(Boltz; Jones, 1989) Dynamic Attending and Responses to Time

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PsycholosicalReview Copyright1989by he AmericanPs~holo#calAssociation, nc.1989,Vol.96, No. 3, 459--491 0033-295X/89/$00.75

D yn am ic Attending and Responses to Tim e

Mari Riess Jones Marilyn BoltzOh io S ta te Un iv e r s i ty Ha v e r f o r d Co l l e g e

A temporally based theory o f attending is proposed that assumes that the structure of world eventsaffords different attending mod es. Future-oriented attending supports anticipatory behaviors andoccurs with highly coherent temp oral events. Time judgm ents, given this attending m ode, axe influ-enced by the w ay an event's ending confirms o r violates temporal expectancies. Ana lytic attendingsupports other activities (e.g., grouping, counting), and if it occurs with events of low temporalcoherence, then time judgments depend o n the attending levels involved. A weighted contrast mode ldescribes over-and underestimations of event durations. The model applies to comparative durationjudgm ents o f equal and unequal time intervals; its rationale extends to temporal prod uctions/extrap-olations. Two experiments co mpa re predictions of he contrast m odel with those derived from othertraditional approaches.

O n e c h a r a c te r i s ti c o f m o d e r n s o c i e ty i s a p r e o c c u p a t i o n w i t h

f ix e d t ime s c h e d u le s a n d s t a n d a r d iz e d t ime k e e p e r s . W e ma in -

t a i n a p p o i n t m e n t s a t h o u r l y i n t e r v a l s , r u s h t o m e e t t h e 5 : 0 0

p . m . b u s , a n d d i n e a t p r e d e t e r m i n e d h o u r s . Y e t o u r n a t u r a l

a b i li t y t o j u d g e t i m e r e m a i n s p o o r l y u n d e r st o o d . H o w o f t e n d o

we e s t ima te th e t im e e la p s e d s in c e l a s t g l a n c in g a t a c lo c k a n d

d i s c o v e r w i th s u r p r i s e th a t we we r e f a i r ly a c c u r a te ? S u r p r i s e i s

u n d e r s t a n d a b le b e c a u s e a t l e a s t a s o f t e n we lo s e t r a c k o f t ime

a n d e rr . Th e v a l id i ty o f th e se im p r e s s io n s i s c o n f i r me d b y l a b o -

r a t o r y r e s ea r c h s h o w i n g t h a t d u r a t i o n j u d g m e n t s d e p e n d n o t

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

te m p o r a l f a c to rs . Th e s e in c lu d e th e s p a t i a l l a y o u t a n d c o m p le x -

i ty of an event as wel l as the a t t en t io na l se t , sk i ll , a f fec t , and

c o n s t i tu t io n a l s t a t e o f th e ju d g e ( A l la n , 1 9 7 9 ; F r a i s se , 1 9 8 4 ;Kr is tof fe r son , 1984) .

Re s e a r c h e r s h a v e a d d r e s s e d m a n y o f th e se i s s u es th a t in c lu d e

b o th p s y c h o p h y s ic a l p r o b le m s ( e. g. , W e b e r ' s La w f o r t ime d i s -

c r imin a t io n ) a n d o r g a n i s mic v a r i a b le s ( e . g . , a g e , d r u g s , a n d

a r o u s a l e f fe ct s) . O f r e c e n t in t e r e s t i s th e in f lu e n c e o f n o n te m p o -

r a l i n f o r m a t i o n o n t i m e j u d g m e n t s , d u e l a r g el y t o a f a s c i n a ti o n

w i t h s u c h p r o b l e m s a s th e fille d interval effect. T h i s p h e n o m e -

n o n r e v e a l s th a t two e q u iv a le n t t ime in te r v a l s ma y n o t b e

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

f il ls th e m . A l t h o u g h t h e m o s t p o p u l a r m o d e l s o f j u d g e d d u r a -

t io n a t t e m p t to e x p la in th i s e f f e ct ( e. g. , B lo c k , 1 9 7 8 ; Or n s te in ,

1 9 6 9 ), t h e e f f e c t i t s e l f r a i s e s p r o b le m s f o r a g e n e r a l th e o r y o f

t im e e s t ima t io n ( Al la n , 1 9 79 ).I n th i s a r t i c l e we f o c u s o n s o m e p r o b le ms r a i s e d b y th e f i ll ed

This research was supported by Gra nt BN S-8204811 from the N a-tional Science Foundation an d by a fellowship from the N etherlandsInstitute for Advanced Study awarded to the senior author (I 986-1987).

The authors tha nk C hris Antons, D avid Buffer , Walter Johnson, G aryKidd, K err i Marsh, Elizabeth Maxshburn, John Michon, Mitch Pratt,Ken Pugh , Jackie Ralston, an d W ithe r wan Vreden. Special thanks axedue to Steve Handel an d two anony mo us reviewers for their excellentcomments on a n earlier version of this ar ticle.

Correspondence concerning this article should be addressed to MarlRiess Jones, Department of Psychology,The Ohio State University, 142Townshend Hall, Columbus, Ohio 432 I0.

45 9

in te r v a l e f f ec t . W e c o n s id e r th e s e a n d r e l a t e d i s s u e s c o n c e r n in g

r e s p o n s e s to t ime f r o m a mo r e g e n e r a l p e r s p e c t iv e , o n e b a s e d

o n a n a n a ly s i s o f e v e n t t i m e i t se l f a n d d y n a m i c a s p e c ts o f a t -

t e n d in g . W e s u g ge s t th a t e v e n t s d e f in e t ime in te r v a l s a n d th a t

th e i r in h e r e n t r h y t h m ic p a t t e r n in g s w i l l a f fe c t th e wa y p e o p le

a t t e n d t o t h e m a n d j u d g e t h ei r d u r a t io n s . T h e g e n e ra l f ra m e -

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

e q u a l a n d u n e q u a l t i m e i n t e rv a l s a s w e ll a s te m p o r a l e x t r a p ol a -

t io n s . A l th o u g h th e s e h y p o th e s e s c a n n o t e x p la in a l l o f th e d i -

v e r se f a c t s o f t ime e s t ima t io n , th e y d o s u g g e s t wa y s o f l in k in g a

g e n e ra l t h e o r y o f a t te n d i n g t o s p ec i fi c m o d e l s o f t i m e j u d g m e n t

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

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

th e i r a s s u m p t io n s in to a mo r e in c lu s iv e f r a me wo r k .Th i s a r t i c l e h a s f iv e p a r t s . P a r t 1 in t r o d u c e s s o m e c o n te m p o -

r a r y t ime mo d e l s . P a r t 2 o u t l in e s a th e o r e t i c a l a p p r o a c h to

e v e n t t i m e a n d d y n a m i c a t t en d i n g , a n d P a r t 3 r e t u r n s t o t i m e

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

t e n d in g in v a r io u s t as k s . P a r t 4 d e s c r ib e s two e x p e r ime n t s r e l e-

v a n t to th e s e h y p o th e s e s th a t p r e s e n t d i f f i c u lt i e s f o r c o n te m p o -

r a r y t ime m o d e l s . P a r t 5 c o n c lu d e s w i th a d d i t io n a l th e o r e t i c a l

i m p l i c a t i o n s o f t h is a p p r o a c h .

P a r t 1: C o n t e m p o r a r y T h e o r i e s a n d Is s ue s

I n P a r t 1 , s e ve r al c o n t e m p o r a r y m o d e l s o f j u d g e d d u r a t i o n

a r e p r e s e n te d a lo n g wi th r e l e v a n t e mp i r i c a l s u p p o r t . Th e s em o d e l s p r i m a r i l y a d d r e s s t h e c a s e i n w h i c h p e o p l e j u d g e i d e n t i-

c a l d u r a t io n s a n d e r r o r s g iv e r i se to th e f i ll e d in t e r v a l e ff ec t. On e

in f lu e n t i a l mo d e l i s Or n s te in ' s ( 1 9 6 9 ) .

Or ns t e in ' s S t o r age S i z e H ypo t hes is

I n f l u e n c e d b y F r a n k e n h a u s e r ' s ( 1 9 5 9 ) o r i g i n a l m o d e l ,

Or n s te in ( 1 9 6 9 ) f u r th e r d e v e lo p e d th e storage size hypothesist o e x p la in th e e s t im a t io n o f t ime p e r io d s l a s t in g a b o u t 1 0 s o r

mo r e . Ac c o r d in g to th i s v ie w , two e q u a l t im e in te r v a l s w i l l s e e m

t o h a v e d i f fe r en t d u r a t i o n s i f o n e i s m o r e c o m p l e x a n d t h e r ef o r e

r e q u i re s m o r e s t o ra g e s p a c e i n m e m o r y : " T h e c e n t r a l m e t a p h o r

i s t h a t t h e e x p e r i en c e o f d u r a t io n o f a n i n t e r v a l i s a c o n s t r u c t i o n



460 MARI RIESS JONES AND MARILYN BOLTZ

form ed from i ts s torage size . As storage size increases, du ra t ion

experienc e lengthens" (O rnste in , 1969, p . 42) .

Expe r ime n t s suppor t ing th i s v i e w ha ve re l i e d on va r ious

de f ini t ions o f s t imu lus c omp le x i ty ( e.g. , nu mb e r o f a ng le s

in v isua l f igures, s t imulus a rrangement in t ime and space)

a nd found tha t t he e xpe r i e nc e d du ra t ion o f i n t e rva l s be tw e e n

30 s a nd I0 m in doe s , i n f a c t , l eng the n w i th i nc re a s ing s t imu lusc omple x i ty (H oga n , 1975 ; O rns t e in , 1969 ; Sc h i ffma n & B obk o ,

1974) . Others , however , have reported confl ic t ing resul ts . For

e xa mple , bo th B loc k (1974) a nd P oyn te r (1983 ) ha ve found tha t

a se que nc e o f w ords i s j udge d longer w he n w ords a re g ro upe d

by se ma n t i c c a t e go ry tha n w he n ra n dom ly a r range d . B e c a use

the l a t t er p re sum a b ly c on ta in s m ore c hunk s , t h i s c on t ra d i c t s

O rns t e in ' s mode l . A s a r e su l t o f t hese d i sc re panc ie s , mode l s a s -

suming a d i f f e ren t r e fe re n t fo r j udge d du ra t ion ha ve be e n p ro -

p o s e d .

Attentional Effort M odels

A mode l o f fe red by U nde rw ood a nd Sw a in (1973 ) pos it s t ha tdu ra t ion judgme n t s a re me d ia t e d by a t t e n t iona l e f fo r t . The y

te s t e d O rns t e in ' s (1969 ) p re d ic t ion tha t i nc re a se d a t t e n t ion

le a ds t o m ore s to re d in fo rm a t ion a nd he nc e to l onge r time e s ti -

ma te s . A t t e n t iona l de m a nds w e re va r ie d inde pe nde n t ly o f i n -

fo rm a t ion c on te n t i n a v ig i la nc e t a sk in w h ic h sub je c t s de te c t e d

t a rge t d ig i t s e mbe dde d in p rose pa ssa ge s t ha t w e re pa r t i a l l y

ma sked by var ious whi te noise in tensit ies . W hen une xpec te dly

asked to judge the re la t ive dura t ion of each passage , subjec ts

repo rted those m ask ed by a h igh-in tensi ty noise ( i .e . , requir ing

mo re a t t e n t ion ) t o be l onger t ha n those ma sk e d by a l ow - in t e n -

si ty noise . However , con tra ry to Or nste i n 's s torage ana lysis , de-

tec t ion leve ls indica ted tha t less i n fo rma t ion w a s e nc ode d in

highly m asked passages.

Suc h f ind ings supp or t t he i de a tha t e xpe r i e nc e d du ra t ion i s

l e ss de pe nde n t on me mory loa d tha n on a t t e n t iona l e f fo r t o r

a rousa l a ssoc i a t e d w i th p re se n te d in fo rma t ion . O the r s , u s ing

ve ry b r i e f s timu l i , ha ve r e a c he d s imi l a r c onc lu s ions (Th om a s &

Cantor , 1978; Th om as & Weaver, 1975).

Contex tual Change Mo del

A nothe r c hal le nge to O rn s t e in ' s (1969 ) p roposa l c ome s f rom

Block 's (1978, 1985, in press) contextual change hypothesis.Judge d du ra t ion i s hypo the s i ze d to i nc re a se a s a l i ne a r func t ion

o f t he num be r o f c on te x tua l c ha nge s oc c u r r ing in b o th the e nv i -

ronmenta l s i tua t ion (e .g . , changes in s t imulus propert ies , task

demands) and in the organism (e .g . , mnemonic ac t iv i t ies) .C ha nge s a re mo n i to re d b y a n in t e rna l c ogn i ti ve de v ice t ha t l a t e r

ou tpu t s a c om ple x i ty i nde x ba se d on the to t a l num be r o f

changes wi th in a t im e in te rva l .

