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Absolute pitch and the perception of sequential musical intervals McGeough, Carol Sigrid Westdal 1987

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ABSOLUTE PITCH AND THE PERCEPTION OF SEQUENTIAL MUSICAL INTERVALS by CAROL SIGRID WESTDAL MCGEOUGH B. Mus., 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 FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES SCHOOL OF AUDIOLOGY AND SPEECH SCIENCES We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September 1987 © C a r o l S i g r i d Westdal McGeough, 1987 4 6 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of AuDlOLO^V / W D Sp f£ (£ CH S c i E N C £ £ The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 D a t e Qcro f3£f? to. )°)%lr-i i ABSTRACT The p e r c e p t i o n of musical i n t e r v a l s by musicians can be en-visaged as being accomplished i n one of two ways. Most musicians appear to have on l y one method f o r i d e n t i f y i n g musical i n t e r v a l s : they d i r e c t l y e v a l u a t e the musical i n t e r v a l between two notes. Musicians with a b s o l u t e p i t c h (AP) appear to have two methods a v a i l a b l e f o r i d e n t i f y i n g i n t e r v a l s : they can e i t h e r d i r e c t l y e v a l u a t e the musical i n t e r v a l , or they can f i r s t i d e n t i f y the two p i t c h e s , and then i n f e r the musical i n t e r v a l between them. T h i s study i n v e s t i g a t e d the p e r c e p t i o n of s e q u e n t i a l musical i n t e r v a l s by two groups of musicians, one group with AP and the other with-out AP. In the f i r s t of four experiments, most s u b j e c t s i n both groups were ab l e to name a c c u r a t e l y standard s e q u e n t i a l musical i n t e r v a l s based on the equal-tempered s c a l e . In the second experiment, most s u b j e c t s i n the AP group were able a c c u r a t e l y and c o n s i s t e n t l y to name notes of the equal-tempered s c a l e , whereas s u b j e c t s without AP were not able to name them c o n s i s t e n t l y or a c c u r a t e l y . In the t h i r d experiment, s u b j e c t s with AP i d e n t i f i e d , with v a r y i n g degrees of accuracy and c o n s i s t e n c y , s i n g l e notes spaced i n 20-cent increments over a 9.4 semitone range, u s i n g the standard musical note names. T h i s experiment a l s o demonstrated t h a t not a l l s u b j e c t s had the same i n t e r n a l p i t c h r e f e r e n c e . In the f i n a l and major experiment, s u b j e c t s i d e n t i f i e d s e q u e n t i a l musical i n t e r v a l s r anging i n 20-cent steps from 260 to 540 ce n t s , u s i n g the standard musical i n t e r v a l names. Su b j e c t s , both with and without AP, appeared to i d e n t i f y the i n t e r v a l s by d i r e c t l y e v a l u a t i n g the musical i n t e r v a l between the two notes, r a t h e r than f i r s t i d e n t i f y i n g the two p i t c h e s and then i n f e r r i n g the musical i n t e r v a l . One s u b j e c t i n the AP group showed a s t r o n g tendency to use the l a t t e r method, but o n l y i n c e r t a i n c o n t e x t s , the reason f o r which remains unexplained. Although more r e s e a r c h i s needed f o r s t r o n g e r c o n c l u s i o n s to be drawn, i t appears t h a t most musicians with AP do not use t h i s a b i l i t y i n the i d e n t i f i c a t i o n of s e q u e n t i a l musical i n t e r v a l s , r e l y i n g i n s t e a d on t h e i r sense of r e l a t i v e p i t c h . i v TABLE OF CONTENTS Page ABSTRACT 1 i TABLE OF CONTENTS i v LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENT v i i i Chapter 1 INTRODUCTION. . 1 Chapter 2 REVIEW OF THE LITERATURE 4 2.1 I n t r o d u c t i o n 4 2.2 Absolute P i t c h 4 2.3 S t r a t e g i e s f o r naming notes and i n t e r v a l s 14 2.4 Tuning Systems 22 Chapter 3 AIMS OF THE EXPERIMENT 28 Chapter 4 MATERIALS AND METHODS 30 4.1 P r e p a r a t i o n of the S t i m u l i 30 4.2 P r e p a r a t i o n of Te s t Tapes 31 4.21 Tape f o r Te s t 1 32 4.22 Tape f o r Te s t 2 35 4.23 Tape f o r Test 3 37 4.24 Tape f o r Te s t 4 39 4.3 Subjec t s 42 4.4 Te s t Procedure 46 V Chapter 5 RESULTS AND DISCUSSION 48 5.1 Data S o r t i n g 48 5.2 Test 1. 48 5.3 Test 2 49 5.4 Test 3 51 5.5 Tes t 4 54 5.6 Summary 67 SELECTED BIBLIOGRAPHY 70 APPENDIX A - Q u e s t i o n n a i r e 73 APPENDIX B - I n s t r u c t i o n s 74 APPENDIX C - Sample Answer Sheets 76 v i LIST OF TABLES Table Page I. Comparison of the major t h e o r e t i c a l systems of temperament 24 I I . Stimulus types f o r T e s t 1 34 I I I . Number of tokens by s t i m u l u s type f o r T e s t 2 36 IV. Stimulus types f o r T e s t 3 38 V. Stimulus types f o r T e s t 4 41 VI. Example Te s t 3 data ( S I ) , showing standard d e v i a t i o n s and mean of standard d e v i a t i o n s 53 V I I . Scores f o r a l l s u b j e c t s on T e s t 1, Test 2, and Test 3...55 V I I I . P r e d i c t i o n m a t r i c e s f o r T e s t 4 57 IX. T e s t 4 r e s u l t s , showing d i s t a n c e s Dl and D2 to RP and AP s t r a t e g i e s 60 X. Examples of d i s t a n c e s to RP and AP i n r e l a t i o n to the number of e n t r i e s d i f f e r i n g from each p r e d i c t i o n matrix 63 v i i LIST OF FIGURES F i g u r e Page 1. T e s t 3 d a t a , SI 52 2. D i s t a n c e s D2 to RP and AP 66 v i i i ACKNOWLEDGEMENT Sin c e r e thanks to Dr. Andre- P i e r r e Benguerel f o r h i s guidance through a l l phases of the p r o j e c t ; to Dr. Don Greenwood f o r h i s h e l p f u l comments; to my s u b j e c t s f o r t h e i r k i nd c o o p e r a t i o n ; and to my husband, Marty, my f a m i l y , and Teresa and L i s a f o r t h e i r support and encouragement. 1 CHAPTER 1 INTRODUCTION P i t c h i s the s u b j e c t i v e c o r r e l a t e of the p h y s i c a l parameter of frequency. I t p l a y s a c e n t r a l r o l e i n music, along with rhythm, timbre, and loudness. Because p i t c h i s a major aspect of music, musicians work hard a t l e a r n i n g to re c o g n i z e p i t c h r e l a t i o n s h i p s . Most musicians develop r e l a t i v e p i t c h , the a b i l i t y to i d e n t i f y a s p e c i f i c tone by i t s musical name when compared to a giv e n r e f e r e n c e tone, or the a b i l i t y to i d e n t i f y the m u s i c a l i n t e r v a l s e p a r a t i n g two p i t c h e s without a r e f e r e n c e tone. Only a s m a l l percentage of musicians possess a b s o l u t e p i t c h , the a b i l i t y to i d e n t i f y a s p e c i f i c tone by name without comparing i t to a r e f e r e n c e tone. Most people who are not m u s i c a l l y t r a i n e d are unable to i d e n t i f y musical i n t e r v a l s or notes with any degree of accurac y or c o n s i s t e n c y , Musicians without a b s o l u t e p i t c h have o n l y one s t r a t e g y a v a i l a b l e f o r i d e n t i f y i n g musical i n t e r v a l s : the l i s t e n e r d i r e c t l y e v a l u a t e s the musi c a l i n t e r v a l between the two notes. Musicians with a b s o l u t e p i t c h , on the other hand, can use two s t r a t e g i e s i n the i d e n t i f i c a t i o n of musical i n t e r v a l s . In one s t r a t e g y , l i k e musicians without a b s o l u t e p i t c h , the l i s t e n e r d i r e c t l y e v a l u a t e s the musical i n t e r v a l between the two notes without f i r s t l a b e l l i n g them ( " r e l a t i v e p i t c h s t r a t e g y " ) ; i n the other s t r a t e g y , the l i s t e n e r f i r s t i d e n t i f i e s the i n d i v i d u a l notes, and then i n f e r s the musical i n t e r v a l s e p a r a t i n g them ("absolute p i t c h s t r a t e g y " ) . Musicians with a b s o l u t e p i t c h have 2 been observed to use the former s t r a t e g y i n s i t u a t i o n s where two notes c o n s t i t u t i n g a s e q u e n t i a l musical i n t e r v a l are c l o s e together i n time ( l e s s than one minute s i l e n c e between the notes) and are both c a t e g o r i z e d with the same musical note name (e.g. D + 20 cents and D - 20 cents are c l o s e s t to the note D, and would both be c a t e g o r i z e d as D by a musician with a b s o l u t e p i t c h and standard r e f e r e n c e ) . Musicians with a b s o l u t e p i t c h have been observed to use the l a t t e r s t r a t e g y i n s i t u a t i o n s where the two notes are f a r a p a r t i n time (at l e a s t one minute s i l e n c e between the notes) and both c a t e g o r i z e d with d i f f e r e n t note names ( i . e . the two notes are each c l o s e s t to a d i f f e r e n t n o t e ) . I t would be of i n t e r e s t to i n v e s t i g a t e which of these two s t r a t e g i e s possessors of a b s o l u t e p i t c h use when the two notes of the musical i n t e r v a l are r e l a t i v e l y c l o s e together i n time (two seconds between the n o t e s ) , but would be l a b e l l e d with d i f f e r e n t m usical note names. I f the notes c o n s t i t u t i n g the i n t e r v a l s d i d not correspond with the notes of the standard equal-tempered s c a l e , i n c o r r e c t i d e n t i f i c a t i o n of some i n t e r v a l s c o u l d be expected with the a b s o l u t e p i t c h s t r a t e g y , caused by compounding of the two s u c c e s s i v e rounding e r r o r s inherent i n t h i s s t r a t e g y . With the r e l a t i v e p i t c h s t r a t e g y , o n l y one e v a l u a t i o n i s necessary f o r the i d e n t i f i c a t i o n of a musical i n t e r v a l : the p i t c h d i f f e r e n c e between the two notes i s rounded up or down to correspond with the c l o s e s t i n t e r v a l . On the other hand, three e v a l u a t i o n s are necessary f o r the i d e n t i f i c a t i o n of a musical i n t e r v a l with the a b s o l u t e p i t c h s t r a t e g y : f i r s t , each tone i s rounded up or down to the c l o s e s t note, and then the i n t e r v a l i s i n f e r r e d from these notes. By rounding two components i n s t e a d of 3 one, e r r o r s can be compounded i n some s i t u a t i o n s , r e s u l t i n g i n i n c o r r e c t i d e n t i f i c a t i o n . For example, with the r e l a t i v e p i t c h s t r a t e g y , the two notes C# + 40 cents and F - 40 cents would be c a t e g o r i z e d as a minor t h i r d (300 c e n t s ) , the i n t e r v a l c l o s e s t to the 320-cent p i t c h d i f f e r e n c e between them. With the a b s o l u t e p i t c h s t r a t e g y , however, C# + 40 cents would be l a b e l l e d as Ctt, and F - 40 cents would be l a b e l l e d as F, and the i n f e r r e d musical i n t e r v a l between the two notes would be a major t h i r d (400 c e n t s ) . 4 CHAPTER 2 REVIEW OF THE LITERATURE 2 .1 I n t r o d u c t i o n A number of r e s e a r c h areas are i n v o l v e d i n the study of ab s o l u t e p i t c h and the p e r c e p t i o n of s e q u e n t i a l musical i n t e r v a l s . S e c t i o n 2.2 reviews d e f i n i t i o n s of a b s o l u t e p i t c h and d e s c r i b e s r e s e a r c h i n t o the p i t c h p e r c e p t i o n a b i l i t i e s of possessors of a b s o l u t e p i t c h . S e c t i o n 2.3 d i s c u s s e s t h e o r i e s of p i t c h coding i n a b s o l u t e p i t c h p o s s e s s o r s , and d e s c r i b e s r e s e a r c h p e r t a i n i n g to p e r c e p t i o n of musical i n t e r v a l s by possessors and nonpossessors of a b s o l u t e p i t c h . S e c t i o n 2.4 d e s c r i b e s the main tu n i n g systems of Western music, and p o s s i b l e e f f e c t s of t u n i n g systems on musical i n t e r v a l judgment. 2.2 Absolute P i t c h Absolute p i t c h i s u s u a l l y d e f i n e d as the a b i l i t y to i d e n t i f y a s p e c i f i c tone by frequency or musical name, or the a b i l i t y to a d j u s t the frequency of a v a r i a b l e tone to some de s i g n a t e d frequency, without comparing the tone to any o b j e c t i v e r e f e r e n c e tone. The ac c u r a c y and c o n s i s t e n c y of p i t c h r e c o g n i z i n g a b i l i t y necessary f o r a b s o l u t e p i t c h i s a matter of c o n t e n t i o n , however. Seashore (1938) s t a t e s t h a t a b s o l u t e p i t c h v a r i e s through degrees from the a b i l i t y to name a piano note without r e f e r e n c e 5 to any other note, to the a b i l i t y to t e l l when an instrument i s tuned " l / 1 0 t h v i b r a t i o n " too high. He r e p o r t s t h a t the a b i l i t y to name s i n g l e notes on a f a m i l i a r instrument i s q u i t e common among t r a i n e d musicians, l i k e l y due to the timbre of the instrument. He a l s o s t a t e s t h a t a b s o l u t e p i t c h can a t t a c h i t s e l f to a p a r t i c u l a r note, and other notes may be i d e n t i f i e d with r e f e r e n c e to t h i s i n t e r n a l s t andard. Bachem (1955) d e f i n e s a b s o l u t e p i t c h as the a b i l i t y to r e c o g n i z e and d e f i n e the p i t c h of a tone without.the use of a r e f e r e n c e tone. T h i s r e c o g n i t i o n and d e f i n i t i o n of p i t c h e s i s f a s t , d e f i n i t e , a c c u r a t e to tones and semitones, a c c u r a t e over at l e a s t a l i m i t e d range i f not the whole musical range, and may be s t r o n g l y i n c l i n e d to octave e r r o r s . Bachem a l s o d e s c r i b e s what he l a b e l s "pseudo-absolute p i t c h " and " q u a s i - a b s o l u t e p i t c h " . Pseudo-absolute p i t c h i s simply e s t i m a t i o n of p i t c h e s based on how high or low they sound, with an average e r r o r of f i v e to nine semitones. Although t h i s e r r o r can be narrowed through p r a c t i c e , the p i t c h e s t i m a t i o n i s s t i l l poor. Singers who compare the p i t c h of a tone to the l i m i t s of t h e i r v o c a l range, or v i o l i n i s t s who compare p i t c h e s with a remembered A440 are s a i d by Bachem to have q u a s i - a b s o l u t e p i t c h . The comparison i s r e l a t i v e l y slow and the p i t c h e s t i m a t i o n i s agai n poor. Pseudo and q u a s i - a b s o l u t e p i t c h are t h e r e f o r e based on the height of the tones and on l y a b s o l u t e p i t c h i t s e l f i s based on chroma or the s u b j e c t i v e " c o l o r " of p i t c h e s . Absolute p i t c h , a c c o r d i n g to Brady (1970), i s a term a p p l i e d to the a b i l i t y of c e r t a i n people to r e c o g n i z e musical notes and i d e n t i f y them by name, or to s i n g any d e s i r e d note. Brady a l s o 6 b e l i e v e s t h a t people with a b s o l u t e p i t c h perform with d i f f e r e n t l e v e l s of acc u r a c y : some remembering a few notes and r e c o n s t r u c t i n g s c a l e s ; and others having memorized a l l notes. In h i s o p i n i o n , the g e n e r a l p o p u l a t i o n appears to be d i v i d e d between those who can i d e n t i f y randomly presented tones with accuracy f a r beyond chance, and those with no f a c i l i t y a t t h i s at a l l . Davies' (1978) view of a b s o l u t e p i t c h i s that i t i s present i n v a r y i n g degrees among p o s s e s s o r s . In i t s extreme form, a b s o l u t e p i t c h i s the a b i l i t y to name i n s t a n t l y any note played, while i n more moderate cases the possessor can i d e n t i f y the key i n which a pie c e of music i s play e d . Spender, i n The New Groves D i c t i o n a r y of Music and Musicians (1980), d e f i n e s a b s o l u t e p i t c h as the a b i l i t y to name the p i t c h of a note without r e f e r e n c e to any p r e v i o u s l y sounded note ( r e c o g n i t i o n ) , or to s i n g a named note without r e f e r e n c e to a p r e v i o u s l y sounded note ( r e c a l l ) , with r e c o g n i t i o n being e a s i e r than r e c a l l . A c c o r d i n g to Spender, no time i s needed to r e l a t e the p i t c h to some sta n d a r d : f o r those with a b s o l u t e p i t c h , r e c o g n i t i o n i s instantaneous. Absolute p i t c h i s d i s t i n g u i s h e d from "absolute t o n a l i t y " , the a b i l i t y to name the key of a chord or harmonic passage without p r e v i o u s l y heard r e f e r e n c e notes. With t h i s a b i l i t y , d i f f e r e n t keys are s a i d to have " d i s t i n c t i v e c o l o u r s or f l a v o u r s " (not the same f o r d i f f e r e n t a b s o l u t e t o n a l i t y p ossessors) t h a t are i n s t a n t l y r e c o g n i z e d . As r e p o r t e d by Spender, Teplov (1966) c l a s s i f i e d a b s o l u t e t o n a l i t y as a sub-stage of a b s o l u t e p i t c h s i n c e a l l those with a b s o l u t e p i t c h would n e c e s s a r i l y have a b s o l u t e t o n a l i t y , but not v i c e v e r s a . 7 According to Spender, average e r r o r i n the task of naming notes or chords should be l e s s than a semitone. In Deutsch (1982), Ward and Burns d e f i n e a b s o l u t e p i t c h as the a b i l i t y to a t t a c h l a b e l s to i s o l a t e d a u d i t o r y s t i m u l i on the b a s i s of p i t c h a l o n e . In Ward's o p i n i o n (1963b), a b s o l u t e p i t c h a b i l i t i e s are on a continuum. Four methods of a s s e s s i n g a b s o l u t e p i t c h have been commonly used i n r e p o r t e d r e s e a r c h . These a r e : musical c a t e g o r i z a t i o n , method of constant s t i m u l i , method of adjustment, and non-musical c a t e g o r i z a t i o n . In experiments u s i n g musical c a t e g o r i z a t i o n , s u b j e c t s are presented with s e r i e s of musical tones which they are asked to i d e n t i f y . The c r u d e s t measure of performance i s the number of tones c o r r e c t l y i d e n t i f i e d . R e s u l t s of musical c a t e g o r i z a t i o n experiments show t h a t many i n d i v i d u a l s with a b s o l u t e p i t c h can c o r r e c t l y i d e n t i f y the notes over the middle 3/4 of the piano. Weinert (1929; c i t e d by Ward and Burns, 1982) presented 85 piano tones from AO to A7 presented i n random order to 22 s u b j e c t s with a b s o l u t e p i t c h on f i v e separate o c c a s i o n s . Percentage e r r o r , i n c l u d i n g octave e r r o r s , ranged from 5.2 to 75% with a median of 25%. Bachem (1937), u s i n g the same method as Weinert with 90 s u b j e c t s p o s s e s s i n g a b s o l u t e p i t c h found seven s u b j e c t s who he d e s c r i b e d as " i n f a l l i b l e " . I t was not c l e a r i n h i s d e s c r i p t i o n , however, whether or not he i n c l u d e d octave and/or semitone e r r o r s . 