bigand, e. (1997). perceiving musical stability- the effect of tonal structure, rhythm, and musical...

7/27/2019 Bigand, E. (1997). Perceiving Musical Stability- The Effect of Tonal Structure, Rhythm, And Musical Expertise. JOUR…

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Journal of Experimental Psychology: Copyright 1997 by the American Psychological Association, Inc.Human Perception and Performance 0096-1523/97/$3.001997, Vol. 23, No. 3 , 808 -822

Perceiving Musical Stabil i ty: The Effect of Tonal Structure,

Rhythm, and Musica l Expert ise

E m m a n u e l B i g a n d

U n i v e r s i t 6 d e B o u r g o g n e

The goal o f this study was to investigate several factors that determine m usical stability inunaccompanied tonal melodies. Following M. R. Jon es's (1987) theory of dynam ic attending,the author assumed that strongly accented tones act as stable melodic reference points. Threemain results were observed: (a) tonal structure, rhythm, and melodic factors (i.e., pitch skipsor change in melodic contour)all contributed to defining the stability experienced on themelodic tones; (b) a linear com bination of 5 m elodic and rhythmic features provided a goodfit to the stability ratings; and (c) som e o f these features contributed differently, dependingon the extent of musical expertise of the participants. The results are interpreted w ithin C. L.Krumhansl's (1990) model of tonal perception and Jones's theory of dynamic attending.

M u s i c a l p i e c e s a r e m o s t c o m m o n l y p e r c e i v e d t o b e s o u n d

s t r u ct u r e s th a t e v o l v e d y n a m i c a l l y t h r o u g h t i m e : A t c e r t a i n

p o i n t s i n a m u s i c a l p i e c e , w e c a n e v a l u a t e w h e t h e r t h e p i e c e

i s f in i shed , when i t wi l l reach i t s f ina l po in t , wha t . the

f o r t h c o m i n g e v en t s s h o u l d b e , a n d w h e n t h e y s h o u l d o c c u r

i n t i m e . T h e p r e s e n t s t u d y i n v e s t i g a t e d s e v e r a l f a c t o r s th a t

c a u s e m u s i c a l p i e c e s t o s o u n d l i k e d y n a m i c s t r u c t u r e s f o r

l is teners .

A c c o r d i n g t o m u s i c t h e o r is t s , th e i m p r e s s i o n t h a t m u s i c

p r o g r e s s e s d y n a m i c a l l y t h r o u g h t i m e s t e m s p r i m a r i l y f r o m

t h e s e q u e n c e o f s ta b l e a n d u n s t a b l e e v e n t s i n ti m e ( L e r d a h l

& Jackendoff , 1983; Meyer , 1956 , 1973; S chenker , 1935) .

I n a g i v e n m u s i c a l c o n t e x t , s o m e e v e n t s ( t o n e s o r c h o r d s )

a r e p e r c e i v e d t o b e m o r e s t a b l e t h a n o t h e r s. U n s t a b l e e v e n t s

ins t i l l s t rong m us ica l t ens ions tha t gene ra te the expec tancyt h a t m o r e s t a b l e e v e n t s w i l l f o ll o w . D u r i n g t h e p a s t d e c a d e ,

s eve ra l em pi r i ca l s tud ies showed tha t m us ica l s t ab i l i ty and

e x p e c t a n c y a r e i n f l u e n c e d b y s e v e r a l f a ct o r s in c l u d i n g m e -

lod ic in te rva l s i zes (B igand , P a rncu t t , & Lerdah l , 1996;

C a r l s e n , 1 9 8 1 ; U n y k & C a r l s e n , 1 9 8 7 ) , m e l o d i c c o n t o u r

(S chm uckle r , 1989 , 1990) , rhy thm ic fea tu res (Bol tz , 1989a ,

1 9 8 9 b ; Jo n e s , B o l t z , & K l e i n , 1 9 9 3 ; P a l m e r & K r u m h a n s l ,

1987a , 1987b) , and tona l and ha rm onic s t ruc tures (Bha-

rucha & S toeck ig , 1986 , 1987; B igand e t a l . , 1996; P a lm er

& Krum hans l , 1987a , 1987b; S chm uckle r , 1989 , 1990;

S c h m u c k l e r & B o l t z , 1 9 9 4 ) . T o d a t e , n o n e o f t h e s e s t u di e s

h a s m a n i p u l a t e d t h e s e f a c t o r s s i m u l t an e o u s l y t o d e t e r m i n e

t h e i r r e l a t i v e w e i g h t i n g . T h e r e f o r e , t h e f i r s t g o a l o f t h ep r e s e n t s t u d y w a s t o d e t e r m i n e h o w t o n a l s t r u c t u r e a n d

r h y t h m a c t i n c o m b i n a t i o n t o a f f e c t t h e p e r c e i v e d m u s i c a l

s t ab i l it y i n r e l a t i v e ly l o n g a n d c o m p l e x m e l o d i e s . T h e s e c -

o n d g o a l w a s t o t e s t a q u a n t it a t iv e m o d e l d e s i g n e d t o p r e d i c t

I thank M.-C. Botte, C. Drake, C. Krnmhansl, P. Lemaire, S.McAdams, and B. Repp for their insightful comments, whichgreatly improved the article.

Correspondence concerning this article should be add ressed toEmmanuel Bigand, LEAD-CNRS URA 1838, 6 B oulevard Gab-riel, Facult6 des Sciences, F-21000 Dijon, France. Electronic mailmay b e sent via Internet to [email protected].

t h e d e g r e e o f s t a b i l i t y e x p e r i e n c e d w i t h e a c h t o n e o f a

m e l o d y . L e t u s c o n s i d e r e a c h o f t h e s e m e l o d i c a n d r h y t h m i cf a c t o r s in g r e a t e r d e t ai l a n d s e e h o w w e c a n q u a n t i f y t h e i r

r e s p e c t i v e e f f e c t s .

T o n a l H i e r a rc h y

M us ica l s t ab i l i ty i s re la ted , in pa r t , to the s ca le degree o f

t h e t o n e s i n t h e m e l o d y ' s u n d e r l y i n g d i a t o n i c s ca l e . A c c o r d -

i n g t o M e y e r ( 1 9 5 6 ) ,

In the major mode in Western music the tonic tone is thetone of ultimate rest toward which all other tones tend tomove. O n the ne xt higher level the third and fifth o f the scale,

though active melodic tones relative to the tonic, join the tonicas structural tones; and all the oth er tones, whether diatonic orchromatic, tend toward one of these. (pp. 214-215)

S u c h a t o n a l h i e r a r c h y h a s r e c e i v e d a g r e a t d e a l o f e m p i r i c a l

s u p p o r t : O n c e t h e k e y o f a m u s i c a l c o n t e x t i s r e c o g n i z e d ,

t h e 1 2 to n e s o f t h e c h r o m a t i c s c a l es a r e p e r c e i v e d i n a

h ie ra rchy of s t ab i l i ty (F ranc~s , 1958/1988; Krurnhans l ,

1990) . In m a jor ke y con tex t s , the ton ic ( f i r s t s ca le degree ) i s

p e r c e i v e d t o b e m o r e s t a bl e t h a n t h e d o m i n a n t ( f i f t h s ca l e

d e g r e e ) , w h i c h i n t u r n i s p e r c e i v e d t o b e m o r e s t a b l e t h a n

t h e m e d i a n t ( t h i r d s c a l e d e g r e e ) . T o n e s o f t h e o t h e r s c a l e

d e g r e e s a r e p e r c e i v e d t o b e l e s s s t a b l e b u t m o r e s t a bl e t h a n

n o n d i a t o n i c t o n e s .

S t a b l e t o n e s i n a g i v e n m u s i c a l c o n t e x t a c t a s c o g n i t i v er e f e r e n c e p o i n t s t o w h i c h t h e o t h e r t o n e s a r e a n c h o r e d

( B h a r u c h a , 1 9 8 4 ; K r u m h a n s l , 1 9 9 0 ; L a d e n , 1 9 9 4 ). C h a n g -

i n g t h e k e y o f t h e c o n t e x t l e a d s t o c h a n g e s i n t h e s e r e f e r e n c e

p o i n t s s o t h a t e v e n t s t h a t w e r e s t a b l e i n a g i v e n c o n t e x t m a y

b e c o m e u n s t a b l e i n a n o t h e r k e y c o n t e x t . A s a n e x a m p l e , th e

t w o - t o n e s e q u e n c e E - F i n s ti l ls a d y n a m i c t e n s io n t o r e la x -

a t i o n re l a t i o n in t h e k e y c o n t e x t o f F m a j o r : E i s p e r c e i v e d

t o b e a n u n s t a b l e t o n e a n d F , a v e r y s t a b l e o n e . T h i s s t a b i l i t yp r o f i l e m a y c h a n g e w i t h t h e C o n te xt . I n t h e k e y c o n t e x t s o fE m a j o r a n d E m i n o r , E i s p e r c e i v e d t o b e m o r e s t a b l e t h a n

F . In these con tex t s , the two tones de f ine a new s tab i l i ty

80 8



PERCEIVING MUSICAL STAB ILITY 8 0 9

prof i l e because they ins t i l l a r e l axa t ion to t ens ion re l a t ion .

Chan ges in the m usica l s t ab i l i ty o f t he t o n e s a r e o f p sy c h o -

log ica l impo r t ance because they a l t e r the dyn am ic shape of

the sequence an d , subsequent ly , mod i fy it s pe rcep tua l i den-

t i ty . Indeed , Dowl ing (1986) s how ed tha t changing the key

c o n t e x t o f a s i x -t o n e m e l o d y m a k e s t h a t m e l o d y d i f f ic u l t t o

recognize . S imi l a r re su l t s were ob ta ined by Bigand and

P inean (1996) w i th longer tone sequences .