In o ne t e s t o f th i s mode l , B loc k a nd R e e d (1978) r e qu i re d

subjec ts to e ncode word l is ts a t d i f fe rent leve ls of process ing (h

l a C ra ik & L oc kha r t , 1972 ). Fo r e xa m ple , some pe op le j udge d

the ty ping sty le o f words ( i .e . , a sha l low task) or ca tegorized

words in to sem ant ic ca tegories (i .e . , a deep task) , whereas o thers

a l t e rna t e d be tw e e n bo th t a sks . A f t e rw a rd , a l l o f the sub je c t s

w e re une xpe c te d ly a ske d to j udge w h ic h a c t iv i ty se e me d longer .

B o th the s to ra ge s iz e a nd a t t e n t iona l e f fo r t mode l s p re d ic t t ha t

de e p p roc e ss ing (more in fo rma t ion , more e f fo r t ) shou ld p ro -

duc e longer t ime e s t ima te s . Th i s w a s no t t he c ase . W he n p e op le

alternated shallow--deep strategies (i .e ., more changes), dura-

t ion seemed longer . They in te rpre ted such f indings as support

fo r B loc k ' s cha nge hypo the s i s a nd a s p gob le ma t i c fo r bo th the

storage size and a t tent iona l e ffor t models .

Evaluation o f Current Mo dels

How successful a re these models? Each is qui te successful

wi th in cer ta in contexts . However , a l l share cer ta in empir ica l

and theore t ica l l imi ta t ions.

Em pir ica l d i f ficul ties s t em fro m seem ingly conflic t ing resul ts

tha t em erge from the l i te ra ture as a whole. A n in te rva l def ined

a s more c om ple x i s some t ime s udge d longer , bu t o n o the r oc c a -

s ions is j udge d sho r t e r t ha n a l e ss c omple x one . Fo r e xa m ple ,

d ive rge n t r e su lt s ha ve be e n obse rve d w i th t he va r i a b l e s o f s t imu-

lus famil ia r i ty (e .g . , Avant & Lym an, 1975, vs. Devane , 1974),

task d i ff icul ty (e .g . , Burnside , 1971, vs. Un derw ood & Swain ,

1973) , and st imulus a rrangement (e .g . , Poynter , 1983, vs.

Sc h i f fma n & B obko , 1974 ) .

Some confl ic t ing f indings may be due to methodologica ldifferences. Others, however, suggest a need for re-evaluating

c e r t a in t a c i t a ssump t ions o f t he m ode l s t he mse lve s (a l so see

Block, in press) . In par t icula r , thr ee issues a re re levant .

The f ir st i nvo lve s t he p re s um e d re fe re n t fo r du ra t ion judg -

m e n t s . E a c h m o d e l a s s u m e s t h a t t i m e j u d g m e n t s a r e i n f e r re d

f rom the a m oun t o f some p roc e ss ing a ct iv ity. H ow e v~ , th i s p ro -

cessing ac t iv i ty s t r ic t ly re fe rs to the nontemporal i n f o r m a t i o n

tha t f i ll s the s t im ulus in te rva l : the nu m be r of spa t ia l angles, the

a r ra nge m e n t o f w ord li st s, t he a m oun t o f ba c kg round no i se ,

a nd so on . B u t t he temporal i n fo rma t ion w i th in a n e ve n t a nd

i t s impa c t o n be h a v io r is i gno re d .

A se c ond p rob le m c onc e rns c omple x i ty . C omple x i ty i s a s -

sum e d to i nc re a se t he a m oun t o f p roce ss ing a c t iv ity a nd

thereb y lengthen experienced dura t ion . B ut i t i sn ' t a lways c lear

w hy . The re l a t ionsh ip o f p syc ho log ic a l c omp le x i ty t o t he s t imu-

lus or i t s dura t ion is ra re ly fu l ly deve loped. For example , the

s to rage s i ze hypo the s i s c l a ims tha t c omp le x i ty is de t e rmine d by

t h e n u m b e r o f m e m o r y c h u n k s . A l t h o u gh r e c en t c o d i n g th e o -

r i e s a dd fo rma l i z a t ion by e qua t ing c omple x i ty w i th me mory

code length (e .g . , Deutsch & Feroe , 1981; Leeuwenberg , 1969;

Simo n, 1972), i t rem ains a d if f icult co nst ruc t . W hat exac t ly i s

a c hunk , a nd w ha t s t imu lus o r t a sk c ha ra c t e r i s t i c s de t e rmine

c hun k bounda r i e s? Suc h que s t ions ha ve ne ve r be e n sa t i s f a cto -

r i l y answ e re d . C om ple x i ty de t e rmina n t s o f a t t e n tiona l e f fo r t

and cog ni t ive change a re equ a l ly e lusive . In a sp eech ut te rance ,

fo r e xa mple , t he re a re c ha nge s i n sound , g ra mma r , me a n ing ,

a n d i n t o n a ti o n , a n d y e t w e d o n ' t k n o w w h i c h k i n d o r h o w m u c h .o f a c ha nge i s r e qu i re d to a f fe c t j udge d du ra t ion . B e c a use c on -

t e m por a ry t im e m ode l s l a c k p re c ise de f in it i ons o f comple x i ty ,

t h i s ma y pa r t i a l ly e xp la in t he c on f l i ct i ng na tu re o f e xpe r ime n ta l

results.

A f ina l p rob le m c onc e rns t he c ho ic e o f e xpe r ime n ta l s t imu l i .

Du ring th e cours e of a day, we in te rac t w i th f r iends, dr ive , l i s ten

to m usic , and so on. Y et , these k inds o f events a re ra re ly se lec ted

for s tudy. Instead, subjec ts must compare in te rva ls f i l led wi th

smile abst rac t drawings (Orns te in , 1969), c l icks (Adam s, 1977),

and l i s ts of unre la ted words or nons ense words (Poynter , 1983) .

A l though the l a t t e r ma y o f fe r t i gh t e xpe r ime n ta l c on t ro l a nd

ma y in f a c t r e p re se n t c e r t a in e ve ryda y e xpe ri e nc e s , the y fa il t o

re f lec t the fu l l range o f s t imul i w e rout ine ly experience .



D Y N A M I C A T T E N D IN G 461

C o m m o n p l a c e e v e n ts d i f fe r f r o m t h o s e t y p i c a l o f t r a d i t i o n a l

t im e s tu d ie s in se v e ral w a y s, n o ta b ly in th e i r s t ru c tu r e a n d fu n c -

t io n . Wi th r e s p e c t t o s t ru c tu re , e v e n t s s u c h a s s p e e c h u t t e r -

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

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

sea rch . Typica l ly , these even ts d isp lay mult ip le leve ls o f in te rre -

l a t e d s t ru c tu r e th a t u n fo ld p re d ic t a b ly o v e r a g iv e n t im e s p a n .O f te n th e re i s d is t in c tiv e n e s s a s n a tu ra l t im e p a t t e rn s , i n c lu d in g

s p e c ia l b e g in n in g s a n d e n d in g s , c h a ra c te r i s t i c t e m p i , a n d

r h y t h m s . A l l o f th i s c o n t r i b u t e s t o t e m p o r a l p r e d ic t a bi l it y . A n d

p re d ic t a b i l i t y a l lo w s p e rc e iv e r s to a n t i c ip a te a n e v e n t ' s fu tu re

c o u rs e , i n c lu d in g w h e n in t im e i t s h o u ld e n d . In in t e ra c t iv e

s p e ec h , f o r e x a m p l e , t h e s m o o t h e x c h a n g e o f s p e a k in g r o l e s a n d

tu rn - t a k in g b e h a v io r s u g g e s ts t h a t p e o p le a n t i c ip a te e n d s o f u t -

t e r a n c e s . I n o t h e r c a s e s , e v e n t s t r u c t u r e c a n c o m m u n i c a t e

m o o d o r i n t e n ti o n . I t i s p o s s ib l e t h a t t h e s t r u c t u r e a n d f u n c t i o n

o f e v e n t s s y s t e m a t i c a l ly a f f ec t t im e e s t im a t io n .

I n s u m , c o n t e m p o r a r y r e s e a r c h o n t i m e e s t i m a t i o n i s c h a r a c -

t e r i z e d b y c o n f l i c t in g e x p e r im e n ta l f i n d in g s . A t th e s a m e t im e ,

q u e s t io n s c a n b e r a i s e d a b o u t t h e s t ru c tu re , fu n c t io n , a n d r e p -re s e n ta tiv e n e s s o f s t im u l i u s e d in th i s r e s e a rc h . We s u g g e s t t h a t

th e s e a re r e la t e d p ro b le m s . D iv e rg e n t e x p e r im e n ta l f i n d in g s

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

t h e w a y s p e op l e r e s p o n d t o t h e m h a v e n o t b e e n c o n s id e r e d .

O v e rv i e w o f a n A l t e rn a t iv e H y p o th e s i s

o f J u d g e d D u r a t i o n

A n a l t e rn a t iv e p e r s p e c t iv e t a k e s i t s c u e f ro m th e id e a th a t

e v e n t s a re , b y d e f in i t i o n , t e m p o ra l a n d th a t t h e i r s t ru c tu re in

t i m e i s c r it i ca l . T h a t i s , t h e t e m p o r a l p a t t e r n in g o f n o n t e m p o r a l

in fo r m a t io n ( e. g. , w o rd s , t o n a l p i t c h e s , l ig h t s, a n d e v e n h a p h a z -

a rd i t e m s ) w i th in a n y in t e rv a l i s c r i t i c a l i n d e t e rm in in g ho w o n e

a t t e n d s to th e e v e n t i ts el f. S o c ie t a l a n d in d iv id u a l n e e d s e n s u re

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

p le a t t e n d d i f f e re n t ly to e v e n t s w i th h ig h a n d lo w s t ru c tu ra l c o -

h e re n c e , a n d th a t t h i s , i n tu rn , d i f f e ren t i a lly a f f e c t s t im e e s t i-

m a te s . In b r i e f, w e p ro p o s e a d i s t in c t io n b e tw e e n tw o d i f f e re n t

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

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

respectively.

E v e n t s I d i f f er i n t e rm s o f t h e i r s t ru c tu ra l c o h e re n c e a n d p re -

d i ct a bi l it y . A n d a l t h o u g h w e a s s u m e a c o n t i n u u m o f c o h e re n c e ,

fo r c o n v e n ie n c e w e d i s t in g u i s h b e tw e e n e v e n t s w i th h ig h a n d

l o w t e m p o r a l c o h e r e n c e . H i g h l y c o h e r e n t e v e n ts , s u c h a s t h o s e

o f s p e e ch , t o n a l m u s ic , a n d b o d y g e s tu re s , o f f e r s t ru c tu ra l p re -

d ic t a b i l i t y a n d d i s p la y c h a ra c te r i s t i c rh y th m ic p a t t e rn s th a t o c -c u r o v e r n o n a r b i t r a r y t i m e s p a ns . E v e n t s o f l o w c o h e r en c e , s u c h

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

t er , u n fo ld o v e r a rb i t r a r y t im e s p a n s th a t c o n ta in l i t t l e s t ru c -

tu ra l p re d ic t a b il i t y .

H ig h ly c o h e re n t e v e n t s a f fo rd fu tu re -o r i e n te d a t t e n d in g . B e -

c a u s e th e y o f fe r h ig h t e m p o ra l p re d ic t a b i l i ty , p e o p le c a n t r a c k

a n d u s e h ig h e r o rd e r t im e p a t t e rn in g s to g e n e ra t e e x p e c ta n c ie s

a b o u t h o w a n d w h e n t h e y w i ll e n d. I n W e s t er n m u s i c , f o r ex a m -

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

o rd e re d f a s h io n , o f t e n w i th s u c h c o h e re n c e th a t l i s t e n e r s c a n

a n t i c ip a te n o t o n ly what n o te s a re l i k ely b u t a l s o when i n t i m e

t h e y " s h o u l d " o c c ur . T h u s , f u t u r e - o r i e n t e d a t t e n d in g e x p l o i ts

th e g lo b a l t im e s t ru c tu r e o f s u c h e v e n t s . In th e s e s itu a t io n s , w e

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

o r v i o l a t i on o f ex p e c t e d e n d i n g t i m e s. W h e n t w o e v e n t s o f

e q u i v a le n t d u r a t i o n b o t h e n d w h e n e x p e c t e d , p e o p l e w i l l co r -

r e c t ly ju d g e th e m to b e th e s a m e d u ra t io n . H o w e v e r, i f o n e v io -

l a t e s a n e x p e c ta n c y b y s e e m in g to e n d l a t e r t h a n a n t i c ip a te d ,

th e n i t w i l l b e in c o r re c t ly ju d g e d a s lo ng er . S im i l a r ly , a n e v e n t

a p p e a r i n g t o e n d too early w i l l b e ju d g e d a s r e l a t iv e ly s h o r t .T h i s r e a s o n i n g e x t e n d s t o j u d g m e n t s o f e v e nt s t h a t a c t u a l l y d o

d i f f e r i n d u ra t io n . A c c o rd in g to th i s v i e w th e n , d u ra t io n e s t i-

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

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

e v e n t ' s a c tu a l a n d e x p e c te d e n d in g .

