1) where l o i s the t h r e s h o l d of human hearing, I i s the sound i n t e n s i t y , and L i s the i n t e n s i t y l e v e l , measured i n d e c i b e l s (dB). 1 . . . the i n t e n s i t y l e v e l i s a purely p h y s i c a l q u a n t i t y . . . . In p r a c t i c e , d i r e c t measurement of the i n t e n s i t y of a sound wave i s d i f f i c u l t . I t i s much ea s i e r to obtain the pressure amplitude of the sound. . . . The i n t e n s i t y of a sound wave progressing i n one d i r e c t i o n i s p r o p o r t i o n a l to the square of the sound p r e s s u r e . 1 9 Backus goes on to demonstrate t h a t , from Equation 1: Lp = 20 Log P/Po where Lp i s the sound pressure l e v e l , and' P i s the Root Mean Square (RMS) sound pressure. The reference pressure Po i s the RMS sound pressure corresponding to the thre s h o l d i n t e n s i t y and has the value 2 X 10" 5 Newtons/M 2. 2 0 0 dB i s , t h e r e f o r e , the thre s h o l d of human hearing. dBA. Sound l e v e l meters t y p i c a l l y have three s c a l e s : A, B, and C. Each of these scales i s designed to reduce the sound pressure reading at c e r t a i n frequencies, i n order to r e f l e c t more a c c u r a t e l y the response of the human ear. This study used the A weighted scale because: 1 8 I b i d . , p. 92. 1 9 I b i d . , p. 93-94. 2 0 I b i d . 9 . . . with [the A weighting] i n s e r t e d , the meter i s l e s s s e n s i t i v e to low frequencies. . . . This designation [dBA] i s seen fr e q u e n t l y i n sound l e v e l measurements, since i t has been found that readings with . . . [A weighting] correspond w e l l to the s u b j e c t i v e impression of the l i s t e n e r to the sound presented. 2 1 Timbre. "Timbre" i s a term with a number of d e f i n i t i o n s . The d e f i n i t i o n given i n American Standard A c o u s t i c a l Terminology i s : Timbre (Musical Q u a l i t y ) . Timbre i s that a t t r i b u t e of auditory sensation i n terms of which a l i s t e n e r can judge that two sounds s i m i l a r l y presented and having the same loudness and p i t c h are d i s s i m i l a r . Note: Timbre depends p r i m a r i l y upon the spectrum of the stimulus, but i t a l s o depends upon the wave form, the sound pressure, and the frequency l o c a t i o n of the spectrum of the s t i m u l u s . 2 2 For the purposes of t h i s study, the term "timbre" w i l l r e f e r to:' . . . the d i f f e r e n c e s perceived by observers i n the tones produced by v a r i o u s conventional and e l e c t r o n i c musical instruments of the same p i t c h and l o u d n e s s . 2 3 C h a r a c t e r i s t i c Timbre. C h a r a c t e r i s t i c timbre i s defined for purposes of t h i s study as being that timbre which p r o f e s s i o n a l musicians and music teachers can agree upon as being a "good tone" for a p a r t i c u l a r instrument. 2 1 I b i d . , pp. 97-98. 2 2 American Standards A s s o c i a t i o n , American Standard  A c o u s t i c a l Terminology (New York: American Standards A s s o c i a t i o n , Inc., 1951), p. 25. 2 3 Gephardt, p. 16. 10 F a m i l i a r timbre. A f a m i l i a r timbre i s defined for purposes of t h i s study as a timbre produced by an instrument which i s the same as the subject's declared major instrument. The exact amount of f a m i l i a r i t y i s described by the measure of PPEM which was gathered i n the p r e l i m i n a r y q u e s t i o n n a i r e . S t a t i s t i c a l Hypotheses There were f i v e hypotheses a r i s i n g from the general research q u e s t i o n : 2 " Hypothesis I : There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t i n t e r a c t i o n between formal ear t r a i n i n g experience (FETE) and playing/performing experience (PPEM) as measured by scores a t t a i n e d on an author-produced t e s t of melodic . i n t e r v a l ident i f i c a t i o n . Hypothesis I I : There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s , as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n , regardless of the amount of PPEM each has had. Hypothesis I I I : There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s , as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n , regardless of the amount of FETE each has had. 2* The .05 l e v e l of s t a t i s t i c a l s i g n i f i c a n c e was used i n t h i s e x p l o r a t o r y study. Hypothesis IV: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s presented using d i f f e r e n t timbres, as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n . Hypothesis V: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s presented using timbres that d i f f e r i n f a m i l i a r i t y , as measured by scores a t t a i n e d on an author produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n . Assumptions, Scope, and L i m i t a t i o n s This study was done with students e n r o l l e d e i t h e r in j u n i o r c o l l e g e or in u n i v e r s i t y who had completed or who were then ta k i n g at l e a s t one f i r s t year theory/harmony course. I t was assumed that the subjects i n v o l v e d , as a r e s u l t of the population d e f i n i t i o n , were f a m i l i a r with the conventions of musical notation and procedures commonly used i n melodic d i c t a t i o n . I t was not assumed that the population under i n v e s t i g a t i o n was r e p r e s e n t a t i v e of a l l music students, since i t i s p o s s i b l e that students from other i n s t i t u t i o n s might be s i g n i f i c a n t l y d i f f e r e n t from the s e l e c t e d population i n terms of musical a b i l i t y , a p t i t u d e , t r a i n i n g , e t c . No attempt was made to deal with i n t e r v a l s , instruments or timbres other than those s p e c i f i e d . Chapter 2 REVIEW OF THE LITERATURE There appears to be a r e l a t i v e l y l a r g e body of work d i s c u s s i n g the a t t r i b u t e s of p i t c h , loudness, and d u r a t i o n , but r e l a t i v e l y l i t t l e p ublished or unpublished m a t e r i a l i n v e s t i g a t i n g the e f f e c t of timbre upon p i t c h perception. Seashore examined timbre only b r i e f l y , c l a i m i n g t h a t : The hearing of timbre. . . gives no new a t t r i b u t e of sound; a tone of a given timbre i s merely a complex of a given number of p i t c h e s i n t h e i r r e s p e c t i v e i n t e n s i t i e s , u s u a l l y blending i n t o the experience of a s i n g l e tone. 1 Farnsworth seemed to disagree with Seashore, saying t h a t : . . . i t i s unfortunate that a u t h o r i t i e s w r i t e at times as though a p e r f e c t f i f t h , a minor chord, or a melody w i l l have i d e n t i c a l - c h a r a c t e r i s t i c s whether sung or played on a marimba, a harmonica, a tuba, or an o l d Cremona v i o l i n . They are n e g l e c t i n g the d i f f e r e n c e s i n t i m b r e . 2 1 C a r l E. Seashore, The Psychology of Musical Talent (Boston: S i l v e r Burdett, 1919),.pp. 1389. 2 Paul R. Farnsworth, The S o c i a l Psychology of Music (New York: The Dryden Press, 1958), p. 56. 1 3 In 1919, C a r l Seashore stated t h a t : . . . Pure tones are r a r e l y used in music, p a r t l y because they cannot be produced byvthe voice or the ordinary musical instruments, and p a r t l y because they are t h i n , and lack richness and f l e x i b i l i t y . 3 More r e c e n t l y , Backus wrote t h a t : . . . In our everyday experience, pure tones are very seldom heard, even i n music. With the exception of the tuning f o r k , most sound sources, i n c l u d i n g musical instruments, produce complex tones that are mixtures of simple tones of various amplitudes and frequencies." Z e i t l i n found that among h i s t e s t subjects there was s i g n i f i c a n t l y b e t t e r p i t c h d i s c r i m i n a t i o n for complex tones than for pure tones, i n the frequency range from 190 Hz to 6000 Hz (approximately G2 to G7). 5 The research of Henning and Grosberg confirmed these r e s u l t s , suggesting that greater exposure to complex tones might f a c i l i t a t e l e a r n i n g : . . . complex tones . . . [presumably] evoke a be t t e r response on the b a s i l a r membrane from which more comprehensive frequency information can be o b t a i n e d . 6 3 Seashore, pp. 128-129. * John Backus, The A c o u s t i c a l Foundations of Music (New York: W. W. Norton, 1969), pp. 107-108. 5 L. R. Z e i t l i n , "Frequency D i s c r i m i n a t i o n of Pure and Complex Tones," Journal of the A c o u s t i c a l Society of America, 36(1964), pp. 1207-1219. 6 G. B. Henning and S. L. Grosberg, " E f f e c t s of Harmonic Components of Frequency D i s c r i m i n a t i o n , " J o u r n a l of the  A c o u s t i c a l Society of America, 44(1968), pp. 1386-1389. 1 4 Stevens commented t h a t : The p i t c h of a sound of given frequency depends to some extent on i t s i n t e n s i t y . I f the loudness of a pure tone i s increased, a change in p i t c h may occur. . . . A number of s t u d i e s have been made of t h i s e f f e c t , but with rather l i t t l e agreement among t h e m . . . . 7 Cohen found rather l e s s e f f e c t , as d i d Verschure and von Meerten. 8 Snow concluded t h a t : The e f f e c t apparently e x i s t s only for pure tones; i t seems g e n e r a l l y agreed that complex tones show no change i n p i t c h with i n t e n s i t y . 9 Chapin and F i r e s t o n e experimented with s h i f t i n g the phase of a lower harmonic of a 108 Hz tone (at 104 dB), with somewhat in c o n c l u s i v e r e s u l t s , 1 0 while F l e t c h e r claimed t h a t : 7 S. S. Stevens, "The" R e l a t i o n of P i t c h to I n t e n s i t y , " J o u r n a l of the A c o u s t i c a l Society of America, 6(1935), p. 153. 8 A. Cohen, "Further I n v e s t i g a t i o n s of the E f f e c t s of I n t e n s i t y upon the P i t c h of Pure Tones," Journal of the  A c o u s t i c a l Society of America, 33(1961), pp. 1363-1376; J . Verschure and A. A. von Meerten, "The E f f e c t of I n t e n s i t y on P i t c h , " A c o u s t i c a , 32(1975), pp. 33-44. 9 W. B. Snow, "Change of P i t c h with Loudness at Low Frequencies," Journa l of the A c o u s t i c a l S o c i e t y of America, 8(1936), pp. 18-19; see a l s o D. Lewis and M. Cowan, "The Influence of I n t e n s i t y on the P i t c h of V i o l i n and C e l l o Tones," Journal of the A c o u s t i c a l Society of America, 8(1.936), pp. 20-22; and E. Terhardt, "The Influence of I n t e n s i t y on the P i t c h of Complex Tones," A c o u s t i c a , 33(1975), pp. 344-48. 1 0 E. K. Chapin and F. A. F i r e s t o n e , "The Influence of Phase on Tone Q u a l i t y and Loudness; The Inter f e r e n c e of Subjective Harmonics," Journal of the A c o u s t i c a l Society of  America, 5(1934), pp. 173-180. 15 The f a c t that considerable timbre d i s t o r t i o n s i n a m p l i f i e r s and e l e c t r o a c o u s t i c transducers could be t o l e r a t e d without any n o t i c e a b l e e f f e c t on the q u a l i t y of reproduced music and speech, supported the [then] g e n e r a l l y accepted opinion that the ear had a l i m i t e d s e n s i t i v i t y i n the d i s c r i m i n a t i o n of timbre under varying phase c o n d i t i o n s . 1 1 Plomp's work i n part confirmed t h i s f i n d i n g , concluding that for the usual musical instruments: . . . harmonics beyond about the seventh cannot be heard o u t . 1 2 This f i n d i n g has i n t e r e s t i n g i m p l i c a t i o n s regarding the minimum frequency range requirements of audio equipment; for a given tone with a fundamental frequency of, for example, 520 Hz, harmonics above a frequency of about 5500 Hz (the seventh p a r t i a l ) may be of l i t t l e or no importance. C. A. Taylor states that there are three major f a c t o r s c o n t r i b u t i n g to d i f f e r e n c e s i n tone q u a l i t y : 1) Simultaneous v i b r a t i o n i n s e v e r a l modes of resonance; 2) a m p l i f i c a t i o n systems with r e s u l t i n g t r a n s i e n t e f f e c t s ; and 3) t r a n s i e n t s caused s p e c i f i c a l l y by the method of i n i t i a t i o n of the sound. 