65 p r o f e s s i o n a l musicians with a b s o l u t e p i t c h were t e s t e d by Wellek (1938; c i t e d by Ward and Burns, 1982) u s i n g Weinert's paradigm, and none were i n f a l l i b l e . 8 Oakes (1955) i n v e s t i g a t e d p i t c h naming and p i t c h d i s c r i m i n a t i o n a b i l i t i e s i n 88 s u b j e c t s . In the p i t c h naming task, 75 recorded piano tones were presented to four groups of students who were asked to g i v e the p i t c h name and octave of each note. The four groups of s u b j e c t s were: music students with a b s o l u t e p i t c h ; music students without a b s o l u t e p i t c h ; a r t s students with some musi c a l t r a i n i n g ; and a r t s students with no musical t r a i n i n g . Oakes found t h a t the d i s t r i b u t i o n of performance on the p i t c h naming t e s t was on a continuum, with a c o r r e l a t i o n f a c t o r of .64 between months of musical t r a i n i n g , and p i t c h naming and d i s c r i m i n a t i o n a b i l i t y . A f t e r c o n s i d e r a b l e s e l f - t r a i n i n g to develop a b s o l u t e p i t c h , Brady (1970) had h i s wife p l a y a random computer-selected note on piano each day as he awakened f o r 57 c o n s e c u t i v e days. Brady's task was to name the note by chroma (note-name) only, d i s r e g a r d i n g the tone-height ( o c t a v e ) . His naming d i s t r i b u t i o n was 65% c o r r e c t , 31.5% semitone e r r o r , and 3.5% wholetone e r r o r . Brady c l a s s i f i e s t h i s as " n e a r - p e r f e c t semitone d i s c r i m i n a t i o n " . Using the method of constant s t i m u l i , names of musical notes are s t i l l used to i d e n t i f y p i t c h e s , but i n t h i s case the s e r i e s of s t i m u l i i s c l o s e l y spaced around a note, and the s u b j e c t judges whether the s t i m u l u s i s too h i g h , too low, or on p i t c h . T h i s experimental method g i v e s a more ac c u r a t e p i c t u r e of the p i t c h judgment a b i l i t i e s of a b s o l u t e p i t c h s u b j e c t s . Abraham (1901; c i t e d by Ward and Burns, 1982) used as s t i m u l i a s e r i e s of f r e q u e n c i e s i n 2-Hz s t e p s , each presented 24 times. His task as s u b j e c t was to decide whether the note 9 presented was too high, too low, or on p i t c h f o r a s p e c i f i c m u s i c a l note. Abraham c o u l d i d e n t i f y 1/4 semitone with 75% accuracy, and 1/2 semitone with 95% accuracy. Van K r e v e l e n (1951) s t u d i e d a b s o l u t e p i t c h i n 17 students who had c o r r e c t l y i d e n t i f i e d o s c i l l a t o r tones c o r r e s p o n d i n g to the 48 notes i n the middle 4 octaves of the piano. They were presented with tones from 404 to 478 Hz i n 2-Hz steps and were asked to respond with "too h i g h " , "too low", or "on p i t c h " r e l a t i v e to G#4, A4, or AS4. The standard d e v i a t i o n of the average s u b j e c t ' s judgments was 6.4 Hz f o r A4 and s l i g h t l y higher f o r the other two p i t c h e s , or an average e r r o r of approximately 30 c e n t s . E x t r a p o l a t i n g on t h i s i n f o r m a t i o n , Ward (1963) computed t h a t f o r a 9 5% c o r r e c t judgment, the s t i m u l i would have to be separated by a semitone. However, van Krevelen's best s u b j e c t performed at about the same l e v e l as Abraham, or 95% a c c u r a c y f o r q u a r t e r tones. S i e g e l (1972) asked 10 a b s o l u t e p i t c h s u b j e c t s and 10 c o n t r o l s u b j e c t s whether a s t i m u l u s tone was too high or too low to correspond to a p a r t i c u l a r note of the equal-tempered s c a l e . A m o d i f i e d s t a i r c a s e method was used, whereby the s t i m u l u s changed i n response to the s u b j e c t ' s previous response, as f o l l o w s : i f the s u b j e c t i n d i c a t e d t h a t the s t i m u l u s was too low, the f o l l o w i n g s t i m u l u s would be a constant amount higher, and v i c e v e r s a . In t h i s way, the s u b j e c t would bracket h i s p i t c h "standard" f o r that p a r t i c u l a r note. R e s u l t s i n d i c a t e d that a b s o l u t e p i t c h and c o n t r o l s u b j e c t s d i f f e r e d s i g n i f i c a n t l y i n v a r i a b i l i t y of t h e i r judgments (p <.01), but not i n accuracy of judgments (p >.05). S i e g e l i n t e r p r e t e d t h i s to i n d i c a t e " t h a t 10 v a r i a b i l i t y , r a t h e r than a c c u r a c y of p r o d u c t i o n i s a good i n d i c a t o r of a b s o l u t e p i t c h . " ( S i e g e l , 1972, p. 84) She a l s o s t a t e s , A pparently, a b s o l u t e p i t c h s u b j e c t s ' mapping of musical notes onto the p i t c h continuum may d i f f e r c o n s i d e r a b l y from t h a t of the well-tempered s c a l e . . . . Because of such i d i o s y n c r a t i c d i f f e r e n c e s . . . , a c c u r a c y of p i t c h p r o d u c t i o n i s not a very good measure of AP [ a b s o l u t e p i t c h ] a b i l i t y . ( S i e g e l , 1972, pp. 84-85) With the method of adjustment, the s u b j e c t must s e t an instrument to a c e r t a i n p i t c h . Experiments of t h i s k i n d r e v e a l how a c c u r a t e l y a s u b j e c t with a b s o l u t e p i t c h can produce a d e s i r e d note. In some s t u d i e s , the s u b j e c t i s allowed to bracket, i n which case he can search f o r h i s " i n d i f f e r e n c e p o i n t " and s e t the c o n t r o l somewhere between too high and too low. In other s t u d i e s , b r a c k e t i n g i s not a l l o w e d . In Petran's (1932) experiment, s u b j e c t s with a b s o l u t e p i t c h were r e q u i r e d to s e t a t o n v a r i a t o r to A4 without b r a c k e t i n g . Petran found t h a t once they entered a "zone of u n c e r t a i n t y " , they tended to s t o p . Although the best s u b j e c t showed o n l y a 1/4-tone d i f f e r e n c e between ascending and descending judgments f o r a given note, the average d i f f e r e n c e f o r a g i v e n s u b j e c t was about two semitones. Van Krevelen's (1951) 17 s u b j e c t s were asked to a d j u s t , u s i n g b r a c k e t i n g , an o s c i l l a t o r 100 times to 3 t a r g e t tones: GS, A, and AS. The r e s u l t s of t h i s t e s t 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 the "too h i g h " , "too low" judgments i n her experiment u s i n g the method of constant s t i m u l i : e r r o r s were i n the range of 30 cents f o r the adjustment of notes. 11 Bramraer (1951) r e q u i r e d 42 randomly-chosen v i o l i n i s t s to a) d i r e c t an experimenter i n t u n i n g the A s t r i n g of a v i o l i n , b) tune the A s t r i n g themselves, and c) d i r e c t an experimenter i n t u n i n g the c l a r i n e t ; each of these 5 times. The 17 s u b j e c t s c l a i m i n g a b s o l u t e p i t c h d i d b e t t e r on average than the r e s t , but there was o v e r l a p between those c l a i m i n g a b s o l u t e p i t c h and those not c l a i m i n g a b s o l u t e p i t c h . V a r i a b i l i t y on the c l a r i n e t was s i g n i f i c a n t l y higher than on the v i o l i n . U n f o r t u n a t e l y , Brammer d i d not r e p o r t any d e t a i l s on the v a r i a b i l i t y of i n d i v i d u a l s u b j e c t s . I f s u b j e c t s are m u s i c a l l y u n t r a i n e d , a r b i t r a r y s t i m u l u s and response c a t e g o r i e s , or nonmusical c a t e g o r i z a t i o n , i s an a p p r o p r i a t e method of t e s t i n g a b s o l u t e p i t c h . With musical s u b j e c t s , t h i s method avoids the ambiguity of black notes, e.g. the d i f f e r e n c e between the concept of G# and Ab, and a l s o avoids the d i f f e r e n c e s i n i n f e r r e d t u n i n g of the s u b j e c t i v e musical s c a l e (Ward, 1963b). P o l l a c k (1952) was the f i r s t to a p p l y i n f o r m a t i o n theory techniques to p i t c h . The i n f o r m a t i o n i n a s i g n a l i s given by the l o g to the base 2 of the number of a l t e r n a t i v e s from which i t might have been s e l e c t e d . I f the l i s t e n e r always i d e n t i f i e s the s i g n a l c o r r e c t l y , then the i n f o r m a t i o n t r a n s m i t t e d i s equal to that of the s i g n a l . The more e r r o r s t h a t are made, the lower the amount of i n f o r m a t i o n t h a t was t r a n s m i t t e d . The p o s s i b l e s t i m u l i are d e f i n e d to the l i s t e n e r , then presented each an equal number of times f o r the s u b j e c t to attempt to i d e n t i f y . The responses are t a b u l a t e d , and i n f o r m a t i o n t r a n s m i t t e d ( I r ) can be c a l c u l a t e d . By r a i s i n g 2 to the power I r , an estimate of the 12 number of stim u l u s c a t e g o r i e s t h a t should have been used i n order to have p e r f e c t i d e n t i f i c a t i o n can be made. P o l l a c k presented m u s i c a l l y u n t r a i n e d s u b j e c t s with tones between 100 and 8000 Hz. He found t h a t no naive l i s t e n e r s c o u l d exceed Ir=2.7 b i t s , or seven tones, no matter how many tones were presented, and t h a t most s u b j e c t s c o u l d d i s c r i m i n a t e a maximum of f i v e tones. Ward (1953) used P o l l a c k ' s procedure, but with a s u b j e c t p o s s e s s i n g well-developed a b s o l u t e p i t c h . The s u b j e c t was presented with 10 pure tones and c o u l d w r i t e down whatever she wanted to i n order to remember each p i t c h . In succeeding t r i a l s , d i s t a n c e between s t i m u l i was manipulated. Over 6 b i t s of i n f o r m a t i o n were t r a n s f e r r e d v i a p i t c h , t h a t i s , over 70 d i f f e r e n t f r e q u e n c i e s i n the 50 to 4500 Hz range c o u l d be i d e n t i f i e d 10 out of 10 times. Maximum i n f o r m a t i o n t r a n s f e r was reached when the s t i m u l i were one semitone a p a r t : no e r r o r s were made, i n c l u d i n g octave e r r o r s , i f s t i m u l i were separated by i n t e r v a l s of one semitone or more. Ten adj a c e n t 1/4-tones as s t i m u l i r e s u l t e d i n o c c a s i o n a l e r r o r s of +/- one ca t e g o r y (80% c o r r e c t ) . At the extremes of the musi c a l range, i n f o r m a t i o n t r a n s f e r dropped. Contro v e r s y remains r e g a r d i n g what c o n s t i t u t e the best s t i m u l i f o r i n v e s t i g a t i o n s of a b s o l u t e p i t c h . B a i r d (1917), t e s t i n g f o r a b s o l u t e p i t c h with piano, organ, t u n i n g f o r k , f l u t e , c l a r i n e t and sung p i t c h e s , found t h a t performance was best on the piano, even though more a l t e r n a t i v e s were gi v e n on t h i s instrument. Seashore (1919) claimed that piano notes should be 13 used as s t i m u l i on t e s t s i n v e s t i g a t i n g a b s o l u t e p i t c h , because musicians are most f a m i l i a r with them. Sergeant (1969) proposed t h a t s t i m u l i f o r i d e n t i f i c a t i o n should be presented on a v a r i e t y of instruments, s i n c e d i f f e r e n t s u b j e c t s are exposed to d i f f e r e n t instruments as c h i l d r e n and may have more a b i l i t y a t p i t c h naming on the instrument they f i r s t p l a y e d . Ward and Burns ( i n Deutsch, 1982) suggest t h a t piano tones are the e a s i e s t of a l l instruments to i d e n t i f y because of extraneous cues. However, depending on the f o r c e with which the piano key i s s t r u c k , the r e l a t i v e i n t e n s i t i e s of the p a r t i a l s may change, making i t u n c l e a r what r o l e p i t c h p l a y s i n the i d e n t i f i c a t i o n of piano tones. Ward (1963a) proposed t h a t i f one i s i n t e r e s t e d i n the a b i l i t y to c l a s s i f y a u d i t o r y events on the b a s i s of p i t c h alone, pure tones should be used as s t i m u l i . Since octave e r r o r s may be the r e s u l t of harmonic s t r u c t u r e , they should be very s m a l l with pure tones. From the l i t e r a t u r e on a b s o l u t e p i t c h , i t appears t h a t there i s g e n e r a l agreement among authors t h a t a b s o l u t e p i t c h i s the a b i l i t y to name the p i t c h of a note without r e f e r e n c e to any p r e v i o u s l y sounded note. There i s , however, disagreement as to whether : (a) s t i m u l i presented should be tones played on a f a m i l i a r instrument or pure tones; (b) r e c o g n i t i o n / p r o d u c t i o n should be i n s t a n t or compared to one (or more) memorized r e f e r e n c e n o t e ( s ) ; (c) a b s o l u t e p i t c h i s r e s t r i c t e d to the a b i l i t y to name notes or whether the a b i l i t y to determine the key 14 of a piece of music should be c l a s s i f i e d as a b s o l u t e p i t c h ; (d) accuracy f o r semitones should be near 100% or " f a r beyond chance". 2•3 S t r a t e g i e s f o r naming notes and i n t e r v a l s The equal-tempered s c a l e d i v i d e s each octave i n t o twelve l o g a r i t h m i c a l l y equal s t e p s , so t h a t the musical i n t e r v a l of a semitone, a frequency r a t i o of 1.0595:1 separates a d j a c e n t notes from one another. Only a few musicians, those with absolute pitch, l e a r n to i d e n t i f y the frequency of a s i n g l e tone presented i n i s o l a t i o n . Because melodies may be transposed i n t o a d i f f e r e n t key, i t i s the relationship of the notes t h a t i s important i n our system. Thus most musicians a c q u i r e r e l a t i v e p i t c h , the a b i l i t y to i d e n t i f y the frequency r a t i o of two notes on an a b s o l u t e b a s i s . Each of the standard i n t e r v a l s i s a s s i g n e d a name, such as unison, tritone, major third, or octave, and "ear t r a i n i n g " c o n s i s t s a t l e a s t i n p a r t of l e a r n i n g to i d e n t i f y the standard i n t e r v a l s . ( S i e g e l and S i e g e l , 1977b, p. 400) Because they are able to a c c u r a t e l y a s s i g n musical note names to f r e q u e n c i e s , i t appears t h a t s u b j e c t s with a b s o l u t e p i t c h have at t h e i r d i s p o s a l two methods of l a b e l l i n g musical i n t e r v a l s . In one case, they may be a b l e to compare the two f r e q u e n c i e s on the b a s i s of t h e i r a b s o l u t e d i f f e r e n c e without f i r s t l a b e l l i n g the i n d i v i d u a l tones, and i n the other case, they may f i r s t l a b e l the i n d i v i d u a l tones and subsequently c a l c u l a t e the i n t e r v a l l i c r e l a t i o n s h i p of the tones. Research by Bachem, and S i e g e l and S i e g e l has shown t h a t possessors of a b s o l u t e p i t c h use both of these s t r a t e g i e s . 1 5 In a frequency d i s c r i m i n a t i o n experiment, Bachem ( 1 9 5 4 ) compared the performance of ten a b s o l u t e p i t c h s u b j e c t s and ten s u b j e c t s with musical t r a i n i n g but without a b s o l u t e p i t c h . A standard tone was f o l l o w e d by a comparison tone with a s i l e n t p e r i o d of from one second to one week between the two tones, and s u b j e c t s were asked to i n d i c a t e whether the tones were the same or d i f f e r e n t . For each l e n g t h of s i l e n c e , Bachem determined the frequency d i f f e r e n c e necessary f o r s u b j e c t s to maintain a t h r e s h o l d l e v e l of performance, t h a t i s , f o r the s u b j e c t ' s judgments to be c o r r e c t 75% of the time. For s i l e n t p e r i o d s of l e s s than one minute, a b s o l u t e p i t c h and c o n t r o l s u b j e c t s had approximately the same t h r e s h o l d . At s i l e n t p e r i o d s g r e a t e r than one minute, the t h r e s h o l d f o r the a b s o l u t e p i t c h s u b j e c t s remained comparable to what i t had been a t one minute, whereas the t h r e s h o l d s of the c o n t r o l s u b j e c t s continued to i n c r e a s e as the s i l e n t p e r i o d between the two tones i n c r e a s e d . Bachem a t t r i b u t e d these d i f f e r e n c e s to the e x i s t e n c e of two mechanisms f o r p i t c h d i s c r i m i n a t i o n . The normal s u b j e c t simply compares tone h e i g h t s f o r i d e n t i t y or d i f f e r e n c e s over the whole time s c a l e . The s u b j e c t with a b s o l u t e p i t c h a l s o compares tone h e i g h t s w i t h i n the s h o r t time range, but s h i f t s to the chroma comparison as soon as t h i s method secures b e t t e r r e s u l t s , i . e . he makes the detour over the v e r b a l a s s o c i a t i o n with the.chroma, which he i s a b l e to remember with high accuracy. (Bachem, 1 9 5 4 , p. 7 5 3 ) For s i l e n t p e r i o d s of l e s s than one minute, t h r e s h o l d s were a t t a i n e d a t approximately 1 / 2 0 semitone to 1 / 2 semitone. These p i t c h d i f f e r e n c e s would be too s m a l l f o r a b s o l u t e p i t c h s u b j e c t s to use a s t r a t e g y i n which they named the notes f i r s t , f o r both notes would i n most cases be given the same note name. 16 Bachem suggested t h a t when standard and comparison tones were s u f f i c e n t l y f a r a p a r t , a b s o l u t e p i t c h s u b j e c t s coded them i n terms of the note of the musical s c a l e and used these codes to decide i f the notes were the same or d i f f e r e n t on the judgment . task. S i e g e l (1974) proposed t h a t s u b j e c t s with a b s o l u t e p i t c h have two modes f o r p r o c e s s i n g tone frequency: a) "sensory t r a c e mode", which maintains a sensory event i n memory f o r a b r i e f time; and b) " v e r b a l mode", i n which