A n a ly t i c a t t e n d in g o c c u r s w i th l e s s c o h e re n t e v e n t s . T h e s e

e v e n t s h a v e lo w t e m p o ra l p re d ic t a b i l i t y , a n d s o p e o p le c a n n o t

a n t i c ip a te th e i r fu tu re c o u r s e . In s t e a d , t h e y a re fo rc e d to a t t e n d

l o c al l y t o a d j a c e n t e l e m e n t s i n a n a t t e m p t t o o r g a n i z e t h e u n -

s t r u c t u r e d i n f o r m a t i o n . D e p e n d i n g o n t h e t a s k , t h is k i n d o f at -

t e n d in g s u p p o r t s s t r a t e g ies d i r e c t e d to w a rd lo w e r le v el r e l a t io n -

s h i ps ( e.g ., g r o u p i n g o r c o u n t i n g t h e n u m b e r o f i t e m s o r c h a n g e s

w i th in th e e v e n t) . F in a l ly , t o e s t im a te th e d u ra t io n o f t h e see v e n t s, p e o p le w i l l b e b i a s e d b y th e i r a t t e n t io n to lo c a l d e t a i l s

a n d w i l l j u d g e e v e n t s f i l le d w i th m o re i t e m s t o b e lon g er .

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

w a y s o f i n t e r a c ti n g w i t h t e m p o r a l e v e nt s. I n t h i s a r ti c l e t h e e m -

p h a s i s w i ll b e o n fu tu re -o r i e n te d a t t e n d in g a n d i t s i n f lu e n c e o n

t im e e s t im a te s , i n a s m u c h a s th i s to p ic h a s r e c e iv e d le s s a t t e n -

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

r a r y t i m e m o d e l s.

S u m m a r y o f P a rt I

C o n t e m p o r a r y t i m e m o d e l s h a v e f o c u s e d o n t h e f il le d i n t er -

v a l e f fe c t i n w h i c h n o n t e m p o r a l i n f o r m a t i o n d i s t o r ts j u d g m e n t s

a b o u t e q u a l t i m e i n te r v al s . T h e i r e x p l a n a t i o n s r e ly o n m e m o r y -b a s e d p r o c e ss e s t h a t g a u g e t h e t o t a l a m o u n t o f a n o n t e m p o r a l

c o n s t ru c t ( i . e . , c o m p le x i ty , e f fo r t , c h a n g e ) . B u t t h e s e a p -

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

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

s e n tat iv e ne s s . A n a l t e rn a t iv e v i e w i s p re s e n te d th a t i s m o re e x -

p l ic i tl y te m p o r a l . I t p r o p o s e s tw o m o d e s o f d y n a m i c a t t e n d in g

( f u t u r e -o r i e n t ed , a n a l y ti c ) t h a t o c c u r w i t h e v e n ts o f h i g h a n d

lo w t e m p o ra l c o h e re n c e , r e s p e ct iv ely . T h i s m o d e l i s d e s ig n e d to

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

m e m o r y - o r i e n t e d a t t e n d i n g ( a n al y t ic ) w i t h f u t u r e - o r i e n t e d a t -

t e n d in g .

P a r t 2: T e m p o r a l E n v i r o n m e n t a n d A t t u n e m e n t s

In th e r e m a in d e r o f t h i s a r ti c l e , w e h a v e th re e g o a l s . T h e f i r s t

i s t o s h o w th a t a n a ly s e s o f e v e n t s t ru c tu re a re c r i t i c a l t o th e o r i e s

Cognitive approaches ha ve traditionally referred t o world objectsand experimental m aterials as stimuli. In protest t o implications regard-ing the impoverished nature o f such materials, some recent approacheshave adopted the term event o refer to ecologicallyvalid objects under-going physical motio n or change (Gibson, 1966, 1979). Ou r frameworkreflects both notions in tha t an event refers to a ny environmental objector activity that varies along a continuu m of s tructural coherence. Some

natural ev ents are very predictable in that em bedded tem poral relation-ships are lawfully interrelated with th e event's nontem poral informa-tion. Other n atural events are less coherent and pred ictable in this re-

gard and, in fact, may contain little internal structure (e.g., silences).



4 6 2 MA R l R IE SS J O N E S A N D MA R IL Y N B O L T Z

o f a t t e n d in g . T h e s e c o n d i s t o d e s c r ib e d i s t in c t w a y s in w h ic h

p e o p l e c a n a t t e n d t o e v e nt s th a t v a r y i n t e m p o r a l c o h e r e n c e .

T h e t h i r d i s t o d e m o n s t r a t e t h a t b o t h e v e n t s t r u c t u r e a n d a t -

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

t im e e s t im a t io n .

P a r t 2 a d d re s s e s th e f i r st g o a l. A n y in t e rp re t a t io n o f r e -

s p o n se s t o ti m e s h o u l d b e b a s e d o n a t h e o r y a b o u t w h a t t i m em e a n s in e v e n t s a n d to p e o p le w h o p e rc e iv e th e se e v e n t s. In th i s

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

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

i t y , a n d c o m p le x i ty . I t a l s o l e a d s to h y p o th e s e s a b o u t t h e e a s e

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

o u s w a y s, s o m e o f w h ic h o p e ra t e in t im e e s t im a t io n s .

T h e o r e ti c a l B a c k g r o u n d

A re l a t iv i s t i c a p p ro a c h to t im e im p l i e s th a t p o in t s i n t im e

a n d a b s o l u t e t i m e i n t e r v al s a r e l e ss i m p o r t a n t t h a n t i m e p e r i o d s

d e t e r m i n e d r e la ti v e t o o t h e r t i m e p e r i o d s ( r h y t h m i c s t r u c t u r e )

a n d t im e p e r io d s d e te rm in e d r e l a tiv e to sp a t i a l e x te n t s (v e lo c i tyo r f lo w s t ru c tu re ; J o n e s , 1 9 76 ) . T h e s e t im e re l a t io n s a re in s e p a -

ra b le f ro m th e e v e n t it se lf . T h i s i d e a i s a t t h e h e a r t o f o u r a s s e r -

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

l e n g th s o f a rb i t r a ry o r i s o l a t e d t im e in t e rv a ls .

O u r th e o re t i c a l e m p h a s i s o n r e l a t iv e t im e i s c o n s i s t e n t w i th

a n e c o l o g ic a l a n a ly s i s o f e v en t s t r u c t u r e i n t e r m s o f r a n s f o r m a -

t io n s ( c h an g e s ) a n d in v a r i a n t s (n o n c h a n g e s ) a n d th e i r fu n c t io n s

fo r th e o rg a n i s m (F re y d , 1 9 8 7 ; G ib s o n , 1 9 7 9 ; J o n e s , 1 9 7 6 ;

S h aw , Mc In ty re , & Ma c e , 1 9 7 4 ; S h e p a rd , 1 9 8 4 ; T u rv e y & C a -

re l lo , 1 9 81 ). P e o p le a n d o th e r l i v in g th in g s b o th c re a t e a n d r e -

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

d a n c e , m u s ic , a n d s o o n . We s u g g es t fu r th e r t h a t t im e t r a n s fo r -

m a t io n s o f t e n s u p p o r t t h e s e in t e ra c t io n s in s p e c ia l w a y s . T h i s

l e a d s to a d i f f e re n t a p p ro a c h to c o m p le x i ty a n d , u l t im a te ly , t o

th e w a y p e o p le r e s p o n d to d y n a m ic e v e n t s t ru c tu re . T o p re v ie w ,

in s u b s e q u e n t s e c t io n s w e p ro p o s e th a t e v e n t s c h a ra c te r i z e d b y

c e r t a in t im e t r a n s fo rm a t io n s a re e a s i e r t o a n t i c ip a te in t im e

(J o n e s , 1 9 7 6 , 1 9 8 1 a , 1 9 8 2 ; D . N . L e e , 1 9 8 0 ; M ic h o n & J a c k s o n ,

1985).

R e l a t i v e T i m e i n E n v i r o n m e n t a l S t r u c t u r e

O u r e n v i ro n m e n t i s f i ll e d w i th a l l s o r t s o f t e m p o ra l e v e n t s ,

s o m e b a s e d o n a c t iv it i e s o f li v in g th in g s a n d o th e r s n o t . A l l l i e

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

b i t r a r y ( l o w c o h e r e n ce ) t o n o n a r b i t r a r y ( h i g h c o h er e n c e ). T h e

g i st o f t e m p o r a l c o h e r e n c e w a s p r e s e n te d i n P a r t 1 w h e r e i t w a sr e l a t e d t o t e m p o r a l p r e d i c t a b i l i t y a n d a t t e n d i n g m o d e . H e r e ,

w e in t ro d u c e g re a t e r fo rm a l i z a t io n b y d i s t in g u i s h in g b e tw e e n

te m p o ra l ly c o h e re n t , o r h i e ra rc h ic a l (H ) t im e s t ru c tu re s , a n d

t e m p o r a l l y i n c o h e r e n t , o r n o n h i e r a r c h i c a l ( N H ) o n e s . U l t i -

m a t e ly , c o m p l e x i t y i s d y n a m i c a l l y c o n c e i ve d i n t e r m s o f t h e se

t im e s t ru c tu re s .

W e b e g i n w i t h s o m e e x a m p l e s o f te m p o r a l l y c o h e r e n t ( h i er -

a rc h ic a l ) e v e n t s i n F ig u re l a a n d lb . B o th e x a m p le s i l l u s t r a t e

o u r u s e o f t h e t e r m coherent t o im p ly o b je c t iv e a c c e n t r e g u la r i -

t ie s ( i . e . , no t necessa r i ly sub jec t ive exper iences ) . In each , non-

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

p re d ic t a b i l i t y in tim e . In F ig u re l a , a m u s ic a l p h ra s e o f 3 , 2 0 0

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

p i t c h e s (C 4 ). 2 L a w fu l ly e m b e d d e d w i th in th i s s p a n a re o th e r

t im e pe r io ds (e .g . , 1 ,600 , 800 m s) , a lso s ign if ican t ly iden t i f ied

b y o n s e t s o f v a r io u s p i t c h es . T h e s m a l l e s t t im e p e r io d (2 0 0 m s )

i s d e t e r m in e d b y th e s m a l l e st o b s e rv a b le to n e - to - to n e o n s e t i n -

t e rv a l. A n o th e r h i e ra rc h ic a l e v e n t is il l u s t r a t e d in F ig u re lb , i n

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

b e d o n -g ro u n d t im e p e r io d s ( e .g ., 2 7 0 m s ) a n d s m a l l e r p e r io d s .N o t i c e t h a t t h e f o r m e r a r e m o r e s t r o n g l y m a r k e d b y c o - o c c u r -

f i n g d o w n s t e p s o f t w o l eg s ( f r o m l e ft h i n d [ L H ] w i t h r i g h t f r o n t

[R F ] ~, t o l e f t f ro n t [L F ] w i th r ig h t h in d [R H ] ~ ) . B e lo w e a c h

e v e n t i s a n a b s t r a c t io n o f i t s n e s t in g p ro p e r t i e s s h o w in g r e l e v a n t

s e ts o f t i m e p e r i o d s ( n = 0 , 1 , 2 . . . ) . O n s e t s o f m o r e p r o m i n e n t

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

in fo r m a t io n (m o re d o t s a t , e .g ., l o c a t io n s x a n d y ) .

T h e s e e x a m p le s h ig h l ig h t tw o p o in t s . O n e in v o lv e s id e n t i f i -

c a t i o n o f d i s ti n c ti v e n o n t e m p o r a l m a r k i n g s o f v a r io n s t i m e l e v-

e ls . T h e o th e r i n v o lv e s c l a r if i c a t io n o f l a w fu ln e ss in t e m p o ra l

n e s t in g s . T h e i s s u e o f d is t in c t iv e m a rk in g s i s a n e x p e r im e n ta l

p r o b l e m t o w h i c h w e r e t u r n i n l a t e r s ec t io n s . T h e i s s ue o f l aw -

f u l ne s s c o n c e r n s t i m e r u l e s t h a t w e f o r m a l i z e a s tim e transfor-mations.

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

w h i l e p r e s e rv i n g s o m e t e m p o r a l p r o p e r t y a s i n v a r i a n t ( J o n e s,

1 9 7 6 , 1 9 8 1 c ) . T h u s , i f a 2 0 0 -m s t im e p e r io d i s n e s t e d w i th in

o n e o f 4 0 0 m s , a n d t h i s , i n t u r n , i s n e s t ed i n a n 8 0 0 - m s p e r i o d ,

a s i n F i g u r e I a , t h e n o n e o f th e s i m p l e s t t i m e t r a n s f o r m a t i o n s

re s u l t s i n w h ic h a l l t im e l e v e l s a re r e l a t e d in a b in a ry f a s h io n

v ia m u l t ip l e s o f 2 (i .e ., p e r io d d o u b l in g ) . T h i s s o r t o f c h a n g e i s

a ratio tim e transformation. I t i s o n e o f t w o t y p e s o f t r a n s f o r m a -

t i o n s th a t e n t e r i n t o t e m p o r a l c o h e r e n c e . T h e o t h e r i s a n addi-tive tim e transformation. I f 2 0 0 m s i s ch a n g ed i n t o 2 5 0 m s a n d

th e n 3 0 0 m s , a n in v a r i a n t a d d i t iv e c h a n g e o f +5 0 m s ex is ts .