1 3 1 1 Harvey F l e t c h e r , "Loudness, P i t c h and the Timbre of Musi c a l Tones, and Their R e l a t i o n to the I n t e n s i t y , the Frequency and the Overtone S t r u c t u r e , " Journal of the A c o u s t i c a l  S o c i e t y of America, 6(1934), pp. 59-69. 1 2 R. Plomp, " P i t c h , Timbre, and Hearing Theory," I n t e r n a t i o n a l Audiology, 7(1967), pp. 322-344. 1 3 C. A. Taylor, The Physics of M u s i c a l Sound (New York: American E l s e v i e r P u b l i s h i n g , 1965), p. 106. 1 6 Taylor c i t e s two other areas as having some a d d i t i o n a l e f f e c t upon tone q u a l i t y : the formants of a tone, and the terminal t r a n s i e n t e f f e c t . 1 " Ward does not appear to consider that the term "timbre" i s used c o r r e c t l y , saying t h a t : Timbre, which i s a f u n c t i o n of the harmonic content of the sound . . . i s often used as a waste basket category; i f two sounds are ' d i f f e r e n t ' though having the same p i t c h and loudness, then they must d i f f e r i n t i m b r e . 1 5 During a conference i n Stockholm, R i s s e t declared t h a t : Ever since Helmholtz, a c o u s t i c s textbooks e x p l a i n that timbre--the d i s t i n c t i v e q u a l i t y of a musical i n s t r u m e n t — i s a s s o c i a t e d with harmonic spect r a ; the c o n f i g u r a t i o n of a spectrum would therefore determine the timbre of the instrument. The research work c a r r i e d out by Schaeffer's group [P. Schaeffer, T r a i t e des objects Musicaux, S e u i l , P a r i s (1966)] pointed out the t o t a l inadequacy of such a simple conception, • as d i d the st u d i e s [of] . . . E. Leipp [ B u l l e t i n s du Groupe d'Acoustique Musicale (1963-1970), A c o u s t i c s Laboratory of the F a c u l t y of Science, 9, quai Saint-Bernard, P a r i s ] and . . . M. Clark [ J . M. C l a r k , Several Problems i n Musical  Acoust i e s , J . Audio Engineering Sty, 7 ( 1959) p~. 2 ]. 1 6 Although R i s s e t does not go i n t o f u r t h e r d e t a i l , Backus e x p l a i n s t h a t : 1" I b i d . , pp. 106-110. 1 5 W. Dixon Ward, "Musical Perception," i n Foundations of  Modern Auditory Theory, ed. J e r r y V. Tobias (New York: Academic Press, 1970), V o l . I , p. 409. 1 6 I b i d . , pp. 125-126. 1 7 For a p a r t i c u l a r instrument, the s t r u c t u r e of a given s i n g l e tone w i l l depend on a number of f a c t o r s . I t changes with loudness. . . . the harmonics i n the sound r a d i a t e d i f f e r e n t l y i n d i f f e r e n t d i r e c t i o n s from the instrument, due to i n t e r f e r e n c e and d i f f r a c t i o n e f f e c t s , so that the harmonic s t r u c t u r e of a tone w i l l depend on where i t i s heard. The spectrum of a tone w i l l a l s o depend on how the player produces i t . I t w i l l a l s o depend on the c h a r a c t e r i s t i c s of the room i n which i t i s played. An a l t e r n a t i v e theory suggests that an instrument has a c e r t a i n f i x e d frequency region or regions in which harmonics of a tone are emphasized, regardless of the frequency of the fundamental. A f i x e d frequency region of t h i s kind i s c a l l e d a formant, and i t i s the l o c a t i o n of these formant regions that c h a r a c t e r i z e s the instrument. . . . . . . there are other aspects of tone that are important i n i d e n t i f y i n g the instrument producing i t . For example, the i n i t i a l t r a n s i e n t . . . i s rather important. . . . The decay t r a n s i e n t can a l s o be important. 1 7 The f i r s t c o n t r o l l e d experiments d e a l i n g with the auditory perception of timbre and wave patterns i n complex tones were reported i n 1862 by H e l m h o l t z . 1 8 Although some of h i s f i n d i n g s are now i n question, he i s given c r e d i t for beginning the e x p l o r a t i o n of the f i e l d of timbre. As r e c e n t l y as 1980, Jameson commented t h a t : The l e a s t amount of research, and a l s o the most recent, has focused on the e f f e c t timbre has upon p i t c h perception and p i t c h matching a b i l i t y i n a m u s i c a l l y relevant s e t t i n g . 1 9 1 7 .Backus, pp. 117-118. 1 8 Hermann L. F. Helmholtz, On the Sensations of Tone as a  P h y s i o l o g i c a l Basis for the Theory of Music, t r a n s . and ed. Alexander J . E l l i s . 2nd ed. (New York: Dover, 1954). 1 9 Jameson, p. 11. 18 Whybrew, commenting on the timbre t e s t p o r t i o n of Seashore's Measures of Musical T a l e n t s , s a i d : Timbre was v a r i e d by a l t e r i n g the balance i n the overtone s t r u c t u r e of the tones used. The authors point out . . . that they had c e r t a i n doubts about the i n c l u s i o n of such a measure, due to d i f f i c u l t i e s occasioned by phonograph f u n c t i o n and room a c o u s t i c s . They expressed the b e l i e f that reasonably constant r e s u l t s might be expected but that f u r t h e r i n v e s t i g a t i o n was needed. 2 0 Cuddy's f i n d i n g s tend to support the premise that a subject who st u d i e s a p a r t i c u l a r instrument for a number of years develops a sense of p i t c h judgement which i s better for tones produced by that instrument than i t i s f o r tones produced for other instruments. Cuddy found t h a t : M u s i c a l l y t r a i n e d subjects who were studying the piano as a major instrument named piano tones more ac c u r a t e l y than pure tones. In general, the accuracy of p i t c h judgement was r e l a t e d to f a m i l i a r i t y with musical t o n e s . 2 1 Leonard, examining t h i s premise from a d i f f e r e n t viewpoint, concluded that students who had not studied instruments i n depth would not be a f f e c t e d by the timbre used. He te s t e d the e f f e c t of s i x f a c t o r s on the p i t c h d i s c r i m i n a t i o n s k i l l of subjects who were non-music majors. The experimental v a r i a b l e s were 2 0 W. E. Whybrew, Measurement and Evaluati o n in Music, 2nd ed. (Iowa: Wm. C. Brown, 1971), pp. 116-117. 2 1 L o l a Lane Cuddy, " P r a c t i c e E f f e c t s i n P i t c h Perception" (D.M.A. d i s s e r t a t i o n , U n i v e r s i t y of Toronto, 1965), p. 91. 1 9 i n t e n s i t y , timbre, r e g i s t e r content, d u r a t i o n , and i n t e r s t i m u l u s time i n t e r v a l . A l l f a c t o r s except timbre were found to a f f e c t p i t c h d i s c r i m i n a t i o n . 2 2 In 1970, Greer t e s t e d the e f f e c t ^ o f timbre on the e x t e r n a l i n t o n a t i o n patterns of c o l l e g e age brass-wind music majors. He used four timbre c o n d i t i o n s , and twelve p i t c h l e v e l s . I t was found to be s i g n i f i c a n t l y more d i f f i c u l t for the brass-wind performers to match the p i t c h produced by a sine wave than to match the p i t c h of t h e i r own instrument, piano, or a f l u t e stop on an o r g a n . 2 3 In a r e l a t e d experiment, Hermanson explored the e f f e c t of timbre on young c h i l d r e n . Among Kindergarten and Grade Three students, he found s i g n i f i c a n t l y fewer degrees of i n t o n a t i o n e r r o r when students matched pi t c h e s produced by a woman's voice than when they matched p i t c h e s produced by other c h i l d r e n , piano, or a sine wave. 2" Sergeant examined p i t c h d i s c r i m i n a t i o n of subjects exposed to both square waves and n a t u r a l s t a t e piano tones. He t h e o r i z e d 2 2 Nels Leonard, J r . , "The E f f e c t of C e r t a i n I n t r i n s i c and Contextual C h a r a c t e r i s t i c s of the Tone Stimulus on P i t c h D i s c r i m i n a t i o n " (Ed. D. d i s s e r t a t i o n , West V i r g i n i a U n i v e r s i t y , 1967) . 2 3 R. Douglas Greer, "The E f f e c t of Timbre on Brass-Wind I n t o n a t i o n , " in Experimental Research in the Psychology of  Music, ed. Edwin Gordon (Idaho: U n i v e r s i t y of Iowa Press, 1970), v o l VI. 2 * L. W. Hermanson, "An I n v e s t i g a t i o n of the E f f e c t s of Timbre on Simultaneous Vocal P i t c h A c u i t y of Young C h i l d r e n " (Ed. D. d i s s e r t a t i o n , Columbia U n i v e r s i t y Teachers' College, 1971). 20 that judgement of p i t c h changes would be b e t t e r for the square wave p i t c h e s than for the n a t u r a l state piano tones. S t a t i s t i c a l v - t e s t i n g , however, d i d not s u b s t a n t i a t e h i s h y p o t h e s i s . 2 5 Grey explored musical timbre using a computer, and suggested that f u r t h e r perceptual research of timbre should be conducted w i t h i n the d i f f e r e n t f a m i l i e s of instruments, e. g. using only woodwinds, or only b r a s s - w i n d s . 2 6 W i l l i a m s , using a t r i a n g l e wave, a square wave, and a sine wave rather than timbres produced by musical instruments, found that timbre d i f f e r e n c e s had a s i g n i f i c a n t e f f e c t on the a b i l i t y of Grade Two and Grade Five c h i l d r e n to i d e n t i f y melodic m o t i o n . 2 7 B l a t t e r , i n a s i m i l a r study, designed and constructed an instrument which was capable of producing a v a r i e t y of frequencies with various wave forms. He then used t h i s instrument to t e s t subjects' a b i l i t i e s to match p i t c h e s . While B l a t t e r , l i k e W i l l i a m s , found a s i g n i f i c a n t timbre e f f e c t , 2 5 Desmond Sergeant, "Experimental I n v e s t i g a t i o n of Absolute P i t c h , " J o u r n a l of Research i n Music Education, 17(Spring, 1969), pp. 135-143. 2 6 J . M. Grey, "An E x p l o r a t i o n of Music a l Timbre using Computer Based Techniques for A n a l y s i s , Synthesis and Perceptual S c a l i n g " (Ph. D. d i s s e r t a t i o n , Stanford U n i v e r s i t y , 1975). 2 7 David B. W i l l i a m s , "An Interim Report of a Programmatic Seri e s of Music Inquiry Designed to I n v e s t i g a t e Melodic Pattern I d e n t i f i c a t i o n A b i l i t y i n C h i l d r e n " ( C a l i f o r n i a : SWRJ Education  Research and Development, 1976). 2 8 A l f r e d Wayne B l a t t e r , "The E f f e c t of Timbre on Pitch-matching Judgements (with) ' R e f l e c t i o n s for Chorus, Narrator, and Fourteen Instruments'" (D. M. A. d i s s e r t a t i o n , U n i v e r s i t y of I l l i n o i s at Urbana-Champaign, 1974). 21 neither author made use of conventional musical i n s t r u m e n t s . 2 8 S i l b e r and Howell had c o n t r a d i c t o r y f i n d i n g s i n t h e i r research. Using undergraduates i n second year or higher, S i l b e r i n v e s t i g a t e d the e f f e c t of f a m i l i a r i t y with a musical medium (v o c a l , s t r i n g , woodwind, and brass q u a r t e t , and piano) on the students' a b i l i t y to analyze and i d e n t i f y four part musical chords. The length of time subjects had been studying t h e i r instruments was c o r r e l a t e d with the chord r e c o g n i t i o n t e s t scores. S i g n i f i c a n t d i f f e r e n c e s were found only for vocal and s t r i n g p e r f o r m e r s . 2 9 Howell a l s o i n v e s t i g a t e d the e f f e c t of timbre on the i d e n t i f i c a t i o n of harmonic i n t e r v a l s by i n s t r u m e n t a l i s t s . He tes t e d f i r s t and second year post-secondary students using p i t c h e s produced by c l a r i n e t , trumpet, piano, "pure tone", and "mixed tone" (a combination of French horn and f l u t e ) . The r e s u l t s showed that p i a n i s t s a t t a i n e d the highest score, and that n e i t h e r timbre nor f a m i l i a r i t y caused a d i f f e r e n c e i n s c o r e s . 3 0 Meyer, i n 1978, i n v e s t i g a t e d p i t c h d i s c r i m i n a t i o n using paired sounds with i d e n t i c a l fundamental frequency and d i f f e r e n t i a l spectra. He used a sawtooth ("normal overtone 2 9 John S. S i l b e r , "Aural A n a l y t i c A b i l i t y i n Harmonic D i c t a t i o n i n Various Musical Media" (Ph. D. d i s s e r t a t i o n , U n i v e r s i t y of Indiana, 1955). 3 0 Ronald Thomas Howell, "The E f f e c t of Timbre on the I n t e r v a l Perception and I d e n t i f i c a t i o n S k i l l of I n s t r u m e n t a l i s t s " (Ed. D. d i s s e r t a t i o n , The U n i v e r s i t y of Oklahoma, 1976) . 