tones are l a b e l l e d with musical names; and that s u b j e c t s without a b s o l u t e p i t c h have on l y the "sensory t r a c e mode" f o r p r o c e s s i n g tone frequency. S i e g e l compared the performance of a b s o l u t e p i t c h and c o n t r o l s u b j e c t s i n judging the i n t e r v a l l i c r e l a t i o n s h i p between two tones separated by e i t h e r 1/10 or 3/4 semitone, with a f i v e -second " r e t e n t i o n i n t e r v a l " between the standard and comparison tones, which was f i l l e d with a l a r g e number of b r i e f t o n a l s t i m u l i . S i e g e l reasoned t h a t i f a b s o l u t e p i t c h s u b j e c t s v e r b a l l y l a b e l l e d s t i m u l i , they should be s u p e r i o r to the c o n t r o l s i n the 3/4 semitone c o n d i t i o n , but have s i m i l a r r e s u l t s i n the 1/10 semitone c o n d i t i o n . Her r e s u l t s confirmed her p r e d i c t i o n s . The p a t t e r n of r e s u l t s . . . corresponds to t h a t p r e d i c t e d by the v e r b a l coding theory of a b s o l u t e p i t c h . A c c o r d i n g to tha t theory, a b s o l u t e p i t c h s u b j e c t s should do b e t t e r than c o n t r o l s i n the 3/4-semitone c o n d i t i o n because they can r e l a t e the s t i m u l i to d i f f e r e n t notes of the s c a l e and s t o r e the a p p r o p r i a t e names i n memory. Such a s t r a t e g y would not be an e f f e c t i v e one i n the 1/10 semitone c o n d i t i o n , s i n c e i t i s h i g h l y l i k e l y t h a t the standard and comparison tones would be as s i g n e d to the same v e r b a l c a t e g o r y . Thus, a b s o l u t e p i t c h s u b j e c t s would s h i f t t h e i r s t r a t e g y to one of remembering the p h y s i c a l c h a r a c t e r i s t i c s of the tones, r a t h e r than v e r b a l l y coding the items on the b a s i s of t h e i r r e l a t i o n to the notes of the s c a l e . ( S i e g e l , 1974, p. 40) 17 When asked to i n d i c a t e t h e i r s t r a t e g y i n the experimental s i t u a t i o n , a l l four of the s u b j e c t s with a b s o l u t e p i t c h who completed the q u e s t i o n n a i r e r e p o r t e d using a " v e r b a l c o d i n g " s t r a t e g y i n the 3/4 semitone c o n d i t i o n and a "sensory coding" s t r a t e g y i n the 1/10 semitone c o n d i t i o n . None of the c o n t r o l s r e p o r t e d having used a " v e r b a l c o d i n g " s t r a t e g y , r a t h e r , they a l l r e p o r t e d u s i n g some form of a "sensory c o d i n g " s t r a t e g y . None of the c o n t r o l s u b j e c t s r e p o r t e d u s i n g d i f f e r e n t s t r a t e g i e s i n the two c o n d i t i o n s . Research i n t o m u s i c a l p e r c e p t i o n has r e v e a l e d t h a t musicians without a b s o l u t e p i t c h p e r c e i v e musical i n t e r v a l s c a t e g o r i c a l l y and t h a t musicians with a b s o l u t e p i t c h p e r c e i v e f r e q u e n c i e s i n the musical range c a t e g o r i c a l l y . S i e g e l and S i e g e l (1977b) s t u d i e d s i x musicians with a good sense of r e l a t i v e p i t c h but without a b s o l u t e p i t c h . Subjects were asked to judge 13 t o n a l i n t e r v a l s i n a magnitude e s t i m a t i o n task and a l a b e l l i n g t a s k . S t i m u l i were spaced i n 20-cent increments over a range of three m u s i c a l i n t e r v a l c a t e g o r i e s : p e r f e c t f o u r t h , t r i t o n e , and p e r f e c t f i f t h . On the l a b e l l i n g task, s u b j e c t s c a t e g o r i z e d the s t i m u l i i n t o r e g u l a r and symmetrical c a t e g o r i e s with l i t t l e o v e r l a p between c a t e g o r i e s . Magnitude e s t i m a t i o n task responses r e v e a l e d three d i s c r e t e steps c o r r e s p o n d i n g to the musical i n t e r v a l s , i n d i c a t i n g t h at s u b j e c t s d i d not d i s c r i m i n a t e between i n t e r v a l s they judged as belonging to the same musical category. On average, s u b j e c t s judged 37% of the i n t e r v a l s as out of tune, while i n r e a l i t y , 77% of the i n t e r v a l s were out of tune by at l e a s t 20 c e n t s . S i e g e l and S i e g e l concluded t h a t "musicians with good r e l a t i v e p i t c h can 18 l a b e l t o n a l i n t e r v a l s a c c u r a t e l y on an a b s o l u t e b a s i s " , that ; "musicians had a s t r o n g tendency to r a t e out-of-tune s t i m u l i as i n tune", and th a t t h e i r "attempts to make f i n e , w i t h i n - c a t e g o r y judgments were h i g h l y i n a c c u r a t e and u n r e l i a b l e . " ( S i e g e l and S i e g e l , 1977b, p. 405) In the f i r s t experiment r e p o r t e d i n t h e i r e a r l i e r paper, S i e g e l and S i e g e l (1977a) had 32 s u b j e c t s with v a r y i n g degrees: of r e l a t i v e p i t c h name 21 d i f f e r e n t t o n a l i n t e r v a l s , ranging over f i v e semitone c a t e g o r i e s , from unison to major t h i r d i n 20-cent s t e p s . Subjects were asked to l a b e l each i n t e r v a l with one of the accepted c a t e g o r y names from unison to major t h i r d . R e s u l t s showed t h a t m u s i c a l l y t r a i n e d s u b j e c t s c o n s i s t e n t l y used a l l f i v e response c a t e g o r i e s , had r e g u l a r , symmetrical naming d i s t r i b u t i o n s , and w e l l - d e f i n e d c a t e g o r y boundaries. M u s i c a l l y naive s u b j e c t s gave i n c o n s i s t e n t responses except f o r the unison category, which can be d i s c r i m i n a t e d from the other c a t e g o r i e s simply by d e t e c t i n g t h a t there i s no d i f f e r e n c e between the two notes i n the i n t e r v a l . S i e g e l and S i e g e l concluded t h a t t h e i r m u s i c a l l y t r a i n e d s u b j e c t s had e s t a b l i s h e d a s e t of a b s o l u t e mnemonic anchors f o r the standard m u s i c a l i n t e r v a l s . In the second experiment r e p o r t e d i n S i e g e l and S i e g e l (1977a), seven s u b j e c t s who possessed a b s o l u t e p i t c h and four non-musicians were asked to i d e n t i f y s i n g l e tone s t i m u l i c o v e r i n g the range from C to E i n 20-cent s t e p s . Subjects were asked to name each note with one of the musical note names C, C#, D, D#, or E. Subjects p o s s e s s i n g a b s o l u t e p i t c h l a b e l l e d the notes a c c u r a t e l y and r e l i a b l y . The performance of the non-musically-19 t r a i n e d s u b j e c t s was r e p o r t e d as extremely i n c o n s i s t e n t on t h i s t a s k . The l a s t two experiments r e p o r t e d i n S i e g e l and S i e g e l (1977a) i n v e s t i g a t e d the e f f e c t of context on the c a t e g o r i z a t i o n of i n t e r v a l s i n musicians not p o s s e s s i n g a b s o l u t e p i t c h , and the c a t e g o r i z a t i o n of s i n g l e notes i n musicians p o s s e s s i n g a b s o l u t e p i t c h . F i r s t , s u b j e c t s were presented with 21 s t i m u l i over a c e r t a i n range of i n t e r v a l s / n o t e s , then without warning, the stim u l u s s e t was changed to i n c l u d e the eleven l a r g e s t i n t e r v a l s / h i g h e s t notes from the previous s e t plus ten l a r g e r i n t e r v a l s / h i g h e r notes. S h i f t i n g the s t i m u l i i n t h i s way had l i t t l e or no e f f e c t on the judgments of the best s u b j e c t s . Thus, S i e g e l and S i e g e l concluded t h a t musicians without a b s o l u t e p i t c h p e r c e i v e musical i n t e r v a l s c a t e g o r i c a l l y , possessors of ab s o l u t e p i t c h p e r c e i v e musical notes c a t e g o r i c a l l y . Burns and Ward (1978) conducted experiments to determine whether or not c a t e g o r i c a l p e r c e p t i o n of musical i n t e r v a l s was dependent on experimental method. In the f i r s t experiment, i d e n t i f i c a t i o n and d i s c r i m i n a t i o n f u n c t i o n s were obtained f o r e q u a l l y spaced s t i m u l i which covered s e v e r a l i n t e r v a l c a t e g o r i e s . F i v e m u s i c a l l y t r a i n e d s u b j e c t s were asked to c a t e g o r i z e i n t o m usical i n t e r v a l c a t e g o r i e s from major second to t r i t o n e , ascending melodic musical i n t e r v a l s ranging from 250 to 500 cents i n increments of 12.5 c e n t s . Burns and Ward found that a l l s u b j e c t s were able to c o n s i s t e n t l y i d e n t i f y the r a t i o s ' as belonging to one of the f i v e musical i n t e r v a l c a t e g o r i e s . In the d i s c r i m i n a t i o n task, s u b j e c t s were asked to judge which of two s u c c e s s i v e melodic i n t e r v a l s , separated by a 1-s ISI, was wider. For each d i s c r i m i n a t i o n f u n c t i o n , the two melodic i n t e r v a l s i n a given t r i a l were adjacent r a t i o s from the set of r a t i o s separated by equal increments over the range from 250 to 550 c e n t s . Three d i s c r i m i n a t i o n f u n c t i o n s were obtained, fo r increment s i z e s of 25, 37.5, and 50 c e n t s . The r e s u l t i n g average d i s c r i m i n a t i o n f u n c t i o n s were of the form t y p i c a l l y a s s o c i a t e d with c a t e g o r i c a l p e r c e p t i o n , i . e . , b e t t e r d i s c r i m i n a t i o n f o r s t i m u l i l y i n g w e l l w i t h i n s u b j e c t i v e c a t e g o r i e s , and poorer d i s c r i m i n a t i o n f o r s t i m u l i l y i n g . a t c ategory boundaries. In some cases, s u b j e c t s were able to d i s c r i m i n a t e w i t h i n - c a t e g o r y s t i m u l i much b e t t e r than p r e d i c t e d . Burns and Ward a t t r i b u t e d t h i s to s u b j e c t s ' a b i l i t y to i d e n t i f y i n t e r v a l s more p r e c i s e l y than semitones. In Burns and Ward's second experiment, four s u b j e c t s were presented with the same s t i m u l i as i n Experiment 1 but with v a r i e d ISI between i n t e r v a l p a i r s i n the d i s c r i m i n a t i o n t a s k . D i s c r i m i n a t i o n f u n c t i o n s , obtained f o r 25 and 50 cents with ISI of 330 ms to 3 s, were not a p p r e c i a b l y d i f f e r e n t from the 1-s ISI c o n d i t i o n . T h e r e f o r e , no> decrease i n w i t h i n - c a t e g o r y d i s c r i m i n a t i o n with i n c r e a s i n g ISI was found, c o n f i r m i n g the assumption t h a t musical i n t e r v a l p e r c e p t i o n i s c a t e g o r i c a l . In Burns and Ward's t h i r d experiment, the s t i m u l i were i d e n t i c a l to those i n Experiment 1, except that the two r a t i o s to be d i s c r i m i n a t e d i n a gi v e n t r i a l were r a t i o s separated by a v a r i a b l e d i s t a n c e i n cents around a f i x e d i n t e r v a l v a l u e . T h i s paradigm was a transformed up-down method a f t e r Z w i s l o c k i (1958; 21 c i t e d by L e v i t t , 1971), i n which i n t e r v a l s e p a r a t i o n converges on the value at which the s u b j e c t ' s performance w i l l be 70.7% c o r r e c t . The task f o r the four s u b j e c t s was to i n d i c a t e which i n t e r v a l was wider. When the 70.7% c o r r e c t t h r e s h o l d estimates of two c o n s e c u t i v e p r e s e n t a t i o n s of the s t i m u l i d i f f e r e d by 5 cents or l e s s (asymptotic performance), another 25-cent e q u a l -s t e p - s i z e d i s c r i m i n a t i o n f u n c t i o n was obtained f o r each s u b j e c t . The i n i t i a l t h r e s h o l d estimates showed good c o r r e l a t i o n with the 25-cent d i s c r i m i n a t i o n c u r v e s . However, a f t e r s u f f i c i e n t t r a i n i n g , i . e . a t asymptotic performance l e v e l s , t h i s c o r r e l a t i o n had l a r g e l y d i s a p p e a r e d . Subjects showed approximately equal d i s c r i m i n a t i o n t h r e s h o l d estimates f o r a l l i n t e r v a l v a l u e s , implying t h a t a f t e r t r a i n i n g , the 25-cent d i s c r i m i n a t i o n f u n c t i o n s should be f l a t . However, a f t e r t r a i n i n g , these d i s c r i m i n a t i o n f u n c t i o n s had the same shape as the p r e - t r a i n i n g 25-cent d i s c r i m i n a t i o n f u n c t i o n s . Burns and Ward s t a t e d t h a t The c o r r e l a t i o n between the i n i t i a l DL [ d i f f e r e n t i a l t h r e s h o l d ] estimates and the 25-cent d i s c r i m i n a t i o n f u n c t i o n s , and the f a c t t h a t many more t r i a l b l o c k s were r e q u i r e d to reach asymptotic performance a t w i t h i n - c a t e g o r y r a t i o s than a t between-category r a t i o s , both i n d i c a t e t h a t c a t e g o r i c a l p e r c e p t i o n i s more than an epiphenomenon a s s o c i a t e d with the e q u a l - s t i m u l u s s e p a r a t i o n d i s c r i m i n a t i o n paradigms u s u a l l y used. However, the f i n d i n g t h a t s u b j e c t s c o u l d , i n g e n e r a l , be " t r a i n e d " so t h a t w i t h i n - c a t e g o r y DL's were equal to between-categoty DL's, but t h a t even a f t e r such t r a i n i n g the e q u a l - s t i m u l u s s e p a r a t i o n d i s c r i m i n a t i o n f u n c t i o n s s t i l l i n d i c a t e d pronounced c a t e g o r i c a l p e r c e p t i o n , shows that the phenomenon i s to a l a r g e extent dependent on experimental procedures. (Burns and Ward, 1978, p. 462) Burns and Ward suggested t h a t , although the e x i s t e n c e of c a t e g o r i c a l p e r c e p t i o n i s l i n k e d with experimental procedure, the concept i n not n e c e s s a r i l y without u t i l i t y . 22 If i t can be shown t h a t the experimental procedures which tend to e l i c i t c a t e g o r i c a l p e r c e p t i o n more c l o s e l y approximate c o n d i t i o n s found i n " r e a l l i f e " p e r c e p t i o n , e.g. p e r c e p t i o n of running speech, or music i n performance, then s t u d i e s of c a t e g o r i c a l p e r c e p t i o n should provide i n s i g h t i n t o higher l e v e l s of a u d i t o r y p r o c e s s i n g , i n v o l v i n g ,e.g., a t t e n t i o n and memory. (Burns and Ward, 1978, p. 464) Burns and Ward t e n t a t i v e l y concluded t h a t c a t e g o r i c a l p e r c e p t i o n of musical i n t e r v a l s " i s r e l a t e d to the degree of s t i m u l u s u n c e r t a i n t y a s s o c i a t e d with the procedures used." In the e q u a l - s t e p s i z e d i s c r i m i n a t i o n task (Experiment 1), s t i m u l i i n a g i v e n t r i a l c o u l d be i n one of f i v e p o s s i b l e p e r c e p t u a l c a t e g o r i e s , and were chosen at random. Thus u n c e r t a i n t y i n the task was much higher than i n the a d a p t i v e procedure (Experiment 3), where s t i m u l i i n any g i v e n t r i a l were i n the r e g i o n of one or two musical i n t e r v a l c a t e g o r i e s and the s t i m u l i f o l l o w e d i n a p r e d i c t a b l e manner based on the s u b j e c t ' s responses. Burns and Ward proposed t h a t . . . s i n c e s t i m u l u s u n c e r t a i n t y i n " r e a l world" p e r c e p t i o n i s , i n g e n e r a l , high, i t might be expected t h a t c a t e g o r i c a l p e r c e p t i o n of musical p i t c h would be the normal s i t u a t i o n . T h i s c o n c l u s i o n i s supported by the r e s u l t s of v a r i o u s i n v e s t i g a t i o n s of i n t o n a t i o n i n performance. (Burns and Ward, 1978, p. 466) 2 . 4 Tuning Systems Ward ( i n To b i a s , 1970) d e s c r i b e s three main systems of t u n i n g used i n Western music: equal temperament, j u s t i n t o n a t i o n , and Pythagorean t u n i n g . In equal temperament, the octave, a frequency r a t i o of 2:1, i s d i v i d e d i n t o 12 equal l o g a r i t h m i c s t e p s , each c a l l e d a semitone. The semitone i s d i v i d e d i n t o 100 23 equal l o g a r i t h m i c steps,each c a l l e d a cent, making an octave 1200 cents wide. Other s c a l e s have s l i g h t l y i r r e g u l a r s p a c i n g . In one v e r s i o n of j u s t i n t o n a t i o n , the steps i n an octave are determined by s m a l l whole-number r a t i o s . For example, i n t h i s t u n i n g system, the i n t e r v a l of a p e r f e c t f i f t h i s a frequency r a t i o of 3:2, f o r a frequency d i f f e r e n c e of 702 cents r a t h e r than 700 cents as i n equal temperament. The frequency r a t i o of a major t h i r d i n j u s t i n t o n a t i o n i s 5:4, f o r a frequency d i f f e r e n c e of 336 cents i n s t e a d of 400 cents as i n equal temperament. The Pythagorean system i s based on a s e r i e s of s u c c e s s i v e p e r f e c t f i f t h s (3:2 r a t i o ) . G, a f i f t h above C, i s 702 cents higher than C. A f i f t h above G i s D, 702 + 702 = 1404 cents above C. S u b t r a c t i n g 1200 cents g i v e s D a value of 204 cents i n s t e a d of the 200 cents i n equal-tempered t u n i n g . A f i f t h above D g i v e s A a value of 906 cents above C, and so f o r t h . Going upward from C f o r h a l f the i n t e r v a l s , and downward from C f o r h a l f the i n t e r v a l s r e s u l t s i n a 1200-cent octave with s l i g h t l y i r r e g u l a r s p a c i n g between the notes (see Table I ) . 