The corm ec t ion i s t mo de l o f t ona l pe rcep t ion deve loped by

Bh arucha (1987) prov ides an e l egant account fo r t he e f fec t s

of key contex t on musica l s t ab i l i t y . In th i s mode l , t he 12

tones of t he chromat i c sca l e a re l i nked to ma jor and minor

c h o r d s a n d t o m a j o r a n d m i n o r k e y s . T o n a l h i e ra r c h ie s a r e

represen ted by the s t rength of t he connec t ions tha t l i nk tone

uni t s t o chord and ke y un i t s . Musica l s t ab i l i t y i s i ns t an t i a t ed

b y t h e a m o u n t o f a c t i v a ti o n t h a t sp r e a ds f r o m k e y u n i ts t o

tone un i t s . The more ac t iva t ed tone un i t s cor re spond wi th

the more s t ab le tones in a g iven contex t and v i ce ve rsa ,

C h a n g i n g t h e k e y c o n t e x t w o u l d m o d i f y t h e a m o u n t o f

ac t iva t ion propaga t ing to the ton e un i t s , so tha t a un i t t ha t i s

s t rongly ac t iva t ed in on e contex t would be l e ss ac t iva t ed inanother ,

T h e f i rs t p u rp o se o f t h e p r e sen t s t u d y w a s t o t e s t h o w k e y

contex t e f fec t s may a f fec t the pe rcep t ion o f me lodies sha r -

ing a long se t o f p i tches in the sam e sequent i a l o rde r. Le t us

cons ide r , fo r example , t he me lodies o f F igure 1 . T1 m e lo-

d ie s a re in A m inor . To ch ange the mu sica l s t ab i li t y , t he key

was changed in T2 by a l t e r ing the p i t ches of t he fa s t t h ree

notes . Accord ing to But l e r and Brown (1984) , t he t r i t one

F#- -C ins t i l l s a s t rong fee l ing of t he key of G in T2 . To

main ta in th i s key in t e rpre t a t ion , t he G#s (Numbers 1 and

20) were low ered by a sem i tone . A l l t he rema in ing no tes a re

the sam e in T1 and 1"2; t he on ly d i f fe rence conce rned the i r

s t ab i li t y . Accord ing to tona l h i e ra rchy , t he A in T1 (Num ber

2) i s a s t ab le ton ic tone , bu t a more uns t ab le tone ( second

sca le degree ) i n T2 . The B (Num ber 3) i s an uns t ab le second

sca le degree in T1 , bu t a more s t ab le th i rd degree inT 2. Bycont ra s t , t he C (Num ber 4) i s a re l a t ive ly s tab le th i rd degree

in T1 , bu t a more uns t ab le four th degree in T2 . By c hanging

a few notes , t he s t ab i l i ty o f t he me lod ic tones has been

c o m p l e t e l y in v e r t ed f r o m T 1 t o T 2 .

R h y t h m i c S t r u c t u r e s

The s t ab i l i t y o f t ones i s no t de t e rmined en t i re ly by the

t o n a l h i er a r c h y o f t h e m e l o d y ' s u n d e r l y i n g k e y . V a r y i n g

som e acou s t i c fea tures ( i .e . , t imbre , i n t ens i ty , dura t ion) cana l t e r s t ab il i t y and , t hus , mo di fy pe rcep t ion o f t he p i ece . Thi s

sugges t s t ha t o the r fea tures should be inc lud ed in a mod e l o ftona l h i e ra rchy so a s t o accoun t fo r the pe rcep t ion of me l -

odies (Bol tz , 1989b; Laden, 1994).Genera l ly , t he s t ab i li t y o f a no te depend s on the rhy thmic

contex t i n which i t appea rs . Accord ing to Le rdahl and

Jacke ndo f f (1983), rhy thm ic s truc tures have a do uble func -

t ion . F ir s t , t hey d iv ide the p i ece in to groups and , t hen , t hey

add rhy thmic va lues to the tona l h i e ra rch ies to de t e rm ine the

musica l func t ion of t he event s conta ined in the groups .

~ 80

Stop n o te s 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3

S top no tes 101112 131415 161718 1920212 2 23

S top n~¢s 1 2 34 56 7 8 9 1011121314 151617181 92021 2223

Stop notes 1011121314 151 617 181 920 21 2223

F i g u r e 1 . Four melodies used in Experiment I. The tonal structure (T) varies from T1 to T2, andthe rhythmic structure (R) varies from R1 to R2.



P ERCEIVING MUS ICAL S TABILITY 811

i n c i d e i n t im e ( J o n e s & B o l t z , 1 9 8 9 ) . C h a n g i n g t h e r h y t h m

o f a m e l o d y c h a n g e s t h e a c c e n t c o u p l i n g , s u c h t h a t s t r o n g

m a r k e r s i n o n e r h y t h m i c s t r u ct u r e m a y h e w e a k m a r k e rs i n

a n o t h e r a n d v i c e v e r s a . C o n s e q u e n t l y , t h e s e c h a n g e s s h o u l d

a l t e r t h e d y n a m i c s h a p e o f t h e s e q u e n c e i n t h a t t h e y m o d i f y

t h e m o d e s o f a t t e n t i o n a l f o l l o w i n g i n l i s t e n e r s . C h a n g i n g

t h e p i t c h s t r u c t u r e p r o v o k e s s i m i l a r c h a n g e s i n t h e s t r e n g t h

o f t h e m a r k e r s i n t h e j o i n t ' a e e e n t s t r u c t u r e a n d , t h u s , in t h ed y n a m i c s h a p e o f t h e s e q u e nc e .

I n t h e p r e s e n t s t u d y , t h e i n f l u e n c e o f s e v e r a l m e l o d i c

r h y t h m i c f e at u r es o n t h e d y n a m i c s h a p e o f a m e l o d y w a s

a d d r e s s e d b y c o n s i d e r i n g t h e e f f e c t s o f t h e s e f e a t u re s o n t h e

p e r c e i v e d m u s i ca l stability profiles. S t a b i li t y p r o f i l e r e f e r s

t o t h e a l t e r n a t i o n o f s t a b l e a n d l e s s s t a b l e t o n e s i n t h e

m e l o d y . S t r o n g m a r k e r s w e r e a s s u m e d t o a c t a s v e r y s t a b le

m e l o d i c r e f e r e n c e p o i n t s b e c a u s e o f t h e p r e s u m a b l y s t r o n g

a t t rac t ion tha t they exe r t on the l i s t ene rs ' a t t en t ion . The

c o m p u t e d s t r e n g t h s o f a c c e n t u a t io n f o r e a c h t o n e o f a m e l -

o d y s h o u l d t h e n p r o v i d e a g o o d f i t t o t h e p e r c e i v e d s t a b i li t y .

F o l l o w i n g J o n e s ( 1 9 8 7 ) , J o n e s a n d B o l t z ( 1 9 8 9 ) , S e -

r a t i n e , G l a s s r n a n , a n d O v e r h e e k e ( 1 9 8 9 ) , a n d B i g a n d( 1 9 9 3 ) , f i v e p r e d i c t o r s w e r e u s e d : t o n a l w e i g h t , d u r a t i o n

w e i g h t , m e t r i c w e i g h t , i n t e r v a l s i z e w e i g h t , a n d m e l o d i c

c o n t o u r w e i g h t . T h e t o n a l w e i g h t s , d e f i n e d a c c o r d i n g t o

K r u m h a n s l ' s ( 1 9 9 0 ) m o d e l o f t o n a l p e r c e p t i o n , r e f l e c t t h e

i m p o r t a n c e o f e a c h t o n e i n t h e t o n a l h i e r a r c h y o f t h e m e l -

o d y ' s u n d e r l y i n g ke y . F o l l o w i n g K r u m h a n s l a n d K e s s l e r 's

f i n d i n g s ( I 9 8 2 , E x p e r i m e n t 2 ), w h e n p a r t o f a m u s i c a l p i e c e

s u g g e s t s a n e w k e y ( t e m p o r a r y m o d u l a t i o n ) , t h e p r e s e n t

m o d e l a s s i g n s t o t h i s p a r t o f t h e p i e c e t h e k e y p r o f i l e v a l u e s

o f t h is n e w t e m p o r a r y k e y ( s e e E x p e r i m e n t 2 ). H o w t h e

t o n a l w e i g h t s ( T W ) w e r e d e f i n e d f o r t h e m e l o d i e s o f E x -

p e r i n ae n t 1 ( F i g u r e 1 ) i s d i s p l a y e d i n T a b l e 1 , w h e r e t h e y a r e

s h o w n t o c o m e f r o m t h e m a j o r a n d m i n o r k e y p r o f i l e s

r e p o r t ed b y K r u m h a n s l a n d K e s s le r ( 1 9 8 2) a n d K r u m h a n s l

( 1 9 9 0 , p . 3 0 ). B e c a u s e t h e m a i n k e y o f th e T 1 m e l o d i e s is

A m i n o r , t h e v a lu e s o f T 1 m e l o d i e s a r e th o s e o f K r u m -

h a n s l ' s A m i n o r p r o fi l e . T h e v a l u e s o f T 2 m e l o d i e s a r e

t h o s e o f K n t m h a n s l ' s G m a j o r p r o f i l e . I l lu s t r a t i v e ly , t h et o n a l w e i g h t o f t h e A ( n u m b e r 2 i n F i g u r e 1 ) i s 6 . 3 3 i n T 1

b e c a u s e A i s th e t o n i c t o n e . T h e t o n a l w e i g h t f o r t h e s a m e

A i n T 2 i s 3 . 4 8 b e c a u s e t h e A i s t h e s e c o n d d e g r e e i n t h i s

k e y c o n t e x t a n d s o o n . C h a n g e s i n v a l u e s r e f l e c t t h e h y p o -

t h e t ic a l c h a n g e s i n m u s i c a l s t a b i l it y c r e a t e d b y t h e t w o k e y

c o n t e x t s i n w h i c h t h e t o n e s a p p e a r . N o t s u r p r i s in g l y , t h e r e

w a s a h i g h n e g a t i v e c o r r e l a ti o n b e t w e e n t h e T 1 a n d t h e T 2

v a l u e s, r ( 2 1 ) = - . 8 1 , p < . 0 0 1 .

T o a c c o u n t f o r t h e c o n t r i b u t i o n o f r h y t h m , t w o s e t s o f

v a l u e s w e r e d e f i n e d : t h e d u r a t i o n w e i g h t s a n d t h e m e t r i c

w e i g h t s . T h e d u r a t io n w e i g h t s ( D W i n T a b l e 1 ) a r e p r o p o r -

t i o n a l t o t h e d i ff e r e n t d u r a t i o n s o b s e r v e d i n t h e m e l o d y : I n

E x p e r i m e n t 1 , a v a l u e o f 1 w a s a s s i g n e d t o t h e e i g h t h n o t e s ,a n d a v a l u e o f 2 w a s a s s i g n e d t o t h e q u a r t e r n o t e s , w h i c h a r e

t w i c e a s l o n g . T h e m e t r i c w e i g h t s ( M W i n T a b l e I ) d e p e n d

o n t h e n u m b e r o f m e t r i c l e v e ls c o n t a i n e d i n th e m e l o d y ( s e e

L e r d a b l & J a c k e n d o f f , 1 9 8 3 ) . H e r e , t h e r e i s a w e a k h e a t a t

t h e e i g h t h n o t e l e v e l ( w i t h a v a l u e o f 1 ) , a m o r e i m p o r t a n t

m e t r i c h e a t o n t h e s e c o n d q u a r t e r n o t e o f t h e m e a s u r e ( w i t h

a v a l u e o f 2 ), a n d a s t r o n g b e a t a t t h e m e a s u r e l e v e l ( w i t h a

v a l u e o f 3 ) .