22 s e r i e s " ) and a square wave ("altered p a r t i a l s " ) . A s i g n i f i c a n t m a j o r i t y of the musicians t e s t e d perceived the sawtooth wave as being sharper i n p i t c h than the square wave. 3 1 In the same year, Gephardt examined f i r s t and second year music majors. Subjects were given the f i r s t note of a d i c t a t e d melody of u n s p e c i f i e d l e n g t h , and asked to notate the remainder of the d i c t a t i o n . Melodies were d i c t a t e d using seven d i f f e r e n t timbres: trumpet, a l t o saxophone, piano, g u i t a r , synthesizer (sawtooth wave), "Mixed I " , and "Mixed I I " . He found that timbre, envelope, melody length, and task experience s i g n i f i c a n t l y a f f e c t e d s u b j e c t s ' scores on the d i c t a t i o n t e s t , and that f a m i l i a r i t y with the timbre source was not a s i g n i f i c a n t f a c t o r . 3 2 Summary From the foregoing examination of the l i t e r a t u r e d e aling with timbre and p i t c h p erception, i t seems c l e a r that tones produced by musical instruments are e a s i e r to i d e n t i f y and to d i s c r i m i n a t e than are tones produced by e l e c t r o n i c sources. There i s some evidence to suggest that previous performance experience on a musical instrument, and the amount of previous 3 1 J . Meyer, "The Dependence of P i t c h on Harmonic Sound Spectra," Psychology of Music, 1978, 6(1), pp. 3-12. 3 2 Donald L. Gephardt, "The E f f e c t s of D i f f e r e n t F a m i l i a r and U n f a m i l i a r Musical Timbres on Musical Melodic D i c t a t i o n " (Ed. D. d i s s e r t a t i o n , Washington U n i v e r s i t y , M i s s o u r i , 1978). 23 ear t r a i n i n g experience, c o n t r i b u t e to p i t c h i d e n t i f i c a t i o n t asks. In g e n e r a l , there appears to be agreement among researchers that timbre does have an e f f e c t on p i t c h judgement; there i s no c l e a r consensus about t h i s e f f e c t , however. Only Gephardt seems to have addressed the question of u n f a m i l i a r timbres, and t h e i r e f f e c t on p i t c h p e r c e p t i o n , as compared to the e f f e c t of f a m i l i a r timbres. Many researchers seem to be agreed that there i s much to be done i n the f i e l d of timbre and i t s e f f e c t on the perception of p i t c h . This study was perceived as an ex p l o r a t o r y i n v e s t i g a t i o n i n t o a f i e l d which has apparently been l i t t l e examined. I t was hoped that some broad g u i d e l i n e s might be discovered which .might serve to o f f e r d i r e c t i o n to future researchers i n t h i s area. In t h i s study, the main area of i n t e r e s t was the e f f e c t of instrumental timbre upon students' a b i l i t y to perceive and describe melodic i n t e r v a l s . As discussed on page 4, t h i s study attempted to answer the f o l l o w i n g four questions: 1) Do d i f f e r e n c e s i n timbre a f f e c t students' a b i l i t y to i d e n t i f y melodic i n t e r v a l s during d i c t a t i o n ? 2) Does the length of time that students have been t r a i n i n g to i d e n t i f y melodic i n t e r v a l s have a r e l a t i o n s h i p with a p o s s i b l e e f f e c t of f a m i l i a r i t y of timbre, as measured by a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? 3) Does the length of time that students have been p l a y i n g t h e i r declared major instrument have a r e l a t i o n s h i p with a p o s s i b l e e f f e c t of f a m i l i a r i t y of timbre, as measured by a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? 24 Does the use of f a m i l i a r or u n f a m i l i a r timbre sources a f f e c t students' a b i l i t y to i d e n t i f y melodic i n t e r v a l s ? 25 Chapter 3 METHODOLOGY Population and Sample A l l subjects were volunteers from among those students e n r o l l e d i n e i t h e r the Music Education Department or the Music Department of the U n i v e r s i t y of B r i t i s h Columbia, or i n the Music Department of Douglas C o l l e g e . 1 Only those students who had taken or were t a k i n g at l e a s t one u n i v e r s i t y l e v e l theory/harmony course were e l i g i b l e for p a r t i c i p a t i o n i n the study. Subjects were c a t e g o r i z e d on the basis of t h e i r answers to a short q u e s t i o n n a i r e , administered immediately p r i o r to the ac t u a l t e s t i n g . At that time information was gathered as to the major instrument played by each su b j e c t , the length of time the subject had been p l a y i n g that instrument, and other p e r t i n e n t d e t a i l s (see Appendix 2). In t o t a l , 220 subjects volunteered for t h i s study: 91 males and 125 females. Of these, eight subjects were excluded. Two were f a c u l t y members, excluded only because of small numbers; the other s i x subjects were d i s q u a l i f i e d from the PPEM/FETE 1 A two-year r e g i o n a l c o l l e g e . 26 p o r t i o n of the study because of incomplete response forms. Only the two f a c u l t y members were excluded from the MAJOR p o r t i o n of the study. The ages of the subjects ranged from 17 to 47 years, with a mean age of 21.8 years. S i x t y subjects were r e g i s t e r e d i n Year One of u n i v e r s i t y or c o l l e g e , 48 i n each of Years Two and Three, 30 i n Year Four, and 29 i n Year F i v e . Seventy-four subjects were from the U n i v e r s i t y of B r i t i s h Columbia Music Education Department, 43 from Douglas Coll e g e , and 101 from the U n i v e r s i t y of B r i t i s h Columbia Music Department. The subjects were c a t e g o r i z e d i n t o three d i f f e r e n t groups, on the b a s i s of Formal Ear T r a i n i n g Experience (FETE): Group 1, one to eight months formal ear t r a i n i n g ; Group 2, nine to s i x t e e n months formal ear t r a i n i n g ; Group 3, seventeen months or more of formal ear t r a i n i n g . These groupings were chosen because the u n i v e r s i t y / c o l l e g e academic year normally c o n s i s t s of eight months. P r e l i m i n a r y examination of the demographic data revealed that there were not s u f f i c i e n t subjects at the higher l e v e l s of FETE to permit a n a l y s i s with both FETE and PPEM, i f more than three l e v e l s of FETE were used. The lack of subjects at the upper l e v e l s of FETE may have been due i n part to n a t u r a l a t t r i t i o n of students throughout the academic process, lack of a v a i l a b i l i t y of advanced courses i n v o l v i n g ear t r a i n i n g , or to some other cause beyond the researcher's c o n t r o l . Subjects were a l s o c a t e g o r i z e d on the basis of Playing/Performing Experience (PPEM): Group 1, l e s s than s i x years PPEM; Group 2, s i x to ten years PPEM; Group 3, more than ten years. PPEM. 27 The c a t e g o r i e s of PPEM were designated a f t e r the work of Cuddy, Leonard, S i l b e r , and Howell. While the o r i g i n a l i n t e n t was to use four l e v e l s of PPEM, examination of the demographic data revealed t h a t , as was the case for l e v e l s of FETE, there were not s u f f i c i e n t subjects to permit a n a l y s i s using four l e v e l s . Subjects were further c a t e g o r i z e d by the declared major instrument (MAJOR), r e s u l t i n g i n f i v e groups: MAJOR 1, C l a r i n e t ; MAJOR 2, Trumpet; MAJOR 3, Piano; MAJOR 4, Voice; MAJOR 5, Other ( a l l those whose Major was not one of the above 4). S e l e c t i o n of I n t e r v a l s and Timbre Sources The twelve melodic ascending i n t e r v a l s shown i n Appendix 1 were chosen as being r e p r e s e n t a t i v e of conventional ear t r a i n i n g t e s t s . I t was the opinion of the author and of se v e r a l experienced music educators that the t e s t would provide s u f f i c i e n t challenge to a l l sub j e c t s . The 13th i n t e r v a l , a pe r f e c t unison, was omitted because i t was f e l t that i t would not have s u f f i c i e n t variance to be a u s e f u l measure. The i n t e r v a l s chosen are s i t u a t e d i n a range which allows each instrument to produce a c h a r a c t e r i s t i c timbre, and which f a l l s w e l l w i t h i n the range of the ma j o r i t y of heard musical m a t e r i a l . By avoiding the extreme ranges of each instrument i t was hoped to c o n t r o l to a c e r t a i n extent the . nuisance v a r i a b l e s of 28 u n c h a r a c t e r i s t i c timbre, inaccurate p i t c h , and embouchure or fi n g e r f a t i g u e . The s i x timbre sources used i n t h i s i n v e s t i g a t i o n were produced by the f o l l o w i n g instruments: c l a r i n e t , trumpet, piano, v i o l i n , xylophone, and syn t h e s i z e r (pure sine wave). These instruments were s e l e c t e d f o r the f o l l o w i n g reasons: C l a r i n e t . The c l a r i n e t i s re p r e s e n t a t i v e of the woodwind f a m i l y , and i s a common instrument i n school and community bands and o r c h e s t r a s . Trumpet• The trumpet i s r e p r e s e n t a t i v e of the brass f a m i l y , and i s a l s o a common instrument i n school and community bands and o r c h e s t r a s . Piano. The basic instrument of ear t r a i n i n g has t r a d i t i o n a l l y been the piano, as discussed i n Chapters One and Two. V i o l i n . The v i o l i n i s re p r e s e n t a t i v e of the s t r i n g f a m i l y , and i s common i n school and community o r c h e s t r a s . Xylophone. The xylophone i s re p r e s e n t a t i v e of the tuned percussion family of instruments, and while not common i n school bands and or c h e s t r a s , i s often found i n elementary school general music c l a s s e s and primary classrooms. Synthesizer. The syn t h e s i z e r was used as a convenient way to provide a pure sine wave. The instrument used i s designed to produce notes of the equi-tempered scale without regard for the 29 wave form ( t i m b r e ) , a t t a c k , or decay being produced. I t was p o s s i b l e , t h e r e f o r e , to make use of an o s c i l l o s c o p e to ensure that a pure sine wave was being produced, and to be confident that notes other than those a c t u a l l y examined, on the o s c i l l o s c o p e would be in tune. The sine wave was included i n the study because of i t s frequent use i n t e s t s of perception by researchers such as Seashore, Bentley, and others. Preparation of the Test Tape The master tape was recorded at 15 inches per second ( i . p . s . ) using the f a c i l i t i e s of B u l l f r o g Recording Company Li m i t e d . During the recording process, each tone was monitored for i n t e n s i t y and for equal temperament frequency l e v e l (see Appendix 3). The e n t i r e recording process was a l s o monitored for p o s s i b l e harmonic d i s t o r t i o n and each recorded tone was adjusted for i n t e n s i t y l e v e l so that the f i n a l recording contained only equal i n t e n s i t y s i g n a l s . Each instrument was played by a p r o f e s s i o n a l performer, who was asked to play a l l i n t e r v a l s at a uniformly moderate volume l e v e l . Figure 1. Rhythmic P a t t e r n used for Melodic I n t e r v a l s . Each i n t e r v a l was played by the performer using the rhythmic p a t t e r n shown i n Figure 1. An e l e c t r o n i c metronome was used to ensure accurate and c o n s i s t e n t performance of both p i t c h and r e s t d u r a t i o n s . The chosen tempo was 2 beats per second ( J =120),' s i n c e : . . . i n order to be heard c l e a r l y as of d e f i n i t e p i t c h , a tone at 128 [Hz] must have a duration of [at l e a s t ] 0.09 sec; for 256, about 0.07 sec; for 384, about 0.04 sec; and f o r 512, about the same.2 A f t e r a l l seventy-two i n t e r v a l s (12 X 6 instruments) had been recorded, each i n t e r v a l was assigned a random number to e l i m i n a t e any s e q u e n t i a l e f f e c t that might i n f l u e n c e scores. I n t e r v a l s , sounded twice, were then t r a n s f e r r e d to a second master tape i n t h e i r p r e v i o u s l y determined random .order, together with a p i t c h reference tone (A = 440 Hz), i n s t r u c t i o n s , and question i d e n t i f i c a t i o n numbers (see Appendix 4). The master 2 C a r l E. Seashore, The Psychology of M u s i c a l Talent (Boston: S i l v e r Burdett, 1919), p. 62. 