2 4 TABLE I Comparison of the major t h e o r e t i c a l systems of temperament Numerical values i n d i c a t e the d i s t a n c e i n cents (1/1200 octave between the unison and the s c a l e s t e p concerned. S o l f e q q i o J u s t Equal Pytl unison do 0 0 0 minor 2nd 112 100 90 major 2nd re 204 200 204 minor 3rd 316 300 294 major 3rd mi 386 400 408 f o u r t h fa 498 500 498 t r i tone 590 600 612 f i f t h s o l 702 700 702 minor 6th 814 800 79 2 major 6th l a 884 900 906 minor 7th 996 1000 996 major 7th t i 1088 1100 1110 octave do 1200 1200 1200 (Ward, i n Tobias , 1970, p. 414 ) 2 5 Proponents of j u s t i n t o n a t i o n and Pythagorean t u n i n g emphasize the p r e f e r e n c e of s m a l l r a t i o s between notes, f o r two reasons: (a) i f the fundamental f r e q u e n c i e s of two s i m u l t a n e o u s l y played complex tones have a small-number r a t i o , many of the p a r t i a l s w i l l c o i n c i d e , so t h a t a minimal number of "beats" w i l l occur when notes are tuned to small-number r a t i o s ; and (b) i t i s hypothesized t h a t humans p r e f e r p a i r s of tones f o r which the f r e q u e n c i e s of n e u r a l d i s c h a r g e agree (Meyer, 1898; c i t e d i n Ward, 1970). Proponents of equal temperament suggest i t i s p r e f e r a b l e i n t h a t an instrument tuned i n equal temperament can be played i n any key, whereas one tuned i n j u s t i n t o n a t i o n or Pythagorean t u n i n g has to be retuned f o r d i f f e r e n t keys (Ward, in Tobias, 1970). Pianos are n o r m a l l y tuned i n equal temperament while s i n g e r s and many i n s t r u m e n t a l i s t s can choose which t u n i n g system to use. Ward ( i n T o b i a s , 1970) r e p o r t s on s t u d i e s by Greene (1937), N i c k e r s o n (1948), Mason (1960), and Shackford (1961, 1962a), which i n d i c a t e t h a t s t r i n g and woodwind p l a y e r s g e n e r a l l y p l a y musical i n t e r v a l s s l i g h l y sharper than i n d i c a t e d by equal temperament. Even the octave, which i s a r a t i o of 2:1 or 1200 cents i n a l l three t u n i n g systems, i s i d e n t i f i e d as "best" at about 1210 cents f o r pure tones (Ward, 1954). G e n e r a l l y , the t u n i n g used by musicians i n these s t u d i e s corresponds f a i r l y c l o s e l y to equal temperament, but with a s m a l l amount of s h a r p i n g of a l l tones i n r e l a t i o n to the t o n i c . 26 Although i t i s s a i d to be tuned to equal temperament, the tu n i n g of a piano i s always s t r e t c h e d to some extent because piano s t r i n g s v i b r a t e i n such a way th a t the p a r t i a l s are not e x a c t l y h a r m o n i c a l l y r e l a t e d . For example, the second p a r t i a l of the A4 s t r i n g on a good piano i s about 1201 to 1202 cents higher than the fundamental, so when a piano tuner matches the A5 fundamental to the A4 second p a r t i a l , the s c a l e i s a u t o m a t i c a l l y s t r e t c h e d . Ward suggests t h a t Perhaps the s t r e t c h e d s c a l e of the piano i s at l e a s t p a r t i a l l y r e s p o n s i b l e f o r the f a c t t h a t the i n t e r n a l s c a l e of musical p i t c h i s a l s o s t r e t c h e d . Indeed, perhaps the correspondence (except f o r s t r e t c h ) between musical p i t c h and equal temperament i s due to the e x t e n s i v e experience a l l musicians have had with the u n i v e r s a l piano. (Ward, i n Tobias, 1970) P o s s i b l y because of the v a r i e t y of t u n i n g systems t h a t musicians are exposed t o , i n t e r s u b j e c t v a r i a b i l i t y i n judgments of musical i n t e r v a l s has been observed. Z a t o r r e and Halpern (1979), i n a study i n which s u b j e c t s i d e n t i f i e d simultaneous musi c a l i n t e r v a l s r a n g i n g from a minor t h i r d to a major t h i r d i n seven equal l o g a r i t h m i c s t e p s , observed t h a t f o r the e i g h t m u s i c a l l y t r a i n e d s u b j e c t s , the major c a t e g o r y was narrower than the minor c a t e g o r y f o r t h i r d s , t h a t i s , the musicians s t u d i e d had a s t r i c t e r c r i t e r i o n f o r a c c e p t i n g major than minor t h i r d s . Z a t o r r e and Halpern a t t r i b u t e d t h i s . . . e i t h e r to a lear n e d narrower tu n i n g of the major t h i r d , or to some p h y s i c a l c h a r a c t e r i s t i c of the major t h i r d [e.g. i t s p l a c e i n the harmonic s e r i e s , or that the major t h i r d approximates the bandwidth of a c r i t i c a l bandwidth i n hea r i n g (Scharf, 1970)]. ( Z a t o r r e and Halpern, 1979, p. 388 ) S i e g e l and S i e g e l (1977a) r e p o r t e d i d i o s y n c r a t i c d i f f e r e n c e s between s u b j e c t s i n c a t e g o r i z a t i o n of musical i n t e r v a l s . Some 27 s u b j e c t s produced c a t e g o r i e s t h a t were wider or narrower than they should have been a c c o r d i n g to p r e d i c t i o n s from the e q u a l -tempered s c a l e . Burns and Ward (1978) a l s o found a r e l a t i v e l y l a r g e i n t e r s u b j e c t v a r i a b i l i t y to be c h a r a c t e r i s t i c of m u s i c a l -i n t e r v a l judgments, and that the l o c a t i o n of c a t e g o r y boundaries v a r i e d among s u b j e c t s . They r e p o r t e d t h a t a v e r a g i n g of s u b j e c t s ' data somewhat obscured the i n f o r m a t i o n seen i n the data of i n d i v i d u a l s u b j e c t s . Since there are many d i f f e r e n t systems of t u n i n g and r e l a t i v e l y l a r g e i n t e r s u b j e c t d i f f e r e n c e s i n musical i n t e r v a l judgment, i t appears t h a t judgments should be compared with " i d e a l " c a t e g o r i z a t i o n f u n c t i o n s f o r each p o s s i b l e s t r a t e g y p r e d i c t e d from the equal-tempered s c a l e , and t h a t data from each s u b j e c t should be examined i n d i v i d u a l l y . 28 CHAPTER 3 AIMS OF THE EXPERIMENT In the study of musi c a l i n t e r v a l p e r c e p t i o n as i t r e l a t e s to possessors of a b s o l u t e p i t c h , some qu e s t i o n s a r e : Does a musician with a b s o l u t e p i t c h p e r c e i v e and i d e n t i f y m usical i n t e r v a l s i n the same manner as a musician without a b s o l u t e p i t c h ? Can a musician with a b s o l u t e p i t c h suppress the i d e n t i f i c a t i o n of notes and d i r e c t l y e v a l u a t e m u s i c a l i n t e r v a l s ? What a b i l i t y does the musician with a b s o l u t e p i t c h r e l y on most h e a v i l y i n a g i v e n s i t u a t i o n , a b s o l u t e p i t c h or r e l a t i v e p i t c h ? S t u d i e s on the p e r c e p t i o n of music have demonstrated t h a t c a t e g o r i c a l p e r c e p t i o n occurs (a) i n the i d e n t i f i c a t i o n of musical i n t e r v a l s by musicians without a b s o l u t e p i t c h , and (b) 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 by musicians with a b s o l u t e p i t c h . Two s t r a t e g i e s are a v a i l a b l e to musicians with a b s o l u t e p i t c h f o r i d e n t i f y i n g s e q u e n t i a l musical i n t e r v a l s . With the " r e l a t i v e p i t c h s t r a t e g y " , the l i s t e n e r d i r e c t l y e v a l u a t e s the musical i n t e r v a l between the two notes, whereas with the "absolute p i t c h s t r a t e g y " , the l i s t e n e r f i r s t i d e n t i f i e s the two notes, and then i n f e r s the musi c a l i n t e r v a l between them. The present study i n v e s t i g a t e s the s t r a t e g i e s used i n the i d e n t i f i c a t i o n of s e q u e n t i a l m u s i c a l i n t e r v a l s by m u s i c a l l y t r a i n e d s u b j e c t s with and without a b s o l u t e p i t c h . These s u b j e c t s are asked to i d e n t i f y i n t e r v a l s which do not correspond to the 29 standard equal-tempered i n t e r v a l c a t e g o r i e s , some of which should be c o r r e c t l y i d e n t i f i e d with the r e l a t i v e p i t c h s t r a t e g y but i n c o r r e c t l y i d e n t i f i e d with the a b s o l u t e p i t c h s t r a t e g y . In p r e l i m i n a r y experiments, s u b j e c t s are asked to i d e n t i f y s e q u e n t i a l musical i n t e r v a l s which correspond to standard musical i n t e r v a l c a t e g o r i e s , and to name s i n g l e notes which correspond to standard equal-tempered p i t c h e s , so t h a t t h e i r sense of r e l a t i v e p i t c h and a b s o l u t e p i t c h can be e v a l u a t e d . In order t h a t t h e i r i n t e r n a l p i t c h r e f e r e n c e can be determined, s u b j e c t s who demonstrate t h a t they have a b s o l u t e p i t c h are then asked to i d e n t i f y s i n g l e notes which correspond to 20-cent increments on the equal-tempered s c a l e , u s i n g the standard note names of the equal-tempered s c a l e . F i n a l l y , s u b j e c t s are asked to i d e n t i f y s e q u e n t i a l m u s i c a l i n t e r v a l s r a n g i n g from 260 to 540 cents i n 20-cent s t e p s , i n t o the standard m u s i c a l i n t e r v a l c a t e g o r i e s . Depending on the s t r a t e g y used, a g i v e n s u b j e c t ' s i d e n t i f i c a t i o n of these i n t e r v a l s should correspond to some extent with one of two s e t s of p r e d i c t e d responses: the f i r s t s e t would correspond to the r e l a t i v e p i t c h s t r a t e g y , based on the p i t c h d i f f e r e n c e between the two notes, and the second s e t would correspond to the ab s o l u t e p i t c h s t r a t e g y , based on naming the two notes i n r e l a t i o n to an i n t e r n a l r e f e r e n c e and then i n f e r r i n g the musi c a l i n t e r v a l between them. T h i s study attempts to d i s c o v e r the f o l l o w i n g : 1. Which of the two s t r a t e g i e s i s used by each s u b j e c t with a b s o l u t e p i t c h when judging s e q u e n t i a l m u s i c a l i n t e r v a l s ? 2. Is there an e v i d e n t d i f f e r e n c e i n the way the two groups of s u b j e c t s i d e n t i f y i n t e r v a l s ? 30 CHAPTER 4 MATERIALS AND METHODS 4 .1 P r e p a r a t i o n of s t i m u l i A l l s t i m u l i c o n s i s t e d of s i n g l e puretones or of p a i r s of puretones which were s y n t h e s i z e d , u s i n g a DEC PDP-12 computer. T h e i r f r e q u e n c i e s corresponded e i t h e r to notes of the e q u a l -tempered s c a l e or to f r e q u e n c i e s between these notes, i n 20-cent s t e p s . A program which s y n t h e s i z e d puretones a t s p e c i f i e d f r e q u e n c i e s was used to generate each one of these notes. Each puretone was generated as a sequence of 1 2 - b i t words, which were s t o r e d on a d i g i t a l tape, and l a t e r p layed back v i a a D-to-A c o n v e r t e r . A l l notes were 500 ms i n l e n g t h . Amplitude envelopes were shaped to produce r i s e and decay times of 25 ms, r e s u l t i n g i n smooth, r a p i d r i s e and decay of the s t i m u l i . Sampling r a t e was se t a t 4096 samples per second. Since the h i g h e s t frequency s y n t h e s i z e d was c l o s e t o 600 Hz, t h i s sampling r a t e was more than adequate to meet the Nyquist c r i t e r i o n and would have i n f a c t accommodated higher f r e q u e n c i e s . A sampling r a t e of 4096 Hz was chosen because the d i g i t a l (LINC) tapes used were d i v i d e d i n t o 256-sample b l o c k s , and thus a 500-ms note would f i t e x a c t l y i n t o a f u l l number of blocks with no s p i l l i n t o a d j a c e n t b l o c k s , making i t e a s i e r l a t e r to t r a n s f e r whole b l o c k s from d i g i t a l tape to audio tape. In order to (a) d i s t r a c t and d i s o r i e n t the s u b j e c t and to some extent " e r a s e " h i s / h e r memory of a p r e v i o u s l y heard p i t c h ; and (b) to a l e r t the s u b j e c t to an upcoming s t i m u l u s and to help him/her keep t r a c k of h i s / h e r p l a c e on the t e s t s , " p i t c h e r a s e r " tones were used between s t i m u l i . These " p i t c h e r a s e r " tones were s h o r t d u r a t i o n s of e i t h e r one of two computer-generated complex tones which g i v e the impression of c o n t i n u o u s l y descending or c o n t i n u o u s l y ascending (Shepard, 1964; R i s s e t , 1971). H e r e a f t e r , they are r e f e r r e d to as "ascending" or "descending p i t c h e r a s e r s " . The " p i t c h e r a s e r s " were t r a n s f e r r e d from analog audio tape to d i g i t a l tape v i a a 1 0 - b i t A-to-D c o n v e r t e r u s i n g WAVES, a se t of computer programs w r i t t e n by L l o y d Rice a t U.C.L.A. The sampling r a t e was a l s o 4096 samples per second. The D-to-A'd s i g n a l was low-pass f i l t e r e d a t 1650 Hz to prevent a l i a s i n g . 200 b l o c k s , or 12.5 seconds of each of the ascending and descending complex tones were sampled and s t o r e d on the d i g i t a l tape. The s t a r t i n g p o i n t of each " p i t c h e r a s e r " tone was randomly chosen, and, depending on the t e s t , i t s l e n g t h was randomly v a r i e d between 1 and 4.4 seconds. 4•2 P r e p a r a t i o n of Test Tapes A l l tones were D-to-A'd with a 1 0 - b i t D-to-A c o n v e r t e r and bandpass f i l t e r e d by a General Radio U n i v e r s a l 1952 F i l t e r s e t to pass o n l y f r e q u e n c i e s i n the range a p p r o p r i a t e f o r the s t i m u l i . The s i g n a l was then fed to a Nagra IV-D f u l l - t r a c k r e e l - t o - r e e l tape r e c o r d e r and recorded on p r o f e s s i o n a l q u a l i t y Ampex audio 32 tape a t a low l e v e l , i n order to e l i m i n a t e problems of p r i n t -through. The puretones and " p i t c h e r a s e r s " were t r a n s f e r r e d from d i g i t a l onto audio tape, u s i n g the WAVES programs. With these programs, i t was p o s s i b l e to p l a y back the tones i n any order r e q u i r e d . The s i l e n t p e r i o d between two notes i n a melodic i n t e r v a l was p r e c i s e l y timed, u s i n g m u l t i p l e s of 62.5 ms, c o r r e s p o n d i n g to a f u l l number of b l o c k s . The tones were moved to the a p p r o p r i a t e p o s i t i o n s on the d i g i t a l tape, then t r a n s f e r r e d to the audio tape. The frequency of each note was t e s t e d on the audio tape (played on the Nagra tape r e c o r d e r ) with a Korg WT-12 q u a r t z chromatic tuner and found to be a c c u r a t e to w i t h i n 3 cents of the d e s i r e d frequency. From one to f i v e b u f f e r items, chosen a t random from among the t e s t items, but f o l l o w i n g the o r d e r i n g c o n s t r a i n t s of the p a r t i c u l a r t e s t , were recorded a t the beginning and end of each t e s t tape. 4.21 Tape f o r T e s t 1 The purpose of t h i s t e s t was to s c r e e n s u b j e c t s f o r t h e i r a b i l i t y to name musical i n t e r v a l s . The subset of s i x i n t e r v a l s from minor t h i r d to minor s i x t h was f e l t to be s u f f i c i e n t l y d i f f i c u l t and v a r i e d to demonstrate a b i l i t y to name musical i n t e r v a l s . S t i m u l i f o r Test 1 c o n s i s t e d of two s e q u e n t i a l l y presented notes of f r e q u e n c i e s c o r r e s p o n d i n g to the notes of the e q u a l -tempered s c a l e between C4 (261.63 Hz) and C5 (523.25 Hz). The two notes of each s t i m u l u s were separated by one of s i x musical i n t e r v a l s : minor t h i r d , major t h i r d , p e r f e c t f o u r t h , t r i t o n e , p e r f e c t f i f t h , and minor s i x t h . There were 120 t e s t items i n Test 1, arranged i n two bl o c k s of 60 s t i m u l i . The 60 s t i m u l i c o n s i s t e d of 10 tokens from each of the s i x musi c a l i n t e r v a l c a t e g o r i e s l i s t e d above. In those cases where ten d i f f e r e n t examples of a s p e c i f i c i n t e r v a l c o u l d not be made u s i n g f r e q u e n c i e s between C4 and C5, i n t e r v a l s from the c e n t r e of the frequency range were repeated f o r t h a t ca t e g o r y (see Table I I ) . H a l f of the s t i m u l i were presented as ascending i n t e r v a l s , and the other h a l f were presented as descending i n t e r v a l s . The s t i m u l i were arranged i n pseudo-random order with the c o n s t r a i n t t h a t two ad j a c e n t s t i m u l i had to be from d i f f e r e n t i n t e r v a l c a t e g o r i e s , and t h a t the second note of a s t i m u l u s had to be d i f f e r e n t from the f i r s t note of the f o l l o w i n g s t i m u l u s . Each s t i m u l u s c o n s i s t e d of two 500-ms tones separated by a 1-s s i l e n t p e r i o d . Between each s t i m u l u s and the next, there was a 6.5-s s i l e n t p e r i o d . F o l l o w i n g every f i f t h s t i m u l u s , there was a 6.5-s s i l e n t p e r i o d , a "descending p i t c h e r a s e r " , and another 6.5-s s i l e n t p e r i o d . The s t a r t i n g p o i n t of each " p i t c h e r a s e r " was randomly chosen from the f i r s t 130 bl o c k s of "descending p i t c h e r a s e r " on the d i g i t a l tape, and the l e n g t h of each " p i t c h e r a s e r " was randomly v a r i e d between 60, 65,and 70 b l o c k s , c o r r e s p o n d i n g approximately to 3.8, 4.1, and 4.4 seconds. 