T o c a p t u r e t h e p o t e n t i a l i n f l u e n c e o f p i t c h s k i p s o n p e r -

c e i v e d m u s i c a l s t a b i l i t y , t h e n u m b e r o f s e m i t o n e s i n e a c h

T a b l e 1Tonal Weights (TW), Duration Weights (DW), Metric Weights (MW), Melodic IntervalWeights (MIW) and Melodic Contour Weights (MCW ) for Melodies TIR1 andT2R2 in Experiment 1

T1R1 T2R2

S to p n o te (s ) T W D W M W M I W M C W T W D W M W M I W

1 3.17 2 2 6 1 6.35 1 3 72 6.33 1 3 1 1 3.48 1 1 23 3.52 1 1 2 0 4.38 1 2 24 5.38 1 2 1 0 4.09 1 1 15 6.33 1 1 3 1 3.48 1 3 36 3.52 1 3 2 1 4.38 1 1 27 6.33 1 1 2 1 3.48 2 2 2

8 3.34 2 2 2 0 6.35 1 3 29 5.38 1 3 7 0 4.09 1 1 710 3.34 1 1 7 1 6.35 1 2 711 5.38 1 2 5 0 4.09 1 1 512 4.75 1 1 8 1 3.66 1 3 813 3.34 1 3 3 1 6.35 1 1 314 6.33 1 1 2 0 3.48 2 2 215 3.52 2 2 2 0 4.38 1 3 216 3.53 I 3 3 0 5.19 1 1 317 5.38 1 1 2 1 4.09 1 2 218 3.52 1 2 1 0 4.38 1 1 119 6.33 1 1 2 0 3.48 1 3 220 3.17 1 3 1 0 6.35 1 1 221 5.38 1 1 4 1 4.09 2 2 522 3.52 2 2 1 1 4.38 2 3 123 6.33 2 3 2 0 3.48 2 2 2



8 1 2 B I G A N D

m e l o d i c i n t e r v a l w a s c o m p u t e d ( M I W v a l u e s i n T a b l e 1 ) .

T o a c c o u n t f o r t h e p o t e n t i a l i r, _f lu en ce o f c h a n g e i n m e l o d i c

c o n t o u r , a v a l u e o f 1 w a s a s s i g n e d t o t h e t o n e s o n w h i c h a

c h a n g e i n c o n t o u r o c c u r s . A v a l u e o f 0 w a s a s s i g n e d i n t h e

o t h e r c a s e s ( M C W v a l u e s i n T a b l e 1 ).

T o s u m m a r i z e , w e h y p o t h e s i z e t h a t s e v e r a l f a c t o r s m a y

a f f e c t t h e p e r c e p t i o n o f s t a b il i t y. T w o o f t h e s e ( i . e ., t o n a l

s t r u c t u r e a n d r h y t h m ) w e r e v a r i e d s y s t e m a t i c a l l y i n t h e

f o l l o w i n g e x p e r i m e n t s a n d t h e o t h e r s ( in t e r v a l s iz e , m e l o d i c

c o n t o u r ) w e r e k e p t c o n s ta n t . T h r e e m a i n a s s u m p t i o n s w e r e

m a d e :

1 . changing the tona l s t ruc tu re o f a me lod y by modify ing on lya few p i tches shou ld s t rong ly a ffec t the s tab i l i ty fo r themajor i ty o f the o the r tones ;

2. changing the rhythmic s tructure should also affect thestability of the melodic tones; and

3 . a comb ina t ion o f f ive k inds o f me lod ic and rhy thmic ac -cents (i.e., tonal, duration, metric, interval size, and me-lod ic con tour we igh ts ) shou ld p red ic t the pe rce ivedstability.

I n a d d i t i o n , g i v e n t h a t s o m e o f t h e s e f a c t o r s r e l y o n m o r es u p e r f i c i a l fe a t u r e s ( d u r a t i o n , m e l o d i c i n t e r v a l s i z e s , c h a n g e

i n m e l o d i c c o n t o u r ) t h a n o t h e r s ( t o n a l a n d m e t r i c s t r u c -

t u re s ), s o m e m a y b e m o r e i m p o r t a n t f o r m u s i c ia n s a n d s o m e

f o r n o n m u s i e i a n s . T h u s , t e s t i n g t h e s e f a c t o r s p r o v i d e d a n

o p p o r t u n i t y t o i n v e s t i g a t e t h e e f f e c t o f m u s i c a l e x p e r t i s e o n

t h e p e r c e p t i o n o f m u s i c a l s t a b i l it y .

E x p e r i m e n t 1

M e ~ o d

Participants. Forty mu sic teachers (hereinafter referred to as

musicians) volunteere d to partic ipate in the experiment. All heldqua li f ica tions f rom a French M us ic Conserva tory and had rece ivedat least 10 years of intensive training in mu sic (i .e . , music thoory ,ear training, an d instrumental performance). Forty college-a gestudents (hereinafter referred to as nomuu sicians) also took part inthe experiment. Th ey had-never played an instrumen t nor s tudiedmusic. All w ere s tudents o f psyc holo gy and partic ipated in theexperiment as volunteers .

Material. Four melod ies T1R1, T1R2, T2R1, and T2R2 weredef ined (F igure 1 ) . The T I melod ies d if fe red from the T2 m elod iesby the key con tex t induced by the f i rs t me lod ic tones . Fo l lowingPa lmer and Krum hans l (1987a , 1987b) , the R2 melod ies weredefined by shifting the rhythm ic s tructure of R1 by on e eighthno te . Consequen t ly , mos t o f the tones tha t fa l l on a s t rong metr icbea t in R1 fa l l on a w eak metr ic bea t in R2 and v ice ve rsa . S evera ltones with a long dura t ion in R1 have a short dura t ion in R2 andvice ve rsa . These four melod ies were segmented in to 23 frag-ments. Each segm ent s tar ted a t the beg inn ing o f the melody ands topped on a d if fe ren t no te ca l led a stop note, For example , inT1R1, the f i rs t f ragment s topped on G# , the second on A, and soon .

The 23 fragments were p layed with sampled p iano soundsp ro d u c ed b y th e E M T IO Y a m a h a S o u n d E x p a n d e r at a t em p o o f80 quar te r no tes pe r minu te . T he Ya mah a sample r was con tro l ledth rough a MIDI in te rface by a Mac in tosh compute r runn ing Per-former software. Velocity, a pa ramete r re la ted to the fo rce withwhich a key is s truck, was held constant for all pitches. Theparticipants were allow ed to adjust the output of the amplifier to a

comfortab le leve l . There was no s i lence be tween the o ffse t o f atone and the onse t o f the succeed ing tone .

Task. The par t ic ipan ts ' ta sk, s imila r to tha t used by Pa lmer andKrum hansl (1987a, 1987b), consis ted of evaluating the musicals tab il ity on each s top no te us ing a judgmen t sca le rang ing from 1(very low stability) to 7 (very great s tability). In a preliminarysession, the partic ipants lis tened to musical exam ples havin g dif-

ferent degrees of s tability. They were told that s trong s tability atth e e n d o f a f r a g m e n t e v o ke s th e f e el in g th a t t h e m e lo d y to d dnaturally s top at this point. On the oth er hand, low stability ev okesthe fee l ing tha t the re mus t be a con t inua t ion o f the melody .Because s tability may be varied in subtle ways in music, thepart ic ipan ts were encou raged to use a l l the degrees o f the judgm entscale . In addition, a t the end of the experiment, the musicians w ererequ ired to iden t i fy the key o f the m elody tha t they had l is tened toand to identify its meter (i .e . , they had to draw the bar lines on as c o r e ) .

Design and procedure. Four independen t g roups o f 10 pa r t ic-ipan ts each were ass igned to the four condi t ions de f ined by c ross -ing the two independen t va r iab les : Key con tex t (2 ) × Rhy thm (2) .Each pa r tic ipant gave a ra t ing fo r each o f the 23 s top no tes o f on lyone melody . The pa r t ic ipan tswere sea ted in g roups o f two , each in

fron t o f a M]DI keyboard , connec ted to the compute r , whichrecorded the ir answers. Seven keys corresponded to the 7 po in ts o fthe judgment sca le . Before runn ing the exper iment , the pa r t ic i -pants practiced evaluation of musical s tability with 12 melodicfragments . No feedback w as p rov ided un less they used the sca le in

the reverse order. The experiment s tarted with the fragment ter-mina t ing on S top N ote 1 . The pa r t ic ipan ts h ad 8 s to g ive the irs tability judgment. After that, the fragment terminating on StopNote 2 w as p layed , then the f ragment end ing on S top No te 3 , andso on . Th is makes the judgments co l lec ted on s top no tes compa-rab le because a l l the s top no tes were judged w hen they w ere f i rs thea rd . As obse rved by Bigand (1993 , Experiment 1 ) randompresentation of the fragments greatly confuses the partic ipantsbecause i t o f ten appears tha t a short f ragm ent fo l lows a longer one .In th is case , the degree o f comple teness is de f ined no t on ly bymus ica l s tabi li ty bu t a lso by the l is tener ' s knowledge o f the con-tinuation of the melody . As a conseq uence, the participants (no-tably the nonmusicians) tended to give higher ratings of s tabilityfor mus ica l f ragm ents o f inc reas ing dura t ion . Th is sugges ted tha tfo r them, regard less o f the m us ica l func t ion o f the la s t tone , thelonge r the fragment, the higher its degree o f completeness . Thisl inea r tendency was no t obse rved when the f ragments were p re -sented in a sequential order(Bigand, 1993, Experiment 2).