O f t e n , a d d i t iv e t im e c h a n g e s e n te r i n to t e m p o ra l n e s t in g s a s

v a r i a t io n s w i th in a g iv e n l ev el . F o r e x a m p le , i n F ig u re lb th e

l ev e l n = 0 (5 0 m s ) re f l e ct s a r e c u r re n t c h a n g e o f - 8 5 m s w i th

re s p e c t t o th e (m is s in g ) p e r io d ic i ty o f le v el n = I (1 3 5 m s ;

d a s h e d l i ne ) . I n c o n t r a s t t o r a t i o t i m e t r a n s f o r m a t i o n s , w h i c h

opera te v e r t ica l ly to change leve l n in to n + I (o r v ice ve rsa ) ,

a d d it i ve t r a n s f o r m a t i o n s o p e r a t e h o r i z o n t a l l y t o m o d u l a t e p e r i -

o d ic i t i e s r e c u r r in g a t s o m e f ix e d l ev e l.

2 A musical scale is defined by a set of pitch classes and relationships

amo ng these pitches. O f m ost relevance to W estern classical music are

diatonic scales, composed of seven pitch classes. Diatonic scales areformed by a series of pitch changes (musical intervals) involving whole

steps (w) and half-steps (s), where w = 2s, and s (also called semitone)is a u nit difference. Th e half-step, or semitone unit, is logarithmicallydefined as a frequency ratio: A ff = .05946. A m ajor diatonic scale ,beginning on th e keynote or tonic, has the followingsequence of wholesteps and half-steps: w, w, s, w, w, w, s. Thus, th e m ost fam iliar m ajordiatonic s cale is C m ajor, in which suoeessive pitch classes of CDEF-GA BC a re separated by w, w, s, w, w, w, s. In this scale, successivepitchclasses are referred to as scale degrees with C b eing the first scale degree,D the second, E the third, and so on (see Hah n & Jones, 1981). Someimportant harmonic relationships within each scale include a majorthird (e.g., C-E in C-major scale), which corresponds to the pitchchanges of(w, w ) from an initial referent pitch, and a p erfect fifth (e.g.,C-G ), which corresponds to th e scale steps of(w, w, s, w). The m ediant(E) is the no te that defines a m ajor third, whereas the dom inant is thenote (G) th at defines a perfect fifth above the tonic (C ). Together thenotes C-E-G form the tonic triad chord in C m ajor.



D Y N A M I C A T T E N D I N G 463

O ) Melodic Phrase

~ 4 D 4 D 4 E 4 F 4 ~ 4 B 3 D 4 C 4

o ~ o s

c- - C s

g~. A ,,

G,,

g ' F, ,

_ C 4o 8 3

- - 1,600ms ~ 1 6 0 O r a l

0 2 4 8 1 2 1 6 2 0 2 4 2 8 3 2

T i m e ( n x l O 0 m s )

1,600

e o o

.hl.

B i n a r y T e m p o r a l N e s t in g

Nolo,lanai equi~lences(durations)

J , , 1 + ,1 . e o o .

b ) L o c o m o t i o n i n C a t

m t L F R F

< O n e C y c l e ) [

Cat RF RF RH RFF e e , ~ ~ , , I. ~ . ;

LH ILF 1 I "Rid m IRF I

T i m e (m s ) ~ ,

L e v e l ( n )

4

3

2

I

O

I,OeOm$

S4Oms

x y x y

B i n a r y T e m p o r a l N e s t i n g

w i t h ( A d d i t iv e ) V a r i a t i o n s

Figure 1. Two coherent events. (Figure I a is a two-measure melo dic phrase in the key of C m ajor. The tonic[C] opens and closes this melody, whereas stress [>] a nd o ther pitch changes m ark various [ratio related]embe dded levels . F igure Ib shows on and of f ground t imes o f legs in a t ro t t ing ca t . Coupled down s teps

m ark ratio-rela ted higher order t im e levels, whereas lower order levels conta in an additive t ime change.

Nesting relations are outline d below each event, where m ore prom inen t contextual changes are shown by

mo re dots [adap ted from Pierson, 1976]. )

1 o n g ro u n d

, o f f g round

Leve l (n )4

52

I (missing)

0

R a t i o a n d a d d i t iv e t im e t r a n s f o r m a t i o n s p r e s e r v e a s i n v a r i-

ant time ratios and time differences, r e s p e ct i v el y . R a t i o t i m e

t r a n s f o r m s i n v o l v e r h y t h m i c e m b e d d i n g s : t i m e r e la t iv e t o t i m e .

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

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

( J o n e s , 1 9 8 7 a ). B o t h k i n d s o f r e l a t iv e t i m e c o n t r i b u t e t o t e m p o -

r a l e v e n t s tr u c t u r e a s s u b s e q u e n t f o r m a l i z a t io n s a n d e x a m p l e s

wi l l s how.

Hierarchical and Nonhierarchical Time Structures:

Some Formalisms

H i e r a r c h i c a l t im e s t r u c t u r e s a r e d i f f er e n t ia t e d f r o m n o n h i e r -

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

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

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

t u r e t h r o u g h c o n s i s te n t t i m e t r a n s f o r m a t i o n s . T h i s i s n o t s o

w i t h n o n h i e r a r c h ic a l e v e n ts , i n w h i c h l o w t e m p o r a l c o h e r e n c e

i s c o n v e y e d b y l e ss r e g u l a r n e st i ng s a n d b y m o r e o b s c u r e c o n -

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

t u r e .

T h e d i s t in c t i o n b e t w e e n h i e r a r c h i c al a n d n o n h i e r a r c h i c a l

s t r u c t u r e s i s l o o s e b e c a u s e , a s P a r t 2 i l l u s t ra t e s , m a n y d e g r e e s

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

o f t i m e s t r u c t u re s c o n t r i b u t e t o t h i s , time markers and distribu-tions of ime markers.

Time Markers: The Rol e o f Nontemporal Information

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

a n d e n d s a r e i n t r in s i c a l ly m a r k e d b y v a r i o u s s t r u c t u ra l c h a n g e s.

H o w e v e~ e x p e r i m e n t a l i s o l at i o n o f t h e se m a r k e r s i s t r i c k y b e -

c a u s e t h e i r s a l i e n c e v a r i e s w i t h c o n t e x t . T h a t i s , m a r k e r s a r e

d e f i n e d r e l a t i o n a l l y a s c o n t e x t u a l c h a n g e . I n a u d i t o r y e v e n t s ,

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

a n d a r e t e r m e d accents. Ac c e n t s o f t he f i r s t ( C4) a nd s i x t h ( G4)

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

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

n e n c e i n m u s i c ( a n d s p e e c h ) . I n v i s u a l e v e n t s, c h a n g e s in d i r e c -

t i o n a n d v e l o c i t y s e r v e s i m i l a r fu n c t i o n s . I n a n y c o n t e x t , n o n -

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

i n g f u l t i m e i n t e r v a l s w i t h i n a n d b e t w e e n e v e n t s. 3

; M usically, this is a conservative definition of accentuation. However,

i t se~ves he funct ion of acknowledging the im por tance o f ser ia l contextand s t ruc tura l changes wi th in a p a t tern . One goal of th is a r t ic le i s to

stimula te theory a nd research that w ill refine ou r knowledge of accents,and w ays in which they are perceived as such, as a function o f serialstructure.



Hierarchical ( rhythm ic) T ime St ructuresLevel (n)

ATI~

3 AT~

IO • • • •

• . : • : • : •

:

B i n a r y T i m e S t r u c t u r e

b ) : . . . . . . " h 1° . . . . . . . . h . l . .

T r i n a r y T i m e S t r u c t u r e

4

c ) , ~T z

~T~

~ - ~ , ,~ ,V o V o V o V

B i n a r y T i m e S t r u c t u r e w i t h V a r i a t i o n s

~ T nC , = ~ T , ~ . I = 2

A T n

C t = ~ T n _ I = 3

A T nC t = ' = 2A T n - I

f o r n > I

d )

No n-Hierarchical T ime St ructures~T 3

oo • oo • oe • el • oo • el •

B i n a r y w i t h T r i n a r y T i m e S t r u c t u r e s

(Polyrhythm)

e ) ~

,c,T~

) / ~ _ _ , . k• . : • :

. ~ . h . h . .N o n - h i e ra r c h ic a l

T o p

C t = 2-

B o t t o m

A T n = 8 / 6 = %C t = A T n . I

O = A c c e n t T y p e I• = A c c e n t T y p e 2

F i r s t H a l f

C t = 2

S e c o n d H a l fC t = 5 , 4

f )

N o n - h i e r a r c h i c a l

O = U n a c c e n t e d( l i g h t o f f )

• = Accented( l i g h t o n )



D Y N A M I C A T T E N D IN G 4 6 5

A c c e n t s d i f fe r i n r e l a t i v e s t r e n g t h ( o r p r o m i n e n c e ) . I n F i g u r e

1 ( l o w e r p o r t i o n s ) m o r e d o t s i n d i c a t e g r e a t e r a c c e n t s t r e n g t h

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

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

p l i t u d e c h a n g e ( i . e. , t h e > s t r e s s n o t a t i o n ) w i t h c e r t a i n s p e c i a l

p i t c h c h a n g e s ( C~ o r (3 4) in F i g u r e 1a , o r t h a t o f a n L H d o w n s t e p

w i t h a n R F o n e i n F i g u r e l b , r e n d e r s th e s e s t ro n g e r m a r k i n g s .C oup le d ac c e n ts a r e i n f a c t t y p i c a l l y s t r o n g e r t h a n decoupled

o n e s. F u r t h e r m o r e , s t r o n g e r a c c e n t s t e n d t o m a r k h i g h e r t i m e

l e v e ls i n c o h e r e n t t i m e h i e r a r c h i e s ( B e n j a m i n , 1 9 8 4; J o n e s ,

1976 , 1987a ; Le r da h l & J a c ke ndo f f , 1983 ; Ma r t i n , 1972 ) . I n

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

f u n c t i o n a l m a r k e r s a t d i f f e r e n t t i m e l e v e ls .

D i s t ri b u t io n s o f T i m e M a r k e r s: R o l e

o f T i m e T r a n sf o rm a t io n s

T h e t e r m hierarchy h a s b e e n v a r i o u s l y u s e d ( J o n e s , 1 9 8 1 b ).

H e r e i t r e fe r s t o a t i m e s t r u c t u r e i n w h i c h t h e t e m p o r a l d i s t r i b u -

t i o n o f m a r k e r s r e v e a l s n e s t e d t i m e l e v e ls t h a t a r e c o n s i s t e n t l yr e l a t e d t o o n e a n o t h e r a t a g i v e n l ev e l b y r a t i o o r a d d i t i v e t i m e

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

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

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

c o m p l e x i t y o c c u r s.

I n h i e r a r c h i c a l e v e n t s , e a c h n e s t e d l e v e l i s a s s o c i a t e d w i t h a

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

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

( n = 0 , 1 , 2 . . . . ) . T h e s m a l l e s t t i m e p e r i o d , d e n o t e d A T o , o c -

c u r s a t t h e l o w e s t l e v el a n d i s o f t e n m a r k e d , e s p e c i a l l y i n i t ia l l y ,

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

o t h e r n e s t e d p e r i o d s a r e r e l a t e d t o A T 0 b y s e ts o f s i m p l e t i m e

r a t i o s ( o r r a t i o t i m e t r a n s f o r m a t i o n s ) . 4 T h u s , t h e t o t a l d u r a t i o n

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

b e d d e d l e v e l.

F i g u r e 2 p r e s e n t s th r e e e x a m p l e s o f h y p o t h e t i c a l t i m e h i e r a r-

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

e r a t e . T h e f i rs t , a n d s i m p l e s t , i s sh o w n i n F i g u r e 2 a . I t i s m e r e l y

a n e x t e n s i o n o f t h e b i n a r y s t r u c t u r e s h o w n i n F i g u r e l a . A l l

n e s t e d t i m e l e v e ls a r e r e l a t e d b y a r a t i o t i m e t r a n s f o r m o f 2 .

T h u s , t h e s m a l l e s t l e v el , A T o , i s r e l a t e d t o A T ~ b y 2 , t o A T 2 b y

4 , a n d s o o n , u n t i l i t s t o t a l d u r a t i o n i s l i n k e d t o a l l o t h e r s . T h i s

i s a b i n a r y t i m e s t r u c t u r e . I t i s h i e r a r c h i c a l b e c a u s e t h e n e s t i n g

i s c o n s i s t e n t , m e a n i n g t h a t t h e s a m e r a t i o ( h e r e 2 ) o b t a i n s o v e r

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

w i l l b e d e n o t e d a s C t , , i n w h i c h C t , = A T J A T n - 1 ( f o r l e v e ls

n , n - 1 ). T h i s t i m e r u l e o p e r a t e s v e r ti c a l l y t o s u m m a r i z e t e m -p o r a l n e s t i n g . F i n a l ly , i n t h i s b i n a r y s t r u c t u r e , C t n i s a n i n v a r i -

a n t i n t h a t i t i s c o n s t a n t o v e r d i f f e r e n t le v e ls , n: C,, = Cz = 2.