34 TABLE II Stimulus types f o r Test 1. " ( a ) " i n d i c a t e s an ascending i n t e r v a l , and " ( d ) " i n d i c a t e s a descending i n t e r v a l . Min3 C ,Eb(a) C#,E (d) D ,F (a) D#,F#(d) E ,G (a) F ,Ab(d) F#,A (a) G ,Bb(d) G#,B (a) A ,C (d) Ma13 C ,E (d) Db,F (a) D ,F#(d) Eb,G (a) E ,G#(d) F ,A (a) F#,A#(d) G ,B (a) Ab,C (d) E ,G#(a) Perf 4 C ,F (a) C#,F#(d) D ,G (a) Eb,Ab(d) E ,A (a) F ,Bb(d) F#,B (a) G ,C (d) D#,G#(a) E ,A (d) T r i t o n e C ,F#(d) C#,G (a) D ,Ab(d) D#,A (a) E ,Bb(d) F ,B (a) F#,C (d) D ,G#(a) D#,A (d) E ,Bb(a) Perf 5 C ,G (a) C#,G#(d) D ,A (a) Eb,Bb(d) E ,B (a) F ,C (d) C#,G#(a) D ,A (d) Eb,Bb(a) E ,B (d) Min6 C ,Ab(d) C#,A (a) D ,Bb(d) D*,B (a) E ,C (a) C ,Ab(d) C»,A (a) D ,Bb(d) D#,B (a) E ,C (d) 35 4.22 Tape for Test 2 The purpose of this test was to screen subjects for the a b i l i t y to name single puretones. Stimulus frequencies covered a two-octave range so that the frequency distance between two stimuli could be more varied, making i t more d i f f i c u l t for subjects to use relative pitch in naming single notes. There were 60 test items in Test 2, arranged in five blocks of 12 stimuli, each block in a different pseudo-random order. Each of the twelve notes of the equal-tempered scale was presented five times in the two-octave range from C3 (130.81 Hz) to C5 (523.25 Hz), twice in one octave and three times in the other octave. Each octave was equally represented, with 30 notes from the lower and 30 notes from the higher octave (see Table III). Adjacent stimuli were separated by a pitch distance of at least 5 semitones. Each stimulus consisted of a 500-ms puretone. The length of time between the beginning of two successive stimuli varied between 8 and 10 seconds. The interval between successive stimuli consisted of (a) a 2.5-s silent period; (b) a "descending pitch eraser", the starting point of which was randomly chosen from the f i r s t 130 blocks of "descending pitch eraser", and the length of which was randomly varied between 3.8, 4.1, and 4.4 seconds; and (c) another 2.5-s silent period. After every f i f t h stimulus, in the place of the "descending pitch eraser", there was an "ascending pitch eraser", with a similarly randomly-chosen starting point and length, to help the subject keep his/her place on the test. 36 TABLE I I I Number of tokens by s t i m u l u s type f o r Tes t 2. Stimulus Type Octave C3-B3 Octave C4-B4 C 3 2 C#/Db 3 2 D 3 2 D#/Eb 3 2 E 2 3 F 2 3 F#/Gb 3 2 G 2 3 Gtt/Ab 2 3 A 2 3 A#/Bb 3 2 B 2 3 37 4.23 Tape f o r Test 3 The purpose of t h i s t e s t was (a) to determine how s u b j e c t s p o s s e s s i n g a b s o l u t e p i t c h would c a t e g o r i z e tones t h a t were a t f r e q u e n c i e s between those of the notes of the standard e q u a l -tempered s c a l e and (b) to t r y to determine each s u b j e c t ' s p i t c h c e n t r e to the n e a r e s t 20 c e n t s . T e s t 3 c o n s i s t e d of 215 t e s t items, arranged i n f i v e b l o c ks of 43 s t i m u l i , each block i n a d i f f e r e n t pseudo-random order. The s t i m u l u s types were 43 s i n g l e puretones based on the e q u a l -tempered s c a l e i n 20-cent s t e p s . These puretones were a l s o used f o r the two-note s t i m u l i i n Te s t 4, to be d e s c r i b e d i n the next s e c t i o n . These two-note s t i m u l i i n c l u d e d a l l the notes from A#3 + 60 cents (241.30 Hz) to G&4 + 0 cents (415.30 Hz) i n 20-cent s t e p s , with the e x c e p t i o n of the notes between B3 + 40 cents and C4 + 60 cents (see Table I V ) . Or d e r i n g c o n s t r a i n t s r e q u i r e d t h a t a d j a c e n t s t i m u l i be a t l e a s t 80 cents away from one another. Each s t i m u l u s was a 500-ms puretone. The l e n g t h or time between s u c c e s s i v e s t i m u l i v a r i e d from 6 to 7 seconds. The i n t e r v a l between s u c c e s s i v e s t i m u l i c o n s i s t e d of (a) a s i l e n t p e r i o d of 3 seconds; (b) a "descending p i t c h e r a s e r " , the s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 175 blo c k s of "descending p i t c h e r a s e r " and the l e n g t h of which was randomly v a r i e d from 1 to 1.5 seconds; and (c) a s i l e n t p e r i o d of 1.5 seconds. A f t e r every f i f t h s t i m u l u s , there was (a) a s i l e n t p e r i o d of 3 seconds; (b) an "ascending p i t c h e r a s e r " , the TABLE IV Stimulus types f o r Test 3. A l l notes are i n the range between A#3 +60 cents (241.30 Hz) and G#4 +00 cents (415.30 Hz). -40/+60 -20/+80 •20 -40 A# + 60 A# + 80 B +00 B +20 B +40 C +60 C# + 60 D +60 D# + 60 E +60 F +60 F# + 60 G +60 C +80 C# + 80 D +80 D# + 80 E +80 F +80 F# + 80 G +80 C» + 00 D +00 D# + 00 E +00 F +00 F# + 00 G +00 G# + 00 C& + 20 D +20 DS + 20 E +20 F +20 F# + 20 G +20 C# + 40 D +40 D& + 40 E +40 F +40 F# + 40 G +40 s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 130 b l o c k s of "ascending p i t c h e r a s e r " , and the l e n g t h of which was randomly v a r i e d between 3.8, 4.1, or 4.4 s e c ; (c) a 1.5-sec. s i l e n t p e r i o d ; (d) a s i l e n t p e r i o d of 3 seconds; (e) a "descending p i t c h e r a s e r " , the s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 175 b l o c k s of "descending p i t c h e r a s e r " and the l e n g t h of which was randomly v a r i e d from 1 to 1.5 seconds; and ( f ) a s i l e n t p e r i o d of 1.5 seconds. 4.24 Tape f o r T e s t 4 The purpose of t h i s t e s t was to determine how s u b j e c t s would c a t e g o r i z e i n t o standard m u s i c a l i n t e r v a l c a t e g o r i e s s e q u e n t i a l i n t e r v a l s whose component tones were not always c o n s i s t e n t with equal-tempered t u n i n g . More s p e c i f i c a l l y , t h i s t e s t was designed to determine which of two s t r a t e g i e s p ossessors of a b s o l u t e p i t c h tend to use: one i n which the l i s t e n e r d i r e c t l y e v a l u a t e s the mus i c a l i n t e r v a l between the two notes, or one i n which he/she f i r s t i d e n t i f i e s the I n d i v i d u a l tones, and then i n f e r s the mus i c a l i n t e r v a l s e p a r a t i n g them. Test 4 c o n s i s t e d of 165 s t i m u l i . The s t i m u l i c o n s i s t e d of two s e q u e n t i a l l y presented notes r a n g i n g from A#3 + 60 cents (241.30 Hz) to G#4 + 00 cents (415.30 Hz), which c r e a t e d melodic m u s i c a l i n t e r v a l s c l o s e s t to the c a t e g o r i e s of minor t h i r d (260 to 340 c e n t s ) , major t h i r d (360 to 440 cents) and p e r f e c t f o u r t h (460 to 540 c e n t s ) . Three s e t s of 55 s e q u e n t i a l musical i n t e r v a l s were c r e a t e d : the frequency of the bottom notes ranged, i n 20-cent s t e p s , from 40 cents below to 40 cents above one of the three notes B3 (246.94 Hz), C#4 (277.18 Hz), or D#4 (311.13 Hz);the frequency of the top notes ranged, i n 20-cent s t e p s , from D4 (293.66 Hz) to E4 (329.63 Hz) f o r the s e t with bottom note B3, from E4 (329.63 Hz) to F#4 (369.99 Hz) f o r the s e t with bottom note C#4, or from F#4 (369.99 Hz) to G#4 (415.30 Hz) f o r the s e t with bottom note D#4 (see Table V ) . Each s e t of i n t e r v a l s was d i f f e r e n t o n l y i n terms of which note of the s c a l e i t was c e n t r e d around. The tones t h a t made up the i n t e r v a l s were spaced around the 0 r e f e r e n c e i n the same manner, and the r e l a t i o n s h i p s between the tones were the same a c r o s s the three s e t s of musical i n t e r v a l s . Thus, i f one ignores the f a c t t h a t the three s e t s of i n t e r v a l s are c e n t r e d around d i f f e r e n t p i t c h e s , one c o u l d say tha t there were 55 s t i m u l u s types, each repeated three times. The 165 s t i m u l i were presented i n a pseudo-random order, with an o r d e r i n g c o n s t r a i n t which r e q u i r e d t h a t a d j a c e n t s t i m u l i be from d i f f e r e n t i n t e r v a l s e t s . Of the 165 s t i m u l i , 85 were presented as ascending i n t e r v a l s , and the remaining 80 were presented as descending i n t e r v a l s . A s h o r t p i l o t t e s t was conducted to determine a s u i t a b l e I n t r a - s t i m u l u s i n t e r v a l f o r Test 4. I t was a concern t h a t the i n t r a - s t i m u l u s i n t e r v a l be long enough f o r the s u b j e c t s to be able to name the component tones before comparing them, but s h o r t enough f o r the s u b j e c t s not to be f o r c e d to use t h i s s t r a t e g y , and such t h a t the s i l e n c e between notes i n an i n t e r v a l was a le n g t h of time t h a t was p l a u s i b l e i n a r e a l m usical s i t u a t i o n . The p i l o t t e s t presented a s e l e c t i o n of i n t e r v a l s t h a t were to be used i n Test 4, and compared the e f f e c t s of an i n t r a - s t i m u l u s i n t e r v a l of .0625, 2, 5, and 10 seconds. The r e s u l t s of t h i s 41 TABLE V Stimulus types for Test 4. Three sets of 55 i n t e r v a l s which made up the 165 s t i m u l i . " ( a ) " - ascending i n t e r v a l s ; " ( d ) " - descending i n t e r v a l s . I n t e r v a l s with bottom In t e r v a l s with bottom Intervals with bottom Distance te A» + 60 to B + 40 note C +60 to C& + 40 note D + 60 to D# + 40 in cents A#+60, D +00 (a) C +60, E + 00 (d) D + 60 , F#+00 (a) 340 A#+60, D +20 (d) C +60, E + 20 (a) D + 60 , F#+20 (d) 360 A#+60, D +40 (a) C +60, E + 40 (d) D + 60 , F&+40 (a) 380 A#+60, D +60 (d) C +60, E + 60 (a) D + 60 , F#+60 (d) . 400 A#+60, D +80 (a) C +60, E + 80 (d) D + 60 , F&+80 (a) 420 A#+60, Dlt + 00 (d) C +60, F + 00 (a) D + 60 , G +00 (d) 440 A#+60, D# + 20 (a) C +60, F + 20 (d) D + 60 , G +20 (a) 460 A#+60, DS + 40 (d) C +60, F + 40 (a) D + 60 , G +40 (d) 480 AS+60, Dft + 60 (a) C +60, F + 60 (d) D + 60 , G +60 (a) 500 A#+60, DS + 80 (d) C +60, F + 80 (a) D + 60 , G +80 (d) 520 A»±60, _E_+00_(al C_+60^. FJ + 00 (d) D + 60 ,_G!+.00_Lal 540 A&+80, D +00 (a) C +80, E + 00 (d) D + 80 , F#+00 (a) 320 Aff + 80, D +20 (d) C +80, E + 20 (a) D + 80 , F#+20 (d) 340 Alf + 80, D +40 (a) C +80, E + 40 (d) D + 80 , F&+40 (a) 360 A#+80, D +60 (d) C +80, E + 60 (a) D + 80 , F#+60 (d) 380 AS+80, D +80 (a) C +80, E + 80 (d) D + 80 , Fft + 80 (a) 400 A#+80, D# + 00 (d) C +80, F + 00 (a) D + 80 , G +00 (d) 420 AS+80, Dft + 20 (a) C +80, F + 20 (d) D + 80 , G +20 (a) 440 A#+80, D# + 40 (d) C +80, F + 40 (a) D + 80 , G +40 (d) 460 A#+80, DS + 60 (a) C +80, F + 60 (d) D + 80 , G +60 (a) 480 A#+80, D# + 80 (d) C +80, F + 80 (a) D + 80 , G +80 (d) 500 A#+80, _E_+00_Lal _ C +80^ Flf + 00 D + 80 ,_Gl+00_Lal ._ 520 B +00, D +00 (a) C#+00, E + 00 (d) D# + 00 , F#+00 (a) 300 B +00, D +20 (d) Clt + 00, E + 20 (a) D# + 00 , F#+20 (d) 320 B +00, D +40 (a) C»+00, E + 40 (d) D# + 00 , F#+40 (a) 340 B +00, D +60 (d) CS+00, E + 60 (a) D# + 00 , Fff + 60 (d) 360 B +00, D +80 (a) cs+oo, E + 80 (d) D& + 00 , Fff + 80 (a) 380 B +00, D# + 00 (d) c»+oo, F + 00 (a) DU + 00 , G +00 (d) 400 B +00, DU + 20 (a) c»+oo, F + 20 (d) D# + 00 , G +20 (a) 420 B +00, D# + 40 (d) Ctf + 00, F + 40 (a) D# + 00 , G +40 (d) 440 B +00, D# + 60 (a) C»+00, F + 60 (d) D# + 00 , G +60 (a) 460 B +00, D# + 80 (d) c»+oo, F + 80 (a) D# + 00 , G +80 (d) 480 B +00, _E_+00_Lal ci+oo^. £# + 00 (<i)_ Dlf + 00 ,_Gt+00_Lal _ 500 B +20, D +00 (a) C#+20, E + 00 (d) D# + 20 , F#+00 (a) 280 B +20, D +20 (d) Ctt+20, E + 20 (a) D# + 20 , F#+20 (d) 300 B +20, D +40 (a) C#+20, E + 40 (d) D# + 20 , FU+40 (a) 320 B +20, D +60 (d) C#+20, E + 60 (a) D# + 20 , Ftt+60 (d) 340 B +20, D +80 (a) C&+20, E + 80 (d) D# + 20 , F&+80 (a) 360 B +20, D# + 00 (d) CS+20, F + 00 (a) D# + 20 , G +00 (d) 380 B +20, D# + 20 (a) CS+20, F + 20 (d) D# + 20 , G +20 (a) 400 B +20, D# + 40 (d) Cff+20, F + 40 (a) D# + 20 , G +40 (d) 420 B +20, Dft + 60 (a) C#+20, F + 60 (d) D# + 20 , G +60 (a) 440 B +20, D# + 80 (d) C#+20, F + 80 (a) D# + 20 , G +80 (d) 460 B ±20, _E_+00_Lal _ _ Cl+20^ F#±00 (d) D# + 20 ,_Gi+00_Lal _ 480 B +40, D +00 (a) C#+40, E + 00 (d) D# + 40 , Ftf + 00 (a) 260 B +40, D +20 (d) C8+40, E + 20 (a) D# + 40 , F#+20 Cd) 280 B +40, D +40 (a) C#+40, E + 40 (d) Dft + 40 , F&+40 (a) 300 B +40, D +60 (d) C&+40, E + 60 (a) D# + 40 , FS+60 (d) 320 B +40, D +80 (a) CS+40, E + 80 (d) Dif + 40 , FS+80 (a) 340 B +40, D& + 00 (d) CS+40, F + 00 (a) Dlt + 40 r G +00 (d) 360 B +40, D# + 20 (a) CS+40, F + 20 (d) DS + 40 , G +20 (a) 380 B +40, D# + 40 (d) CS+40, F + 40 (a) D# + 40 , G +40 (d) 400 B +40, Dit + 60 (a) CS+40, F + 60 (d) Dtt + 40 , G +60 (a) 420 B +40, DS + 80 (d) CS+40, F + 80 (a) D# + 40 , G +80 (d) 440 B +40, E +00 (a) CS+40, F& + 00 (d) D# + 40 , G#+00 (a) 460 t e s t combined with s u b j e c t s ' o b s e r v a t i o n s i n d i c a t e d t h a t an i n t r a - s t i m u l u s i n t e r v a l of 2 seconds should be s u f f i c i e n t f o r s u b j e c t s to name the notes i n the i n t e r v a l , without f o r c i n g them to use t h i s s t r a t e g y . Each s t i m u l u s i n Tes t 4 c o n s i s t e d of two 500-ms puretones sep a r a t e d by a 2-s s i l e n t p e r i o d . The l e n g t h of time between s u c c e s s i v e s t i m u l i v a r i e d between 8.5 and 9 seconds. Each s t i m u l u s was f o l l o w e d by (a) a 3-s s i l e n t p e r i o d ; (b) a "descending p i t c h e r a s e r " , the s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 175 bl o c k s of "descending p i t c h e r a s e r " and the l e n g t h of which was randomly v a r i e d between 1 and 1.5 seconds; and (c) a 1.5-s s i l e n t p e r i o d . Every f i f t h s t i m u l u s was f o l l o w e d by (a) a 3-s s i l e n t p e r i o d ; (b) an "ascending p i t c h e r a s e r " the s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 130 bl o c k s of "ascending p i t c h e r a s e r " and the l e n g t h of which was randomly v a r i e d between 3.8, 4.1, and 4.4 seconds; (c) a 1.5-s s i l e n t p e r i o d ; (d) a 3-s s i l e n t p e r i o d ; (e) a "descending p i t c h e r a s e r " , the s t a r t i n g p o i n t of which was randomly chosen from the f i r s t 175 bl o c k s of "descending p i t c h e r a s e r " and the le n g t h of which was randomly v a r i e d between 1 and 1.5 seconds; and ( f ) a 1.5-s s i l e n t p e r i o d . 4.3 Subjects Unpaid v o l u n t e e r s u b j e c t s were r e c r u i t e d from among f r i e n d s and acquaintances of the experimenter, and from the Departments of Music of both the U n i v e r s i t y of B r i t i s h Columbia and Douglas C o l l e g e . A group of ten a d u l t s who b e l i e v e d they had ab s o l u t e 43 p i t c h (SI to S10) and a group of f i v e a d u l t s who b e l i e v e d they d i d not have a b s o l u t e p i t c h ( S l l to S15) p a r t i c i p a t e d i n the experiment. A l l s u b j e c t s answered a q u e s t i o n n a i r e , a sample of which i s found i n Appendix A. Si x females and four males made up the f i r s t group. Piano was the f i r s t instrument played by a l l the s u b j e c t s i n t h i s group. Nine s u b j e c t s began p l a y i n g the piano between the ages of three and f i v e , and one s u b j e c t (S2) began p l a y i n g the piano a t age seven. F i v e of the s u b j e c t s (SI, S3, S4, S5, and S8) r e p o r t e d f i r s t l e a r n i n g to p l a y the piano by ear, three (S2, S7, and S10) r e p o r t e d both p l a y i n g by ear and r e a d i n g w r i t t e n music when f i r s t l e a r n i n g the piano, and the remaining two s u b j e c t s (S6 and S9) r e p o r t e d f i r s t l e a r n i n g to p l a y the piano by r e a d i n g w r i t t e n music. Two s u b j e c t s (S2 and S4) had s t u d i e d no instrument other than the piano, and the other e i g h t s u b j e c t s had s t u d i e d one to four other instruments. Piano was s t i l l the major instrument f o r f i v e of the s u b j e c t s (S2, S3, S4, S9, and S10). Two s u b j e c t s s t a t e d t h a t t h e i r major instrument was now v o i c e ( S i and S8); one r e p o r t e d the trumpet as h i s major instrument (S5); one r e p o r t e d the s y n t h e s i z e r keyboard as h i s major instrument (S6); and one s u b j e c t (S7) r e p o r t e d h i s major instruments as the organ and v o i c e . S u b j e c t s i n the a b s o l u t e p i t c h group were asked how they d i s c o v e r e d t h e i r a b i l i t i e s a t p i t c h naming. Most r e p o r t e d that they had been s u r p r i s e d a t some p o i n t to f i n d out t h a t not everyone c o u l d name p i t c h e s as they c o u l d . Three s u b j e c t s (S2, S4, and S8) r e p o r t e d being a b l e to hear a piano p i e c e and subsequently p l a y the pie c e by ear i n the c o r r e c t key. Two s u b j e c t s (S2 and S6) r e p o r t e d p l a y i n g games with f a m i l y members i n which they named notes a f t e r they were played, without l o o k i n g a t the keyboard. One s u b j e c t (S6) d i s c o v e r e d he had a b s o l u t e p i t c h a f t e r he was accused of c h e a t i n g on a music t e s t . One s u b j e c t (SI) r e p o r t e d n o t i c i n g t h a t she c o u l d f i n d the A to tune her v i o l i n w i t h i n her head, while other v i o l i n i s t s needed to hear a note p l a y e d . One s u b j e c t (S7) s t a t e d t h a t he knew what p i t c h to s t a r t on i n a c h o i r , before the p i t c h had been p l a y e d . One s u b j e c t (S9) r e p o r t e d n o t i c i n g i f a c h o i r was s i n g i n g sharp or f l a t , and one s u b j e c t (S5) r e p o r t e d n o t i c i n g d i f f e r e n c e s i n the sounds of d i f f e r e n t keys. Subjec t s g e n e r a l l y found i t d i f f i c u l t to d e s c r i b e what they thought happened when they named p i t c h e s . Four s u b j e c t s ( S i , S3, S4, and S6) r e p o r t e d t h a t i t was seemingly automatic and t h a t the name f o r the note seemed to pop i n t o t h e i r heads without them having to t h i n k a t a l l . One s u b j e c t (S2) r e p o r t e d t h a t she v i s u a l i z e d p l a y i n g a piano keyboard. Two s u b j e c t s (S5 and S7) s t a t e d t h a t some notes came a u t o m a t i c a l l y to them and they used r e l a t i v e p i t c h to r e l a t e other notes to the ones t h a t came a u t o m a t i c a l l y . One s u b j e c t (S9) r e p o r t e d f i n d i n g a "muscular memory" i n her t h r o a t to which to r e l a t e the p i t c h e s . Two s u b j e c t s r e p o r t e d t h a t naming p i t c h e s was u s u a l l y automatic but when the p i t c h e s were not i n tune, they each had a d i f f e r e n t s t r a t e g y : one (S8) imagined the sound of an A and then r e l a t e d the p i t c h i n q u e s t i o n to the A; and the other (S10) p i c t u r e d a piano keyboard to f i n d the c l o s e s t note to the p i t c h he heard. Subjects a l s o found i t d i f f i c u l t to d e s c r i b e the way i n which they named i n t e r v a l s . Three s u b j e c t s (SI, S4, and S10) 45 r e p o r t e d naming the two notes and then c a l c u l a t i n g the i n t e r v a l between them. Three s u b j e c t s (S2, S8, and S9) s t a t e d t h a t they d i d not name the notes, but l i s t e n e d to the p i t c h d i f f e r e n c e between the two notes. Three s u b j e c t s (S3, S5, and S7) r e p o r t e d t h a t they used a combination of the aforementioned s t r a t e g i e s , and one s u b j e c t (S6) r e p o r t e d t h a t he f i r s t thought of a chord t h a t the two notes would be found i n , named the two p i t c h e s , and f i n a l l y c a l c u l a t e d the i n t e r v a l s e p a r a t i n g the two notes. Three females and two males made up the group of s u b j e c t s who b e l i e v e d they d i d not have a b s o l u t e p i t c h . Piano was the f i r s t instrument played by four s u b j e c t s , who a l l r e p o r t e d s t a r t i n g to p l a y a t an age of four t o f i v e y e a r s . F l u t e was the f i r s t instrument played by the remaining s u b j e c t (S14); she began l e a r n i n g t o p l a y the f l u t e a t age e i g h t . One s u b j e c t (S12) re p o r t e d t h a t she f i r s t l e a r n e d to p l a y by ear, two s u b j e c t s ( S l l and S13) s t a t e d t h a t they played both by ear and from music when f i r s t l e a r n i n g , and the remaining two s u b j e c t s (S14 and S15) r e p o r t e d b e g i n n i n g by l e a r n i n g from w r i t t e n music. Subjec t s i n t h i s group had a l l s t u d i e d from two to s i x other instruments. One s u b j e c t ( S l l ) r e p o r t e d t h a t h i s main instrument was the piano; one s u b j e c t ' s main instrument was the h a r p s i c h o r d (S12); one s u b j e c t ' s main instrument was the g u i t a r (S13); one s u b j e c t ' s main instrument was v o i c e (S14); and one s u b j e c t ' s main instruments were the piano and v o i c e (S15). Subjects i n t h i s group a l s o had d i f f i c u l t y d e s c r i b i n g t h e i r s t r a t e g i e s f o r naming i n t e r v a l s . A l l s u b j e c t s r e p o r t e d naming i n t e r v a l s by d e c i d i n g the s i z e of the i n t e r v a l between the two 46 notes; none r e p o r t e d attempting to name the notes f i r s t and then i n f e r the i n t e r v a l . One s u b j e c t ( S l l ) r e p o r t e d u s u a l l y naming i n t e r v a l s a u t o m a t i c a l l y , but i f he was i n doubt, c o n f i r m i n g h i s judgement of the i n t e r v a l with a s e t of " t o n a l a s s o c i a t i o n s " ( f o r example, a p e r f e c t f o u r t h sounded l i k e "dominant to t o n i c " ) . One s u b j e c t (S12) r e p o r t e d u s i n g s o l f e g g i o t o name i n t e r v a l s . One s u b j e c t (S13) r e p o r t e d u s i n g mnemonics i n the form of f a m i l i a r tunes t h a t c o n t a i n e d known i n t e r v a l s , and matching the i n t e r v a l to the song. One s u b j e c t (S14) r e p o r t e d checking i n t e r v a l s m e l o d i c a l l y both ascending and descending, to v e r i f y her naming of an i n t e r v a l . One s u b j e c t (S15) r e p o r t e d a r b i t r a r i l y choosing the name of the f i r s t note of the i n t e r v a l , and then a u t o m a t i c a l l y v i s u a l i z i n g the two notes on the keyboard. None of the s u b j e c t s r e p o r t e d any known or suspected h e a r i n g problems. 