R e s u l t s

Par t i c ipant agreement . T o a s s e s s i n t e r p a r ti c i p a n t a g r e e -

m e n t , t h e K e n d a l l c o e f f i c ie n t o f c o n c o r d a n c e w a s c o m p u t e d

s e p a r a t e l y f o r t h e m u s i c i a n s a n d t h e n o n m u s i e i a n s i n e a c h

e x p e r i m e n t a l s i t u a t i o n . T h e o b s e r v e d c o e f f i c i e n t s w e r e a l l

s ig n i f i c a n t (p < . 0 1 ) . T h i s r e s u l t i n d ic a t e d a s ig n i f i c a n t

a g r e e m e n t a m o n g t h e p a r t i c i p a n t s ' r a t i n g s i n a l l e x p e r i m e n -

t a l si t u a ti o n s . T h e c o r r e l a t i o n s b e t w e e n t h e m u s i c i a n s ' a n d

t h e n o n m u s i c i a n s ' m e a n r a t i n g s w e r e a l s o s i g n i f i c a n t i n

e a c h e x p e r i m e n t a l c o n d i t i o n . T h e l o w e s t c o r r e l a t i o n w a s

o b s e r v e d f o r t h e T 1 R 1 m e l o d y , r ( 2 1 ) = . 6 0 , p < . 0 1, a n d

t h e h i g h e s t f o r t h e T 2 R 1 m e l o d y , r ( 2 1 ) = 6 7 , p < . 0 1. T h e

d a t a f o r T 1 R 1 a n d T 1 R 2 w e r e t h e n c o m p a r e d w i t h t h o s e

o b t a i n e d b y B i g a n d ( 1 9 9 3 , E x p e r i m e n t 2 ) w i t h t h e s a m e

m e l o d i e s . A l l c o r r e l a ti o n s w e r e s i g n i f i c a n t f o r b o t h g r o u p s ,



PERCEIVING MUSICAL STABILITY 813

indica t ing the re l i ab i l i t y o f t he expe r imenta l me thod . The

lowest coe f f i c i en t was obse rved for t he music i ans in T1R 1,

r (21) = .77 , p < .01 , and the h ighes t fo r t he nonm usic i ansin T1R 1, r(21) = .85, p < .01.

F igure 2 d i sp l ays the mean ra t ings ac ross l i s t ene rs fo reach s top no te in each exper imenta l s i t ua t ion . These mean

ra t ings de f ine va r i ed mu sica l s t ab i l i ty p rof i l e s t ha t d i f fe red

s t rongly f rom one exper imenta l s i t ua t ion to anothe r . Forboth groups of l i s t ene rs , t hese d i f fe rences were t e s t ed w i th

a 2 × 2 × 2 3 (K e y C o n t e x t × R h y t h m × S t o p N o t e )

mul t iva r i a t e ana lys i s o f va r i ance (MANOVA), w i th the

th i rd fac tor be ing a w i th in-pa r ti c ipan t fac tor , and the f i r s t

two fac tors be ing be tween -pa r t i c ipan t va r i ab les .

K e y c o n t e x t e f f e c t . Over the 23 s top no tes , t he T1 pro-

f i l e s d i f fe red s ign i f i can t ly f rom the T2 p rof i l e s amon g the

music i ans , F (22 , 15) = 13 .75 , p < .001 (Wi lks ' s l ambd a

tes t) , and among the nonmusic i ans , F (22 , 15) = 3 .75 , p <

.005 . P rof i l e ana lyses were pe r formed aga in w i thout S top

Notes 1 and 20 , w hich d i f fe r i n p i tch be tween T1 and T2 .

T h e m a i n e f f e c t o f t h e k e y c o n t e x t p e r s is t e d b o t h f o r m u -

sic ians, F(20 , 17) = 12.26, p < .001, and for non mu sicians,F(20 , 17) = 2.91, p < .02. W ith the mu sicians , the stabi l i typrof i l e s o f t he T1 and T2 me lodies were even s ign i f i can t ly

nega t ive ly cor re l a t ed , r (44) = - .3 0 , p < .05 .

To ev a lua te the ex ten t t o which these changes in s t ab i l i t y

prof i l e s m ay be l i nked to the tona l h i e ra rchy o f t he in fe r red

key , t he ave raged ra t ings of T1 and T 2 w ere cor re l a ted wi th

K r u m h a n s l ' s ( 19 9 0) A m i n o r a n d G m a j o r k e y p r o f il e s. F o r

both groups of pa r t ic ipan t s , T1 ra t ings were s ign i f i can t ly

cor re l a t ed wi th the A minor h i e ra rchy and nega t ive ly cor -

re l a t ed wi th the G ma jor h i e ra rchy (Table 2) . For bo th

groups , T2 ra t ings were s ign i f i can t ly cor re l a t ed wi th the G

major key prof i l e and nega t ive ly cor re l a t ed wi th the A

min or ones . Thi s sugges t s t ha t bo th groups o f li s t ene rs wereor i en ted toward the A minor tona l h i e ra rchy in T1 and

toward the G ma jor t ona l h i e ra rchy in T2 . The music i ans '

r e sponses g iven a t t he end o f t he expe r iment conf i rmed tha t

15 ou t o f 20 m usic i ans iden t i f i ed the A m inor key in T1

melodies ; and 17 ou t o f 20 , t he G ma jor key in T2 me lodies .

For bo th T1 and T2 me lodies , t he music i ans ' r a t ings were

m o r e h i g h l y c o r r e l a t e d w i t h t h e K r u m h a n s l k e y p r o f i l e s

t h a n w e r e t h o se o f t h e n o n m u s i c i a n s .

I t might be a rgued tha t , i n sp i te o f t he key iden t i f i ca tion

responses g iven by the music i ans a t t he end of t he expe r i -m e n t , t h e T 2 m e l o d i es m a y h a v e b e e n h e a r d i n a C m a j o r

k e y f r o m t h e b e g i n n i n g o f t h e f i f th m e a su r e t o t h e e n d o f t h e

melod y . To address th i s i ssue , the ave rage ra t ings reg i s t e redfor S top Notes 8 to 23 in the T2 me lodies were cor re l a t ed

w i t h t h e K r u m h a n s l G k e y a n d C k e y p r o f i l e s . F o r t h e

music i ans , t he cor re l a t ion coe f f i c i en t s were h ighe r w i th the

G m ajor key prof i l e , r (14) = .51 , t han wi th the C ma jor key

prof i le , r (14) = .17 . S imi l a r f i nd ings were obse rved amon g

71

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el

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1 .S 2

s t o ~

n o t e s

~ r

6.s~

T IR1• N o n m u s i d a n s O M u s ic i an s

b ~ ] r f k ~ g T t l l l A : ~ i l ~ = k I ~ 1 1

T I R 2

• N o n m u s i d a n s o M u s ic ia n s

. . . , . , . . : . . ' . . . V : : . , , - . . : . , ,

1 3 5 7 9 i l 1 3 1 5 1 7 1 9 2 1 2 3 1 3

T E R 1

e N o n m u s i d a n s

S 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3

T 2 R 2

e~

s.s!i

L . . . .

1 .~ ,l°°°°,°,oo,°..°°. , , . .oo.,i .°°°,°,°°°l. , , ,

o H u s i d a n s • N o n m u s i c i a n s o M u s i d a n s

E

. . . . . . . . . . .

' . , , o . . . . . . . . . . , . . . , . . o . . . , . . . . . .. . . . . . . . ..

S t o p I

n o t e s

' ~ T " 7 " " T " T ' , ' 7 " " 7 , ' T ' T ' T " T " ' ' T " ' T ' " 7 " " ' 7 " ' "

t , J I t l / ~ . - I " ~ -

, ~ . - . . 7 . . Z ? Z . . . - . - } r T t ~ . - - ~ - , , . ~ .- .....

, , . , , , : , : . .. .. .. .. .. . .. .. .. . - V . . . . . . . . . . . . . . . . . . .. . . . . . . . . . ' . - . . . . . . . . . . .. . . . . . . . .

1 3 5 7 9 11 13 15 17 19 21 23 1 3 5 7 9 11 13 15 17 19 21 23

Figure 2 . Mean ratings of m usical stability observed for each m elody used in E xperiment 1. T =tonal structure; R = rhythmic structure.



814 BIGAND

Table 2Correlat ion (Pearson r) Comparing TI and T2 Ratings

Wi th Krumhan s l ' s Key Pro f i les

r for:

Participants Ke y T1 T2

Musicians A minor .69** - .5 4" *

G major -.4 5* .58**Nonmusicians A minor .53** -.4 2"

G major - .2 8 .40

* p < . 0 5 . * * p < . 0 1 .

t he nonmusic i ans so tha t t he cor re l a t ion wi th the G ma jor

key prof i l e was .43 , and the cor re l a t ion wi th the C ma jor

k e y p r o f i l e w a s - . 0 3 . T h i s su g g e s t s t h a t e v e n t h o u g h T 2

melodies could theore t i ca l ly he hea rd in C ma jor on these

s top no tes , t he pa r t i c ipan t s ' r e sponses w ere mo re in agree -

mer i t w i th the G ma jor k ey prof i l e s .

Effect o f rhythm. T h e M A N O V A a l so r e v e a l e d t h a t

changing the rhy thmic s t ruc tures f rom R1 to R2 l ed tos ign i f i can t changes in the m usica l s t ab i l i ty p rof i l e s fo r t he

music i ans , F (22 , 15) = 2 .87 , p < .02 (W i lks ' s lamb da te s t ),

and for t he nonm usic i ans , F (22 , 15) = 2 .99 , p < .02 . The

c lea res t i l l us t ra t ion of t h i s rhy thmic e f fec t was obse rved

wi th S top Notes 5 and 7 in T1 me lodies . The musica l

s t ab i l i t y o f t hese tones inc reased s t rongly f rom R1 to R2,

l ending to a s t rong change in the mu sica l s t ab i li t y p rof i le . In

the presen t case , t h i s i nc rease in s t ab i l i t y was due to the

fac t s tha t S top Note 5 fe l l on a s t rong me t r i c bea t in R2 (and

n o t i n R 1 ) a n d t h a t S t o p N o t e 7 w a s o f l o n g e r d u ra t io n i n R 2

than in R1. Fur the rmore , ana lyses were then pe r formed to

inves t iga t e th is rhy thmic e f fe c t i n g rea t e r de t a i l .