31 tape was then re-recorded at 7.5 i . p . s . , and leader tape was i n s e r t e d to mark the various s e c t i o n s where pauses would occur during a d m i n i s t r a t i o n of the t e s t . T e s t ing Procedure The t e s t s were conducted i n various music classrooms i n the U n i v e r s i t y of B r i t i s h Columbia Scarfe and Music B u i l d i n g s , and in the Douglas College Music f a c i l i t i e s . The placement of the t e s t equipment was kept as c l o s e l y i d e n t i c a l as f e a s i b l e i n each t e s t l o c a t i o n . Ambient background noise was measured p r i o r to each a d m i n i s t r a t i o n of the t e s t , and was found to be c o n s i s t e n t l y l e s s than 60 dBA i n every instance. S i m i l a r l y , tape speed was measured before each a d m i n i s t r a t i o n , and was found to be c o n s i s t e n t to ±.5 Hz for the reference tone of A = 440 Hz. Playback l e v e l s were set to y i e l d an SPL of 85 dBA at four feet in f r o n t of the speakers when p l a y i n g the p i t c h reference tone. This s e t t i n g produced an average SPL of 68 to 78 dBA throughout the room f o r the recorded i n t e r v a l s . The playback equipment c o n s i s t e d of a Sony TC-630 combined tape recorder, a m p l i f i e r , and speakers. The t e s t s were made in a "free f i e l d " , using loud speakers, s i n c e : 32 I t appears that s c i e n t i f i c i n v e s t i g a t o r s can sometimes s i m p l i f y the a n a l y s i s of t h e i r experiments i f sounds are sent from source to l i s t e n e r i n an anechoic chamber. They can often f u r t h e r s i m p l i f y t h e i r labors by working with e l e c t r i c a l l y generated sound supplied d i r e c t l y to the ears by means of headphones. However, i t i s almost u n i v e r s a l l y true that the human ear's a b i l i t y to d i s c r i m i n a t e small changes of p i t c h , loudness, or tone c o l o r , or otherwise to 'make sense' out of a combination of s i g n a l s , i s immensely better i n a room than i t i s under a c o u s t i c a l l y more s t e r i l e surroundings. 3 I t was f e l t that t h i s free f i e l d procedure d u p l i c a t e d , more c l o s e l y than might otherwise be the case, a r e a l i s t i c s i t u a t i o n i n which music might be heard. In every instance, the speakers were l o c a t e d at the f r o n t of the room, i n a p o s i t i o n approximately equivalent to that of the piano u s u a l l y used for ear t r a i n i n g i n that room. Subjects heard Part A of the t e s t i n s t r u c t i o n s , and then were given a short time to complete the Background Information Sheet. Subjects then heard Part B of the i n s t r u c t i o n s followed by three " p r a c t i c e i n t e r v a l s " (P4, P5, and P8, played on piano) which were not scored. A f t e r being given an opportunity to ask questions, subjects then began the a c t u a l t e s t , recording t h e i r answers i n the appropriate boxes on the answer sheet (see Appendix 2). The t e s t took approximately 20 minutes from s t a r t to f i n i s h . Test scores were not i d e n t i f i e d with i n d i v i d u a l s i n any way, and subjects were assured of c o n f i d e n t i a l i t y . 3 Arthur H. Benade, Fundamentals of M u s i c a l Acoustics (New York: Oxford U n i v e r s i t y Press, 1976), p. 197. 33 S t a t i s t i c a l Design and A n a l y s i s Subjects' answers were hand coded, t r a n s f e r r e d to a computer disk f i l e , and then recoded from the o r i g i n a l t h i r t e e n item code to a two item code. This process was necessary to make them s u i t a b l e for machine s c o r i n g by the computer program LERTAP.* D e t a i l s of t h i s recoding procedure may be found in Appendices 7 and 8. I n i t i a l examination of the data revealed that the variance-covariance matrixes appeared to be heterogeneous, and that the d i s t r i b u t i o n curves were not normal. I t was decided that the lack of normality was the r e a l cause of the d i f f i c u l t y , and p o s s i b l e s o l u t i o n s were explored. A f t e r i n v e s t i g a t i n g the e f f e c t s of various transformations, i t was decided to use an a r c s i n e transformation. A t o t a l of three transformations were c a r r i e d out, i n order to e l i m i n a t e any v a r i a t i o n i n scores due to the p a r t i c u l a r c l a s s or l o c a t i o n of a subject, and i n order: 1. to achieve homogeneity of e r r o r v a r i a n c e , and, 2. to achieve normality of t r e a t m e n t - l e v e l d i s t r i b u t i o n s . 5 The f i r s t transformation involved r e c a l c u l a t i n g subjects' scores as proportions by d i v i d i n g each of the s i x t e s t s by " L a r r y Richard Nelson, Laboratory of Educational Research  Test Package (New Zealand, 1974) . 5 Roger E. K i r k , Experimental Design: Procedures for the  Behavioural Sciences ( C a l i f o r n i a : Brooks/Cole P u b l i s h i n g , 1968), p. 63. 34 twelve, the t o t a l number of items. The proportions thus obtained were then converted using an a r c s i n e transformation to obtain a more normal d i s t r i b u t i o n of a l l scores. The formulas given i n Marascuilo and McSweeney were used for t h i s t r a n s f o r m a t i o n . 6 This procedure y i e l d e d scores with values expressed i n radians. F o l l o w i n g the a r c s i n e transformation, scores were then converted i n t o standard scores (mean zero, standard d e v i a t i o n one) by f i r s t s t a n d a r d i z i n g across the s i x dependent v a r i a b l e s w i t h i n each c l a s s , then s t a n d a r d i z i n g across each c l a s s w i t h i n each i n s t i t u t i o n , and f i n a l l y s t a n d a r d i z i n g across each i n s t i t u t i o n . This procedure produced scores with a mean value of zero and a standard d e v i a t i o n of one for the t o t a l d i s t r i b u t i o n of scores. Comparison of any score with any other score could, t h e r e f o r e , be meaningfully made since a l l scores were e f f e c t i v e l y on the same s c a l e . 7 A m u l t i v a r i a t e a n a l y s i s of variance (MANOVA) was performed, using PPEM and FETE as the independent v a r i a b l e s (three l e v e l s each) and the s i x scores a t t a i n e d on the melodic i n t e r v a l i d e n t i f i c a t i o n t e s t as the dependent v a r i a b l e s (Table 1). A separate MANOVA was performed on the same dependent 6 Leonard A. Marascuilo and Maryellen McSweeney, Nonparametric and D i s t r i b u t i o n - F r e e Methods for the S o c i a l Science"s ( C a i i f o r n i a : Brooks/Cole Publ i s h i n g , 1977) , pp. 147-151. 7 The computer program which performed these transformations was w r i t t e n by Dr. R. E. Bruce, of the Educational Research Service Center at the U n i v e r s i t y of B r i t i s h Columbia. A copy of the program w i l l be found i n Appendix 9. 35 v a r i a b l e s but using the subj e c t s ' declared major instrument (MAJOR) as the only independent v a r i a b l e . This two stage a n a l y s i s was necessary since there was an i n s u f f i c i e n t number of subjects to permit blocking on a l l three independent v a r i a b l e s simultaneously. TABLE 1  3 X 3 MANOVA DESIGN PPEM GROUP ONE GROUP TWO GROUP THREE GROUP ONE N = 22 N=1 2 N=8 GROUP.TWO N = 31 N=30 N = 33 GROUP THREE N=22 N=21 N=33 TOTAL N=212 36 Chapter 4 RESULTS Summary of the Problem This i n v e s t i g a t i o n was c a r r i e d out i n an attempt to explore the e f f e c t of musical timbre on subjects' a b i l i t y to p a s s i v e l y i d e n t i f y d i c t a t e d melodic i n t e r v a l s . The independent v a r i a b l e s were playing/performing experience (PPEM), formal ear t r a i n i n g experience (FETE), and f a m i l i a r i t y of timbre (MAJOR).. The dependent v a r i a b l e s were the scores a t t a i n e d on s i x aut h o r - w r i t t e n t e s t s of melodic d i c t a t i o n . For purposes of a n a l y s i s , subjects were grouped i n t o three l e v e l s of PPEM and three l e v e l s of FETE. An a d d i t i o n a l f i v e - l e v e l grouping was made on the basis of declared major instrument (MAJOR). A m u l t i v a r i a t e a n a l y s i s of variance (MANOVA) a n a l y s i s was used to determine which of the data r e s u l t s were s t a t i s t i c a l l y s i g n i f i c a n t . Where appr o p r i a t e , Scheffe post-hoc m u l t i p l e comparison t e s t s were performed. 37 S t a t i s t i c a l Results I n t r o d u c t i o n The m u l t i v a r i a t e a n a l y s i s of variance (MANOVA) t e s t s were performed on the data using the MULTIVAR computer package. 1 This s t a t i s t i c a l package performs a MANOVA as ge n e r a l l y described by H a r r i s . 2 The a n a l y s i s was performed at the U n i v e r s i t y of B r i t i s h Columbia Computer Center on the Amdahl 470 V/8 computer, operating under the Michigan Terminal System (MTS). The r e s u l t s of the s t a t i s t i c a l t e s t s are reported from the most complex to the l e a s t complex, since the presence of an i n t e r a c t i o n between two f a c t o r s makes d i f f i c u l t any i n t e r p r e t a t i o n of one of those f a c t o r s alone. The MANOVA a n a l y s i s of PPEM and FETE w i l l be discussed f i r s t , followed by the MANOVA a n a l y s i s of MAJOR. A s i g n i f i c a n t m u l t i v a r i a t e F r a t i o i n the summary ta b l e i n d i c a t e s a r e l a t i o n s h i p between the dependent v a r i a b l e s and the appropriate independent v a r i a b l e . The absence of a s i g n i f i c a n t u n i v a r i a t e F r a t i o i m p l i e s that the r e l a t i o n s h i p among the dependent v a r i a b l e s and the independent v a r i a b l e may be a complex one. No i n t e r p r e t a t i o n was made of such a r e l a t i o n s h i p , s i n c e , for example, i t would make l i t t l e sense to present a 1 MULTIVAR: Version 6.2 (Chicago: N a t i o n a l Educational Resources" 1972). 2 Richard J . H a r r i s , A Primer of M u l t i v a r i a t e S t a t i s t i c s (New York: Academic Press, 1975). ' 38 r e s u l t which says that "The scores on the piano timbre of Level 2 of PPEM are s i g n i f i c a n t l y d i f f e r e n t from one-half of the score on the c l a r i n e t timbre of PPEM Level 3 plus one-half of the score on the trumpet timbre of PPEM Level 1." I f there was at l e a s t one s i g n i f i c a n t u n i v a r i a t e F r a t i o , then appropriate post hoc comparisons were made to determine where the s i g n i f i c a n t d i f f e r e n c e s were l o c a t e d . S t a t i s t i c a l t e s t s were c a r r i e d out, for main e f f e c t s , at the c = .05 l e v e l of s i g n i f i c a n c e . For post hoc analyses, the s i g n i f i c a n c e l e v e l was maintained at a = .05, since t h i s was an expl o r a t o r y study. A l l post hoc t e s t s were conducted using Scheffe's F r a t i o t e s t . Tests of Hypothesis I N u l l Hypothesis: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t i n t e r a c t i o n between formal ear t r a i n i n g experience (FETE) and playing/performing experience (PPEM) as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l ident i f i c a t i o n . From Table 2, i t may be seen that the PPEM/FETE i n t e r a c t i o n F r a t i o was n o n - s i g n i f i c a n t for both the m u l t i v a r i a t e and the u n i v a r i a t e t e s t s . 3 A c c o r d i n g l y , the n u l l hypothesis was accepted; there was no i n t e r a c t i o n between PPEM>and FETE. 3 Shown as "PF I n t e r a c t i o n " i n the t a b l e . 39 TABLE 2 MANOVA SUMMARY TABLE FOR PPEM AND FETE Multivariate Test Univariate Statstics Source F (df) df Cl Tr Pi -.. Vi Sy (PPEM) 3.52 (12,396) 2 9.81* 10.31* 10.51* 9.68* 10.79* 15.70* (FETE) 1.97* (12,396) . 