S i m p l e t i m e h i e r a rc h i e s a r e b a s e d o n C t v al u e s th a t a r e s m a l l

a nd c on s t a n t i n t e ge r s ( i . e ., C t = 1 , 2 , 3 , e t c . ) . W he n C t = 3 , a

t r i n a r y s t r u c t u r e r e s u l t s a s i n F i g u r e 2 b . T h i s h i e r a r c h y i s l e s s

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

l a r g e r i n te g e r . W h e n d i f f e r e n t C , v a l u e s a p p e a r a t d i f f e r e n t l e v e ls

(e.g ., C,m --'-2 , a n d C tn = 3; n = 1 . . . m . . . p . . . ) m o r e c o m p l e x

h i e r a r c h i e s a r e s p e c i fi e d .5

F i n a ll y , a m o d e r a t e l y c o m p l e x h i e r a r c h y i s s h o w n i n F i g u r e

2 c . T h i s i s a b i n a r y h i e r a r c h y w i t h a d d i t i v e t im e c h a n g e s ( s h o w na s k ) . T h i s c h a n g e e s s e n t i a l ly s h i f ts t h e ( m i s s i n g ) A T I t o f o r m

t h e l o w e st t i m e l e v e l, m u c h a s i n t h e c a t e x a m p l e o f F i g u r e l b .

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

c e n t s ( h i g h e r l e v e l ), i n t e r e s t in g s y n c o p a t e d v e r s i o n s o f t h i s h i e r -

a r c h i c a l f o r m m a y b e s p e c i fi e d . A l l s u c h s t r u c t u r e s a r e h i e r a r -

c h i c a l f o r t w o r e a s o n s : ( a ) T h e a d d i t i v e t r a n s f o r m i s i n v a r i a n t

f o r a l l p e r i o d s a t a g i v e n l e v el , a n d ( b ) o t h e r t i m e l e v e ls ( h e r e

n > 1 ) a r e c o n s i s t e n t l y r e l a t e d b y C t = 2 .

A l l o f t h e se t i m e s t r u c tu r e s e x h i b i t c o n s is t e n t t e m p o r a l n e s t -

i n g . I n t h o s e w i t h s i m p l e t i m e s y m m e t r i e s (e . g ., C t = 1 , 2 , 3 . . . ) ,

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

i n v a r ia n c e . A n y h i g h e r t i m e p e r i o d ( A T , ) c a n b e r e l a t e d t o t h e

u n i t p e r i o d b y a p o w e r o f t h e c o n s t a n t r a t i o , C ,:

A T n = A T o C tn ( wh e r e n = 0 , 1 , 2 , . . . ) . ( 1 )

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

h o w i t t ie s a n e v e n t to g e t h e r d y n a m i c a l l y b y s h o w in g t h a t a n y

e m b e d d e d t i m e l e v el c a n b e c o n s i st e n tl y t r a n s f o r m e d i n t o a n y

o t h e r v i a t i m e r a t i o s .

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

b a s e d t e m p o r a l n e s t in g s w i t h i n a n e v e n t 's t o t a l d u r a t i o n , a s w e l l

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

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

r i e s : t h o s e t h a t d o n o t i n c o r p o r a t e a d d i t i v e t i m e r u l e s ( F i g u r e

2 a a n d 2 b ) a n d t h o s e t h a t d o ( F i g u r e 2 c) . D e g r e e o f t e m p o r a l

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

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

i n t o t h e f i rs t ca t e g o r y . C o n v e r s e l y , d y n a m i c c o m p l e x i t y i s

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

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

4 One may argue th a t ATn ref lec ts t rans la tory t ime t ransformat ions

forming an inf in i te symm etry group, and tha t Ctn (n = 0, + 1 + 2 +- 3)reflects d i la tory ime t ransformat ions tha t a l so form an inf in ite symm e-

try gro up (e.g., Hahn & Jones, 1981; Cox eter & Greitzer, 1967). For amore genera l trea tment in te rm s of t ime t ransformat ions tha t speci fy

the logar i thmic spi ra l , see Hahn and Jones .5 Th is analysis assumes an established t ime s tructure an d func tional

markers. If the t ime struc ture refers to meters, for exam ple, i t is not

concerned w ith issues of meter identification a nd ways in which c ertainmarkers, beat periods, and rh ythm ic figures may facil i tate meter identi-

fication on the p art o f an attend er (Essens & Povel, 1985; Longnet-Hig-gins & Lee, 1982, 1984). These issues involve attending and de tectionof tempo ral invariants and are considered in a la ter section.

Figure 2. Six examples of t ime s t ruc tures tha t could hypothet ica lly charac ter ize a g iven envi ronmenta l

event. (Examples range from the bin ary t ime stru cture o f (a) that is highly coherent (hierarchical) to th eirregular one of low coherence in (f) tha t is nonhierarchical. The latter represents a tem pora l pattern oflights, in on [O] or off [O] posit ions, from a judged dura tion study by P oynte r and Ho ma [ 1983]. In allpattern s the stronger accents are signified by m ore dots. Temporal level, AT , , correspo nds to the r ecurre nt

perio d at n = 0, 1 . . . . Nesting prope rties are given by ratio t ime transformations, Ct, = A Tn/ATn-~.)



46 6 MARI RIESS JONES AND MARILYN BOLTZ

reasoning extends to assessments of nonhierarc hieal t ime s t ruc-

tures , three o f which appe ar in F igure 2 ( i .e . , 2d , 2e, 2f) .

F i gu re 2d i l l u st r at es an i mpo r t an t k i nd o f nonh i erarch iea l

t ime st ructure. I t i s a polyrhy thm . A polyrhYthm involves two

s i mul taneous ly r ecu r ren t per i od i c it i es t ha t fo rm a non i n t eger

t im e rat io (e.g., 4:3 and 4:5; Ape l, 1972). It is l i teral ly a tem po -

ral phasing of two t ime hierarchies . In th i s case, b inary a ndt r i nary t i me s t ruc t u res a r e i nvo l ved , each i den t i f i ed by a

d i f fe r en t accen t t ype (O o r O) t ha t becomes coup l ed (O) on l y t o

ma rk higher levels . Thu s, Figure 2d ha s a h ierarchical counte r-

par t in Figure 2c: Both display a h igher level b ina ry t ime st ruc-

ture. But the polyrhythm lacks the consis tent addi t ive t ime

changes of Figure 2c at i t s lower levels (in w hich t im e rat ios a re

4:3 or 8:6; Ha nde l, 1984; Han del & Oshinsky, 1981; Yeston,

1976).

A d i f fe r en t so r t o f v i o l a t ion o f h i e r a rch i ca l t ime sym met ry

occu r s i n F i gu re 2e. Here , p rom i nen t accen t s r evea l a t em pora l

nesting t ha t is ini t ial ly hierarc hical . However, this reg ulari ty of

8 beats i s clear ly v iolated in the se cond ha l f of the sequ ence, in

which higher order t ime spans o f 10 and 6 beats occur . A m orecomp l ex ti me r a t i o i s t hus needed t o fo rmal i ze th i s s t ruc tu re .

F ina ll y, t he m os t i r r egu l ar t i me pa t t e rn (F i gu re 2 0 embeds

durat ions th at are h apha zardly m arked at h igher levels , y ield ing

l ow t emp ora l coherence . Th i s t i me s t ruc t u re i s one we hypo t he-

s ize may co r r espond t o t he sequence o f li gh ts u sed by Poyn t er

and Ho m a (1983) in a judge d durat ion s tudy. St ronger accents

(mo re dots) are assum ed to occ ur at (a) sequenc e beginnings,

(b) l ight onsets (O), and (c) l ight onsets following pauses (no

lights, 0).In sum , nonhierarch ieal t ime s t ructure s do no t d isplay s im-

ple temp oral recursiv i ty (as in Eq uat ion 1). Dynamical ly , they

are m ore com pl ex because r a t i o and add i ti ve ti me t r ans fo rma -

t ions are inconsis tent ly appl ied . Consequent ly , t ime relat ions

between an e vent ' s em bed ded t ime levels and i t s to tal dura t ion

are obsc ured. Together wi th h ierarchical ar rangem ents , a con-

t i nuum o f t empora l cohe rence is suggest ed i n wh i ch coherence

i s l oosel y i ndexed by t he r a t i o com pl ex i t y o f t he rhy t hm genera-

tor, Ct~ (i .e. , i ts inva rianc e ov er levels and i ts integer value). P re-

c ise fo rmal i za ti on o f temp ora l coherence m ay com e wi t h p rog -

ress in m athem at ics of dynam ical systems (e.g . , chaos theory) .

Meanwhi le , t he ru l e o f t hu mb a l go r i thm i mpl i ed by t h i s ana ly -

sis involves the rh ythm generator, Ct~: As th is para me ter ap-

p rox i mat es a p rom i nen t l y ou tl i ned b i nary t i me s t ruc t u re , t em-

poral cohere nce increases.

Examples o f Environmental Coherence

Of t en when one ven t u res a guess abou t how m uch t i me has

elapsed, on e is coping with t im e interv als fil led w~th things su ch

as act ion pat terns, music, and speech. How d o the formal iza-

t i ons j u s t ou t l ined advance ou r under s tand i ng o f t he s t ruc t u re

and funct ion o f such events? Th ey suggest that var ious k inds

and degrees o f tem poral c oheren ce wil l emerge and that assess-

men t o f t h is coherence wil l depend on i den ti f ica t ions o f app ro -

pr iate t ime markers , character i s t ic t ime t ransformat ions, and

mul t ip le under ly ing t ime st ructures .

Body Gestures and Locomotion

Body movem en t s a r e c lassi ca ll y rhy t hmi ca l . L i mb mot i ons

recu r wi th f ixed per iods and phase locking in which m arkers of

these per iods are of ten speci f ied by dis t inct ive d i rect ional

changes in mov em ent . Emerging research suggests that a range

of under ly ing t ime st ructures exis ts , wi th some sup por t ing a dy -

nam i c i n t e rp l ay o f com pl ex , co -occu r r i ng body gest ures .

In some cases , t he t em pora l coo rd i na t i on amon g l i mbs i s

very coheren t and can be descr i bed by s imp l e harm on i c t i me

rat ios (e.g ., Klapp, 1979, 1981; Kelso , Hol t , Rubin , & K ug l~1981). Fur therm ore, locom ot ion pat terns in va r ious species , in-

cluding huma ns, reveal that episodes of walking a re del imi ted

by special beginning and ending phases and are character ized

by h i gh l y regu l ar ti mi ngs o f l i mb , t o r so , and head movem en t

changes (Barclay, Cutt ing, & Koslowski, 1978; Carlsoo, 1972;

Gray, 1968; Inman, 1966; Johansson, 1973, 1975; Pierson,

1976; Winter, 1983). Di f ferent locom otor s ty les appe ar at char-

acter i s t ic locomot ion rates ( tempi) , yet each i s , nonetheless ,

suggestive of a h ierarchical t ime s t ructure. F or example, a cat ' s

faster t ro t co mb ines l imbs in a d i f ferent rhy thm than i t s s lower

walk . Yet both gai ts suggest the h ierarc hy of Figure 2c. Th ey

are d i f ferent iated pr im ar i ly by dist inctive addi t ive t ime changes

that cap ture c orrespond ing veloci ty d i f ferences associated wi thon-grou nd t ime di f ferences in the two gai ts (Pierson, 1976). In

shor t , one ap pl icat ion of the prev ious formal i sms suggests that

ca t ego ri es o f rhy t hmi c s ty le ex i s t and can be fo rma l i zed by par -

t icular combina t ions of rat io and addi t ive t ime invar iants . Both

t ime t rans forma t ions have meaning: Th e rat io base offers pre-

dictabi l i ty for coordinat ive gestures , whereas addi t ive t ime

changes n ot o nly character ize an individual ' s s ty le hut th ey can

also s ignal under ly ing veloci ty proper t ies .

O f cou r se , any sys t emat ic pa t t e rn i ng i n t i m e l ends p red ic t -

abil ity . And wi th m otor gestures th i s not only af fords a basis fo r

i nd iv i dua l mo t o r coo rd i na t i on and se l f synchrony , ! t a lso m eans

that v isual act ion pat terns created by one individual can

suppor t var i ous i n t e rac t ive nonverba l com muni ca t i ons w i t h

others , including turn- taking behavior , dance, nur tur in~ and

prey-stalking, al l of which par take of in teract ionai sync hron y

(Condon & Sander, 1974; Kolata, 1985; Laws, 1985; Newtson,

Hairfield,.Bloomingdale, & Cu tino , 1987).

On the othe r hand, v ar ious comple x gestures der ive me aning

from violat ions of tem pora l predictabi l i ty (e.g ., Figure 2e) . For

exam ple, a danc er ' s ski ll can b e s ignaled by s ingular and sur-

pr i s ing s tr ide changes, leaps, or turn s based o n on e or m ore dis-

t inct ive t ime in tervals. Final ly , co mp lex polyrh ythm ic gestures

rou t i ne l y occu r as when on e does t wo t h ings a t once i n t wo-

handed tap ping and typing (Gentner , 1987; Klap p, 1979; Jaga-

cinski , Marshhurn, Klapp, & Jones, 1988; Kla pp et al ., 1985).