The music i ans ' r e sponses , g iven a t t he end of t he expe r -

iment , were cons ide red f i r s t t o conf i rm tha t a sh i f t i n t herhy thm ic s truc ture f rom R1 to R2 e f fec t ive ly provok ed a

sh i f t i n t he loca t ion of t he me t r i c s t rong hea t s . Among the

20 pa r t i c ipan t s who l i s t ened to the R1 m e lodies , 16 repor t ed

a m e t r i c s t ruc ture ( iden t ica l t o t he one d i sp lay ed in F igure

1), in wh ich a ba r l i ne occurs be tween S top N otes 1 and 2 ,

5 and 6 , 8 and 9 , 11 and 12 , and so on . Among the 20music i ans who l i s t ened to the R2 me lodies , 17 repor t ed amet r i c s t ruc ture ( iden t i ca l t o t he o ne d i sp layed in F igure 1),

i n which a ba r l i ne occurs jus t be fore S top No te 1 and , then

be tween s top no tes 4 and 5 , 7 and 8 , 11 and 12 , and so on .

To assess how these sh i f t s i n the loca t ion of t he me t r i cs t rong bea t s ma y have a f fec t ed the pe rce ived mu sica l s t a-

b i l i ty , t he ra t ings reg i s t e red for t he s top no tes tha t changedo n l y i n m e t r i c p o s i t i o n f r o m R I t o R 2 w e r e c o m p a r e d .

F igure 3a d i sp l ays the ave rage ra t ings reg i s t e red for S topNotes 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 16, 17, 18, 19, and 20,t h e m e t r i c p o s i t i o n o f w h i c h c h a n g e d i n R 1 a n d R 2 . A l l

pa ramete rs be ing equa l , t he tones t ended to be pe rce ived a sbe ing m ore s t ab le when they fe l l on a s t ronger me t r i c bea t.W i t h t h e m u s i c i a n s , u n i v a r i a t e a n a l y s e s o f v a r i a n c e

(ANO VA) ind ica t ed tha t these d i f fe rences in s t ab i l i ty weresta t ist ical ly signif ic ant for Stop N otes 3, 5, 11, 17, 18, 19,and 20 . Wi th the nonmusic i ans , on ly the d i f fe rences instabi l i ty recor ded on Stop No tes 3, 5, 9, 12, 18, and 19 were

s t a t is t i ca lly s ign i f ican t . Taken toge the r , t hese f ind ing s sug-ges t t ha t t he re was a gene ra l t endency to pe rce ive s t rong

met r i c bea t s t o be more s t ab le than weak me t r i c bea t s , a l l

pa ramete rs be ing kep t cons t an t .

C h a n g i n g t h e r h y t h m i c s t ru c t ur e f r o m R 1 t o R 2 n ot o n l y

provokes seve ra l sh i f ts i n the loca t ion of t he me t r i c s t rong

bea t s bu t p rovokes dura t ion pa t t e rn changes a s we l l . Seve ra l

tones w i th a l ong du ra t ion in R1 have a shor t dura t ion in R2(i .e . , S top No tes 1, 8, 15, and 21) , an d vice versa ( i .e . , S top

Notes 7 and 14) . To t e s t t he e f fec t o f dura t ion pa t t e rn

changes , t he ra t ings reg i s t e red on no tes fo r which the du-

r a ti o n c h a n g e d f r o m R 1 t o R 2 w e r e c o m p a r e d ( F i g u r e 3 b ).

Wi th the music i ans , ANOVAs ind ica t ed tha t t he pe rce ived

mus ica l s t ab il i ty was s ign i f i can t ly h ighe r w hen S top Notes

I , 7 , 14 , and 15 were o f l ong dura t ion ( i . e. , qua r te r no tes) .

For the nonmusic i ans , t he d i f fe rences in s t ab i l i t y ra t ings

were s ign i f i can t on ly for S top Notes 14 and 15 . These

resu l t s sugges t t ha t i nc reas ing the dura t ion of t he tone had a

modera t e e f fec t on the pe rce ived s t ab i l i t y . I t should be

noted , howev er , t ha t , by sh i f t i ng the rhy thm ic s t ruc ture , t he

e f fec t o f changes in dura t ion in t e r fe res w i th the e f fec t o fchanges in the me t r i c l oca t ion , a po in t t ha t we w i l l re tu rn to

in Exper iment 2 .

Tonal × R hythm ic Structures in teraction. T h e r e w a s n o

s ign i f i can t g loba l i n t e rac t ion be tween p i t ch and rhy thmic

s t ructure . Sh i f t ing the rhy thm ic s t ruc ture by one e igh th no te

wi th rega rd to the p i t ch s t ruc ture d id no t mo di fy the musica l

s t ab i li t y p rof i l e s d i f fe ren t ly for T1 and T2 me lodies . AN O-

V A s p e r f o r m e d o n e a c h s t o p n o t e p r o v i d e d e v i d e n c e f o r

on ly one s ign i f i can t i n t e rac t ion . On the l a s t t one of t he

melo dy , t he d i f fe rence in s t ab i l it y ra tings be tween the A in

T1 ( ton ic tone ) and the A in T2 ( second sca l e degree ) was

s ign i f i can t ly grea t e r when these As fe l l on a s t rong hea t i n

R1 (4 .8) t han w hen they fe l l on a we aker me t r i c bea t i n R2

(2.9) , F(1, 36) = 5,36, p < .05. Ho we ver, this interact ive

e f fec t is f a r f rom comp e l l ing because the s t ab i l i t y o f A in T1

melodies rema ined ve ry h igh (6 .9 vs . 6 .8 , r e spec t ive ly) i n

sp i te o f t h e c h a n g e i n r h y t h m f r o m R 1 t o R 2 .

Mu ltiple regression analyses. A f i r s t mul t ip l e regress ion

ana lys i s was pe r formed to pred ic t t he ave rage s t ab i l i t yra t ings in a l l expe r imenta l condi t ions w i th f ive pred ic tors

( i .e . , t ona l we igh t , me t r i c w e ight , dura t ion w e ight , i n t e rva l

s i ze we ight s , and me lodic contou r we ight s ) and the ex ten t o f

musica l expe r t i se . A l inea r combina t ion of t hese s ix va r i -ab le s p rov ided a s ign i f i can t f it t o t he ave rage ra t ings , R =

,69; F(6 , 183) = 26.51, p < .001. Sem ipart ia l corre la t ion

coe f f i c i en t s (sr) i nd ica t ed tha t t ona l we igh t s made the m ost

impor t an t d i rec t con t r ibu t ion , s r = .57, t = 10.5 6,p < .001,wi th m usica l s t ab i l it y rat ings h ighe r fo r m ore s t ab le tones in

the tona l h i e ra rchy . The second most impor t an t p red ic torwas the dura t ion we ight , s r = .26, t = 4.8 2, p < .001, wi thmusica l s t ab i l i t y ra t ings h ighe r fo r t ones o f l onger dura t ion .The me lodic in t e rva l s i zes and the me t r i c we ight s made

di rec t con t r ibu t ions of equ a l impor t ance to ave rage ra t ings ,sr = .16, t = 3 .00 ,p < .01, a n d s r = .15, t = 2 .74 ,p < .01,re spec t ive ly , w i th musica l s t ab i l i t y ra t ings be ing h ig he r fo rtones preceded b y a sma l l i n t e rva l and for t hose fa l l i ng ona s t rong me t r i c beat . Ne i the r t he change in me lodic con tournor the m usica l expe r t i se made s ign i f i can t con t r ibu t ions to




( a ) M us idans N o n m u s i c i a n s

O S t r o n g b e a t o W e a k b e a t7,

6 . 5 - : . . . . . . .

s.5 - ' :

, : . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . .. . . . . . . .

S.S L..--. ~

1 S

s t o p 'n o t e s

• S t r o n g b e a t o W e a k b e a t

; _ ! 7 . . . . . . . : v _ _ : _ : :_ _ _ _ _ _ : :7 ; I I I T I J I T ; ~ ; I I I T I I 7 7 1 ! I I T I T I _ ~ V ~ / ; I I I I I I 7 7 7 ~ ; I I ; I I I I T I T ; ~ I ~ 7 1 ; ; I I I , ; ; 1 7 1 i ; i i 7 1 ~ i i i i i

2 3 4 5 6 9 1 0 1 1 1 2 1 3 1 6 1 7 1 8 1 9 2 0 2 3 4 $ 6 9 1 0 1 1 1 2 1 3 1 6 1 7 1 8 1 9 2 0

( b ) M us idans N onm us lc ians

. • Q~Jarter no te o E ighth no te *Quar te r n o t e 0 E i g h th n o t e7

6.s!

ei

s.s~s:

4.s~o) , .

s.s'S2

S t o p

n o t e s

] = = . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .

i i i i i i i i ! ! ! i i i i i i i i i i i i ! i ! ! i ! i i i ! ! i ! i i i i ! ! ! i i i i i ! i i i i ! i i ii i i i i i i i i i ! i i i i ii i i i i i i i i i i i i ! i i i i i i ! i i i i i i !! i i i i i ! i i ! i i !! i i i i i i i i i i i i i !! i i i i i i1 7 8 1 4 1 5 2 1 I 7 8 1 4 1 5 2 1

Figure 3. Effects of m etric (a) and duration (b) o n mu sical stability.

a v e r a g e r a t i n g s . H o w e v e r , a d d i t i o n a l a n a l y s i s r e v e a l e d a

s i g n i f ic a n t i n te r a c t i o n b e t w e e n t o n a l w e i g h t s a n d t h e e x t e n t

of m us ica l expe r t i s e , t = 3 . 22 , p < . 01 , sugges t ing tha t tona l

w e i g h t s c o n t r i b u t e d d i f f e r e n t l y f o r m u s i c i a n s a n d

n o n m u s i c i a n s .

T o a n a l y z e t h e T o n a l W e i g h t s X M u s i c a l E x p e r t i s e i n -

t e r a c t io n f u r t h e r , m u l t i p l e r e g r e s s i o n a n a l y s e s w e r e p e r -

f o r m e d s e p a r a t e l y f o r e a c h g r o u p o f p a r t i c ip a n t s ( T a b l e 3 ) .