2 1.22 0.70 0.54 2.4.2 r 0.00 0.14 PF Interaction 0.86 (12,692) 4 0.69 0.42 0.85 0.26 0.44 0.11 •-Within 203 *p<05 CL, Clarinet, Tr, Trumpet, Pi, Piano, Vi, Violin, Xy, Xylophone, Sy, Synthesizer. TABLE 3 SCHEFFE POST HOC COMPARISON OF PPEM LEVELS INSTRUMENT 1-2 1-3 2-3 CLARINET 0.003 1 1 .43* 17.59* TRUMPET 0.288 9.07* 19.36* PIANO 0.301 14.97* 15.88* VIOLIN 0.492 8.47* 19.99* XYLOPHONE 0.413 9.17* 20.59* SYNTHESIZER 0.999 23.52* 23.30* * p<.05 40 TABLE 4 SCHEFFE POST HOC PAIRWISE COMPARISON OF PPEM LEVELS COMPARISON 1-2 1-3 2-3 VLN/SYNTH 6.12* 4.65 0.08 XYLO/SYNTH 4.65 6.05* 0.22 * p<.05 TABLE 5 SCHEFFE POST HOC COMPARISON OF PPEM COMPARISON 1 2 3 CLAR/PNO 0.27 4.31 0.51 CLAR/TPT 4.57 18.92* 7.48* CLAR/VLN 0.38 4.08 0.04 CLAR/XYLO 2.12 0.48 1 .35 CLAR/SYNTH 2.37 0.01 1 .66 TPT/PNO 6.83* 41.29* 11.51* TPT/VLN 0.21 0. 07 0.26 TPT/XYLO 3.95 8. 37* 3.62 TPT/SYNTH 0.72 4.37 3.29 PNO/VLN 4.07 34.51* 7.31* PNO/XYLO 0.48 17.82* 3.09 PNO/SYNTH 1 3.02* 16.54* 1 .77 VLN/XYLO 2.14 6.49* 1 .74 VLN/SYNTH 2.36 4.65 2.40 XYLO/SYNTH 8.88* 0. 34 0.01 * p<.05 42 CL : Clarinet TR: Trumpet PI: Piano VI: Violin XY: Xylophone SY: Synthesizer 6 4 i 2 0 •.2 .4 CL TR Level 3. PI VI XY SY CL TR All Levels. PI VI LEGEND L E V E L 1 L E V E L 2 L E V E L 3 Figure 2. PPEM COMPARED WITH SCORES. 43 Tests of Hypothesis II N u l l Hypothesis: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e in the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s , as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n , regardless of the amount of PPEM each has had. As can be seen from Table 2, the PPEM m u l t i v a r i a t e F r a t i o and a l l of the r e l a t e d u n i v a r i a t e F r a t i o s were s i g n i f i c a n t at the a = .05 l e v e l . Post hoc i n v e s t i g a t i o n s revealed that t e s t scores achieved by subjects at Level 1 of PPEM were not s i g n i f i c a n t l y d i f f e r e n t from those at Level 2, but that subjects at Level 2 were s i g n i f i c a n t l y d i f f e r e n t from those at Level 3. A d d i t i o n a l l y , . subjects' scores .at Level 1 were s i g n i f i c a n t l y d i f f e r e n t from subjects' scores at Level 3 (Figure 2, Table 3). Post hoc i n v e s t i g a t i o n s a l s o revealed that the d i f f e r e n c e s between the scores on c e r t a i n instruments changed as the l e v e l s of PPEM changed (Table 4), and a l s o that the d i f f e r e n c e s between the scores on c e r t a i n p a i r s of instruments changed as the l e v e l s of PPEM changed (Table 5). In view of these r e s u l t s , the n u l l hypothesis was r e j e c t e d ; there were s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s i n the a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s , when the -amount of PPEM each has had was taken i n t o c o n s i d e r a t i o n . Tests of Hypothesis I I I 44 N u l l Hypothesis: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s , as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n , regardless of the amount of FETE each has had. As can be seen from Table 2, only the m u l t i v a r i a t e F r a t i o was s i g n i f i c a n t for the FETE f a c t o r . This f i n d i n g suggests that there was some s i g n i f i c a n t l y d i f f e r e n t combination of v a r i a b l e s among the l e v e l s of FETE. Such a combination was not, however, meaningful i n terms of t h i s study. Post hoc i n v e s t i g a t i o n revealed that while the l e v e l s of FETE were not d i f f e r e n t from one. another, there were s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s between scores a t t a i n e d on various instruments at each l e v e l of FETE (Table 6). I t was a l s o found that the d i f f e r e n c e s between the scores on c e r t a i n t e s t timbres changed as the l e v e l of FETE changed (Table 7, and Figure 3). A c c o r d i n g l y , the n u l l hypothesis was r e j e c t e d ; there was a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s when the amount of FETE each has had was taken i n t o c o n s i d e r a t i o n . 45 TABLE 6 SCHEFFE POST HOC COMPARISON OF FETE COMPARISON 1 2 3 CLAR/PNO 7.22* 2.11 5.16 CLAR/TPT 8.99* 14.09* 7.68* CLAR/VLN 1 .45 3.03 0.08 CLAR/XYLO 0.12 6.70* 0.10 CLAR/SYNTH 0.33 1 .43 0.06 TPT/PNO 33.73* 3.14 26.70* TPT/VLN 2.47 9.64* 6.02 TPT/XYLO 10.24* 0.62 3.85 TPT/SYNTH 4.29 0.28 3.85 PNO/VLN 15.02* 25.66* 5.31 PNO/XYLO 9.47* 1 .39 8.26* PNO/SYNTH 12.01* 5.77 8.67* VLN/XYLO 2.11 16.97* 0.29 VLN/SYNTH 0.38 8.97* 0.29 XYLO/SYNTH 0.84 1 .97 0.32 * p<.05 46 TABLE 7 SCHEFFE POST HOC PAIRWISE COMPARISON OF FETE LEVELS COMPARISON 1-2 1-3 2-3 CLAR/TPT 9.18*. 0.08 7.57* TPT/PNO 6.85* 0.18 4.84 TPT/VLN 11.23* 0.40 15.57* VLN/XYLO 4.21 0.98 8.95* VLN/SYNTH 3.21 0.67 6.00* * p<.05 47 LEGEND CL TR D: All Levels. PI L E V E L 1 L E V E L 2 L E V E L 3 Figure 3 . FETE COMPARED WITH SCORES. 48 Tests of Hypothesis IV N u l l Hypothesis: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s presented using d i f f e r e n t timbres, as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n . Since FETE and PPEM were both found to be s i g n i f i c a n t , no e x p l i c i t t e s t s were made of t h i s hypothesis. The r e j e c t i o n of t h i s hypothesis was a consequence of the r e j e c t i o n of Hypotheses II and I I I . Tests of Hypothesis V N u l l Hypothesis: There w i l l be no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e i n the mean a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s presented using timbres that d i f f e r in f a m i l i a r i t y , as measured by scores a t t a i n e d on an author-produced t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n . As seen i n Table 8, a l l MAJOR F r a t i o s , both m u l t i v a r i a t e and u n i v a r i a t e , were s i g n i f i c a n t at the a = .05 l e v e l . Post Hoc comparisons revealed that there were s i g n i f i c a n t d i f f e r e n c e s among the scores a t t a i n e d on c e r t a i n timbres for only two declared major instruments ("voice" and " o t h e r " ) , but there were many s i g n i f i c a n t d i f f e r e n c e s among declared major instruments for each of the t e s t timbres (Tables 9 and 10, Figures 4 and 5). Accordingly, the n u l l hypothesis was r e j e c t e d ; there was a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e in the a b i l i t y of subjects to i d e n t i f y c e r t a i n melodic i n t e r v a l s when the d e c l a r e d m a j o r i n s t r u m e n t w a s t a k e n i n t o c o n s i d e r a t i o n . TABLE 8 MANOVA SUMMARY TABLE FOR MAJOR Multivariate Test Univariate Statistics  Source F (df) df Cl Tr Pi Vi Xy Sy Major 1.77* (24,727) 4 3.75* 3.52* 2.80* 4.36* 6.34* 3.78* Within 213 *P<.05 NOTE - Cl., Clarinet, Tr, Trumpet, Pi, Piano, Vi, Violin, Xy, Xylophone, Sy, Synthesizer. TABLE 9 SCHEFFE POST HOC COMPARISON OF MAJOR COMPARISON VOICE OTHER TPT/PNO 0 . 2 8 3 3 . 1 0 * PNO/SYNTH 1 2 . 6 9 * 1 0 . 5 1 * XYLO/SYNTH 1 4 . 6 6 * 0 . 0 6 * p < . 0 5 50 TABLE 10 SCHEFFE POST HOC COMPARISON OF DECLARED MAJOR MAJOR CLAR TRPT PIANO VIOLIN XYLO SYNTH CLAR/TPT 1 .94 1 .50 3.83 0.08 31.54* 11.28* CLAR/PNO 45.61* 33.83* 32.93* 65.43* 30.42* 29.16* CLAR/VOICE 20.28* 13.48* 12.25* 20.26* 22.38* 0.25 CLAR/OTHER 3.28 0.13 3.62 7.01 0.28 0.34 TPT/PIANO 66.35* 49.66* 59.25* 69.95* 123.90* 76.71* TPT/VOICE 34.76* 24.03* 29.76* 22.81* 107.10* 14.88* TPT/OTHER 10.26* 2.51 14.90* 8.54 25.85* 15.52* PIANO/VOICE 5.00 4.60 5.03 12.87* 0.62 24.03* PIANO/OTHER 24.42* 29.83* 14.73* 29.60* 36.58* 23.22* VOICE/OTHER 7.24 11.00* 2.54 3.43 27.70* 0.01 * p<.05 51 Figure 4. MAJOR COMPARED WTTH SCORES. 52 A: C L TR CLARINET. B: C L TR TRUMPET. C L TR VIOLIN. L E G E N D CL : Clarinet TR : Trumpet PI : Piano VO. Voice OT: Other C L T R XYLOPHONE, F: C L TR PI SYNTHESIZER. OT Figure 5 . SCORES COMPARED WITH MAJOR. 53 Chapter 5 CONCLUSIONS Introduct ion The purpose of t h i s study was to explore the e f f e c t of timbre upon the i d e n t i f i c a t i o n of melodic i n t e r v a l s . The question was asked: "Do d i f f e r e n c e s i n timbre a f f e c t students' a b i l i t y to i d e n t i f y melodic i n t e r v a l s during d i c t a t i o n ? " Since i t was suggested by some researchers that t h i s a b i l i t y might be a f f e c t e d by a subject's f a m i l i a r i t y with a p a r t i c u l a r timbre (the MAJOR instrument), the amount of playing/performing experience on that instrument (PPEM), and the length of time he has been fo r m a l l y studying ear t r a i n i n g (FETE), these three f a c t o r s were used i n d e f i n i n g the formal hypotheses. Five n u l l hypotheses were formulated and t e s t e d , using a t e s t of melodic i n t e r v a l i d e n t i f i c a t i o n created by the author. The r e s u l t s of the study, as discussed i n Chapter 4, have l e d to the f o l l o w i n g c o n c l u s i o n s : N u l l Hypothesis I : PPEM/FETE i n t e r a c t i o n — a c c e p t e d ; N u l l Hypothesis I I : e f f e c t of playing/performing experience (PPEM)--rejected; N u l l Hypothesis I I I : e f f e c t of formal ear t r a i n i n g experience ( F E T E ) — r e j e c t e d ; 54 N u l l Hypothesis IV: d i f f e r e n c e s in t i m b r e - - r e j e c t e d ; N u l l Hypothesis V: f a m i l i a r i t y of timbre (MAJOR)—rejected. Summary of Results The population i n v e s t i g a t e d c o n s i s t e d of c o l l e g e and u n i v e r s i t y students with a minimum of two months of formal ear t r a i n i n g i n u n i v e r s i t y / c o l l e g e l e v e l harmony/theory courses. For t h i s p o p u l a t i o n , v a r i a t i o n s in timbre seemed to have an e f f e c t on students' a b i l i t y to perform simple melodic d i c t a t i o n tasks. This e f f e c t was present when e i t h e r the amount of PPEM or the amount of FETE was considered, and a l s o was true for each instrumental timbre examined. I n v e s t i g a t i o n of the r e l a t i o n s h i p of PPEM and timbre showed c l e a r l y that students who had the l a r g e s t amount of PPEM (more than ten years of experience) a t t a i n e d the highest scores. There were no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s between the scores a t t a i n e d by students at Level 1 of PPEM and those a t t a i n e d at Level 2 ( l e s s than s i x years and s i x to ten years, r e s p e c t i v e l y ) . When d i f f e r e n c e s among instrumental timbres were examined at each l e v e l of PPEM, i t became evident that there was no c l e a r pattern of v a r i a t i o n . For a l l l e v e l s , there were no d i f f e r e n c e s between the scores a t t a i n e d on c l a r i n e t and those a t t a i n e d on v i o l i n . S i m i l a r l y , there were no d i f f e r e n c e s at any l e v e l of PPEM between scores on c l a r i n e t and xylophone, c l a r i n e t and s y n t h e s i z e r , trumpet and v i o l i n , trumpet and s y n t h e s i z e r , or 55 v i o l i n and s y n t h e s i z e r . The number of s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s at each l e v e l of PPEM and the r e l a t i v e scores at each l e v e l suggest that Level 1 students may be unable to i d e n t i f y melodic i n t e r v a l s w e l l enough to be a f f e c t e d by timbre, while Level 3 students may be able to i d e n t i f y melodic i n t e r v a l s so w e l l that they are not misled or confused by timbre. Level 2 students, as might perhaps be expected, scored between Levels 1 and 3. An a l t e r n a t i v e i n t e r p r e t a t i o n might be that c l a r i n e t , trumpet, v i o l i n , xylophone and s y n t h e s i z e r timbres y i e l d e d e s s e n t i a l l y the same scores, but that the e f f e c t of the piano timbre was d i f f e r e n t . This a l t e r n a t i v e i n t e r p r e t a t i o n implies that scores a t t a i n e d on piano i n t e r v a l s may have been higher because of f a m i l i a r i t y with the piano from the students' regular ear t r a i n i n g sessions. While the nature of the r e l a t i o n s h i p i s not c l e a r , there appears to be a d e f i n i t e r e l a t i o n s h i p between PPEM and timbre. In a d d i t i o n , i t i s c l e a r that the score a t t a i n e d , regardless of the timbre, increases with the amount of a