4•4 Test Procedure The s u b j e c t s were seated, one a t a time, i n a sound t r e a t e d room with the experimenter. The t e s t tapes were played on a Nagra IV-D f u l l - t r a c k r e e l - t o - r e e l tape r e c o r d e r and presented over Beyer Dynamic DT-48 headphones a t a l e v e l of 60 to 65 dB SPL, as measured on a B r u e l and K j a e r 6 cm3 4152 a r t i f i c i a l e a r . A comfortable l e v e l was determined f i r s t as the t e s t tape was played over TDH-49 Maico headphones, and found to be between 58 and 63 dB. A s u b j e c t i v e l y equal i n t e n s i t y was then determined f o r the Beyer headphones. T h i s l e v e l was measured through the Beyer headphones u s i n g an adaptor custom-made to a l l o w the headphones to f i t over the a r t i f i c i a l e a r . The r e s u l t i n g measurement was higher by approximately 2 dB. The 60 and 65 dB marks were noted on the volume c o n t r o l of the Nagra tape r e c o r d e r and the volume was s e t between these two marks f o r the t e s t s e s s i o n s . S u b j e c t s were i n s t r u c t e d v e r b a l l y , from a w r i t t e n s e t of i n s t r u c t i o n s , to l i s t e n to each n o t e / i n t e r v a l and to mark the c o r r e c t or c l o s e s t n o t e / i n t e r v a l on the answer sheet (see Appendix B f o r complete i n s t r u c t i o n s , and Appendix C f o r sample answer sheets f o r each of the t e s t s ) . Answer sheets f o r T e s t s 1, 3, and 4 were s i m i l a r . For each item on the t e s t , a range of answer c h o i c e s was p r i n t e d on the answer sheet, and s u b j e c t s were asked to c i r c l e or u n d e r l i n e the c h o i c e they thought best f i t the note or i n t e r v a l t h a t was presented. The answer sheet f o r Test 2 c o n s i s t e d of item numbers with blank spaces a d j a c e n t to them. Subject s were asked to w r i t e the name of the note t h a t best f i t the note t h a t was presented. S u b j e c t s were requested to mark an answer f o r each item on every t e s t , even i f they found i t d i f f i c u l t to decide on an answer. The t o t a l t e s t time f o r the four t e s t s was a p p r o x i m a t e l y one and a h a l f hours. S u b j e c t s c o u l d choose e i t h e r to do a l l four t e s t s i n one s e s s i o n , or to do the f i r s t two t e s t s a t one s e s s i o n and the l a s t two t e s t s a t another s e s s i o n . 48 CHAPTER 5 RESULTS AND DISCUSSION 5.1 Data S o r t i n g Raw data were entered i n t o a computer, or g a n i z e d i n a v i s u a l l y l o g i c a l d i s p l a y , p r i n t e d , and a n a l y z e d . The d i s p l a y f o r the data of each t e s t i s d e s c r i b e d i n the s e c t i o n s f o l l o w i n g . 5.2 Te s t 1 As s t a t e d i n s e c t i o n 4.21, the purpose of t h i s t e s t was to determine each s u b j e c t ' s a b i l i t y a t naming standard s e q u e n t i a l m u s i c a l i n t e r v a l s . S u b j e c t s were asked t o name 120 s e q u e n t i a l m u s i c a l i n t e r v a l s c o r r e s p o n d i n g to the c a t e g o r i e s minor t h i r d , major t h i r d , p e r f e c t f o u r t h , t r i t o n e , p e r f e c t f i f t h , and minor s i x t h , u s i n g the standard m u s i c a l i n t e r v a l names. The s i x c a t e g o r i e s were d e f i n e d r e l a t i v e to the standard equal-tempered s c a l e . The data of each s u b j e c t were rearranged so t h a t responses f o r each i n t e r v a l c a t e g o r y were grouped t o g e t h e r . For each i n t e r v a l c ategory, the data were d i v i d e d i n t o two columns, one f o r ascending, the other f o r descending i n t e r v a l s . Each of these columns was f u r t h e r s u b d i v i d e d i n t o two columns, one f o r each block of s t i m u l i . Examination of the data d i d not r e v e a l t h a t e i t h e r manner of p r e s e n t a t i o n (ascending or descending) or p o s i t i o n i n the p r e s e n t a t i o n order had any n o t i c e a b l e e f f e c t on s u b j e c t s ' responses. Scores on Test 1 f 01? the''ten s u b j e c t s with a b s o l u t e p i t c h ranged from 80 to 100% c o r r e c t , -with a median of 96%. Scores f o r the f i v e s u b j e c t s without a b s o l u t e p i t c h group ranged from 83 to 100% c o r r e c t , a l s o with a median of 96%. Seven of the a b s o l u t e p i t c h s u b j e c t s ( S i , S2, S3, S7, .£T8, S9, and S10), and four of the non-absolute p i t c h subjects' ( S l l , S12, S14, and S15) had s c o r e s of over 90% c o r r e c t on Test 1. -These s c o r e s are shown i n Table VII below. 5.3 Test 2 -As s t a t e d i n s e c t i o n 4.22, the purpose of t h i s t e s t was to determine each s u b j e c t ' s a b i l i t y a t naming s i n g l e puretones. S u b j e c t s were asked to name 60 s i n g l e puretones c o r r e s p o n d i n g to notes of the equal-tempered s c a l e , u s i n g standard m u s i c a l note names. The data were r e o r d e r e d so t h a t the f i v e responses to each note were d i s p l a y e d a d j a c e n t to each other i n rows. Each response was compared to the c o r r e c t response f o r t h a t s t i m u l u s , and the d i s t a n c e between them i n semitones was c a l c u l a t e d . The r e s u l t s of T e s t 3 (to be d e s c r i b e d i n the next s e c t i o n ) i n d i c a t e d t h a t the i n t e r n a l p i t c h r e f e r e n c e of most s u b j e c t s was not c e n t r e d e x a c t l y on one note, but l o c a t e d between two notes of the equal-tempered s c a l e ; i t ranged (S to S) from 40 cents below to 20 cents above the standard equal-tempered t u n i n g . Because of 50 t h i s v a r i a b i l i t y , i t was f e l t t h a t a response to a giv e n s t i m u l u s should be regarded as c o r r e c t i f i t was w i t h i n one semitone (up or down) from the expected response. Since i n d i v i d u a l p i t c h r e f e r e n c e s c o u l d be e i t h e r above or below the standard p i t c h r e f e r e n c e , i t was necessary to determine f o r each s u b j e c t whether the semitone above or the semitone below the expected response would be regarded as c o r r e c t . The number of responses which were one semitone above the expected response were counted, as were the number of responses which were one semitone below the expected response. The l a r g e r of these two sums was added to the unadjusted s c o r e , r e s u l t i n g i n an a d j u s t e d score r e v e a l i n g the percentage of items c o r r e c t +/- 1/2 semitone. One s u b j e c t (S6) had an i n t e r n a l p i t c h r e f e r e n c e which was one whole semitone below the st a n d a r d : the m a j o r i t y of h i s responses on Test 2 were one semitone above the c o r r e c t response, and Test 3 r e s u l t s confirmed t h i s i n t e r n a l p i t c h r e f e r e n c e . T h e r e f o r e , f o r t h i s s u b j e c t , expected responses were one semitone below the standard equal-tempered t u n i n g . For the a b s o l u t e p i t c h group, % c o r r e c t +/- 1/2 semitone ranged from 62 to 100% with a median of 90%. F i v e s u b j e c t s i n t h i s group ( S i , S6, S8, S9, and S10) surpassed the 90% mark. One s u b j e c t who b e l i e v e d she had a b s o l u t e p i t c h (S2) was unable to a c c u r a t e l y name the puretones i n Test 2, a c h i e v i n g o n l y 62%. She re p o r t e d t h a t she f e l t the lack of harmonics i n the s t i m u l i h indered her naming of the notes. She was the o n l y s u b j e c t i n the a b s o l u t e p i t c h group to score below 85% on Test 2. For the group without a b s o l u t e p i t c h , s c o r e s on Test 2 ranged from 23 to 60% with a median of 32%. Thus, there were two q u i t e d i s t i n c t d i s t r i b u t i o n s of s c o r e s , one f o r each group of s u b j e c t s . In a l l but one case (S2), the r e s u l t s confirmed the s u b j e c t s ' own judgements of t h e i r a b s o l u t e p i t c h a b i l i t i e s . Scores f o r Test 2 are shown i n Table VII below. 5.4 Te s t 3 The purpose of t h i s t e s t was to determine how, and with which a c c u r a c y and c o n s i s t e n c y , s u b j e c t s i n the a b s o l u t e p i t c h group c o u l d name puretones i n 20-cent frequency increments u s i n g the twelve standard note name c a t e g o r i e s of the equal-tempered s c a l e , and a l s o to determine each s u b j e c t ' s i n t e r n a l p i t c h r e f e r e n c e . S u b j e c t s were asked to name the notes c o r r e s p o n d i n g to 5 blocks of 43 puretones. There were o n l y twelve p o s s i b l e responses to the 43 d i f f e r e n t s t i m u l u s types, f o r c i n g s u b j e c t s to use the names of the c l o s e s t standard notes. Responses were converted to numbers from 1 to 12, cor r e s p o n d i n g t o the notes from A to G#, and then rearranged so th a t the f i v e responses f o r each s t i m u l u s type were d i s p l a y e d a d j a c e n t to each o t h e r . For each s u b j e c t , the mean of the f i v e responses f o r each s t i m u l u s type was c a l c u l a t e d , and these means were p l o t t e d on a graph, an example of which i s seen i n F i g u r e 1. For each s u b j e c t , the standard d e v i a t i o n from the mean f o r each s t i m u l u s type and the mean of these standard d e v i a t i o n s were c a l c u l a t e d . The mean of the standard d e v i a t i o n s ranged from 0.15 to 0.78 semitones, with a median of .41 semitones. A subset of Test 3 data f o r SI with a mean standard d e v i a t i o n of l e s s than 52 CO CO u_ LiJ h- Li 3 1 f id 53 0.5 semitones i s shown below, i n Table VI. SD's f o r a l l s u b j e c t s are shown i n Table V I I . TABLE VI Example Test 3 data ( S I ) , showing standard d e v i a t i o n s and mean of standard d e v i a t i o n s . Stimulus Token Mean SD Mean type 1 2 3 4 5 E+60 9 9 9 9 9 9.0 0.0 E+80 9 9 9 9 9 9.0 0.0 F+ 0 9 8 9 9 9 8.8 0.4 F+20 9 9 9 9 10 9.2 0.4 F+40 9 9 10 9 11 9.6 0.9 0.34 Using a b e s t - f i t program, a s t r a i g h t l i n e y = mx + h was f i t t e d through the data p o i n t s of each s u b j e c t ; another s t r a i g h t l i n e was c a l c u l a t e d f o r the p r e d i c t e d d a t a . The o r d i n a t e s of the s u b j e c t ' s data r e g r e s s i o n l i n e were compared with those of the p r e d i c t e d l i n e a t three p o i n t s along the l i n e , each c o r r e s p o n d i n g to the c e n t r e of one of the three s e t s of i n t e r v a l s to be used i n Test 4. The d i f f e r e n c e between the o r d i n a t e s of the p r e d i c t e d data and the s u b j e c t ' s data was taken to be equal to the number of cents by which the i n t e r n a l p i t c h r e f e r e n c e of the s u b j e c t d i f f e r e d from 0 a t each one of these three p o i n t s . I t was assumed t h a t the i n t e r n a l p i t c h r e f e r e n c e of the s u b j e c t a t each of the th r e e p o i n t s was r e p r e s e n t a t i v e of the s u b j e c t ' s i n t e r n a l p i t c h r e f e r e n c e a c r o s s t h a t whole s e t of i n t e r v a l s i n Test 4. Much i n d i v i d u a l v a r i a t i o n was observed i n i n t e r n a l p i t c h r e f e r e n c e s . S i x s u b j e c t s (S2, S3, S4, S8, S3, and S10) had i n t e r n a l p i t c h r e f e r e n c e s h i f t s which were c o n s i s t e n t over the whole range of s t i m u l i . These r e f e r e n c e s h i f t s ranged from - 40 cents to 0 c e n t s . The remaining four s u b j e c t s had i n t e r n a l p i t c h r e f e r e n c e s h i f t s which v a r i e d , over the 9.5 semitone range of Test 3, by as much as 40 c e n t s . R e s u l t s f o r a l l s u b j e c t s on T e s t s 1, 2 and 3 are shown i n Table V I I . 5.5 Test 4 T e s t 4 was the main t e s t of t h i s study. I t s purpose, as s t a t e d i n S e c t i o n 4.24, was to determine how s u b j e c t s would c a t e g o r i z e s e q u e n t i a l m u s i c a l i n t e r v a l s whose component tones were not always c o n s i s t e n t with equal-tempered t u n i n g , and to determine which of two p o s s i b l e s t r a t e g i e s these s u b j e c t s would use. S u b j e c t s were asked to name 165 s e q u e n t i a l musical i n t e r v a l s which ranged i n 20-cent s t e p s from 260 cents to 540 c e n t s . Responses were converted to numbers from 2 to 6, c o r r e s p o n d i n g to the i n t e r v a l s major second (2), minor t h i r d (3), major t h i r d ( 4 ) , p e r f e c t f o u r t h ( 5 ) , and t r i t o n e ( 6 ) . The data were rearranged i n t o three matrices a c c o r d i n g to the lower note of each s t i m u l u s (B, C#, and D#). There was one data matrix f o r the s e t of i n t e r v a l s with bottom note from 40 cents below to 40 cents above B, one f o r the s e t of i n t e r v a l s with bottom note from 40 cents below to 40 cents above C#, and one f o r the s e t of i n t e r v a l s with bottom note from 40 cents below to 40 cents above TABLE VII 55 Scores f o r a l l s u b j e c t s on Test 1, Test 2, and Test 3. Subject Test 1 % c o r r e c t Test 2 % c o r r e c t +/- 1/2 semit SD Test 3 Reference i n cents B C# D# (a) Absolute p i t c h group 1 92 93 .49 0 -20 -20 2 93 62 .78 -20 -20 -20 3 89 87 .36 0 0 0 4 100 88 .46 -40 -40 -40 5 84 85 .46 -40 -20 -20 6 80 92 .31 -20 0 +20 7 99 88 .29 0 -20 -20 8 99 93 .25 -40 -40 -40 9 100 93 .67 -20 -20 -20 1 0 ( i ) 100 100 .15 0 0 0 1 0 ( i i ) - - .18 + 20 +20 +20 (b) Non - a b s o l u t e p i t c h group 11 100 37 - - -12 93 60 - - -13 83 23 - - -14 96 30 - • - -15 100 32 _ _ 56 Each of the s u b j e c t ' s data matrices was compared to two ma t r i c e s which would each be p r e d i c t e d by a p a r t i c u l a r s t r a t e g y : (a) a matrix r e p r e s e n t i n g the " r e l a t i v e p i t c h (RP) s t r a t e g y " , i n which the d i f f e r e n c e between the two tones i n semitones and cents would be determined, and then rounded o f f to the c l o s e s t i n t e r v a l , and (b) a matrix r e p r e s e n t i n g the "absolute p i t c h (AP) s t r a t e g y " , i n which the two tones would each be f i r s t rounded o f f to the c l o s e s t semitone, and then the d i f f e r e n c e between the two notes would be c a l c u l a t e d . For the AP s t r a t e g y , f i v e p r e d i c t i o n m a t r i c e s were made, co r r e s p o n d i n g to f i v e i n t e r n a l p i t c h r e f e r e n c e s : - 40 c e n t s , - 20 c e n t s , 0 c e n t s , + 20 c e n t s , and + 40 c e n t s . The RP s t r a t e g y matrix and the f i v e AP s t r a t e g y matrices are d i s p l a y e d i n Table V I I I . For each data matrix of each s u b j e c t , o n l y two p r e d i c t i o n m a t r i c e s were used i n the comparison, the RP s t r a t e g y matrix and one of the f i v e AP s t r a t e g y m a t r i c e s , namely the one which corresponded most c l o s e l y with the s u b j e c t ' s i n t e r n a l p i t c h r e f e r e n c e f o r t h a t data matrix as determined i n Test 3. Using the AP s t r a t e g y , because the two notes are f i r s t rounded o f f to the c l o s e s t note and then the d i f f e r e n c e between them c a l c u l a t e d , rounding e r r o r s can be compounded, ca u s i n g the i n c o r r e c t i d e n t i f i c a t i o n of some i n t e r v a l s . For example, i f a s u b j e c t with a b s o l u t e p i t c h was presented with the i n t e r v a l C + 60 cents to E + 20 cents (360 c e n t s ) , one would expect t h a t , u s i n g the AP s t r a t e g y , t h i s s u b j e c t would, because of a s t r o n g tendency to name the notes f i r s t , i d e n t i f y the notes as C# and E, and then i d e n t i f y the i n t e r v a l between those notes as a minor t h i r d (300 c e n t s ) . Using the RP s t r a t e g y , the a c t u a l p i t c h 57 TABLE VI I I P r e d i c t i o n m a t r i c e s f o r Test 4. Marked c e l l s are o u t l i n e d . Bottom note (BN) i s from 40 cents below to 40 cents above the note B, Cft, or D#. Top note (TN) i s i n cents from bottom note 0. 