T h e s e m i p a r t i a l c o r r e l a t i o n c o e f f i c i e n t s in d i c a t e d t h a t t h e

t o n a l w e i g h t s m a d e a g r e a t e r d i r e c t c o n t r i b u t io n t o s t a b i l it y

r a t in g s f o r t h e m u s i c i an s t h a n f o r t h e n o n m u s i e i a n s . B y

c o n t r a st , t h e d u r a t i o n w e i g h t s m a d e a g r e a t e r d i r e c t c o n t r i-

b u t i o n f o r t h e n o n m u s i c i a n s t h a n f o r t h e m u s i c i a n s. F o r b o t h

g r o u p s , t h e m e t r i c w e i g h t s a n d t h e m e l o d i c i n t e r v a l s i z e sm a d e d i r e c t c o n t r i b u t i o n s o f n e a r l y e q u a l i m p o r t a n c e , a n d

t h e c h a n g e s i n m e l o d i c c o n t o u r n e v e r s i g n i fi c a n t l y c o n t r i b -

u ted to the m us ica l s t ab i l i ty ra t ings .

D i s c u s s i o n

T h i s e x p e r i r n e n t d e m o n s t r a t e s t h a t m e l o d i e s w i t h h i g h l y

s im i la r supe r f i c ia l s t ruc tu res ( i . e . , the s am e rhy thm and

s a m e m e l o d i c c o n t o u r ) a n d a l o n g s e t o f i d e n t i c a l p i t c h e s i n

t h e s a m e s e q u e n t i a l o r d e r m a y b e p e r c e i v e d i n d i f fe r e n t

w a y s . T h e p i t c h s t r u c t u r e ' o f T 1 a n d T 2 ( 2 9 t o n e m e l o d i e s )

d i f f e r e d o n f i v e t o n e s . I n s p i t e o f t h is , t h e p e r c e p t u a l d i f -

f e r e n c e s b e t w e e n t h e s e m e l o d i e s w e r e i m p o r t a n t a n d v e r y

s p e c i f i c . A s p r e v i o u s l y s h o w n , t h e p e r c e i v e d m u s i c a l s t a -

b i l i ty o f t h e T 1 a n d T 2 m e l o d i e s w a s s i g n i f i c a n t ly c o r r e l a t e d

w i t h t h e t o n a l h i e r a r c h y o f d i f fe r e n t k e y s ( T 1 t o A m i n o r

k e y a n d T 2 t o G m a j o r k e y ) : T h e g r e a t e r ' t h e t o n e ' s s t r u c -

T a b l e 3

Summ ary o f Mul tip le Regress ion Ana lyses Pred ic t ing theAverage Ra t ings by a Com bina tion o f the F iveFactors in Exper imen t I

Participants and facto r sr t pMusicians"

Tonal .65 8.7 5 <.001Duration .19 2.51 <.001Metric .15 2.01 <.0 2Interval size .14 1.95 <.0 5Melodic contour .07 <1 <.06

NonmusieiansbTonal .48 6.28 <.001Duration .37 4.81 <.001Metric .15 1.98 <.00 1Interval size .19 2.48 <.0 6Melodic contour .00 < 1 <.0 2

aR = .72; F(5, 86) = 18.6 4. b R = .69; F(5, 86) = 16.13.



8 1 6 B I G A N D

t u r a l i m p o r t a n c e i n t h e k e y , t h e h i g h e r t h e p e r c e i v e d m u s i c a l

s t a bi l it y . T h i s p r o v i d e s s o m e e v i d e n c e t h a t c h a n g i n g o n l y a

f e w n o t e s i n a m e l o d y c a n i n f l u e n c e l i s t e n e r s ; t h e y i n f e r

d i f f e r e n t k e y s , m a i n t a i n a g i v e n k e y i n t e r p r e t a t i o n o v e r a

re la t ive ly long t im e span , and then a t t r ibu te d i f fe ren t s t a -

b i l i ty t o t h e t o n e s o f t h e m e l o d y . S u c h k e y c o n t e x t s e f f e c t s

l e d t h e p a r t ic i p a n t s t o p e r c e i v e p h y s i c a l l y i d e n t ic a l a c o u s t i c

e v e n t s a s b e i n g v e r y d i f f e r e n t a u d i to r y e v e n t s .

I n a d d i t i o n , t h is e x p e r i m e n t d e m o n s t r a t e s t h a t p e r c e i v e d

s t a b il i ty i s n o t e n t i r e l y d e t e r m i n e d b y t h e t o n a l s t r u c t u r e s o f

t h e m e l o d y : C h a n g i n g t h e r h y t h m i s s u f f i c i e n t t o p r o v o k e

s ign i f i can t changes in the pe rce ived s tab i l i ty p rof i l e s . The

p r i m a r y t e n d e n c y a p p e a r s t o b e t h a t t o n e s a r e p e r c e i v e d a s

b e i n g m o r e s t a b le w h e n t h e y a r e o f l o n g d u r a t i o n o r w h e n

t h e y f a l l o n a s t r o n g m e t r i c b e a t. C o n s i s t e n t fi n d i n g s w e r e

r e p o r t e d b y L a d e n ( 1 9 9 4 ) . T h e s e r h y t h m i c e f f e c t s m a y b e

u n d e r s t o o d f u r t h e r in l i g h t o f t h e o v e r a l l l a c k o f i n t e r a c t io n

b e t w e e n p i t c h a n d r h y t h m i c s t r u c tu r e . I n d e e d , w e a s s u m e d

t h a t a n i n c r e a s e i n d u r a t i o n o r a c h a n g e i n m e t r i c p o s i ti o n

w o u l d h a v e a d i f f e r e n t e f f e c t o n m u s i c a l s t a b i li t y d e p e n d i n go n t h e l o c a t i o n o f t h e n o t e s i n s i d e t h e t o n a l h i e r a r c h y .

H o w e v e r , a m o n g t h e 2 3 s t o p t o n e s t es t e d , t h e o n l y e v i d e n c e

f o r s u c h a n i n t e r a c t io n w a s o b s e r v e d a m o n g t h e m u s i c i a n s

o n t h e l a s t t o n e o f t h e m e l o d i e s . T h i s r e s u l t d i f f e r e d f r o m t h e

o n e p o i n t e d o u t b y B i g a n d ( 1 9 9 3 ) , w h o o b s e r v e d a n o v e r a l l

s i g n i f ic a n t i n t e ra c t i o n b e t w e e n p i t c h a n d r h y t h m w i t h i n t h e

m u s i c i a n s. T h e o n l y d i f f e r e n c e b e t w e e n t h e p r e s e n t e x p e r -

i m e n t a n d t h a t c o n d u c t e d b y B i g a n d i s t h a t t h e c h a n g e i n

t o n a l s t r u c t u r e w a s a c h i e v e d h e r e w i t h o u t c h a n g i n g t h e

p i t c h e s a n d t h e m e l o d i c i n t e r v a l s o f t h e T 1 a n d T 2 m e l o d i e s .

T h a t t h e p r e s e n t e x p e r i m e n t f a i l e d t o r e p l i c a t e th e i n t e ra c -

t i o n o b s e r v e d b y B i g a n d s u g g e s t s t h a t t o n a l s t r u c t u r e a n d

r h y t h m d o n o t n e c e s s a r i l y i n t e r a c t w h e n a l l o t h e r f e a t u r e s( i . e . , m e lod ic con tour , in te rva l s i zes , p i t ches ) a re kep t

cons tan t .

F i n a l l y , th e p r e s e n t e x p e r i m e n t p r o v i d e d e v i d e n c e t h a t a

l i n e a r c o m b i n a t i o n o f f i v e p r e d i c t o r s a c c o u n t e d f o r a s i g -

n i f i can t pa r t o f the va r iance in the s t ab i l i ty ra t ings rec ord ed

t h r o u g h o u t t h e e n t i r e e x p e r i m e n t a l s i t u at i o ns . E x c e p t f o r t h e

m elod ic con tour we igh t , a l l p red ic to rs ( i . e . , tona l , dura t ion ,

m e t r i c , and in te rva l s i ze we igh t s ) m ade s ign i f i can t con t r i -

b u t i o n s t o t h e p a r t ic i p a n t s ' r a t in g s . S o m e o f t h e m c o n t r i b -

u t e d d i f f e r e n t l y , ac c o r d i n g t o t h e i r e x t e n t o f m u s i c a l e x p e r -

r is e . T h e t o n a l w e i g h t w a s a m o r e i m p o r t a n t c o n t r i b u t o r f o r

t h e m u s i c i a n s t h a n f o r t h e n o u m u s i c i an s . T h e o p p o s i t e w a s

o b s e r v e d f o r t h e d u r a t i o n w e i g h t . T h i s i n t e r a c t i o n w i t hm u s i c a l e x p e r t i s e s u g g e s ts t h a t m u s i c i a n s m a y h a v e b a s e d

t h e i r r e s p o n s e s p r i m a r i l y o n t h e t o n a l h i e r a r c h y o f t h e

m e l o d y ' s u n d e r l y i n g k e y , w h e r e a s t h e n o u m u s i c i a n s w e r e

m o r e i n f l u e n c e d b y t h e m o r e s u p e r f i c i a l f e a t u r e s o f t h e

m e l o d i e s ( t o n e d u r a t i o n ).

I n s u m m a r y , t h e f w s t e x p e r i m e n t d e m o n s t r a t e s t h a t s t a -

b i l i t y a r i s e s f r o m a c o n v e r g e n c e o f m e l o d i c a n d t e m p o r a l

f a c t o rs , th e i n f l u e n c e s o f w h i c h m a y b e q u a n t i f i e d a n d s e e m

t o v a r y d e p e n d i n g o n m u s i c a l e x p e r t i s e . T h e p u r p o s e o f

E x p e r i m e n t 2 w a s t o r e p l i c a t e t h e p r e v i o u s f i n d i n g s w i t h

m o r e d y n a m i c m e l o d ie s .

E x p e r i m e n t 2

T h e o r i g i n a l m e l o d y ( F i g u r e 4 ) f o r E x p e r i m e n t 2 w a s

c h o s e n f r o m a m u s i c t e x t b o o k a n d i s c l a i m e d t o b e i n th e

s t y l e o f R o s s i n i ( G a r t e n l a u b , 1 9 7 8 ) . T h i s m e l o d y i s m u c h

m o r e c o m p l e x t h a n t h a t u s e d i n E x p e r i m e n t 1 . F i r s t , t h e

t o n a l p i t c h s t r u c t u r e c o n t a i n s a d e s c e n d i n g c i r c l e o f f i f t h

p r o g r e s s i o n i n M e a s u r e s 5 t o 8 t h a t s t r o n g l y s u g g e s t s t h ek e y o f A ( M e a s u re s 5 a n d 6 ) a n d t h e n t h e k e y o f G

( M e a s u r e s 7 a n d 8 ) . T h e m a i n k e y o f F m a j o r i s th e n c l e a r l y

r e a f f i r m e d . I w i l l r e f e r t o t h i s t o n a l p r o g r e s s i o n a s F - A - G - F .