subject's p l a y i n g or performing experience. An examination of the e f f e c t of FETE a l s o leaves some questions unanswered. There seems no doubt that FETE d i d i n t e r a c t with the instrumental timbre to produce scores which were d i f f e r e n t at d i f f e r e n t l e v e l s of FETE; i t i s not c l e a r as to the nature of that i n t e r a c t i o n . In some ways, i t would appear that Levels 1 and 3 are very s i m i l a r : both l e v e l s have almost i d e n t i c a l combinations of s i g n i f i c a n t r e s u l t s . This s i m i l a r i t y i s supported by the pairwise comparisons. Examination of the graphs, however, tends to suggest that Level 1 and Level 2 may 56 have more i n common. The r e s u l t s of the study i n d i c a t e , then, that FETE and timbre are i n t e r r e l a t e d , but f a i l to make c l e a r the d e t a i l s of that r e l a t i o n s h i p . The e f f e c t of f a m i l i a r i t y of timbre i n t h i s study seems to suggest that while there i s a r e l a t i o n s h i p between the declared major instrument and the timbre presented, there i s not a d i r e c t r e l a t i o n s h i p . That i s , a student who i s f a m i l i a r with a p a r t i c u l a r timbre does not n e c e s s a r i l y a t t a i n a higher score on d i c t a t i o n presented with that p a r t i c u l a r timbre than with other timbres. I t i s c l e a r that students with experience on piano or on voice a t t a i n e d s i g n i f i c a n t l y higher scores than d i d students with experience on other instruments; i t i s not c l e a r how formal ear t r a i n i n g experience i n t e r a c t s with timbre. Conclusions The timbre i n which melodic i n t e r v a l s are presented during d i c t a t i o n does make a d i f f e r e n c e to the scores a t t a i n e d , at l e a s t for the population examined i n t h i s study. Timbre then, i s of s u f f i c i e n t importance that educators should not: . . . ignore i t and concern [themselves] e x c l u s i v e l y with rhythm and p i t c h . 1 Depending upon the amount of FETE and PPEM a subject has, the r e s u l t s of t h i s study would seem to suggest that presenting m a t e r i a l with d i f f e r e n t timbres can make the task of i d e n t i f y i n g 1 W i l l i a m E. Thomson and Richard P. Delone, I n t r o d u c t i o n to Ear T r a i n i n g ( C a l i f o r n i a : Wadsworth P u b l i s h i n g , 1968), p. ~. 57 i n t e r v a l s d i f f e r e n t from the task of i d e n t i f y i n g i n t e r v a l s presented with a c o n s i s t e n t l y uniform timbre. The nature of that d i f f e r e n c e i s not c l e a r from t h i s study, and has not been c l e a r i n s t u d i e s done p r i o r to t h i s one. Although the r e s u l t s of t h i s study are somewhat ambiguous regarding the e f f e c t of f a m i l i a r i t y of timbre, i t appears that being f a m i l i a r with a timbre source used, through playing/performing experience with an instrument producing that timbre, does not a i d i n the i d e n t i f i c a t i o n of p i t c h e s produced with that timbre. I t i s p o s s i b l e that subjects d i d not respond a c c u r a t e l y to the question regarding t h e i r "major instrument", since many u n i v e r s i t y / c o l l e g e students change t h e i r major instrument during t h e i r academic s t u d i e s . The r e s u l t may be that some students have more experience on t h e i r "secondary" instruments than on t h e i r declared majors. I t i s i n t e r e s t i n g to note, however, that students who claimed voice as t h e i r declared major instrument achieved the same scores as d i d piano students. I t may be that voice students, by v i r t u e of making frequent use of piano i n t h e i r s t u d i e s , are not very d i f f e r e n t from piano students i n terms of f a m i l i a r i t y with the timbre of the piano. I t appears that the timbre i n which d i c t a t i o n m a t e r i a l i s presented can a f f e c t a student's a b i l i t y to perform i d e n t i f i c a t i o n of melodic d i c t a t i o n i n t e r v a l s . Since ear t r a i n i n g i s , presumably, a p r e l i m i n a r y stage i n l e a r n i n g to work with more complex musical m a t e r i a l s , i t would seem that students should be exposed to various timbres as part of t h e i r t r a i n i n g i n i n t e r v a l i d e n t i f i c a t i o n . 58 S u g g e s t i o n s f o r F u r t h e r Study S e v e r a l s u g g e s t i o n s f o r f u r t h e r i n v e s t i g a t i o n have a r i s e n from t h i s s t u d y : 1. The e f f e c t of f a m i l i a r i t y of t i m b r e needs t o be e x p l o r e d i n depth, u s i n g s u b j e c t s w i t h a wide range of exper i e n c e . 2. The e f f e c t of f i x e d and moveable doh s h o u l d be e x p l o r e d i n r e l a t i o n t o t i m b r e , s i n c e t h e r e i s ev i d e n c e t o suggest t h a t t o n a l i t y i n f l u e n c e s m u s i c a l p e r c e p t i o n . 3. The e f f e c t of the t y p e of i n t e r v a l used ( a s c e n d i n g , d e s c e n d i n g , harmonic, and m e l o d i c ) s h o u l d be e x p l o r e d , as s h o u l d the speed of p r e s e n t a t i o n . 4. The e f f e c t of the t y p e s of t i m b r e s p r e s e n t e d s h o u l d be examined more t h o r o u g h l y , i n c l u d i n g d i f f e r e n t c o m b i n a t i o n s of i n s t r u m e n t s , and a l s o i n c l u d i n g the e f f e c t of removing the a t t a c k and r e l e a s e from the sound. I t i s suggested i n the l i t e r a t u r e t h a t the a t t a c k and r e l e a s e may be of g r e a t importance i n i d e n t i f i c a t i o n of t i m b r e . 5. There a r e now a v a i l a b l e a number of ear t r a i n i n g programs f o r use on microcomputers f i t t e d w i t h s y n t h e s i z e r s . An e x a m i n a t i o n of the e f f e c t s of u s i n g s y n t h e s i z e d i n s t e a d of r e a l i n s t r u m e n t s s h o u l d be made, t o determine the a p p l i c a b i l i t y of such s y n t h e s i z e r s t o ear t r a i n i n g c o u r s e s . 6. The q u e s t i o n of s u b j e c t s ' d e c l a r e d major i n s t r u m e n t 59 needs to be re-examined, t a k i n g i n t o acount the length of time spent studying the major instrument, and the v-length of time spent studying any secondary instruments. 7. A recent change i n the Secondary Music Curriculum of the B r i t i s h Columbia p u b l i c school system should soon make i t p o s s i b l e to r e p l i c a t e t h i s study, since ear t r a i n i n g i s now to be o f f e r e d as a regular part of the music c l a s s in secondary schools. The information gathered might shed greater l i g h t upon the e f f e c t of c h r o n o l o g i c a l age on i n t e r v a l i d e n t i f i c a t i o n , and should provide a wider range of FETE f o r study. 60 SOURCES CONSULTED Books A l i f e r i s , James. A l i f e r i s Music Test. Minnesota: U n i v e r s i t y of Minnesota, 1952. ; and S t e c k l e i n , John E. A l i f e r i s - S t e c k l e i n Music Achievement Test, College Midpoint L e v e l . Minnesota: U n i v e r s i t y of Minnesota Press, 1962. American Standards A s s o c i a t i o n . American Standard A c o u s t i c a l  Terminology. New York: American Standards A s s o c i a t i o n , 1951. Apel, W i l l i , ed. 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"An Interim Report of a Programmatic S e r i e s of Music Inquiry Designed to I n v e s t i g a t e Melodic Pattern I d e n t i f i c a t i o n A b i l i t y i n C h i l d r e n . " C a l i f o r n i a : SWRL  Education Research and Development, 1976. Z e i t l i n , L. R. "Frequency D i s c r i m i n a t i o n of Pure and Complex Tones." Journal of the A c o u s t i c a l Society of America, 36(1964), 1207-1219. 68 Unpublished M a t e r i a l s Beyer, George Heydrick. "The Determination of P i t c h D i s c r i m i n a t i o n i n High School Students with Musical T r a i n i n g . " M a g i s t r a l t h e s i s , C a l i f o r n i a State U n i v e r s i t y , 1977. B i l y c i a , Demetria Marcia. "Auditory D i s c r i m i n a t i o n of P i t c h D i f f e r e n c e s Among Pure Tone and Voice S t i m u l i . " M a g i s t r a l t h e s i s , Western Michigan U n i v e r s i t y , 1977. B l a t t e r , A l f r e d Wayne. "The E f f e c t of Timbre on Pitch-matching Judgements (with) ' R e f l e c t i o n s f o r Chorus, Narrator, and Fourteen Instruments.'" Doctoral d i s s e r t a t i o n , U n i v e r s i t y of I l l i n o i s at Urbana-Champaign, 1974. Cuddy, L o l a Lane. " P r a c t i c e E f f e c t s i n P i t c h Perception." Doctoral d i s s e r t a t i o n , U n i v e r s i t y of Toronto, 1965. Gephardt, Donald L. "The E f f e c t s of D i f f e r e n t F a m i l i a r and U n f a m i l i a r Musical Timbres on Musical Melodic D i c t a t i o n . " Doctoral d i s s e r t a t i o n , Washington U n i v e r s i t y , M i s s o u r i , 1978. Grey, J . M. "An E x p l o r a t i o n of Musical Timbre using Computer Based Techniques for A n a l y s i s , Synthesis and Perceptual S c a l i n g . " Doctoral d i s s e r t a t i o n , Stanford U n i v e r s i t y , 1975. Hermanson, L. W. "An I n v e s t i g a t i o n of the E f f e c t s of Timbre on Simultaneous Vocal P i t c h A c u i t y of Young C h i l d r e n . " Doctoral d i s s e r t a t i o n , Columbia Teachers' Coll e g e , 1971. 69 Howell, Ronald Thomas. "The E f f e c t of Timbre on the I n t e r v a l Perception and I d e n t i f i c a t i o n S k i l l of I n s t r u m e n t a l i s t s . " Doctoral d i s s e r t a t i o n , The U n i v e r s i t y of Oklahoma, 1976. Jameson, R. P h i l i p . "The E f f e c t of Timbre Conditions on the Prompted and Simultaneous P i t c h Matching of Three A b i l i t y Groups of Trombone Performers." Doctoral d i s s e r t a t i o n , Columbia U n i v e r s i t y Teachers' Colle g e , 1980. Leonard, Nels J r . "The E f f e c t of C e r t a i n I n t r i n s i c and Contextual C h a r a c t e r i s t i c s of the Tone Stimulus on P i t c h D i s c r i m i n a t i o n . " Doctoral d i s s e r t a t i o n , West V i r g i n i a U n i v e r s i t y , 1967. S i l b e r , John S. "Aural A n a l y t i c A b i l i t y i n Harmonic D i c t a t i o n i n Various Mu s i c a l Media." Doctoral d i s s e r t a t i o n , U n i v e r s i t y of Indiana, 1955. Tunks, Thomas W.; and Harvey, Jay R. "Defining Tuning E r r o r : Is Frequency Mismatch S u f f i c i e n t ? " Paper presented at the Music Educators N a t i o n a l Conference Convention, A p r i l 12, 1980, Miami, F l o r i d a . Vander Gheynst, Paul John. "The E f f e c t of Timbre on A u d i t o r y - V i s u a l D i s c r i m i n a t i o n . " Doctoral d i s s e r t a t i o n , The U n i v e r s i t y of I l l i n o i s , at Urbana-Champaign, 1978. Wang, C e c i l i a . "Timbre Perception and Tonal Duration." Paper presented at the Music Educators N a t i o n a l Conference Convention, A p r i l 12, 1980, Miami, F l o r i d a . 70 Appendix 1 Melodic I n t e r v a l I d e n t i f i c a t i o n — I n s t r u c t i o n s to Performers The f o l l o w i n g pages are the i n s t r u c t i o n s that were given the performers who were doing the recording of i n t e r v a l s . 71 Melodic I n t e r v a l I d e n t i f i c a t i o n — I n s t r u c t i o n s to Performers Piano, V i o l i n , Xylophone, Syn t h e s i z e r ("Concert P i t c h Instruments") Please play each note at a mezzo f o r t e volume. Use a normal tone, and use v i b r a t o i f you would normally do so. You are attempting to produce a "good" tone which c o u l d serve as an examplar. Stop at each double bar; the recording engineer w i l l advise you when he i s ready for the next bar. Make use of the stroboscope to ensure you are p l a y i n g e x a c t l y on p i t c h (A = 440 Hz ), and the metronome to ensure that you are p l a y i n g e x a c t l y in time. A. 4 *i 1 ^ 7 J. ' U 7 ^ 71 V L M • " «/ g j . 