1• AP s t r a t e g y with - 40 cent r e f e r e n c e BN -40 -20 0 + 20 + 40 TN 300 320 340 360 380 400 420 440 460 480 500 3 3 _3_ 2 2 4 _4_ 3 3 4 J_ _4_ 3 3 4 4 4 3 3 4 4 4 4 4 J_ 3 5 _5_ 4 4 5 _5_ _5_ 4 4 5 5 5 4 4 5 5 5 5 5 5 4 Jj 2 • AP s t r a t e g y with -20 cent r e f e r e n c e TN 300 320 340 360 380 400 420 440 460 480 500 BN -40 3 ! 3 I 4 4 4 4 1 4 | 5 5 5 5 -20 3 3 4 4 4 4 4 5 5 5 5 0 3 3 4 4 4 4 4 5 5 5 5 + 20 3 3 4 4 4 4 4 5 5 ! 5 5 + 40 I I 2 ! 3 3 3 3 3 4 4 4 m 3• AP s t r a t e g y with 0 cent r e f e r e n c e BN -40 -20 0 + 20 + 40 TN 300 320 340 360 380 400 420 440 460 480 500 3 3 3 3 3 3 3 3 3 3 _3_ 3 3 3 4 4 _4_ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 _4_ 4 4 4 5 5 _5_ 5 5 5 5 5 5 5 5 5 5 5 4• AP s t r a t e g y with + 20 cent r e f e r e n c e TN 300 320 340 360 380 400 420 440 460 480 500 BN -40 . 1 4 ! 4 4 4 f 5 5 5 5 5 1 6 61 -20 3 3 3 3 4 4 4 4 4 5 5 0 3 3 3 3 4 4 4 4 4 5 5 + 20 3 3 3 3 4 4 4 4 4 5 5 + 40 3 3 3 3 I 4 1 4 4 4 4 1 5 I 5 5 • AP s t r a t e g y with + 40 cent r e f e r e n c e BN -40 -20 0 +20 + 40 TN 300 320 4 JL 3 3 3 3 3 3 340 360 380 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 400 420 440 460 480 500 5 _5_ 4 4 4 4 4 4 5 5 4 4 4 5 _5_ _4_ 4 4 5 _5_ 4 4 6 _6 5 5 5 6. RP s t r a t e g y TN 300 320 340 360 380 400 420 440 460 480 500 BN -40 3 4 4 4 4 4 5 5 5 5 5 -20 3 3 4 4 4 4 4 5 5 5 5 0 3 3 3 4 4 4 4 4 5 5 5 + 20 3 3 3 3 4 4 4 4 4 5 5 + 40 3 3 3 3 3 4 4 4 4 4 5 58 d i f f e r e n c e of 360 cents would be rounded o f f to the c l o s e s t i n t e r v a l , a major t h i r d (400 c e n t s ) . Two measures were d e v i s e d to show how c l o s e s u b j e c t s ' data m a t r i c e s were to each of the p r e d i c t i o n m a t r i c e s . Each AP s t r a t e g y p r e d i c t i o n matrix d i f f e r s from the RP s t r a t e g y matrix o n l y on a c e r t a i n number of e n t r i e s (12 to 14). These are o u t l i n e d i n Table VIII and r e f e r r e d to as 'marked c e l l s ' or 'marked e n t r i e s ' . The c e l l s t h a t d i f f e r between any AP s t r a t e g y p r e d i c t i o n matrix and the RP s t r a t e g y p r e d i c t i o n matrix always correspond to one of the f o l l o w i n g two groups: (a) one group of i n t e r v a l s which, i n terms of a c t u a l p i t c h d i f f e r e n c e u s i n g the RP s t r a t e g y were 40 cents away from a standard i n t e r v a l c ategory, but would be i d e n t i f i e d as the neighbour i n t e r v a l 60 cents away with the AP s t r a t e g y ( c a l l e d NI60 i n t e r v a l s ) ; and (b) another group of i n t e r v a l s which, i n terms of a c t u a l p i t c h d i f f e r e n c e u s i n g the RP s t r a t e g y were 20 cents away from a standard i n t e r v a l c a tegory, but would be i d e n t i f i e d as the neighbour I n t e r v a l 80 c ents away with the AP s t r a t e g y ( c a l l e d NI80 i n t e r v a l s ) . The f i r s t measure, DI, g i v e s NI80 i n t e r v a l s a weight of 25, NI60 i n t e r v a l s a weight of 5, and unmarked e n t r i e s a weight of 1. I t i d e n t i f i e s f o r each data matrix, those e n t r i e s which are d i f f e r e n t from the c o r r e s p o n d i n g e n t r y i n the p r e d i c t i o n matrix (RP or AP), and computes the sum of the weights c o r r e s p o n d i n g to these e n t r i e s , thus y i e l d i n g one d i s t a n c e to the RP p r e d i c t i o n and one d i s t a n c e to the AP p r e d i c t i o n . Each one of these numbers i s taken to be the " p r e l i m i n a r y d i s t a n c e " to the s a i d p r e d i c t i o n . In order to s u b t r a c t out the e f f e c t s of random e r r o r , the maximum sum of the p r e l i m i n a r y d i s t a n c e to the RP s t r a t e g y and of the 59 p r e l i m i n a r y d i s t a n c e to the AP s t r a t e g y without random e r r o r (MSWRE) i s determined. T h i s i s done by adding together the weights of a l l the marked e n t r i e s . For example, the maximum sum of the p r e l i m i n a r y d i s t a n c e to the RP s t r a t e g y p l u s the p r e l i m i n a r y d i s t a n c e to the AP s t r a t e g y f o r a p i t c h r e f e r e n c e s h i f t of -40 cent s i s (5 X 25) + (9 X 5) = 170. There are 5 NI80 i n t e r v a l s each with a weight of 25, and 9 NI60 i n t e r v a l s each with a weight of 5. Without random e r r o r , these are the o n l y e n t r i e s which should d i f f e r between the two p r e d i c t i o n m a t r i c e s , and each e n t r y should d i f f e r on o n l y one of the two p r e d i c t i o n m a t r i c e s . I t can be assumed t h a t the number by which the sum of the two d i s t a n c e s of each data matrix exceeds the MSWRE i s the r a t e of random e r r o r . One h a l f of t h i s random e r r o r r a t e i s s u b t r a c t e d from each of the " p r e l i m i n a r y d i s t a n c e s " f o r the gi v e n data matrix. The two r e s u l t i n g numbers are taken to be the " d i s t a n c e s " to the p r e d i c t i o n m a t r i c e s . The second measure, D2, uses no weights. I t computes the e r r o r r a t e on the unmarked e n t r i e s and assumes the e r r o r r a t e t o be s i m i l a r f o r the marked e n t r i e s . The " d i s t a n c e " computed i n t h i s case i s the sum of marked e n t r i e s d i f f e r i n g from the marked e n t r i e s i n the p r e d i c t i o n matrix (RP or AP), decreased by the product of the e r r o r r a t e by the number of marked e n t r i e s . Dl and D2 d i s t a n c e s were normalized by d i v i d i n g the t o t a l of the two d i s t a n c e s f o r each data matrix by the sum of the two d i s t a n c e s , r e s u l t i n g i n sco r e s from 0 to 100. Table IX r e p o r t s normalized s c o r e s u s i n g measures Dl and D2. I t i s ev i d e n t t h a t s c o r e s on the two measures are q u i t e w e l l c o r r e l a t e d . A l l but three of the 64 data m a t r i c e s have d i s t a n c e s which are c l o s e r t o 60 TABLE IX Tes t 4 r e s u l t s , showing normalized d i s t a n c e s DI and D2 to RP and AP s t r a t e g i e s . Subject M a t r i x O f f s e t DI D2 To RP To AP To RP To AP (a) Absolute p i t c h group 1 B 0 28.57 71.43 26.47 73.53 C# -20 30.36 69 .64 34.54 65.46 D# -20 23.21 76.79 55.72 44.28 2 B -20 5.36 94.64 5.71 94.29 -20 8.93 91.07 18.47 81.53 D# -20 1.79 98.21 0.45 99.55 3 B 0 35.71 64.29 50.00 50.00 C* 0 25.71 74.29 44.74 55.26 D# 0 32.14 67.86 36.11 63.89 4 B -40 0.00 100.00 11.69 88.31 C# -40 -7.14 107.14 -2.36 102.36 D# -40 -3.57 103.57 6 .37 93.63 5 B -40 37.50 62.50 24.32 75.68 C# -20 42.86 57.14 50.00 50.00 D# -20 16.07 83.93 -3.85 103.85 6 B -20 23.21 76.79 15.55 84.45 Ctt 0 32.14 67.86 39.82 60.18 D# + 20 43.93 56.07 24.00 76.00 7 B 0 53.57 46.43 60.18 39.82 C# -20 17.86 82.14 24 .23 75.77 D# -20 12.50 87.50 27.48 72.52 8 B -40 17.86 82.14 21.26 78 .74 C# -40 0.00 100.00 9.68 90.32 Dft -40 3.57 96.43 22.58 77.42 9 B -20 48.21 51.79 45.50 54.50 C» -20 30.36 69 .64 35.24 64.76 D# -20 37.50 62.50 54.70 45.30 10 ( i ) B 0 92.86 7.14 94.74 5.26 C# 0 7.14 92.86 -2.36 102.36 D# 0 57.14 42.86 71.32 28 .68 1 0 ( i i ) B + 20 1.79 98.21 -24.32 124.32 C* + 20 63.57 36 . 43 78.95 21.05 D# + 20 11.79 88.21 20.51 79.49 61 TABLE IX (continued) Subject M a t r i x O f f s e t D l To RP To AP D2 To RP To AP (b) Non--absolute p i t c h group 11 B (0) 25.00 75.00 16.44 83.56 C# (0) 32.14 67.86 39 .82 60.18 D# (0) 14.29 85.71 27.63 72.37 12 B (0) 28.57 71.43 31.31 68.69 C# (0) 7.14 92.86 9.27 90.73 D# (0) 25.00 75.00 16.44 83.56 13 B (0) 48.21 51.79 63.86 36.14 C# (0) 30.36 69.64 37.18 62.82 D# (0) 8.93 91.07 18.92 81.08 14 B (0) 21.43 78.57 50.00 50.00 C# (0) 25.00 75.00 19.45 80.55 D# (0) 7.14 92.86 16.67 83.33 15 B (0) 35.71 64.29 50.00 50.00 C* (0) 10.71 89 .29 19 . 45 80.55 D# (0) 14.29 85.71 31.31 68.69 the same p r e d i c t i o n matrix, whether u s i n g Dl or D2. Table X g i v e s examples of s c o r e s f o r e n t r i e s i n a h y p o t h e t i c a l data matrix which g r a d u a l l y change from being e x a c t l y i n accordance with one s t r a t e g y to being e x a c t l y i n accordance with the other s t r a t e g y , without random e r r o r s . Based on Table X, i t was d e c i d e d t h a t d i s t a n c e s would be c l a s s i f i e d i n the f o l l o w i n g manner: data m a t r i c e s on which e i t h e r d i s t a n c e Dl or D2 was below 10.00 would be c a l l e d "very c l o s e " t o a g i v e n s t r a t e g y ; data m a t r i c e s on which e i t h e r d i s t a n c e Dl or D2 was between 10.00 and 33.33 would be c a l l e d " c l o s e " t o a g i v e n s t r a t e g y ; and data m a t r i c e s on which e i t h e r d i s t a n c e Dl or D2 was between 33.33 and 50.00 would be c a l l e d "mixed" between both s t r a t e g i e s . I f a s u b j e c t used the RP s t r a t e g y , h i s / h e r d i s t a n c e s to RP should be low and h i s / h e r d i s t a n c e s to AP should be h i g h . I f a s u b j e c t used the AP s t r a t e g y , these trends should be r e v e r s e d . I t was the hope of the experimenter t h a t s u b j e c t s would c l e a r l y use one or the other s t r a t e g y , a c r o s s a l l three m a t r i c e s . For f i v e s u b j e c t s i n the a b s o l u t e p i t c h group ( S i , S2, S4, S6, and S8) and three s u b j e c t s i n the non-absolute p i t c h group ( S l l , S12, and S14) a l l t h r e e data m a t r i c e s corresponded c l o s e l y or v e r y c l o s e l y with the RP s t r a t e g y . For four s u b j e c t s i n the a b s o l u t e p i t c h group (S3, S5, S7, and S9) and two s u b j e c t s i n the non-a b s o l u t e p i t c h group (S13 and S15) a t l e a s t one data matrix corresponded c l o s e l y or v e r y c l o s e l y with the RP s t r a t e g y , and a t l e a s t one data matrix corresponded to a mix of both s t r a t e g i e s . No c o r r e l a t i o n s with s c o r e s on other t e s t s c o u l d be found to d i f f e r e n t i a t e these two groups of r e s u l t s . I n d i v i d u a l v a r i a t i o n i n the p e r c e p t i o n of m u s i c a l i n t e r v a l s , d i s c u s s e d i n Chapter 2, 63 TABLE X Examples of d i s t a n c e s t o RP and AP i n r e l a t i o n to the number of e n t r i e s d i f f e r i n g from each p r e d i c t i o n matrix. S t r a t e g y used Dl D2 To RP To AP To RP To AP A l l RP 0.00 100.00 0.00 100.00 1 NI60 to AP 3.57 95.71 8.33 91.67 1 NI60, 1 NI80 to AP 21.43 78.57 16.67 83.33 2 NI60, 1 NI80 to AP 25.00 75.00 25.00 75.00 2 NI60, 2 NI80 to AP 42.86 57.14 33.33 66.67 3 NI60, 2 NI80 to AP 46.43 53.57 41.67 58.33 4 NI60, 2 NI80 to AP 50.00 50.00 50.00 50.00 5 NI60, 2 NI80 to AP 53.57 46.43 58.33 41.67 6 NI60, 2 NI80 to AP 57.14 42.86 33.33 66.67 6 NI60, 3 NI80 to AP 75.00 25.00 75.00 25.00 7 NI60, 3 NI80 to AP 78.57 21. 43 83.33 16.67 7 NI60, 4 NI80 to AP 95.71 3.57 91.67 8.33 8 NI60M 4 NI80 to AP 100.00 0.00 100.00 0.00 64 may have caused the r e s u l t s to correspond more or l e s s c l o s e l y with the RP s t r a t e g y . Only one s u b j e c t , S 1 0 ( l ) , who had shown the s t r o n g e s t a b s o l u t e p i t c h a b i l i t y i n the f i r s t three t e s t s , had r e s u l t s t h a t corresponded w i t h the AP s t r a t e g y ; however, t h i s correspondence was not c o n s t a n t over a l l three data m a t r i c e s . His r e s u l t s had a v e r y c l o s e correspondence with the AP s t r a t e g y on the "B" s t i m u l u s s e t , a v e r y c l o s e correspondence with the RP s t r a t e g y on the "C#" s t i m u l u s s e t , and a c l o s e correspondence with the AP s t r a t e g y on the "D#" s t i m u l u s s e t . These r e s u l t s are p u z z l i n g , as the responses seem to i n d i c a t e t h a t one s t r a t e g y was used f o r one s e t of i n t e r v a l s , and the o p p o s i t e s t r a t e g y was used f o r another s e t of i n t e r v a l s , although these i n t e r v a l s were randomly i n t e r l e a v e d i n the t e s t . A t h i r d p r e d i c t i o n matrix f o r the data of S10 was made, based on h i s responses to the s i n g l e note s t i m u l i of Test 3. The t h r e e data m a t r i c e s were each compared to the RP matrix and to the above p r e d i c t i o n matrix, i n the same manner as they had been compared i n the D2 measure. R e s u l t s of t h i s comparison o n l y confirmed the e a r l i e r r e s u l t s . In order to attempt t o c l a r i f y h i s s t r a t e g y f o r i d e n t i f y i n g i n t e r v a l s , S10 was asked to repeat T e s t s 3 and 4, approximately one month a f t e r h i s f i r s t t e s t s e s s i o n . New r e s u l t s f o r Test 3 i n d i c a t e d the same high degree of a c c u r a c y and c o n s i s t e n c y of note naming as on the f i r s t t e s t s e s s i o n . The s u b j e c t ' s i n t e r n a l p i t c h r e f e r e n c e s h i f t was now c l o s e r to + 20 c e n t s , as opposed to 0 cents on the f i r s t t e s t s e s s i o n , but was a g a i n c o n s i s t e n t over 65 the e n t i r e range of s t i m u l i . Table IX ( S l O ( i i ) ) shows h i s r e s u l t s i n T e s t 4 f o r the second t e s t s e s s i o n . The d i s t a n c e s D l and D2 show p a t t e r n s which are the r e v e r s e of those of the f i r s t s e s s i o n : on the B and D# matrix, responses correspond v e r y c l o s e l y and c l o s e l y to the RP s t r a t e g y , and on the C# matrix, responses correspond c l o s e l y t o the AP s t r a t e g y . F i g u r e 2 shows the d i s t a n c e s D2 f o r three s u b j e c t s : S8, whose data matrices corresponded c l o s e l y to the RP s t r a t e g y ; S3, whose data m a t r i c e s corresponded to a mixture of RP and AP s t r a t e g i e s ; and S10 ( i ) and ( i i ) , whose data m a t r i c e s have been d e s c r i b e d above. SlO's a b s o l u t e p i t c h a b i l i t y appeared to be the s t r o n g e s t among the a b s o l u t e p i t c h s u b j e c t s i n the study, and thus he might be expected to be the most i n c l i n e d t o use the AP s t r a t e g y ; however, examination of the r e s u l t s from a l l t e s t s c o u l d not g i v e an e x p l a n a t i o n f o r the changing of s t r a t e g y from one s e t o f . I n t e r v a l s t o the o t h e r . SD's f o r both Test 3 s e s s i o n s were examined f o r each note, i n each s e t of i n t e r v a l s . SlO's use of d i f f e r e n t s t r a t e g i e s does not appear to c o r r e l a t e with c e r t a i n t y or u n c e r t a i n t y of note naming, s i n c e v a r i a b i l i t y was v e r y low a c r o s s a l l the notes on both t e s t s e s s i o n s . Random e r r o r s f o r both T e s t 4 s e s s i o n s were examined. These remained approximately the same a c r o s s a l l m a t r i c e s and a c r o s s both t e s t s e s s i o n s . I t appears t h a t S10 was u s i n g both s t r a t e g i e s , but i t i s u n c l e a r why he seems to have changed h i s s t r a t e g y depending on which p i t c h e s were used i n the s t i m u l i , and a l s o p u z z l i n g t h a t the s t r a t e g i e s used should have r e v e r s e d between t e s t s e s s i o n s . 66 K : X V X ' X ^ y / / '•• '•• '•: \ \ '•• V \ \ , \ 'S '"% 'S ' ) '' j' ) '' ' •*•. X *••. v v v / ' / / / / -L. i- L. £ L— '//////..' '' {'', f (' /' / /' i A A J . X . X V .. y • V . A A A A A A A / < x x x x x x x x , , y v y W v y . . ^ • X . y,. y .K \ >:. ',. y . y , '\ • r • '//'// / ' / ///// /////'//// / - s / / / / / / / / / / / / / / / / / L . A . . A . . A . . A . . A . / . . .  .IX. .X„ A A A / ' y , ' . ' / > • / / / / ..' j ./ / ,.' / ..' y .•' / 1 ' yy yy yyyyy / y / / y y X-* v ••. v. *». *•. v v v *•. *•. v *. — . . v—~ X / ' / >' i 1 r" " i" f y'' \W \ \ 'v \ \ A A A • \ > V A A X A ; A ; A . A . A > \ XxXxXXX: V V V V V V V ;;xx v ' W > : ! X X X X . X X X X X X . u-VVVu-VVVVV -"*/ X V V X X X - V . X X - •••'//////// ''/'/'///////// / / / / / / / / / / ••' / / / / / . / / / / / / / / / / / " l — r \ \ \ C4 ~ c> c> c> !j> d> r- f. > I 1?J L-li'l' Q :*"-= 'y< D C< " • — " 4 " / . ' 4 £ it: \ \ 7 .ID. .ID. "xi" V) ( T . U S C U S d ) OCiU DT.5| p 67 5.6 Summary The present study examined the p e r c e p t i o n of musical i n t e r v a l s by musicians with and without a b s o l u t e p i t c h . P r e v i o u s r e s e a r c h i n t o the p e r c e p t i o n of music has e s t a b l i s h e d two p o i n t s : (a) musicians without a b s o l u t e p i t c h p e r c e i v e musical intervals c a t e g o r i c a l l y , t h a t i s , a l l m u s i c a l i n t e r v a l s i n s m a l l increments over a c e r t a i n range are c o n s i s t e n t l y i d e n t i f i e d as the same i n t e r v a l (Burns and Ward, 1978); (b) musicians with a b s o l u t e p i t c h p e r c e i v e p i t c h e s c a t e g o r i c a l l y , t h a t i s , a l l notes i n s m a l l increments over a c e r t a i n range are c o n s i s t e n t l y i d e n t i f i e d as the same p i t c h ( S i e g e l and S i e g e l , 1977a). In order f o r these two p o i n t s to be t r u e the i n t e r v a l s , r e s p e c t i v e l y p i t c h e s , being i d e n t i f i e d must be e f f e c t i v e l y rounded o f f to the c l o s e s t standard i n t e r v a l / n o t e . In the p e r c e p t i o n of i n t e r v a l s , musicians with a b s o l u t e p i t c h presumably use e i t h e r of the aforementioned modes of c a t e g o r i c a l p e r c e p t i o n : (a) the RP s t r a t e g y , d i r e c t l y e v a l u a t i n g the I n t e r v a l , and rounding i t o f f to the c l o s e s t s t a n d a r d i n t e r v a l ; or (b) the AP s t r a t e g y , f i r s t rounding o f f the two notes to the c l o s e s t standard notes and then i n f e r r i n g the m u s i c a l i n t e r v a l between them. Most s u b j e c t s i n the present study appear to e v a l u a t e m u s i c a l i n t e r v a l s d i r e c t l y u s i n g the RP s t r a t e g y . One s u b j e c t appears to use the AP s t r a t e g y i n the context of s p e c i f i c p i t c h e s , and the RP s t r a t e g y i n the context of other p i t c h e s . His use of a s p e c i f i c s t r a t e g y f o r s p e c i f i c p i t c h e s does not remain constant over d i f f e r e n t t e s t s e s s i o n s . No reasonable e x p l a n a t i o n can be found f o r t h i s behaviour. 