As s ingle t im e sequences, such co ordinat ive pat terns are less

coheren t (hence nonh i erarch i ca l ) acco rd i ng t o t he p resen tdefinit ion.

Musical Structure 6

Ani mal s p rod uce song t h rough bo dy ges tu res tha t a r e coo rd i -

na t ed wi t h i n t hemsel ves and wi t h o t her s. Bo t h m o t o r p roduc-

t ions and musical convent ions g ive r i se to composi t ions wi th

distinctively m arke d t ime levels (Be njam in, 1984; Berry, 1976).

6The authors are indebted to Helen Brow n (Purdue U niversity,De-partment of M usic) and David Butler (Ohio State Department of M u-sic) for com men ts on an earlier version of this sec tion. Any interpreta-tive errors, howeve~are the authors'.



D Y N A M I C A T T EN D IN G 4 6 7

M u s i c n o t o n l y e x e m p l if i es m e a n i n g f u l n es s i n t i m e s t r u c t u r e ,

b u t i t a l so i ll u s t r a te s h o w th o s e fo rm a l i s m s o u t l in e d e a r l i e r h a v e

p o te n t i a l fo r e x p re s s in g d e g re e s o f m e a n in g fu ln e s s . T h i s i s b e -

c a u s e n o n t e m p o r a l m a r k i n g s c a n r e v ea l d if f e r en t k i n d s a n d l e v -

e ls o f t e m p o r a l c o h e r e nc e t h r o u g h t h e d y n a m i c p l ay o f m u l ti p le

u n d e r ly in g t im e h ie ra rc h ie s ( s t ru c tu ra l , m e t r i c ) .

Nontemporal markings in music: Structural time hierarchiesand harmonic markers. A m e l o d y i s a s e q u e n c e o f p h r a s e d

p i t c h c h a n g es . E a c h p h r a s e h a s a b e g i n n i n g a n d e n d a n d t r a n -

s p i r e s o v e r a g iv en d u ra t io n . In W e s te rn m u s ic , b e g in n in g s a n d

e n d i n g s o f t e n c o r r e s p o n d t o c e r t a i n p i t c h e s a s so c i a te d w i t h a

to n a l s y s t e m (D o w l in g & H a rw o o d , 1 9 8 5 ; P i s to n , 1 9 78 ) . T o n a l -

i ty re l ie s on spec ia l p i tch re la t ions (e .g . , a s in a d ia ton ic se t )

a n d m u s ic a l ru l e s th a t p ro v id e l is t e n e r s w i th a m u s ic a l r e fe re n c e

f r a m e i n w h i c h o n e p i t c h , t h e t o n i c, d e f in e s t h e m e a n i n g o f o t h -

e rs . T h u s , a l th o u g h lo w e r t im e l ev e ls m a y b e in d ic a t e d b y to n e

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

re l a t e d p i t c h e s . S u c h h ig h e r l e ve l m a rk in g s a re s h o w n in F ig u re

3 f o r a n e x c e r p t f r o m a G - m a j o r m e l o d y. T h i s e x c e r p t is s h o w n

t o e n d ( r e s o l v e ) o n t h e t o n i c ( G ) , a n d e m b e d d e d p h r a s e s a r em a r k e d e i t h er b y t h e t o n i c i t s e l f o r b y h a r m o n i c a l l y r e l a te d

p i t c h e s s u c h a s th e d o m in a n t ( i .e ., D ) a n d th e m e d ia n t ( i. e. , B )

f o u n d i n t h e t o n i c t r i a d c h o r d ( G - B - D ) . P r o v i d e d a k e y i s c l e ar l y

e s ta b l is h e d , m a r k e r s s u c h a s t he s e a d d p r o m i n e n c e t o h i g h e r

t im e l e v e l s . T h e y a re t e rm e d harmonic accents a n d d e n o t e d

h e r e a ~ e r a s h ( H . B r o w n , 1 9 8 8 ; B u t l e r & B r o w n , 1 9 8 4 ; K r u m -

hans l , 1979; K ru m ha ns l & Kess le r , 1982) . 7

Me lo d ic li n e s w i th in a p h ra s e ty p ic a l ly p o in t t o c e r t a in f in a l

to n a l g o a l s o r a c c e n t s t h a t a re d i s t r ib u te d q u i t e l a w fu l ly in t im e

(C o n e , 1 9 6 8 ; B o l t z & J o n e s , 1 9 8 6 ; J o n e s , 1 9 8 7 a ; L e r d a h l &

J a c k e n d o f f , 1 9 83 ). F u r th e rm o re , n e s t in g o f s u c h p h ra s e s i s o f_

t e n r e c u rs i v e a n d a s s u m e s b i n a r y a n d / o r t r i n a r y t i m e s t r u c t u r e s

(F ig u re 2 a o r 2 1) ). F o l lo w in g L e rd a h l a n d J a c k e n d o f f (1 9 8 3 ) , w ere fe r t o th e s e p h ra s e -b a s e d h i e ra rc h ie s a s structural ime hierar-chies a n d l e t S d e n o t e t h e c l a s s o f s t r u c t u r a l a c c e n t s t h a t f u n c -

t i o n a s t i m e m a r k e r s o f p h ra s e s.

F in a l ly , i f m u s ic a l c o h e re n c e s im p ly in v o lv e d th e id e n t i fi c a -

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

t i o n s w o u l d b e s t r a ig h t f o r w a r d . B u t o t h e r k i n d s o f t i m e m a r k e r s

e x i s t. T h e s e c a n l e a d to a d i f f e re n t s o r t o f t im e h ie ra rc h y ,

n a m e l y a m e t r i c h i e r ar c h y , o r t o o t h e r s t r u c t u r a l a c c e n t s t h a t

m u s t b e f ig u re d in to s t ru c tu ra l h i e ra rc h ie s , n a m e ly , t e m p o ra l

accen ts ( t ).

Temporal relationships: Metric time hierarchies, rhythm, andtempo. Meterp r o v i d e s a n u n d e r l y i n g t i m e f r a m e f r o m w h i c h

r h y t h m a n d t e m p o d e v i at e o n a rt f u l t e m p o r a l j o u r n e y s . T h i sf r a m e t u r n s o u t t o b e a m e t r i c t i m e h i e ra r c hy . T h a t i s, a m e t e r

in v o lv e s a r a t io r e l a t io n s h ip b e tw e e n a t l e a s t tw o t im e l e v e l s

(Y e s to n , 1 9 7 6 ). O n e i s a r e fe re n t t im e l ev e l, t h e b e a t p e r io d , a n d

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

b e a t p e r io d s , t h e m e a s u re (v e r t ic a l b a r l i n e s d e n o te m e a s u re s ) .

M e t r i c l ev e ls a re d e s ig n a te d in a tu n e ' s t im e s ig n a tu re . F o r e x -

a m p le , a 4 /4 m e te r i s s h o w n in F ig u re 3 a ; t h e lo w e r 4 in d ic a t e s

t h a t a q u a r t e r n o t e 0 ) i s t h e b e a t p e r i o d , a n d t h e u p p e r 4 i n d i -

c a t e s th a t t h e re a re fo u r b e a t s t o a m e a s u re . I n o th e r w o rd s , t h e

4 /4 m e te r i s b a s e d o n a 4 :1 = 2 ~ :1 t im e ra t io . I n f a c t , sp e c ia l,

i n v a r i a n t r a t i o s d e f in e a ll c o m m o n m e t e r s : D u p l e a n d q u a d r u -

p l e m e t e r s r es t o n b i n a r y t i m e s t r u c t u r e s ( C tn = 2 n ) , a n d t r ip l e

m e t e r s i n v o lv e t r i n a r y o n e s ( s ee F o o t n o t e 9 ). I n s h o r t , th e s e

c h a ra c te r i s t i c t im e in v a r i a n t s d e f in e m e t r i c c a t e g o r i e s in We s t -

e rn m u s ic ( J o n e s , 1 9 8 1 a , 1 9 8 1 c ) .

M a r k e r s o f m e t r i c h i e r a r ch i e s a r e o f t e n a s s o c i at e d w i t h a m -

p l i tu d e c h a n g e ( st r e ss ) a t m e a s u re 6 n s e t s (i .e ., g re a t e r d o w n b e a t

e n e rg ie s ; L e rd a h l & J a c k e n d o f f , 1 9 8 3 ) , b u t i n fo rm a t io n o th e r

th a n s t r e s s w i l l al s o c o n v e y m e te r (B e n ja m in , 1 9 8 4 ; C . S . L e e ,

1 9 8 5 ; S lo b o d a , 1 9 8 3 , 1 9 8 5 ) . In f a c t , p e rc e iv e d m e t r i c a c c e n t sd o n o t a l w ay s c o r r e s p o n d t o n o t a t e d s t re s s p o i n t s , t h u s u n d e r -

s c o r i n g t h e n e e d t o i d e n ti f y p s y c ho l o g i ca l l y c o r r e c t t i m e m a r k -

e r s (S te e d m a n , 1 9 7 7 ; V o s & H a n d e l , 1 9 8 7 ; V o s, L e e u w e n b e rg ,

& C o l l a rd , 1 9 78 ) . We d e n o te b y M th e c l a s s o f m e t r i c a l a c c e n t s

th a t r e l i a b ly m a rk m e t r i c t im e h ie ra rc h ie s ( a s in F ig u re 3 ) . N o te

t h a t m e t r i c h i e r ar c h i e s a ri s e f r o m d u r a t i o n s o f m e a s u r e s a n d

t h u s d i f f er f r o m s t r u c t u r a l h i e r a rc h i e s t h a t a r i s e f r o m d u r a t i o n s

o f m e l o d i c p h r a s es .

Tempo o f fe r s a y a r d s t i c k o f m e t e r a n d o f a m e a s u r e ' s d u r a -

t io n . I t d e p e n d s o n th e u n i t t im e p e r io d s e l e c t e d b y a p e r fo rm e r ,

n a m e ly , t h e b e a t p e r io d . T h i s e s t a b l i s h e s a p i e c e ' s c h a ra c te r i s t i c

pac e s (e .g . , la rgo , a l legro) . For e xam ple , a l l o the r th ings b e ing

e q u a l , a b e a t p e r io d o f a n e ig h th n o te ( ) ) r e s u l t s i n a fa s t e r p a c e( t e m p o ) t h a n o n e o f a q u a r t e r n o t e ( J) .

Rhythm r e f er s t o p a t t e r n e d t i m e c h a n g e s w i t h i n a m e t r i c

f r a m e . A n i m p o r t a n t f e a t u r e o f r h y t h m i c p a t t e rn s i s t h a t t h e y

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

t i n g t im e c h a n g e s , n a m e ly , l o n g e r o r s h o r t e r d u ra t io n s (m u l t i -

p l e s o r s u b d iv i s io n s o f t h e b e a t p e r io d ) . T h u s , t h e lo n g e r h a l f

n o t e s ( J) i n t h e t u n e o f F i g u r e 3 t e n d t o b e m o r e s a l ie n t. S u c h

t e m p o r a l a c c e n t s f o r m p o w e r f u l ti m e m a r k e r s t h a t o f t e n f u n c -

t i o n a s s t r u c tu r a l a c c e n t s t h a t , l ik e h a r m o n i c o n e s , m a r k b e g i n -

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

h i e ra rc h ie s (C o n e , 1 9 6 8 ; K ra m e r , 1 9 8 2 ; T o d d , 1 9 85 ).

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

t e st i fy t o t h e f a c t t h a t m u s i c c a p t u r e s t i m e s y m m e t r i e s f o r m a l -

i z e d e a r li e r b y d i f fe re n t tim e s t ru c tu re s . I t m ig h t b e a rg u e d th a t

t h i s i s n ' t s o b e c au s e n o t a t e d t i m e r a t i o s d o n ' t a l w a y s a p p e a r i n

p ro d u c e d m u s ic (G a b r i e l s s o n , 1 9 8 5 ; S te rn b e rg e t a l. , 1 9 78 ). 9

7 This analysis of tonality is oversimp lified. Th e psychological sa-

lience of pitches in an y m usical context depends no t only on prevailingtonality and grammatical con siderations (H. Brow n, 1988; Krum hansl,1979; Krum hansi & Kessler, 1982)but on temporal context provided by

rhythm (Monahan & Carterette , 1985) and temporal order (e.g., variousnotes identifying intervals such as tritone; H. Brown & Butler, 1981;

Butler & Brow n, 1984, Kidd, 1984). Finally, temporal ordering o f har-mon ically significant pitches, as in Figure 3, can establish, via impliedharmony, a sense of certain chordal progressions that move to resolu-

tion o n the final note as a tonic triad. Th us, shifting accenting ma y alsoaffect coherence in tonal melodies by creating con flicting tonalities andinappropriate implied harmonic progressions.

8 For additional definitions of tempo, see Kron man and Sundberg

(1987) and Clyn es ( 1978). In particular, C lynes has proposed an organis-mic tempi that uniquely specifiesa compo ser or performer's pulse. Thisidea, although compatible with ou r general approach, should n ot beconfused with more traditional definitions of tempi (e .g., Kronm an &Sundherg). In produced sound oatterns, i t is quite possible tha t charac-teristic tempi follow Clynes' exposition, a notion that reinfo rces ourapproach, rather th an contradicting it.