S e c o n d , t h e r h y t h m i c s t r u c t u r e c o n t a i n s r i c h e r p a t t e r n s o f

d u r a t i o n ( 1 6 t h n o t e , d o t t e d e i g h t h , e t c ,) a n d c o m p l e x m e t r i c

p a t t e r n s s u c h a s t h e s y n c o p a t e d t o n e s i n M e a s u r e s 5 , 7 , a n d

9 . F i n a l ly , t h e r e a r e n u m e r o u s l a r g e p i t c h s k i ps a n d c h a n g e s

i n t h e m e l o d i c c o n t o u r . T h e r e f o r e , t h e m e l o d y c o n t a i n s a

s t r o n g d y n a m i c s t r u c t u re d e f i n e d b y a b a l a n c e d c o m p l e x i t y

o f t h e f i v e m u s i c a l f e a t u r e s o f i n t e r e s t . C o n s e q u e n t l y , w e

e x p e c t e d s t r o n g e r e f f e c t s f r o m t h e c h a n g e i n t h e p i t c h a n d

r h y t h m i c s t r u c t u r e s , a g r e a t e r n u m b e r o f i n t e r a c t i o n s b e -

t w e e n t o n a l a n d r h y t h m i c s t r u c t u re s , a n d g r e a t e r d i f f e r e n c e sb e t w e e n t h e t w o g r o u p s o f l i s t e n e r s . I n a d d i t i o n , w e e x -

p e c t e d a g r e a t e r c o n t r i b u t i o n f r o m t h e d u r a t i o n a n d t h e

m elod ic we igh t s ( i . e . , in te rva l s i zes and changes in m e lod ic

c o n t o u r ) t o t h e m u l t i p l e r e g r e s s i o n a n a l y s e s.

Me~od

Material. Figure 4 displays the melodies used in the experi-ment. Because they were long, 19 stop notes were defined. The laststop note (20) was used only to ve rify the ke y interpretation of themusicians and the nonmusicians. Until Stop No te 19, the key wasvaried by shifting 8 notes one semitone up or down, 3 notes b y twosemitones, and 1 note by three semitones. The T 2 melodies start in

D major and modulate from Stop Note 10 to the end toward Gmajor. I will refer to this tonal progression as D-G. TI and T2melodies share identical melodic contours and rhythm ic structuresove r the 19 stop notes and identical pitches on 12 of them (1, 2, 3,4, 5, 6, 9, 13, 14, 16, 18, and 19). Several rhythmic changes wereeffected that were designed to alter musical stability withoutrendering the melodies as being too awkwardsounding. Moreover,these rhythmic changes allow us to define notes changing induration but not in metric position (Stop Notes 2, 6, 10, and 14)and notes changing in metric position w ithout changing in duration(Stop Notes 8, 12, 16 ). The fo ur melodies (T1R1, TI R2 , T2R1,and T2R2) were segmented into several fragments; each startedfrom the beginning of the melody an d stopped on a different stopnote. The 20 fragments were produced in the same manner as inExperiment 1.

Th e predicted values for stability were defined as in Experiment1. Th e tonal weights of the T1 melodies are those of the Krumhansl(1990) F major key profile to Stop Note 6 (TW in T able 4). Th e Amajor key profile values are used from Stop N otes 7 to 10, and theG m ajor key profile values from Stop Notes 11 to 14. The F majorkey profile values are then used again. These values are referred toas the F-A-G-F key profile. In the T2 melodies, the D major keyprofile values are used fro m Stop Notes 1 to 10, and the G majorkey profile values from Stop Note 11 to the end of the melody.These values are labeled as the D -G k ey profile. The correlationbetween the tonal weights of T1 and T2 was positive but notsignificant, r(18) = .25.

The duration weights (DW in Table 4) are proportional to the




J . 1 1 0

^ T I R 1 . . . . . r l l , , , J I , I • - . , ,, ~ , ~ i , . , I . 1 . , . , , . , i

. . . . . 2 , : ' - ' ,d Stop 1' . . . .t e 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

, ~ . . . . . , _ . , ~ i i , I ~ , ,' r i i t t , I l l - - i ~ , I . 1 0 ~ I . . . . .

i ' ~ ~ 1 . . . . . . . . .i l . . . . . . . . I - -~ g , . - - . l . . , I ) ~ ' I

. . - , " ] , . . I . I " 1 " " - I -~'-"-'-,,~-~ ..

Stopno tes 1 2 3 4 5 6 7 8 91 0 1112 13 14 1516 1718 19 20

Stopnotes 1 2 3 4 5 6 7 8 9 1 01 1 12 13 1415 16 17 18 19 20

t I r m a l ] 1 ] ~ ~ ! i ! I [ ! i l l n ~- . . . . . . : - _ - - , _ , _ - . , , , ~ . . ~ ; , . ~ -I | 1 ] l ~ ' l m [ I II . [ I II v ' -- l ~ d I | 1I I v I I Wll v i ~ , l l l 8 1 I I I I l i p I ~ l I .

i n , i - i l r i ~ i i i l , ~ , 11 | q l w i n m w ~ l i ~ i .

e J w •Stopnotes 1 2 3 4 5 6 7 8 9 1011 12 131415 16 1718 19 20

Figure 4. Four melodies used in Experiment 2. The tonal structure (T) varies from T1 to T2, and

the rhythmic slructure (R) varies from R1 to R2.

different durations observed in the'melody: A value of 4 was

assigned to the quarter note, a value of 3 to the dotted eighth notes,and so on. The metric weights (MW in Table 4) depend on the

number of metric levels that the melody contains. Here, there i s a

strong beat at the measure level (which has a value of 4), a less

important metric beat on the second quarter note of the measure

(which has a value of 3), and so on. To express the potentialinfluence of pitch skips on stability, the number of semitones in

each melodic interval was computed (MIW values in Table 4). To

account for the potential influence of change in the melodic

contour, a value of 2 was assigned to the tones on which a change

in contour occurs. A value of 1 was assigned to repeated tones

Table 4

Tonal Weights (TW), Duration Weights (DW), Metric Weights (MW), Melodic IntervalWeights (MIW), and Melodic Contour Weights (MCW) for the MelodiesTIR1 and T2R2 in Experiment 2

TIR1

Stop note(s) TW DW MW MIW MCW

T2R2

TW DW MW MIW

1 4.38 3 4 2 0 5.19 3 4 22 4.38 4 3 1 2 5.19 2 3 13 3.48 4 4 2 0 3.48 2 2 24 3.48 2 3 0 1 3.48 4 4 05 3.66 4 4 4 0 6.35 2 2 36 4.38 4 3 5 2 5.19 2 3 57 2.68 2 4 1 0 4.38 2 2 38 2.39 4 2 9 2 4.38 4 4 129 4.09 4 4 0 1 6.35 2 2 0

10 4.38 4 3 1 1 2.29 2 3 2I 1 3.66 2 4 7 0 3.66 2 2 812 2.39 4 2 9 2 3.66 4 4 1213 4.09 4 4 0 1 4.09 2 2 014 4.38 4 3 1 1 4.38 2 3 115 2.88 2 4 7 0 5.19 2 2 916 3.66 4 2 10 2 5.19 4 4 1217 4.09 2 4 0 1 4.38 2 2 018 4.38 4 2 1 1 3.48 2 3 219 3.48 3 4 0 1 6.35 4 4 020 6.35 6 4 1 2 6.36 4 3 1



8 1 8 B I O A N D

(e.g., Stop No te 4) because repeated notes introduce o nly a w eakchange in the melodic contour. F or the sam e reason, a value of 1was assigned to the tones that immediately follow a repeated tone(e.g., Stop N ote 10). A value o f 0 was assigned in the other cases(MCW values in Table 4).

Participants, procedure, and design. Experiment 2 was con-ducted w ith the 40 you ng music teachers and the 40 undergraduatestudents in psychology who participated in Experiment 1. Theparticipants' task, the procedure, and the design were identical tothose of Experiment 1.

R e s u l t s

Pa r t i c ip a n t s ' a g re e m e n t . T h e K e n d a l l c o e f f i c i e n t o f

c o n c o r d a n c e w a s c o m p u t e d s e p a r a t e l y f o r th e m u s i c i a n s a n d

t h e n o n m u s i c i a n s f o r e a c h e x p e r i m e n t al s it u at io n. T h e o b -

s e r v e d c o ¢ If i c i e n ts w e r e a l l s i gn i fi c a nt , < , 0 1 . T h e c o r -

r e la t io n s b e t w e e n t h e m e a n r a t in g s o f t he m u s i ci a n s a n d t h e

n o n m u s i c i a n s w e r e s i g n if i c a nt i n e a c h e ) ( p e r i m e n t a l c o n d i -

t io n. T h e l o w e s t c o r r e l at i o n w a s o b s e r v e d f o r t h e T I R 2

m e l o d y , r ( 1 8 ) = . 7 0 , < . 0 1 , a n d t h e h i g h e s t w a s o b s e r v e d

f o r t h e T I R I m e l o d y , r ( 1 8 ) ---- . 8 9 , p < . 0 1 . T h e m e a n

r a t in g s a c r o s s l i st e ne r s f o r e a c h s t o p n o t e a n d f o r e a c h

e x p e r i m e n t a l s i t u a ti o n a r e s h o w n i n F i g u r e 5 . T h e d i ff e r-

e n c c s i n st a bi l it y r o f i l e s r e c o r d e d f o r S t o p N o t e s 1 t o 1 9

w e r e e x a m i n e d w i t h a 2 × 2 × 1 9 ( K e y C o n t e x t ×

R h y t h m × S t o p N o t e ) M A N O V A , w i t h t h e t h ir d f a c t o r a s

t he r e pe a te d va r i a b le . S top N o te 20 w a s no t i nc lude d in th i s

a na ly s i s be c a us e i t i s t he ton ic in a l l t he e xpe r ime n ta l

c ond i t ions , a nd i t w a s no t a s s ume d to in s t i l l a d i f f e re n t

d e g r e e of s t a b i li t y .