7 7 4 —L . / 1 •/ 1 J. 7 & 7 1 *7 r j j . V 1 U 7 J- 71 t 7 \. ml U 7 ' 1 1 72 Melodic I n t e r v a l I d e n t i f i c a t i o n - - I n s t r u c t i o n s to Performers C l a r i n e t , Trumpet ("Transposing" Bb instruments) Please play each note at a mezzo f o r t e volume. Use a normal tone, and use v i b r a t o i f you would normally do so. You are attempting to produce a "good" tone which could serve as an examplar. Stop at each double bar; the recording engineer w i l l advise you when he i s ready for the next bar. Make use of the stroboscope to ensure you are p l a y i n g e x a c t l y on p i t c h (A = 440 Hz ) , and the metronome to ensure that you are p l a y i n g e x a c t l y i n time. 9p 0* g _ L _ J . •< II j J 7 jj. X 1 1 J T T — —i—H—#^  — i — — 1 H a H *—H J . 7 =:J J 7 d a / i 7 1 5 7 fff* 1 73 Appendix 2 Questionnaire and I n t e r v a l Answer Form The f o l l o w i n g pages contain the information and answer sheets which were given to su b j e c t s . 74 Questionnaire and I n t e r v a l Answer Form  INSTRUCTIONS PART A This t e s t i s designed to explore the e f f e c t of timbre (tone c o l o u r ) on the perception of p i t c h . The t e s t w i l l take approximately 20 minutes. Although your p a r t i c i p a t i o n i s appreciated, you are free to withdraw at any time or to refuse to answer any questions without p r e j u d i c e . I f the questi o n n a i r e i s completed, your consent w i l l be assumed. Please turn to the next page, "Background Information", and answer the questions. Complete the questions and the answer form anonymously. Do not w r i t e your name on these pages. PART B You are going to hear a s e r i e s of melodic i n t e r v a l s . Each i n t e r v a l w i l l be played twice, with an announcement of the question number between each p a i r . Only i n t e r v a l s i n the octave C4 (middle C) to C5 w i l l be used, as shown in the l i s t below. m2 M2 m3 M3 P4 X4(dim5) P5 m6 M6 m7 M7 P8 Six d i f f e r e n t instruments w i l l be used to produce the i n t e r v a l s . YOU DO NOT NEED TO IDENTIFY THE INSTRUMENT BEING USED. Write down the name of each i n t e r v a l i n the space provided. Ignore the smaller numbers to the r i g h t of each box. Try to answer every question, even i f you are not sure of the answer; guessing i s permitted. THIS TEST IS ANONYMOUS, AND DOES NOT COUNT TOWARD ANY EVALUATION. Are there any questions? The f o l l o w i n g s e c t i o n i s a sample quiz only, to give you a chance to p r a c t i s e . I t w i l l not be scored. NUMBER NAME 9 NUMBER NAME 1 0 NUMBER NAME 1 2 3 1 1 This completes the p r a c t i c e s e s s i o n . Are there any f u r t h e r questions? Please turn to the Answer Sheet — in a moment, we w i l l begin the a c t u a l q u i z . 75 BACKGROUND INFORMATION 1 . In what year of u n i v e r s i t y / c o l l e g e are you c u r r e n t l y e n r o l l e d ? (Use 9 i f you are F a c u l t y ) I 1 7 , Age? (Years) 9 - 1 0 Sex? (M or F) 1 2 4. What i s your MAJOR instrument ( i . e . the instrument on which you spend most of your time and energy)? — 1. CLARINET 2. TRUMPET 3. PIANO 4. VIOLIN 5. XYLOPHONE 6. SYNTHESIZER 7. NONE 8. OTHER (INCLUDING VOICE--PLEASE SPECIFY) L_ 1 « 5. How long have you played t h i s instrument? (Years) 1 6 - 1 7 What i s your SECONDARY instrument ( i . e . the instrument on which you spend somewhat l e s s of your time and energy)? 1. CLARINET 2. TRUMPET 3. PIANO 4. VIOLIN 5. XYLOPHONE 6. SYNTHESIZER 7. NONE 8. OTHER (INCLUDING VOICE~-PLEASE SPECIFY) 1 9 7. How long have you played t h i s instrument? (Years) 2 1 - 2 2 How many a c t u a l MONTHS of u n i v e r s i t y / c o l l e g e l e v e l theory/harmony courses have you taken? [Note: one u n i v e r s i t y / c o l l e g e year equals eight months.] 2 4 - 2 6 Now turn back to PART B on the I n s t r u c t i o n page and l i s t e n to the tape. 76 MELODIC INTERVAL IDENTIFICATION ANSWER SHEET NUMBER NAME 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 1 4 1 5 1 6 17 18 19 20 21 22 23 24 1 0 1 1 1 2 1 3 1 a 1 5 1 e 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 a 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 NUMBER NAME 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 3 3 3 4 3 5 3 e 3 7 3 8 3 9 n o 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 4 9 5 0 5 1 5 2 5 3 5 4 5 5 5 6 NUMBER NAME 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 5 7 5 8 5 9 6 0 e 1 6 2 6 3 6 4 E 5 6 6 6 7 6 8 6 9 7 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 7 8 7 9 8 0 77 Appendix 3 L i s t and S p e c i f i c a t i o n s of Equipment used for the Study The f o l l o w i n g i s the l i s t of equipment which was used for the study. 78 L i s t and S p e c i f i c a t i o n s of Equipment used for the Study Recording: Microphone: Mixing Board: Tape deck; Tape: Synthesizer; Analyzer; E q u a l i z e r : Noise Gate; Osc i l l o s c o p e ; Playbac k: AKG C34 Soundcraft S e r i e s Two O t a r i MX 5050 q u a r t e r - i n c h h a l f track Ampex #456, recorded at 15 i . p . s . Roland 100M Klark Technic Model DN60 Real Time Spectrum Analyzer Audio Design Scamp Sweep Eq u a l i z e r Orange County E l e c t r o n i c s Model CLX Dynamic Range Processor Heathkit Model IO-4550 DC to 10 MHz Dual-trace o s c i l l o s c o p e Tape Recorder Frequency Response: Wow and F l u t t e r : Harmonic D i s t o r t i o n : Signal/Noise R a t i o : Sony TC-630 combined tape recorder, a m p l i f i e r , and speakers 30 Hz - 18000 Hz ±3 dB at 7.5 i.p.s, .08 % at 7.5 i . p . s . .4 % at 0 VU at 7.5 i . p . s . -56 dB at 7.5 i . p . s . Meters: R e a l i s t i c Model 42-3019 Sound Level Meter, set on dBA scale Peterson Model 400 Stroboscope (±2 cents) P e a r l Model TC-102 Tuning Meter (±2 cents) Boss Model DB-33 e l e c t r o n i c metronome 79 Appendix 4 Contents of the Test Tape The. f o l l o w i n g i s the sequence i n which items were recorded on the t e s t tape which was played to su b j e c t s . 80 Contents of the Test Tape A one minute reference tone (A = 440 Hz) was placed on the tape, followed by the i n s t r u c t i o n s . Appropriate pauses were i n s e r t e d to allow time for subjects to complete the quest i o n n a i r e and to ask any questions. Three p r a c t i c e i n t e r v a l s were placed on the tape a f t e r the i n s t r u c t i o n s . These three i n t e r v a l s c o n s i s t e d of P4, P5, and P8, played on piano. No answers were provided for the p r a c t i c e i n t e r v a l s . Following these i n s t r u c t i o n s was the a c t u a l t e s t , which had the f o l l o w i n g p a t t e r n : question # i n t e r v a l pause i n t e r v a l pause 6 seconds 2 sec. 2 sec . 2 sec . 2 sec. At the end of the tape, subjects were t o l d : "This completes the t e s t i n g . Thank you for your a s s i s t a n c e and cooperation." 81 Appendix 5 I n t e r v a l Randomization Program The f o l l o w i n g program was w r i t t e n by Mr. Steve White of the Educational Research Service Center of the U n i v e r s i t y of B r i t i s h Columbia. I t i s designed to run on an Apple micro-computer with a minimum memory of 16K. 82 I n t e r v a l Randomization Program 101 , 102,103,104,105,106 107,108,109,110,111,112 201 ,202,203,204,205,206 207,208,209,210,211,212 301 ,302,303,304,305,306 307,308,309,310,311,312 401 ,402,403,404,405,406 407,-408,409,410,41 1,412 501,502,503,504,505,506 507,508,509,510,511,512 601 ,602,603,604,605,606 607,608,609,610,611,612 "DT J M n -O" " D T I M n + 9 " " 10 DIM A(72),S$(72),V(72),U(72) 20 FOR I = 1 TO 72 39 READ A(I) 40 NEXT I 60 FOR I = 1 TO 72 69 READ S$(I) 70 NEXT I 100 DATA 101 DATA 102 DATA 103 DATA 104 DATA 1 05 DATA 106 DATA 107 DATA 108 DATA 109 DATA 110 DATA 111 DATA 200 DATA 201 DATA 2 02 DATA 203 DATA 204 DATA 205 DATA 2 06 DATA 207 DATA 208 DATA 209 DATA 2 1 0 DATA 211 DATA 212 DATA 213 DATA 214 DATA 215 DATA 216 DATA 2 1 7 DATA 218 DATA 2 1 9 DATA 220 DATA 221 DATA 222 DATA 223 DATA "PIANO -2" , "PIANO +2 ","PIANO -3" "PIANO +3", "PIANO P4 ","PIANO X4" "PIANO P5" "PIANO -6 ","PIANO +6" "PIANO -7" "PIANO +7 ","PIANO P8" "CLAR -2 II T 'CLAR +2", "CLAR -3" "CLAR +3 II 1 'CLAR P4", "CLAR X4" "CLAR P5 II 1 'CLAR -6", "CLAR +6", "CLAR -7 II » 'CLAR +7", "CLAR P8" "TPT -2 t l 1 'TPT +2", "TPT -3" "TPT +3 II 1 'TPT P4", "TPT X4" "TPT P5 II 1 'TPT -6", "TPT +6" "TPT -7 II 1 'TPT +7", "TPT P8" "VIOLIN -2' ',"VIOLIN +2","VIOLIN -3" "VIOLIN + 3' ,"VIOLIN P4","VIOLIN X4" "VIOLIN P5' ',"VIOLIN -6","VIOLIN + 6" "VIOLIN -7' ',"VIOLIN +7","VIOLIN P8" "XYLOPH -2' ' ,"XYLOPH +2","XYLOPH -3" "XYLOPH + 3' ,"XYLOPH P4","XYLOPH X4" "XYLOPH P5' ' ,"XYLOPH -6","XYLOPH + 6" "XYLOPH -7' ' ,"XYLOPH +7","XYLOPH P8" "SYNTH -2' ',"SYNTH +2","SYNTH -3 n "SYNTH + 3' ,"SYNTH P4","SYNTH X4 t i "SYNTH P5' '/'SYNTH -6","SYNTH +6 H "SYNTH -7 ',"SYNTH + 7","SYNTH P8 t i 83 300 OLDN = INT (72 * RND (1) + 1) 310 V(1) = OLDN:U(OLDN) = 1 320 1 = 2 400 N = INT (72 * RND (1) + 1) 410 IF INT (A(N) / 100) = INT (A(OLDN) / 100) THEN 400 420 T1 = INT (A(OLDN)) - ( INT (A(OLDN) / 100) * 100) 422 T2 = INT (A(N)) - ( INT (A(N) / 100) * 100) 423 IF T1 = T2 THEN 400 425 IF U(N) = 1 THEN 400 430 U(N) = 1 440 V(I) = N:OLDN = N:I = 1 + 1 450 IF I = 73 THEN 1000 460 GOTO 400 1000 REM PRINTOUT 1111 FOR I = 1 TO 72 1122 PRINT SPC( I < 10)1;" 1125 " SPC( V(I) < 100) SPC( V(I) < 10)V(I) TAB( 10)A(V(I));" 1130 TAB(20)S$(V(I)) 1133 NEXT I 333 3 END 84 Appendix 6 Order of I n t e r v a l s as Played to Subjects The f o l l o w i n g pages contain the order i n which the various i n t e r v a l s were presented to s u b j e c t s . 85 Order of I n t e r v a l s as Played to Subjects J =120 No. 1 Synthesizer No. 2 V i o l i n 2fc 5 No. .3 C l a r i n e t No. 4 V i o l i n & 1 l. 1 '• J 1 ,1 a No. 5 Trumpet No. 6 Xylophone t i if J. i No. 7 C l a r i n e t No. 8 V i o l i n No. 9 C l a r i n e t No. 10 Piano : I 7 . 7 -^s bars • I 7 jjJ. —=#5 " No. 11 Trumpet No. 12 V i o l i n 5 No. 13 C l a r i n e t No. 14 V i o l i n No. 15 C l a r i n e t No. 16 Synthesizer E; i if U. T No. 17 V i o l i n No. 18 Trumpet a m : j 1 y 1 EIEE3 » I No. 19 Piano I If |„, 7 J . 7 No. 20 Xylophone 7 l J , 7 86 J =120 No. 21 Piano No. 22 Trumpet No. 23 Piano No. 24 Xylophone No. 25 Synthesizer No. 26 C l a r i n e t : I 7 ,1 1 5 3 No. 27 V i o l i n No. 28 ' C l a r i n e t 5 7 r 7 No. 29 Xylophone No. 30 Trumpet 5 g . -» I 7 : ; i 7 J . 7 No. 31 Synthesizer No. 33 V i o l i n ; i 7 J . 7 No. 34 Synthesi zer t I LZi No. 35 =3= Trumpet No. 37 Synthesizer M No. 39 Piano" P S No. 36 CH a r i n p t -=3 No. 38 C l a r i n e t ! I / P No. 40 Synthesizer i; I 7 j . 7 87 J. 120 No. 41 Xylophone No. 42 Piano 4 - r — 3 - : I 1 f | 7 I i No. 43 Xylophon > . ~2* No. 44 Trumpet i 1 L J 1 No. 45 -i r— 8—r-V i o l i n -i a — U J * No. 46 I a i Synthesizer • 1 i 7 — f ' f - r - 7 - v 0 * 7 • I-J>7 u. 7 1 No. 47 V i o l i n No. 48 C l a r i n e t No. 49 Xylophone No. 50 Trumpet • • 7 j 7 No. 51 Xylophon ie < No. 52 V i o l i n 7 1*1 • 7 7 bi. 7 No. 53 Piano No. 54 Synthesizer _ e : I 7 7 •3* i No. 55 C l a r i n e t : I 7 i f No. 56 Piano ; I 7 j 7 No. 57 Synthesizer : i 1 f 1 3 No. 59 Synthesizer ~ l 7 | No. 58 Trumpet No. 60 Trumpet 88 J =120 No. 61 V i o l i n No. 62 Trumpet No. 63 f • a , Xylophon mJ - * — e w • No. 64 i a | Clarinet. • . W J^* Sl— • 1-g ^ No. 65 •i r—3 r-Piano • mJ MM # No. 66 r±' 7 ' Synthesizer • i ^ J 7 S> h ^ No. 67 * 7 - i — b * Trumpet • No. 68 F j , 7 J ' 1 Xylophone • W —| u— No. 69 1 , 3 , 1 Piano • \~ ..I 1_| No. 70 I'J.7 kl-Xylophone • ; ...ti ^_ • *_ No. 71 Piano t «J J «V • 1 U No. 72 ~~H*—r r j . ' IH- 7 Xylophone • ^—1 L • ' ' J . 7 bJ. 89 Appendix 7 Coding Method Used for I d e n t i f y i n g Responses The f o l l o w i n g page contains the d e t a i l s of the coding method used to i d e n t i f y subjects' responses i n order to f a c i l i t a t e computer s c o r i n g and a n a l y s i s . 