9 Sternberg. Knoll, & Z ukofsky (1978) used a psychopliysical ask tostudy the perception and production of time ratios and found system-atic distortions o f responses to time ratios. H owever; heir analyses of

production times, which relied on a reaction-time correction factor,



468 MA R I R IESS JO N ES A N D MA R ILY N B O LTZ

But , the picture i s more c omple x . The re i s e v ide nc e fo r p re -

fe r re d , s imp le t ime ra t i o s i n p roduc e d rh y thm s (Esse ns , 1986 ;

Fraisse, 1956, 1964, 1982; Povel, 1981; Essens & Povel, 1985).

Fu r the rm ore , sk il le d mus ic ihns o f t e n a c c u ra t e ly p roduc e h ighe r

o rde r t ime spa ns a nd c omp le x rhy th mic r a t i o s ~° (C la rke , 1985a ,

1985b; Shaffer , 1981, 1982) . We c la im th a t m an y devia t ions

tha t do o c c u r a re m os t r e a sona b ly r e p re se n te d a s add i t ive t imec ha nge s t ha t a r i se e i the r f rom a p e r fo rm e r ' s ( a ) f a i lu re t o c a p -

tu re d if fi cu lt r a t i o no ta t ions a nd /o r (b ) c onsc ious a t t e m p t s t o

c om mun ic a t e rhy th mic s ty le ( e .g ., l e ga to , s ta c c a to ) o r e mo t ion

via tem po change (Clarke , 1984; Gab rie lsson, 1974; Gab rie ls-

son, Bengtsson, & G abrie lsson , 1983; Sha lfe r , C larke , & Todd,

1985) . The se f a c to rs r e l at e t o w a ys a pe r fo rm e r c omm unic a t e s

by se ri al ly mod u la t ing me lod ic t im ing a nd a re d i sc usse d m ore

ful ly e lsewhere (Jon es, 1987a) . A f ina l reason fo r b lurr ing o f

tem po ra l proport ion a l i t ies is found in the score i tse lf . This fac-

tor i s considered next .

Temporal coherence in music: Structural and metric hierar-

chies. A mus ic a l sc o re d i sp l a ys t e mp ora l c ohe re nc e b y the w a y

i t c ombine s s t ruc tu ra l a nd me t r i c t ime s t ruc tu re s . Se pa ra t e ly ,e a c h o f t hese s t ruc tu re s c a n fo rm a c ohe re n t h i e rarc hy . B u t t o -

ge ther , overa l l coheren ce depends on h ow they com bine in t ime .

F igu re 3 show s how d i f fe re nce s i n t e m pora l c ohe re nc e c a n

c ome f rom va r i a t i ons i n mus ic a l ph ra s ing . H e re , a l l t im ing

c ha nge s c onc e rn r e l a t ive ph ra se du ra t ions o f a s t ruc tu ra l h i e ra r -

chy re la t ive to fa i r ly constant pro per t ies of a me tr ica l h ie ra rchy.

Object ive ly , mo st coherence appe ars in Figure 3a in which bo th

(b ina ry ) h i e rarc h ie s c o incide in t ime . E a c h m e a su re ope ns w i th

a metr ica l (s t ress) accent , and a l though the 8-bea t melodic

ph ra se s a re l onger t ha n me a su re s , e a c h re so lve s (h c oup le d w i th

t a c c e n t s) p re d ic t a b ly a t t he e nd o f a l t e rna t e me a su re s . T h i s

y i e ld s a s ing le p rom ine n t ly m a rke d t im e s t ruc tu re a s i n F igu re

2a . B y c on t ra s t , a ga in s t t he sa me m e t r i c f r a me , m e lod ic ph ra s -

ing (signa led aga in by jo in t h and t s t ruc tura l acce nts) form s a

l ess c ohe re n t t ime pa t t e rn (F igu re 3b ). Th i s p i e c e ope ns w i th

re gu la r a nd s t rong ly ma rke d me lod ic ph ra s ings , bu t i t c lo se s

w i th a mus ic a l su rp r ise c re a t e d by de v ia n t ph ra s e l e ng ths o f 6

and 10 bea ts , respec tively . In th is , i t shares the for m at of Figure

2e . Th e psychologica l im pac t of such devia t ions is considered

in la te r sec t ions. Fina l ly , even more tempora l uncer ta in ty is

found in F igu re 3c , in w h ic h a sub t le mo du la t ion o f t he s t ruc -

tu ra l h i e ra rc hy o f F igu re 3a oc c u rs . In t h i s c a se , t he t a c c e n t s

re m a in h i e rarc h ica l . In f a c t, t he y re in fo rc e the m e t r i c t ime h i e r -

a rc hy . N o t i c e t ha t on ly ha rmon ic a c c e n t s a re sh i f t e d to va ry

ph ra se du ra t ions . The y a lone c re a t e a nonh ie ra rc h ica l fo rm .

In sum, mus ic a l c ohe re nc e va r i e s i n me a n ing fu l w a ys tha t

l e nd the mse lve s to c e r t a in fo rma l i sms . W e shou ld unde r sc o retha t w e do no t c l a im tha t t he m ore c ohe re n t m us ic a l e ve n t s a re

the m ore in t e re st i ng o r a ppe a l ing one s ; o f te n the y a re no t . U n-

questionably , a cer ta in leve l of a r t fu l an d even sys tema t ic v io la -

t ion (e .g . , syncopat ion) of very cohe rent s t ru c tures i s necessa ry

to c re a t e a e s the t ic a ppe a l . W e me re ly c l a im tha t t he se va r i a t i ons

spe a k to t e m pora l p re d ic t a b il i ti e s . In t h i s r e ga rd , c ohe re nc e de -

c re a se s a nd dyna mic c omple x i ty i nc re a se s w he ne ve r s imp le

t ime h i e ra rc h ie s a re v io l a t e d by a dd i ti ve t ime c ha nge s a nd /o r

by o the r t e mpo ra l ly pha se d h i e ra rch ie s .

failed to take accoun t of anticipatory behaviors, and thu s are not con -

elusive.

Speech

A m o n g o t h e r h u m a n s on gs i n t e n d ed t o s e rv e c o m m u n i c a t i o n

goa l s a re t hose c re a t e d b y dyna m ic a l ly c oo rd ina t e d voc a l ges -

tu re s , na m e ly spe e c h pa t t e rn s . Spe e c h , l i ke mus ic , p re se n t s a p -

parent rhythmic i t ies tha t , on c loser inspec t ion , fa i l to l i t the

s imp le s t t ime h i e ra rc h ie s . A ga in , t he ke y to un loc k ing the set iming mys te r i e s ma y tu rn on the i de n t i f ic a t ion o f a pp rop r i a t e

t ime ma rke r s a s w e ll a s c l a r i f ic a t ion o f d i f fe re n t t ime s t ruc tu re s

and the i r in te rre la t ions.

Eng l i sh i s a s t r e ss - t ime d l a ngua ge w i th a pp rop r i a t e t ime in -

t e rva ls t hus d e f ine d be tw e e n s t r ess po in t s . Th e s im p le s t rhy th -

mic pa t t e rn p ropose d fo r t he d i s t r i bu t ion o f s t re ss po in t s i s iso -

c h rony , i n w h ic h a c c e n t s w i th in unb roke n u t t e ra nc e s shou ld

be tem pora l ly equidistant (Pike , 1945). However, only l imi ted

e mpi r i c a l sup po r t e x i st s fo r t he i soc h rony p r inc ip l e e ve n in a

sophist ica ted version based on b inary t ime hie rarchies (e .g . ,

Lehiste , 1976; Mart in , 1972; Shie lds, McHugh, & Mart in ,

1974), there by ra is ing ques t ions ab ou t i t s suffic iency (e .g ., L ib-

e rm a n & Pr inc e , 1977 ).

Some inve s t iga to r s a rgue tha t de v ia t ions f rom i soc h rony

func t ion me a n ing fu l ly i n c om mu nic a t ion (Le h i s t e , 1977) . Fo r

e xa mp le , spoke n ph ra se s a re o f t e n ma rke d by e nd l e ng the ning

and prop ort ion a l s i lences as in mu sic (Pacc ia -Cooper, & Cooper,

1981 ) . O the r me a n ing fu l de v ia t ions , s t e m min g f rom sh i f ts i n

spe a ke r a r ti c u l a t ion r a t e , ma rk e r s t r e ng th , a n d in tona t iona l

c on tou r c a n c om mu nic a t e e m o t iona l s t a t e s (Sc he re r, 1979 ) , i n -

tent ions (Lehiste , 1976; Picke t t , 1980), and turn- taking goa ls of

spe a ke rs (S i e gma n , 1978; W ie m a nn & K n a pp , 1975 ) . In m a ny

cases, these devia t ions a re ad di t ive t ime chang es tha t der ive con-

t e x tua l me a n ing by v io l a t ing the p re d ic t a b i l it y c on fe r re d by un -

de r ly ing t ime symm e t r i e s .

In s igh t i n to unde r ly ing t ime sym me t r i e s i s sugges te d b y C u t -

l e r a nd I sa rd 09 80 ) . U s ing c a re fu l me a su re m e n t s o f i n t e rs t r e ssin t erva l s , a c ous t ic a l m a n i fe s t a ti ons o f a n i soc h rony w e re fou nd

to r e ve a l a n unde r ly ing inva r i a n t rhy thm. In t e r s t re ss i n t erva l s

w i th in a syn ta c t i c boun da ry a re i soc h ronous , ma in t a in ing a r a -

t io o f 1 ,00; however, the re la t ive dura t ion of adjacent in te rva ls

se pa ra t e d b y a syn ta c t i c boun da ry i s c ons is t e n tly l e ng the ne d

to a r a t i o o f 2:1. C u t l e r a nd I sa rd a rgue d : " Inc re a se d du ra t ion

re su l ts no t f ro m a c om ple t e d i s rup t ion o f isoc h rony, bu t r a the r

f rom ' sk ipp ing a be a t ' so t ha t t he du ra t ion o f l onger i n t e rva ls i s

tw ic e tha t o f sho r t e r one s" (p . 258 ). O the r e v ide nc e suppor t s

c e r t a in r a t i o t im ing p rope r t i e s i n spe e c h (e .g ., K oz h e n ikov &

Christovich , 1965; TuUer, Kelso , & Ha rr is , 1983).

Thus , i t a ppe a r s t ha t bo th t e mp ora l r e gu la r i ty a nd sys t e ma t i c

de v ia tions f rom re gu la r i ty do e x i s t in spe e c h pa t t ern s . N e ve r -the le ss , t o a l ign r e gu la r i t y s imp ly w i th b ina ry t im e s t ruc tu re s

based on st ress markers i s too rest r ic t ive for severa l reasons.

First , even wi th s t ress- t imed in te rva ls , o ther t ime st ruc tures

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

moCom plex metric time ratios refer to C,n = ATJ AT~ _I, values thatform nonintegers such as 6/4 and 9/8 (or compound m eters, e.g., simplemeters such as 2/2 6/4 multiplied by 3). Also, ratios that differ withrespect to level--as in 3 /4 m eter, where Ct = 3 at one level and Ct = 2at oth ers --are on ly a slightly more com plex time h ierarchy. Metric ra-tios form either simple or complex invariants in time and thus p rovidethe basis for specifying hythm ic patterns, as Jones (1981a, 1987a) has

shown.



O ~ .A M I C ~ E . O . . O

a ) ~ 2 B E A Ts i.~ B E A T S ,~ ~ A T S

B B E A T S B B E A T S II B B E A T S ~ B E A T S

I I I I I IA c c en t T y p e S M i M S IM [M S IM i M S IM i M S, O ~ . i . . . . . . . . . . . . i ~, ,

[ . , . . " .~ ; J r r ~ i J - ~ ' . - ' : '

, c c .o , . '~ ' - ' ( ? ) : - ' - " ' ( ~ i ' " - ( ? ) : - : " - ( ' ~ i ~ " ( : )N o t e s G B G B G

Hierarchical Tim e Structure

A c c e n t s C o u p l e d ( ~ )

4 6 9

b ) I 1 6 BEATS 1 6 BEATS ]

8 BEATS 8 BEATS II 6 BEATS I 0 BEATS

1] I] 11~ ? . s ~ ~ c c . o , . . ,M s , ~ , M S ~ M S ~ M S

,.. ,. ^ ;. }. 2~ ], j l. . l , . ~ i , : ~ ' ~ . , 4 1 . " J!. J f - " i , ;'

- % : ( ~ ) ( ? ) i ~ ) . . . . . ( i ic c e n t s

N o t e s G B G B G

N o n - h i e r a r c h i c a l T i m e S t r u c t u r e

A c c e n t s C o u p l e d ( ~ ,)

c )

A c c e n t T y p e ~ . . ~ , S

A c c e o t s ' ~ ( '

N o t e s G

6 BEATS 8 BEATS ,, B BEATS I0 BEATS

M M S S M M M M M M S

I I, , w l = = = i , I . , . J = , , , ~ . . , J I , l ' l ~ l h ' 1 , .t

( ~ , , . , ( . ( t , "~I""h ) l t )

B G B G

N o n - h i e r a r c h i c a l T i m e S t r u c t u r e - h

A c c e n t s D e c o u p l e d ( h ) ( t )

Figure 3. Variations in temporal coherence that arise from differences in relative durations of melodicphrases. (Properties of a structural time hierarchy a re changed, whereas those of the metric hierarchy arenot. M ost coherence occurs in (a) in which S and M hierarchies coincide because coupled S accents [t plush] end each phrase and these also coincide with alternate m easure endings. Less coherence occurs in (h) in

which S accents [t plus h] are again coupled, but they create a nonhierarchical ev ent. In (c), t and h accentsare deeoupled via an additive time separation; the t accents remain hierarchical [dotted lines], whereas h

accents mark nonhierarchieal time levels [solid lines].)

o p e ra t iv e . S e c o n d , s ig n i f i c a n t t im e m a rk e r s o th e r t h a n a m p l i -

tu d e c h a n g e s ( s t r e s s ) a re a l s o c r i t i c a l i n s p e e c h t im in g . P i t c h

a n d t im e a c c e n t s fu n c t io n to o u t l in e r e c u r s iv e ly r e l a t e d m e lo d ic

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

m us ic (e .g . , Bol inger, 1958; Fry , 1958; Ladd , 1986). F ina l ly , jus t

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

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

c o m b i n e t o s u p p o r t c o m p l e x t e m p o r a l a c c e n t p h a s i n g s ( e . g . ,

F ig u re 2 d ) . F o w le r ' s (1 9 8 3 ) s u g g e s t io n th a t v o w e l s a n d c o n s o -

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



4 7 0 MA R I R IE SS J O N E S A N D MA R IL Y N B O L T Z

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

m ic ) s t ru c tu re .