Ke y c o n te x t e f f e c t . O v e r t h e 1 9 s to p n o t e s , t h e m u s i -

c i a n s ' T l p r o f i le s d i f f e re d s i g n i f ic a n t ly f r o m t h o s e o f T 2 ,

]7(18 , 19 ) = 4 .52 , p < .005 (W i lk s ' s l a mb da te s t ) a s d id

thos e o f t he nonm us ic i a ns , F (18 , 19 ) = 3 .18 , p < .01 .

P r o f d e a n a l y s e s w e r e p e r f o r m e d a g a i n o n t h e 1 2 s to p n o t e s

s ha r ing the s a m e p i~che s (S top N o te s l , 2 , 3 , 4 , 5 , 6 , 9 , 13 ,

14 , 16 , 18, a nd 19 ). The m a in e f fe c t o f t he ke y w a s s ign i f -

i c a n t fo r bo th the mus ic i a ns , F (11 , 26 ) = 3 .94 , p < .005 ,

a nd the nonm us ic i a ns , F ( l l , 26 ) = 3 .26 , p < .01 .

T h e a v e r a g e r at i n g s o b t a in e d f r o m T 1 a n d T 2 m e l o d i e s

w e r e t h e n c o r r e la t e d w i t h t h e F - A - G - F k e y s p r of i le , a n d

w i t h th e D - G k e y p r of il e . h e T I r a t i n g s : we r e m o r e h i g h l y

c o r r el a te d w i t h t h e F - A - G - F k e y p r of i le & a n w i t h t h e D - G

k e y p r o fi l e , n o t a b l y f o r t h e m u s i c i a n s ( T a b l e 5 ) . R e c i p r o -

c al ly , t h e T 2 r a t i ng s w e r e m o r e h i g h l y c o r r e l a te d w i t h t h e

D - G p r of i le t h a n w i t h t h c F - A - G - F k e y p ro fi le . h i s s u g g e s t

t h a t b o t h g r o u p s o f l is t e n er s w e r e m o r e o r i e n t e d t o w a r d t h eF - A - G - F k e y s , i n th e T 1 m e l o d i e s , a n d t o w a r d t h e D - G

ke ys , i n t he T2 me lod ie s . Th i s po in t w a s c on fn - rne d by the

m e a n r a t i n g s o b s e r v e d f o r S t o p N o t e 2 0 . R e g a r d l e s s o f

d i f fe re nc e s in p i t c h , t he F in T1 a nd the G in T2 ha ve the

s a me ton ic mus ic a l func t ion . O n th i s s top no te , t he me a n

T 1 R 1

e N o n m u s i d a n s O M u s id a n s

" ' : : : : : : : " ; : : ; . . .. . .. . .. . .. . .. . .. . . . . .. . .. . . .. . .. . .. . . : ; 4. . . . . . . . 7": - -

1 . S . ~

1 '

i- -

T I R 2

• N o n m u s i d a n s O M u s i d a n s

: : : : : : : : : : : : : : :: : : : : : : : : : : : : : : :: : : : : : : : : : : : :. . . . . .: : : : : : : : : : : : : : : :: : : : : : : : : : : : : : : :: : : : : : : : : : : : : : : ::

' ~ 4t " " , V \ I ~ / . .

: : . : . . . L . . . . . . . . . . . . . , _ , I L . _ . . . . . . . , . . . : . _ ~ : . . .. . .. . . . , : . . . , , . . L : . . . . . . : : . .. .. .. .

Stop 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

n o t e s

T 2 R 1 T 2 R 2

• N o n m u sid an s o M u sid an s • N o n musician s OM u sid an s

7 t . . . . . . . . . . , ~ - . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .

S t o p 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 i 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0n o t e s

Figure 5. M ean stability ratings in Experiment 2 for each melody. T = tonal structure; R =rhythmic structure.



P ERCEIVING MUS ICAL S TABILITY 821

m e l o d i c s e q u e n c e . I n t e r m s o f B h a r u c h a ' s c o n n e c t i o n i s t

m o d e l ( 1 9 8 7 ) , t h i s i n te g r a t i o n m a y b e i n s t a n t i a te d b y m o d -

n l a t in g t h e a m o u n t o f a c t i v a t i o n p r o p a g a t i n g t o t o n e u n i t s b y

s e v e r a l o t h e r p a r a m e t e r s r e l a t e d t o t o n e d u r a t i o n , m e t r i c

l o c a t i o n o f t h e t o n e s , p i t c h i n t e r v a l , a n d m e l o d i c c o n t o u r .

H o w e v e r , t h e m o d e l d e f i n e d i n t h e p r e s e n t s t u d y c o u l d b e

f i n e - t u n e d b y g r e a t e r r e f i n e m e n t s . O n e w e a k n e s s o f t h e

p r e s e n t m o d e l i s t o q u a n t i f y t h e t o n a l s t r u c tu r e b y c o n s i d -e r i n g o n l y t h e s c a l e d e g r e e o f t h e t o n e i n t h e m e l o d i c

u n d e r l y i n g k e y . I n s p i t e o f t h e f a c t t h a t s u c h a s i m p l e

q u a n t i f i c a t io n c a p t u r e d a s i g n i f ic a n t p a r t o f t h e p e r c e i v e d

m us ica l s t ab i l i ty , one m ay ob jec t tha t tona l sm ac ture i s too

c o m p l e x t o b e c h a r a c t e r i z e d in s u c h a u n i d i m e n s i o n a l f a s h -

i o n . I n d e e d , t h e s t a b i li t y o f a t o n e i n a g i v e n m e l o d i c c o n t e x t

n o t o n l y d e p e n d s o n t h e t o n a l h i e r a r c h y o f t h e u n d e r l y i n g

k e y b u t a l s o o n i t s c h o r d a l p o s i ti o n i n t h e i m p l i e d h a r m o n i c

p r o g r e s s io n . T h e p r e s e n t m o d e l d o e s n o t e x p r e s s t h e p o t e n -

t i a l i n f l u e n c e o f t h e i m p l i e d h a r m o n i c p r o g r e s s i o n o n m u -

s ica l s t ab i l i ty . The re fore , quan t i fy ing the tona l s t ab i l i ty o f

t h e m e l o d i c t o n e s i n r e f e r e n c e t o b o t h t h e t o n a l h i e r a r c h y

a n d t h e t o n a l f u n c t i o n o f t h e t o n e s i n t h e i m p l i e d h a r m o n i cp r o g r e s s i o n w o u l d p r o b a b l y b e a m o r e s o p h i s t i c a te d w a y t o

f o r m a l i z e t h e i n f l u e n c e o f t h e t o n a l s t r u c t u r e o n m u s i c a l

s t ab i l i ty . Le rdah l ' s tona l p i t ch space theory (Le rdah l , 1988 ,

1 9 9 6 ) o f f e r s o n e p o s s i b l e f r a m e w o r k f o r s u c h a

quan t i f i ca t ion .

T h e f i n a l g o a l o f t h is s t u d y w a s t o i n v e s t i g a te t h e e f f e c t o f

m u s i c a l e x p e r t i s e o n p e r c e i v e d m u s i c a l s t a b i li t y . O n e o f t h e

m o s t s t r ik i n g f i n d i n g s c o n c e r n s t h e v e r y s l i g h t d i f fe r e n c e s

i n m u s i c a l s t a b i li t y p r o f i l e s f o r m u s i c i a n s a n d n o n m u s i c i a n s

i n a l l e x p e r i m e n t a l s i t u a ti o n s a n d i n b o t h e x p e r i m e n t s . T h i s

r e s u l t i s c o n s i s t e n t w i t h o t h e r r e s u l ts r e p o r t e d w i t h m e l o d i e s

( B h a r u c h a , 1 9 8 4 ; B i g a n d , 1 9 9 3 ; B i g a n d & P i n e a u , 1 9 9 6 ;

B o l t z , 1 9 8 9 a ; L a d e n , 1 9 9 4 ; S m i t h & C u d d y , 1 9 8 9 ) a n d w i t h

c h o r d s e q u e n c e s ( B i g a n d , 1 9 9 3 ; B i g a n d e t a l ., 1 9 9 6 ; B i g a n d& P inea u , in p res s ) . Th i s sug ges t s tha t the exp l ic i t l ea rn ing

o f m u s i c m a y n o t b e n e c e s s a r y t o p e r c e i v e s u b t l e s t r u c tu r e s

in tona l m us ica l s equences .

A b o v e a n d b e y o n d s i m i l a r p a t t e rn s o f re s u l t s a m o n g

m u s i c i a n s a n d n o n m u s i c i a n s , t h e p r e s e n t s t u d y r e v e a l e d

s o m e d i f f e r e n c e s b e t w e e n b o t h g r o u p s o f l i s te n e r s. I n b o t h

e x p e r i m e n t s , w e a k i n t e r a c t i o n s w e r e f o u n d i n m u l t i p l e r e -

g r e s s i o n a n a l y s e s b e t w e e n t h e t o n a l a n d t h e d u r a t i o n

w e i g h t s a n d m u s i c a l e x p e r t i se . T h e f o r m e r v a r i ab l e c o n t r i b -

u t e d m o r e t o t h e m u s i c i a n s ' r a t in g s ; t h e l a t t e r c o n t ri b u t e d

m o r e t o t h e n o n m u s i c i a n s ' r a t i n g s . S i m i l a r i n t e r a c ti o n s w e r e

a l s o o b s e r v e d b y B i g a n d e t a l . ( 1 9 9 6 ) w i t h s h o r t c h o r d

s e q u e n c e s i n w h i c h t h e m u s i c i a n s ' r a t in g s w e r e d e t e r m i n e dp r i m a r i l y b y t h e t o n a l f u n c t i o n o f t h e c h o r d , w h e r e a s t h o s e

o f t h e n o n m u s i c i an s w e r e i n f lu e n c e d m o s t l y b y m o r e s u -

pe r f i c ia l fea tu res (no tab ly p i t ch in te rva l ) . Mus ic ians and

n o n m u s i c i a n s m a y r o u g h l y b e s e n s i t iv e t o t h e s a m e k i n d s o f

m u s i c a l f e a t u r e s , b u t t h e f o r m e r t e n d e d t o e m p h a s i z e t h e i r

k n o w l e d g e o f t o n a l h i e r a r c h y .

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R e c e i v e d D e c e m b e r 1 0 , 19 9 3

R e v i s i o n r e c e i v e d D e c e m b e r 2 0 , 1 9 9 5

A c c e p t e d F e b r u a r y 1 6, 1 9 9 6 •

bigand, e. (1997). perceiving musical stability- the effect of tonal structure, rhythm, and musical...

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