90 Coding Method Used for I d e n t i f y i n g Responses Subjects' response forms were hand coded, and the coding checked for accuracy according to the f o l l o w i n g code: m2 M2 m3 M3 P4 X4 P5 m6 M6 m7 M7 P8 Blank 1 2 3 4 5 6 7 8 9 0 - + The subjects' answers to the background information q u e s t i o n n a i r e were a l s o coded, with a l e t t e r code being used for those instruments which subjects l i s t e d under "OTHER". Once these codings had been done and the data had been keypunched, a l l response codings and the keypunched cards were checked to ensure accuracy. The few e r r o r s which were found were c o r r e c t e d , and a n a l y s i s of the data was then c a r r i e d out. In order to s i m p l i f y the a n a l y s i s , a program was w r i t t e n to t r a n s l a t e the i n t e r v a l answers from the o r i g i n a l t h i r t e e n l e v e l code to a two l e v e l code which i n d i c a t e d only whether an answer was c o r r e c t or i n c o r r e c t : Wrong Right 1 2 The LERTAP output of scores was subsequently used as input for SPSS and MULTIVAR programs. 91 Appendix 8 The Computer Program used f o r Conversion of Scores The f o l l o w i n g program was w r i t t e n by Dr. R. E. Bruce of the Educational Research Service Center (ERSC) at the U n i v e r s i t y of B r i t i s h Columbia. 92 The Computer Program used for Conversion of Scores 00050 REM THIS PROGRAM RUNS UNDER WATEROO BASIC V2.0 00100 REM THIS CODE CONVERTS DATA FROM '1 THRU 9,0,-,+,?' 00150 REM TO '00-12'. 00200 REM DHDATA CONTAINS INPUT DATA IN FORM 'XXXX YY:::Y' 00225 REM WHERE XXXX IS THE RECORD ID, 00250 REM AND Y EQUALS THE RESPONSE-72 RESPONSES ALLOWED. 00300 REM DATA CONTAINS OUTPUT IN THE FORM '00-05' FOR LERTAP 00350 REM -CONVERTS CONTAINS DATA IN THE FORM '00-12'. 00400 REM DALMUSKEY CONTAINS THE CORRECT RESPONSES FOR 00425 REM QUESTION AT 1 PER CARD. 00450 00500 DIM CHAR$(151) fRIGHT(151) 00550 ON EOF IGNORE 00600 OPEN #2,'DHDATA',INPUT 00650 OPEN #3,'-CONVERTS',OUTPUT 00700 FORMAT $ ="#.#####################################"& 00750 &+"#########################################" 00800 PRINT "PLEASE ENTER THE NUMBER OF CASES" 00850 INPUT CASES 00900 FOR J=1 TO CASES 00950 INPUT #2,USING FORMAT$,A$ 01000 B$ = STR$(A$,1,7) 01050 FOR 1=8 TO 79 01100 CHAR$(I) = STR$(A$,I,1) 01150 IF CHAR$(I) = "0" 01200 CHAR$(I) = "10" 01250 ELSEIF CHAR$(I) = "-" 01300 CHAR$(I) = "11" 01350 ELSEIF CHAR$(I) = "+" 01400 CHAR$(I) = "12" 01450 ELSEIF CHAR$(I) = "?" 01500 CHAR$(I) = "00" 01550 ELSE 01600 CHAR$(I) = "0"+CHAR$(l) 01650 ENDIF 01700 B$ = B$ + CHAR$(I) 01750 NEXT I 01800 PRINT #3,B$ 01850 NEXT J 01860 01870 01900 REM THIS CODE CONVERTS DATA FROM '00-12' TO '01-02' 01925 REM FOR LERTAP RUN 93 01950 OPEN #4,'DALMUSKEY',INPUT 02000 OPEN #5,'-CONVERTS',INPUT 02050 OPEN #6,'DATA',OUTPUT 02100 FORMS$="####################################"& 02150 & + " # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # 02200 &+»####################################"& 02250 &+»###########################################" 02300 FOR 1=8 TO 150 STEP 2 02350 INPUT #4, RIGHT(I) 02400 NEXT I 02450 FOR C=1 TO CASES 02500 INPUT #5,USING FORMS$,A$ 02550 B$ = STR$(A$,1,7) 02600 FOR 1=8 TO 150 STEP 2 02650 CHAR$(I) = STR$(A$,I,2) 02700 IF CHAR$(I)="00" 02750 ANS$="01" 02800 GOTO 3650 02850 ENDIF 02900 WRONG = RIGHT(I) - VALUE(CHAR$(I)) 03000 IF WRONG = 0 03050 ANS$="02" 03100 ELSE 03150 ANS$="01" 03600 ENDIF 03650 B$ = B$ + ANS$ 03700 NEXT I 03750 PRINT #6,B$ 03800 NEXT C 03850 END 94 Appendix 9 The Computer Program used for Transformation and S t a n d a r d i z a t i o n of Scores The f o l l o w i n g program was w r i t t e n by Dr. R. E. Bruce of the Educational Research Service Center (ERSC) at the U n i v e r s i t y of B r i t i s h Columbia. «. 95 The Computer Program used for Transformation and St a n d a r d i z a t i o n of Scores 00100 REM THIS PROGRAM RUNS UNDER WATERLOO BASIC V2.0 00100 DIM TOTAL(19),DEV(19),MEAN(19),STDDEV(19),NUMSCORE(19) 00110 PRINT "DATA MUST BE IN SCORES 1 IN FOLLOWING FORMAT: 00115 FORMAT ICLCAbbbS1S2S3S4S5S6"; 00120 PRINT " WHERE I=INSTITUTE, CL=CLASS, CA= CASE, S1-S6 00122 ARE SCORES" 00125 PRINT"RESULTS WILL BE IN '-AZSCORES6' A SCRATCH FILE!" 00130 CASES=0 00150 ON EOF IGNORE 00200 OPEN #2,'SCORES 1' ,INPUT 00250 OPEN #3,'-ASCORES2',OUTPUT 002 53 OPEN # 4,'-ASCORES3' ,OUTPUT 00255 FORMAT$="####################" 00260 INPUT #2,USING-FORMAT$,A$ 00265 FIRST$=A$ 00270 GOTO 280 00275 INPUT #2,USING FORMAT$,A$ 00280 IF IOSTATUS(2)=1 THEN GOTO 730 00282 REM NO RECORD FOUND IN SCORES 1 00285 CASES=CASES+1 00295 C = VALUE(STR$(A$,2,2)) 00300 FOR 1=9 TO 19 STEP 2 00350 B$ = STR$(A$,1,8) 00400 OLDSCORE=VALUE(STR$(A$,I,2)) 00405 OLDSCORE = OLDSCORE/12 00410 IF OLDSCORE=0 00420 NEWSCORE=2*ASIN(SQR(1/48)) 00430 ELSEIF OLDSCORE=1 00440 NEWSCORE=PI - 2*ASIN(SQR(1/48)) 00450 ELSE 00460 NEWSCORE=2*ASIN(SQR(OLDSCORE)) 00470 ENDIF 00480 NEWSCORE$ = VALUE$(NEWSCORE) 00490 B$= B$ + NEWSCORE$ 00500 PRINT #3,B$ 00510 TOTAL(C) = TOTAL(C) + NEWSCORE 00520 NUMSCORE(C) = NUMSCORE(C) + 1 00600 NEXT I 00720 GOTO 275 00730 FOR C = 1 TO 19 00733 IF NUMSCORE(C) = 0 THEN GOTO 750 00740 MEAN(C) = TOTAL(C)/NUMSCORE(C) 96 00745 SUMM = SUMM + NUMSCORE(C) 00750 NEXT C 00760 CLOSE #3 00765 PRINT "TOTAL # OF CASES AND FIRST CASE =";CASES,FIRST$ 00770 OPEN #3,'-ASCORES2',INPUT 00800 INPUT #3,A$ 00850 D = VALUE(STR$(A$,2,2)) 00900 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 00950 DEV(D) = DEV(D) + (SCORE - MEAN(D))**2 01000 FOR L = 2 TO SUMM 01025 INPUT #3,A$ 01040 D = VALUE(STR$(A$,2,2) ) 01050 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 01100 DEV(D) = DEV(D) + (SCORE - MEAN(D))**2 01150 NEXT L 01155 FOR C = 1 TO 19 01160 IF TOTAL(C) = 0 THEN GOTO 1170 01165 STDDEV(C) = SQR(DEV(C)/(NUMSCORE(C)- 1)) 01170 NEXT C 01180 CLOSE #3 01 182 01 183 01185 PRINT"CALCULATING ZSCORES FOR EACH CLASS" 01190 OPEN #3,'-ASCORES2',INPUT 01200 INPUT #3,A$ 01225 B$ = STR$(A$,1,8) 01250 D = VALUE(STR$(A$,2,2)) 01300 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 01330 ZSCORE = (SCORE - MEAN(D))/STDDEV(D) 01350 B$ = B$ + VALUE$(ZSCORE) 01360 FORMS$ ="###########.######" 01390 PRINT #4,USING FORMS$,B$ 01400 FOR L = 2 TO SUMM 01450 INPUT #3,A$ 01 475 B$ = STR$(A$,1,8) 01500 D = VALUE(STR$(A$,2,2)) 01550 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 01600 ZSCORE = (SCORE - MEAN(D))/STDDEV(D) 01605 IF ZSCORE > 0 01610 IF ZSCORE < 1 01613 CORRANS$ ="0"+VALUE$(ZSCORE) 01614 B$ = B$ +CORRANS$ 01615 GOTO 1630 01617 ENDIF 01619 "ENDIF 01620 B$ = B$ +VALUE$(ZSCORE) 01630 PRINT #4,USING FORMS$,B$ 01650 NEXT L 01700 CLOSE #2 01725 CLOSE #3 01750 CLOSE #4 01760 01 770 97 01800 PRINT"CALCULATING ZSCORES FOR EACH INSTITUTION" 02000 DIM INSTOTALO),INSDEV(3),INSMEAN(3),INSSTDDEV(3), 02005 INSNUMSCORE(3) 02010 OPEN #2,'-ASCORES3',INPUT 02020 OPEN #4,'-ASCORES5',OUTPUT 02030 FOR J=1 TO SUMM 02040 INPUT #2,A$ 02050 IF STR$(A$,1,1)<>" " 02060 C = VALUE(STR$(A$,1,1)) 02070 ELSEIF STR$(A$,2,1)<>" " 02080 C = VALUE(STR$(A$,2,1)) 02090 ELSEIF STR$(A$,3,1)<>" " 02100 C = VALUE(STR$(A$,3,1)) 02110 ELSEIF STR$(A$,4,1)<>" " 02120 C = VALUE(STR$(A$,4,1)) 02130 ENDIF 02140 NEWSCORE = VALUE(STR$(A$,9,9)) 02150 INSTOTAL(C) = INSTOTAL(C) + NEWSCORE 02160 INSNUMSCORE(C) = INSNUMSCORE(C) + 1 02170 NEXT J 02180 FOR C = 1 TO 3 02190 IF INSNUMSCORE(C) = 0 THEN GOTO 2220 02200 INSMEAN(C) = INSTOTAL(C)/INSNUMSCORE(C) 02210 PRINT "C AND INSNUMSCORE(C) ARE";C,INSNUMSCORE(C) 02220 NEXT C 02230 OPEN #3 r'-ASCORES3' ,INPUT 02240 INPUT #3,A$ 02260 IF STR$(A$,1,1)<>" " 02270 D = VALUE(STR$(A$,1,1)) 02280 ELSEIF STR$(A$,2,1)<>" " 02290 D = VALUE(STR$(A$,2,1)) 02300 ELSEIF STRS(A$,3,1)<>" " 02310 D = VALUE(STR$(A$,3,1)) 02320 ELSEIF STR$(A$,4,1)<>" " 02330 D = VALUE(STR$(A$,4,1)) 02340 ENDIF 02350 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 02370 INSDEV(D) = INSDEV(D) + (SCORE - INSMEAN(D))**2 02380 FOR L = 2 TO SUMM 02390 INPUT #3,A$ 02400 IF STR$(A$,1,1)<>" " 02410 D = VALUE(STR$(A$,1,1)) 02420 ELSEIF STR$(A$,2,1)<>" " 02430 D = VALUE(STR$(A$,2,1)) 02440 ELSEIF STR$(A$,3,1)<>" " 02450 D = VALUE(STR$(A$,3,1)) 02460 ELSEIF STR$(A$,4,1)<>" " 02470 D = VALUE(STR$(A$,4,1)) 02480 ENDIF 02490 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 02500 INSDEV(D) = INSDEV(D) + (SCORE - INSMEAN(D))**2 02510 NEXT L 02520 FOR C = 1 TO 3 98 02530 IF INSTOTAL(C) =0 THEN GOTO 2550 02540 INSSTDDEV(C) = SQR(INSDEV(C)/(INSNUMSCORE(C)-1)) 02550 NEXT C 02560 CLOSE #3 02570 OPEN #3,'-ASCORES3',INPUT 02580 INPUT #3,A$ 02600 B$ = STR$(A$,1,8) 02610 IF STR$(A$,1,1)<>" " 02620 D = VALUE(STR$(A$,1,1)) 02630 ELSEIF STR$(A$,2,1)<>" " 02640 D = VALUE(STR$(A$,2,1)) 02650 ELSEIF STR$(A$,3,1)<>" " 02660 D = VALUE(STR$(A$,3,1)) 02670 ELSEIF STR$(A$,4,1)<>" " 02680 D = VALUE(STR$(A$,4,1)) 02690 , ENDIF 02700 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 02710 ZSCORE = (SCORE - INSMEAN(D))/INSSTDDEV(D) 02720 B$ = B$ + VALUE$(ZSCORE) 02730 PRINT #4,USING FORMS$,B$ 02740 FOR L = 2 TO SUMM 02750 INPUT #3,A$ 02760 B$ = STR$(A$,1,8) 02770 IF STR$(A$,1,1)<>" " 02780 D = VALUE(STR$(A$,1,1)) 02790 ELSEIF STR$(A$,2,1)<>" " 02800 D = VALUE(STR$(A$,2,1)) 02810 ELSEIF STR$(A$,3,1)<>" " 02820- D = VALUE(STR$(A$,3,1)) 02830 ELSEIF STR$(A$,4,1)<>" " 02840 D = VALUE(STR$(A$,4,1)) 02850 ENDIF 02860 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 02870 ZSCORE = (SCORE - INSMEAN(D))/INSSTDDEV(D) 02880 IF ZSCORE > 0 02890 IF ZSCORE < 1 02900 CORRANS$ ="0"+VALUE$(ZSCORE) 02910 B$ = B$ +CORRANS$ 02920 GOTO 2960 02930 ENDIF 02940 ENDIF 02950 B$ = B$ +VALUE$(ZSCORE) 02960 PRINT #4,USING FORMS$,B$ 02970 NEXT L 02980 CLOSE #2 02985 CLOSE #3 02990 CLOSE #4 02992 02993 02995 PRINT "CALCULATING ZSCORES FOR WHOLE STUDY" 03000 OPEN #2,'-ASCORES5',INPUT 03010 OPEN #4,'-AZSCORES6',OUTPUT 03020 FOR J=1 TO SUMM 99 03030 INPUT #2,A$ 03040 NEWSCORE = VALUE(STR$(A$,9,9)) 03050 TOTAL = TOTAL + NEWSCORE 03060 NUMSCORE = NUMSCORE + 1 03070 NEXT J 03080 MEAN = TOTAL/NUMSCORE 03100 OPEN #3,'-ASCORES5',INPUT 03110 INPUT #3,A$ 03130 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 03150 DEV = DEV + (SCORE - MEAN)**2 03160 FOR L = 2 TO SUMM 03170 INPUT #3,A$ 03180 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 03190 DEV = DEV + (SCORE - MEAN)**2 03200 NEXT L 03210 STDDEV = SQR(DEV/(NUMSCORE-1)) 03220 CLOSE #3 03230 OPEN #3,'-ASCORES5',INPUT 03240 INPUT #3,A$ 03260 B$ = STR$(A$,1,8) 03270 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 03280 ZSCORE = (SCORE - MEAN)/STDDEV 03290 B$ = B$ + VALUE$(ZSCORE) 03300 PRINT #4,USING FORMS$,B$ 03310 FOR L = 2 TO SUMM 03320 INPUT #3,A$ 03330 B$ = STR$(A$,1,8) 03340 SCORE = VALUE(STR$(A$,9,LEN(A$)-8)) 03350 ZSCORE = (SCORE - MEAN)/STDDEV 03360 IF ZSCORE > 0 03370 IF ZSCORE < 1 03380 CORRANS$ ="0"+VALUE$(ZSCORE) 03390 B$ = B$ +CORRANS$ 03400 GOTO 3440 03410 ENDIF 03420 ENDIF 03430 B$ = B$ +VALUE$(ZSCORE) 03440 PRINT #4,USING FORMS$,B$ 03450 NEXT L 03460 END 100 Appendix 10 C e l l Means, Variance, and Standard Deviation for PPEM and FETE 101 C e l l Means, Variance, and Standard D e v i a t i o n for PPEM and FETE 1 2 3 4 5 6 CLAR TPT PIANO VIOLIN XYLO SYNTH 1 -0. 093367 -0.47118 1 -0. 078006 -0. 217 122 -0. 159962 -0. 38-3301 2 -0. 72834 1 -0.201781 -0. 180303 -0. 591973 -0. 1795 10 -0.53037 1 3 0. 034976 -0.054967 0 . 373590 0. 134626 o. 2619 14 -O.291S97 4 -0. ,190111 -O.438849 0. 1.82536 -o. . 326C63 -0. 199174 - C . 1739 17 5 . -0. . 357 150 -0 223257 -0. 093314 -0. 669506 -0. 191807 -0.275256 6 -0 .202091 -0.577450 0. 096C61 -0. ,211612 -o. 193966 -0.262738 7 0. .340628 0.2238 19 0. 6205 12 0. , 319088 0. 519422 0.451820 8 0 .323035 0.328169 0. 618532 0. .22438 1 0. .493131 0.4508C2 9 0 .382758 0.306526 0. .510326 0. ,420357 0. .381271 0.475596 CELL N FACTOR LEVELS PPEM FETE 22 12 8 31 30 33 22 21 33 TOTAL N= 212. VARIABLE VARIANCE ( E R R O R M E A N S Q U A R E S ) 1 CLAR 0.865008 2 TPT 1.085915 3 PIANO 0.682431 4 VIOLIN 1.127537 5 XYLO 0.85OS9S 6 SYNTH 0.902126 STANDARD DEVIATION 0.9301 1 .042 1 0.8261 1 .06 19 0.9223 0.9498 1 02 Appendix 11 C e l l Means, Variance, and Standard Deviation for MAJOR 1 03 C e l l Means, Variance, and Standard D e v i a t i o n f o r MAJOR OBSERVED CELL MEANS 1 2 3 4 5 6 CLAR TPT PIANO VIOLIN XYLO SYNTH 1 15 -0. .353136 -0. 399545 -0. 016087 -0. 557783 -0. •109476 -O. 188768 2 18 -0, .478090 -o. 522879 -0. 175050 -0. .586022 -0. .596281 -0. 502687 3 73 0. .252929 0. 183662 0. 449624 0. .273159 0. 368608 0. 316087 4 39 0. 051041 -0. 031357 0. 267674 -0. 09540O 0. . 300601 -0. 142131 5 73 -0. .190509 -0. 363950 0. 138231 -0. 285756 -0. , 155613 -O. 134370 TOTAL N= 218 VARIABLE VARIANCE (ERROR MEAN SOUARES) 1 CLAR 0.877934 2 TPT 1.095814 3 PIANO 0.717905 4 VIOLIN 1.150263 5 XYLO 0.819196 6 SYNTH 0.952603 STANDARD DEVIATION 0.9370 1 .0468 0.8473 1 .0725 0.9051 0.9760 

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