68. Since the use of the AP s t r a t e g y i n i n t e r v a l i d e n t i f i c a t i o n would r e s u l t i n no b e t t e r i d e n t i f i c a t i o n of i n t e r v a l s than the RP s t r a t e g y , and i n f a c t would r e s u l t i n i n c o r r e c t i d e n t i f i c a t i o n of i n t e r v a l s i n some cases, i t would be to the advantage of a possessor of a b s o l u t e p i t c h to suppress the i d e n t i f i c a t i o n of notes and to d i r e c t l y e v a l u a t e i n t e r v a l s . I t would appear t h a t those s u b j e c t s with the most c o n s i s t e n t a b s o l u t e p i t c h would be more l i k e l y to use the AP s t r a t e g y , as they would have the most con f i d e n c e i n t h e i r a b s o l u t e p i t c h a b i l i t i e s . I t would a l s o seem t h a t s u b j e c t s who had not played tunable instruments would be more l i k e l y to use the AP s t r a t e g y than s u b j e c t s who had played tunable instruments, because they may have had l e s s experience u s i n g r e l a t i v e p i t c h . For example, i n order to p l a y a well-tuned m u s i c a l I n t e r v a l on the piano, the p l a y e r has o n l y t o f i n d the l o c a t i o n of the two notes and p l a y them. Since a p r o f e s s i o n a l piano tuner tunes the piano, u s u a l l y a c c o r d i n g t o the e q u a l -tempered s c a l e , the p i a n i s t does not have to concern h i m s e l f with the t u n i n g of each note. On the other hand, when p l a y i n g a music a l i n t e r v a l on the v i o l i n , a f t e r d e t e r m i n i n g the g e n e r a l l o c a t i o n of the notes the p l a y e r must l i s t e n c l o s e l y t o the two notes to c r e a t e an " i n - t u n e " i n t e r v a l , be l t i n the e q u a l -tempered, j u s t , or another t u n i n g system. When p l a y i n g with other instruments, the v i o l i n i s t must l i s t e n to the r e l a t i v e p i t c h between the notes he p l a y s and those p l a y e d by the other i n s t r u m e n t a l i s t , to c r e a t e " i n - t u n e " i n t e r v a l s . 69 For a future study, i t might be wise to do a preliminary test to discover each subject's pitch reference sh i f t , and then create and present only the intervals that would be identified differently depending on the strategy used. With the equipment used in the present study this would be very time-consuming, as i t would be necessary to make individual audio tapes for each different pitch reference s h i f t . However, with the use of a computer and of programmable sound-generating hardware, with which the stimuli could be presented to the subject directly from the computer terminal and possibly modified as a function of the previous response(s), this could be very manageable. One could present each interval a greater number of times in each testing session without fatiguing the subject, as intervals which would be identified the same way regardless of strategy would not have to be presented, rather, only those intervals which would yield information regarding strategy would be presented. In this way, more precise knowledge might be gained about the strategies used in the identification of musical intervals by possessors of absolute pitch. More research is needed for stronger conclusions to be drawn; however, i t appears that most musicians with or without absolute pitch use their relative pitch a b i l i t y to identify musical intervals. It remains to be seen whether any musicians with absolute pitch consistently use their absolute pitch in the identification of musical intervals. 70 SELECTED BIBLIOGRAPHY Abraham, 0. (1901). Das a b s o l u t e Tonbewusstsein. Sammelbaende  der I n t e r n a t i o n a l e n M u s i k q e s e l l s c h a f t , 3., 1-86. Bachem, A. (1937). V a r i o u s types of a b s o l u t e p i t c h . J o u r n a l of  the A c o u s t i c a l S o c i e t y of America, 9, 146-151. Bachem, A. (1954). Time f a c t o r s i n r e l a t i v e and a b s o l u t e p i t c h d e t e r 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 S o c i e t y of  America,. 26, 751-753. Bachem, A. (1955). Absolute p i t c h . J o u r n a l of the A c o u s t i c a l  S o c i e t y of America. 27. 1180-1185. B a i r d , J.W. (1917). Memory f o r a b s o l u t e p i t c h . In S t u d i e s i n  Psychology. T l t c h e n e r Commemorative Volume, E.C. Sanford (Ed.). L.N Wilson: Worcester, Mass., 43-78. Brady, P.T. (1970). F i x e d s c a l e mechanism of a b s o l u t e p i t c h . J o u r n a l of the A c o u s t i c a l S o c i e t y of America, 48, 883-887. Brammer, L.M. (1951). Sensory cues i n p i t c h judgement. S t u d i e s  i n psychology, 11/ 336-340 Burns, E.M., and Ward, W.D. (1978). C a t e g o r i c a l p e r c e p t i o n -phenomenon or epiphenomenon: evidence from experiments i n the p e r c e p t i o n o£ melodic m u s i c a l i n t e r v a l s . J o u r n a l of the  A c o u s t i c a l S o c i e t y of America, 63, 456-468 Davies, J.B. (1978). The Psychology of Music. London: Hutchinson. Greene, P.C. (1937). V i o l i n i n t o 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 S o c i e t y of America, 9, 43-44. L e v i t t , H. (1971). Transformed up-down methods i n p s y c h o a c o u s t i c s . J o u r n a l of the A c o u s t i c a l S o c i e t y of  America. 49, 467-477. Mason, J.A. (1960). Comparison of s o l o and ensemble performances with r e f e r e n c e to Pythagorean, j u s t and equl-tempered i n t o n a t i o n s . J o u r n a l of Research i n Music E d u c a t i o n , 8, 31-38. Meyer, M. (1898). Zur The o r i e der D i f f e r e n z t o e n e und der Gehoersempfindungen ueberhaupt. B e i t r a e g e zur Akustischen  Muslkwlssen3chaft. 2, 25-65. Ni c k e r s o n , J.F. (1948). A comparison of performances of the same melody played i n s o l o and i n ensemble with r e f e r e n c e to equi-tempered, j u s t , and Pythagorean i n t o n a t i o n s . Unpublished d o c t o r a l d i s s e r t a t i o n , U n i v e r s i t y of Minnesota. 71 Oakes, W.F. (1955). An experimental study of p i t c h naming and p i t c h d i s c r i m i n a t i o n r e a c t i o n s . The J o u r n a l of G e n e t i c  Psychology P 86, 237-259. P e t r a n , L.A. (1932). An experimental study of p i t c h r e c o g n i t i o n . P s y c h o l o g i c a l Monograph, 42., No. 6. P o l l a c k , I. (1952). The i n f o r m a t i o n of elementary a u d i t o r y d i s p l a y s . J o u r n a l of the A c o u s t i c a l S o c i e t y of America, 24, 745-749. R i s s e t , J.C. (1971). Paradoxes de hauteur: l e concept de hauteur sonore n'est pas l e meme pour t o u t l e monde. Seventh  I n t e r n a t i o n a l Congress on A c o u s t i c s , Budapest, 1971, 20 S 10, 613-616. Seashore, C.E. (1919). The Psychology of M u s i c a l T a l e n t . New York: S i l v e r , B urdett and company. Seashore, C.E. (1938). Psychology of Music. New York: McGraw-H i l l . Sergeant, D. (1969). Experimental i n v e s t i g a t i o n of a b s o l u t e p i t c h . J o u r n a l of Research i n Music E d u c a t i o n , 17., 135-143. Shackford, C. (1961). Some asp e c t s of p e r c e p t i o n , P a r t I. J o u r n a l of Music Theory, 5, 162-202. Shackford, C. (1962a). Some as p e c t s of p e r c e p t i o n , P a r t I I . J o u r n a l of Music Theory. 6_, 66-90. Shepard, R.N. (1964). C i r c u l a r i t y i n judgements of a b s o l u t e p i t c h . J o u r n a l of the A c o u s t i c a l S o c i e t y of America, 36, 2346-2353. S i e g e l , J.A. (1972). The nature of a b s o l u t e p i t c h . In S t u d i e s i n the Psychology of Music, V o l . 8, I.E. Gordon (Ed.). Iowa C i t y : U n i v e r s i t y of Iowa P r e s s , 65-89. S i e g e l , J.A. (1974). Sensory and v e r b a l coding s t r a t e g i e s i n s u b j e c t s with a b s o l u t e p i t c h . J o u r n a l of Experimental  Psychology. 103 (1), 37-44 S i e g e l , J.A., and S i e g e l , W. (1977a). Absolute i d e n t i f i c a t i o n of notes and i n t e r v a l s by musicians. P e r c e p t i o n and  Psvchophyslcs, 21. 143-152. S i e g e l , J.A., and S i e g e l , W. (1977b). C a t e g o r i c a l p e r c e p t i o n of t o n a l i n t e r v a l s : musicians can't t e l l sharp from f l a t . P e r c e p t i o n and Psychophyslcs, 21, 399-407 Spender, N. (1980). Absolute p i t c h . In The New Grove D i c t i o n a r y  of Music and M u s i c i a n s . S. Sadie (Ed.). London: MacMillan P u b l i s h e r s L i m i t e d , 27-29. Teplov, B. (1966). P s y c h o l o g i e des A p t i t u d e s M u s i c a l e s . P a r i s : Presses U n i v e r s i t a i r e s de France. 72 Van K r e v e l e n , A. (1951). The a b i l i t y to make a b s o l u t e judgments of p i t c h . J o u r n a l of Experimental Psychology, 42, 207-215. Ward, W.D. (1953). Information and a b s o l u t e p i t c h . J o u r n a l of  the A c o u s t i c a l S o c i e t y of America, 25, 833. Ward, W.D. (1954). S u b j e c t i v e musical p i t c h . J o u r n a l of the  A c o u s t i c a l S o c i e t y of America, 26, 369-380. Ward, W.D. (1963a). Absolute p i t c h P a r t I. Sound, 2 (3), 14-21. Ward, W.D. (1963b). Absolute p i t c h P a r t I I . Sound, 2 (4), 33-41. Ward, W.D. (1970). M u s i c a l p e r c e p t i o n . In Foundations of Modern  A u d i t o r y Theory, 1, J.V. T o b i a s , (Ed.). New York and London: Academic P r e s s , 407-447. Ward, W.D. and Burns, E.M. (1982). Absolute p i t c h . In The Psychology of Music, D. Deutsch (Ed.). New York: Academic P r e s s , 431-451. Weinert, L. (1929). Untersuchungen ueber das a b s o l u t e Gehoer. A r c h l v f u r d i e Gesamte P s y c h o l o g i e , 73, 1-128. Wellek, A. (1938). Das a b s o l u t e Gehoer und s e i n e Typen. Z e l t s c h r i f t f u r Angewandte P s y c h o l o g i e & Charakterkunde- B e i h e f t e . 8_3, 1-368. Z a t o r r e , R.J., and Halpern, A.R. (1979). I d e n t i f i c a t i o n , d i s c r i m i n a t i o n , and s e l e c t i v e a d a p t a t i o n of simultaneous mu s i c a l i n t e r v a l s . P e r c e p t i o n and Psychophysics, 26 ( 5 ) , 384-395. Z w i s l o c k i , J . , Maire, F., Feldman, A.F., and Rubin, H. (1958). On the e f f e c t of p r a c t i c e and m o t i v a t i o n on the t h r e s h o l d of a u d i b i l i t y . J o u r n a l of the A c o u s t i c a l S o c i e t y of America, 3jp_, 254-262. APPENDIX A Q u e s t i o n n a i r e I d e n t i t i e s of a l l s u b j e c t s w i l l remain c o n f i d e n t i a l . 1 . Name: ; Subject #_ 2 . Phone: Date: 3. Age: Address: 4. Sex: 5. What was the f i r s t instrument you played? 6 . At what age d i d you s t a r t p l a y i n g t h i s instrument? 7. Did you begin by p l a y i n g w r i t t e n music or p l a y i n g by ear? What other instruments have you s t u d i e d ? What i s your major instrument now? Do you b e l i e v e you have a b s o l u t e p i t c h ? I f yes, ple a s e answer a and b below: a. How d i d you r e a l i z e you had a b s o l u t e p i t c h ? b. Ple a s e t r y to d e s c r i b e what happens when you hear a note and name i t : 1 1 . Please t r y to d e s c r i b e how you name i n t e r v a l s : 1 2 . Do you have any h e a r i n g problems? I f yes, ple a s e d e s c r i b e : APPENDIX B 74 I n s t r u c t i o n s to Subjects I'm l o o k i n g a t how people with a b s o l u t e p i t c h and people without a b s o l u t e p i t c h p e r c e i v e s i n g l e notes and melodic i n t e r v a l s . You w i l l hear s i n g l e notes and i n t e r v a l s made of puretones. Each note or i n t e r v a l w i l l be played once, and you w i l l have 3 or 4 seconds between items to decide on your answer. There w i l l be 4 t e s t s which take about 1 hour and 30 minutes i n a l l . You may take a break a f t e r each t e s t i f you wish. I f f o r any reason you f e e l you must sto p d u r i n g the t e s t , p lease say "Stop", and I w i l l s t o p the tape. However, Items w i l l not be repeated. Before we s t a r t , I'd l i k e t o ask you some qu e s t i o n s and have you read and s i g n t h i s consent form. The o n l y r i s k i n v o l v e d i n t h i s experiment i s of p o s s i b l e boredom. Test 1 I n s t r u c t i o n s In t h i s t e s t , you are going t o hear a s e r i e s of melodic i n t e r v a l s , both ascending and descending. Each i n t e r v a l w i l l be played once, f o l l o w e d by a s i l e n t p e r i o d . A f t e r e very f i v e i n t e r v a l s , you w i l l hear a descending sound which corresponds with a space on your answer sheet. T h i s descending sound i s simply a marker to a l l o w you to c o n f i r m your p l a c e on the t e s t . I want you to l i s t e n c a r e f u l l y to each i n t e r v a l and c i r c l e or u n d e r l i n e the name of each i n t e r v a l on your answer sheet. Please g i v e an answer f o r every item, even i f you f i n d i t d i f f i c u l t to decide on an answer. There are 127 items on t h i s t e s t . A f t e r the f i r s t f i v e items, i f you have any q u e s t i o n s , j u s t say "Stop" and I w i l l stop the tape. I f you wish, the f i r s t f i v e items w i l l be repeated, but remember, these are the o n l y items t h a t can be r e p l a y e d . Test 2 I n s t r u c t i o n s You are now going t o hear a s e r i e s of s i n g l e notes. Each note w i l l be played once, f o l l o w e d by a s i l e n t p e r i o d , a descending sound, and another s i l e n t p e r i o d . A f t e r e very f i v e notes, you w i l l hear an ascending sound which corresponds with a space on your answer sheet. The ascending sound i s a marker t o a l l o w you to c o n f i r m your p l a c e on the t e s t . I would l i k e you to w r i t e the name of each note i n the space p r o v i d e d on your answer sheet. Please name every note, even i f you f i n d i t d i f f i c u l t t o decide on an answer. There are 66 items on t h i s t e s t . 75 »st 3 I n s t r u c t i o n s You are now going to hear a s e r i e s of s i n g l e notes. You 111 hear a descending sound, a s h o r t s i l e n t p e r i o d , then the one t h a t I want you to name, and another s i l e n t p e r i o d . A f t e r v e r y f i v e notes, you w i l l hear an ascending tone to help you onfirm your p l a c e on the t e s t . C i r c l e or u n d e r l i n e the name of each note on your answer sheet. Your answer sheet has a l l the names of the musical s c a l e Erom A to GU. They are s e t out i n a l p h a b e t i c a l order - the order on the page has nothing to do with notes being higher or lower than each other. Please name every note, even i f you f i n d i t d i f f i c u l t to decide on an answer. There are 220 items on t h i s t e s t . Test 4 I n s t r u c t i o n s You w i l l now hear a s e r i e s of melodic i n t e r v a l s , both ascending and descending. Each i n t e r v a l w i l l be played once. You w i l l hear a descending sound, a short s i l e n t p e r i o d , then the melodic i n t e r v a l that I want you to name, and another s i l e n t p e r i o d . After every f i v e i n t e r v a l s you w i l l hear an ascending tone to help you c o n f i r m your p l a c e on the t e s t . C i r c l e or u n d e r l i n e the name of each i n t e r v a l on your answer sheet. Please name every i n t e r v a l , even i f you f i n d i t d i f f i c u l t to decide on an answer. There are 170 items on t h i s t e s t . 76 APPENDIX C Sample Answer Sheets T E S T Subject!* Date 1. 2. 3. 4. 5. min3 min3 min3 min3 min3 Maj3 Maj3 Maj3 Maj3 Maj3 P 4 P4 p4 p4 p4 TT TT TT TT TT p5 p5 p5 p5 p5 min6 min6 min6 min6 min6 6. 7. 8. 9. 10 min3 min3 mln3 min3 min3 Maj3 Maj3 Maj3 Maj3 Maj3 p4 p4 p4 p4 P4 TT TT TT TT TT p5 P 5 P5 p5 P5 min6 min6 min6 min6 min6 11, 12, 13, 14, 15, min3 min3 mln3 min3 min3 Maj3 Maj3 Maj3 Maj3 Maj3 P4 p4 P4 P4 P4 TT TT TT TT TT P5 P5 p5 p5 p5 min6 min6 min6 min6 min6 16 17 18 19 20 min3 min3 min3 min3 min3 Maj3 Maj3 Maj3 Maj3 Maj3 p4 p4 P4 p4 p4 TT TT TT TT TT p5 P5 P5 P5 P5 min6 min6 min6 min6 min6 T E S T 2 Subject)* Date 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29 . 30. 31. 32. 33. 34. 35. 36. 37. 38. 39 . 40. T E S T 3 Subject tt Date 78 1. A Bb Alt B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 2. A Bb Att B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 3. A Bb Alt B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 4. A Bb Att B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 5. A Bb A# B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 6. A Bb Att B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 7. A Bb A# B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 8. A Bb A* B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 9. A Bb Att B C Db ctt D Eb Dtt E F Gb Ftt G Ab Gtt 10. A Bb Att B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 11. A Bb Alt B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt 12. A Bb Att B C Db Ctt D Eb Dtt E F Gb Ftt G Ab Gtt T E S T 4 Subject & Date 79 1. Maj2 min3 Maj3 per£4 T r i t o n e 2. Maj2 min3 Maj3 p e r f 4 Tr itone 3. Maj2 min3 Maj3 p e r f 4 T r i t o n e 4. Maj2 min3 Maj3 p e r f 4 T r i t o n e 5. Maj2 min3 Maj3 perf 4 T r i t o n e 6. Maj2 min3 Maj3 p e r f 4 Tr itone 7. Maj2 min3 Maj3 p e r f 4 T r i t o n e 8. Maj2 min3 Maj3 p e r f 4 Tr i t o n e 9. Maj2 min3 Maj3 p e r f 4 T r i t o n e 10. Maj2 min3 Maj3 per f 4 Tr itone 11. Maj2 mln3 Maj3 p e r f 4 T r i t o n e 12. Maj2 min3 Maj3 per f 4 Tr i t o n e 13. Maj2 min3 Maj3 per f 4 T r i t o n e 14. Maj2 min3 Maj3 per f 4 T r i t o n e 15. Maj2 min3 Maj3 p e r f 4 T r i t o n e 16. Maj2 mln3 Maj3 p e r f 4 T r i t o n e 17. Maj2 min3 Maj3 p e r f 4 T r i t o n e 18. Maj2 min3 Maj3 per f 4 T r i t o n e 19 . Maj2 min3 Maj3 p e r f 4 T r i t o n e 20. Maj2 min3 Maj3 per f 4 T r i t o n e 

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