In s u m , th e s e a rc h fo r a s in gle p e r io d ic i ty in s p e e c h p a t t e rn s

i s u n l ik e ly to b e r e w a rd e d . In s t e a d , t h e c h a ra c te r i s t i c t e m p o ra l

p a t t e rn in g s in s p e e c h m u s t b e a d d re s s e d b y id e n t i fy in g (a ) fu n c -

t io n a l m a rk e r s , (b ) m e a n in g fu l d e v ia t io n s f ro m c h a ra c te r i s t i c

t im e h ie ra rc h ie s , a n d ( c ) t e m p o ra l p h a s e r e l a t io n s a m o n g v a r i -o u s k in d s o f s p e e c h t im e h ie ra rc h ie s.

F i na l ly , a t h e m e o f P a r t 2 i s t h a t a l t h o u g h t e m p o r a l c o h e r e n c e

in g e s tu re s , m u s ic , a n d s p e e c h v a r i e s , i t d o e s s o m e a n in g fu l ly

b y p la y in g a g a in s t c e r t a in p re d ic t a b le t im e b a s e s. A n d b e c a u s e

w e w i l l c l a im th a t c o h e re n c e i s c r i t i c a l t o d y n a m ic a t t e n d in g ,

s o m e fo rm a l i z a t io n i s im p o r t a n t . I n th e lo n g ru n , a p re c i se fo r -

r e a l i z a t io n w i ll d e p e n d o n id e n t i f i c a t io n o f t im e m a rk e r s a n d

a p p ro p r i a t e t im e s t ru c tu re s . H e re , w e su g g e s t t h a t a p ro v i s io n a l

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

T h i s r a t io t im e t r a n s fo rm a t io n c h a n g e s in v a lu e s y s t e m a t i c a l ly

a s a f u n c t i o n o f t h e k i n d o f t im e s t r u ct u r e ( s) i n v o l v e d a n d t h e

n u m b e r o f a d d i ti v e t i m e c h a n g e s p re s e n t.

A t t e n d in g t o D y n a m i c E n v i r o n m e n t a l S t r u c t u re

I f e n v i ro n m e n t a l e v e n ts a r e s t r u c t u r e d , m o r e o r l e ss c o h e r -

e n t ly in t im e , w h a t d o e s th i s im p ly fo r a n a t t e n d e r? In th i s s e c -

t io n w e c o n s id e r t h i s q u e s t io n w i th th e g o a l o f p ro p o s in g d i s -

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

even ts .

We b e g in b y a s s u m in g th a t a t t e n d in g i s i ts e l f a t e m p o ra l a c -

t iv i ty th a t s e rv es c e r t a in g o a l s a n d i s g u id e d b y th e w a y n o n te m -

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

n a m i c i n t e r a ct i o n s b et w e e n a n a t t e n d e r a n d s o m e e n v i r o n m e n -

t a l e v e n t o c c u r i n t h e f o r m o f attunements. O n e i m p o r t a n t

d i s t in c t io n to e m e rg e i s t h a t b e tw e e n d i f f e re n t k in d s o f a t tu n e -

ments , spec if ica l ly between uture-oriented and analytic a t t e n d -

i n g m o d e s . F i n al ly , c o n s t r ai n t s a s s o c ia t e d w i t h d y n a m i c c o m -

p le x i ty a re s h o w n to a f f e c t t h e l i k e l ih o o d o f t h e s e k in d s o f a t-

t u n e m e n t s a n d t o e n t e r i n t o a t t u n e m e n t f a il u re s .

A t t u n e m e n t s

T h e i d e a o f a t t u n e m e n t r e s ts o n a n a s s u m p t i o n t h a t a t t e n d i n g

is sens i tive to env iron me nta l rhy thm ic i t ie s (Jones , 1976) . At-

t e n d in g to s p e e c h , b o d y g e stu re s , m u s ic , a n d m a n y o th e r w o r ld

e v e n t s is a rh y th m ic a l a c t iv ity . T h a t i s, rh y th m i c i ty i s i n h e re n t

to l i v in g th in g s in c lu d in g th e a c t iv i ty o f a tt e n d in g . B io lo g ic a lly

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

t im e p e r io d s u n d e r l i e a t t e n d in g . T h e s e in t e rn a l rh y th m s h a v ein d e p e n d e n t ly v a r i a b le a m p l i tu d e s th a t p ro v id e p o te n t i a l w a y s

o f m e a s u r in g th e p h y s ic a l b a s i s o f a t t e n d in g , t l T o g e th e r, f r e -

q u e n c ie s a n d a m p l i tu d e s w i th in s e t s o f re c u r s iv e ly r e l a t e d a t -

t e n d i n g r h y t h m s u n d e r li e f o c u s in g o f a t t e n ti o n a l e n e r g y o v e r

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

s e l ec t ive a t t e n d in g fo r p a r t i c u la r g o a l s .

In t e ra c t iv e a t te n d in g i s t e rm e d attunement. I t i n v o lv e s a s y n -

c h r o n o u s i n t e rp l a y b e tw e e n a n a t t e n d e r a n d a n e v e n t i n w h i c h

t h e f o r m e r c o m e s t o p a r t i a ll y s h a r e t h e e v e n t ' s r h y t h m i c p a t -

t e rn . T h i s i n v o lv e s a n e n l i s t m e n t o f o r g a n i s m i c r h y t h m s w h o s e

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

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

i t y ( S h e p a rd , 1 98 1) . O n e o r m o r e a t t e n d i n g r h y t h m s b e c o m e

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

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

e n t e v e n t s a n d , i n f a c t , w e a s s u m e th a t o rg a n i s m s o p e ra t e w i th

a n in i t ia l b i a s fo r h ig h t e m p o ra l c o h e re n c e , a s i f a n id e a l h i e ra r -

chy ob ta ine d (Essens , 1986 ; Fra is se , 1964; Pove l , 1981; see

F o o tn o te 1 1 ). F o r e x a m p le , b e c a u s e th e h i e ra rc h ic a l s t ru c tu re

o f t h e m e l o d y i n F i g u r e , 3 a h a s d y n a m i c s i m p l ic i ty , i t of f er sr e a d y a t t u n e m e n t t o o n e o r m o r e o f i ts e m b e d d e d t i m e l ev e ls

a s w e l l a s t o i t s t o t a l t im e s p a n . T o i l l u s t r a t e th e s e id e a s , w e

c o n s id e r t h e fu n c t io n s o f r e fe re n t le v el , fo c a l a t te n d in g , a n d a t -

ten t iona l sh if ts .

R e fe re n t L e v e l

We a s s u m e th a t a n a t t e n d e r in i t i a l ly e n t r a in s to s o m e re l a -

t ive ly r e g u la r, p ro m in e n t ly m a rk e d t im e p e r io d w i th in a n e v e n t .

P e rh a p s in a n u t t e ra n c e , i t is a p e r s o n ' s c h a ra c te r i s t i c a r t i c u la -

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

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

leve l fo r the pe rceiver . In the even t i t se l f, i t i s den o ted AT j , bu t

w i t h i n t h e o r g a n i s m i t d e n o t e d b y A ~ , w h e r e t h e p r i m e i n d i -

c a t e s a n e n t r a in e d rh y th m a n d j ( i .e ., w h e n n = j ) r e fe r s t o a

re fe re n t l ev e l. T h i s r e fe re n t p e r io d p ro v id e s ( a ) a t e m p o ra l r e fe r -

e n c e f r a m e , " lo c k in g " th e a t t e n d e r to th e e v e n t , a n d (b ) a n

e v e n t -d e te rm in e d t im e s c a l e th a t " c a l ib ra t e s " t im e s p a n s . In

F ig u re 3 a , fo r e x a m p le , t h e q u a r t e r n o te , J , i s t h e b e a t p e r io d ;

i t d e t e r m i n e s AT a s a t e m p o ra l a n c h o r a s w e ll a s s p e c i fy in g th e

l e n g th o f o th e r h i e ra rc h ic a l t im e l e v el s.

A r e f e r e n t p e r i o d i s j o i n t l y d e t e r m i n e d b y c o n t e x t a n d a n

a t t e n d e r' s b i o lo g i c al m a k e - u p . I t d e p e n d s o n e n v i r o n m e n t a l f a c -

to rs , (e .g . , p res en ta t ion m oda l i ty , in i t ia l pat te rn ing~ tem po ) as

wel l a s o rgan is mi c ones (e .g . , spec ies , age , a rousa l leve l ; Hirsh ,

Bi lge r , & De a therag e , 1969; Kole rs & Brews ter , 1985; Pove l &

E s s e n s, 1 9 85 ) . F o r e x a m p le , t h i s c o n s t ru c t fo rm a l i z e s th e id e at h a t m o d a l a t t e n d i n g r h y t h m s s h i f t w i t h m a t u r a t i o n ( J o n e s ,

1976). In fan ts ma y be d iffe ren t ia l ly se lec t ive to ev en ts tha t o ffe r

re la t ive ly smal l re fe ren t pe r iods (e .g . , h igher tone f requenc ies ,

p h o n e m ic p a t t e rn s ) , w h e re a s o ld e r p e o p le m a y in c re a s in g ly e n -

t r a in w i th lo n g e r p e r io d s a s r e fe re n t s. I t fo l lo w s th a t t e m p o ra l

s c a l in g ( ca l ib ra t in g ) w i l l s h if t w i th a g e ; t h i s h a s d i r e c t im p l i c a -

t i o n s f o r t i m e j u d g m e n t s .

F o c a l A t t e n d in g

A t tu n e m e n t s h i f t s i n v o lv e d i r e c t in g s o m e a t t e n d in g e n e rg ie s

a w a y f ro m th e r e fe re n t p e r io d t o a n o t h e r l e v el ( J o n e s, 1 9 8 1 a ) .

T h i s i s foca l attending, a n d a t t e n d e d - to l ev e ls a re r e fe r r e d to a sfocal t ime periods (o r l e ve ls ). F o c a l a t t e n d in g r e a l i ze s t e m p o -

ra l ly s e l e c t iv e a t t e n d in g in w h ic h e n e rg y c a n b e t a rg e te d o v e r

'~ Biological energies of attending rhythm s are p hysical, not psych i-cal. They are directly fled to the time structure of the organism and,through attunements, to specific relative time properties of events. Fur-thermore, the term recursivelyrelatedsets of attending rh ythm refers tothe assump tion th at those periods that are mu ltiples (divisors) of simpleinvariant integer tirne ratios form a m ore coherently related set. In theserespects , the concept o f energy differs in an impo rtant way from that of,for example, attentional resource theory, in which it assumes a moremetaphorical than structural-specific role (e.g., Navon & G opher,1979).



D Y N A M I C A T T E N D I N G 4 7 1

s o m e t i m e l e v el s a n d n o t o t h e r s t o s e r v e c e r t a in g o a l s (J o n e s ,

B o l t z , & K i d d , 1 9 82 ; J o n e s , K i d d , & W e t z e l, 1 9 8 1 ; N e i s s e r &

B r e c k l e n , 1 9 7 5 ) . F o r e x a m p l e , i f a l i s te n e r ' s g o a l i s t o " c a t c h "

t h e g l o b a l i d e a o f a s p e a k e r, a t t e n d i n g w i ll b e t a r g e t e d o v e r

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

m u s t c o n c e n t r a t e o n t h e s p e a k e r ' s v o w e l p r o n u n c i a t i o n . B e -

c a u s e f o c a l a t t e n d i n g i n v o l v e s e n e r g y s h i f ts , it i s m o r e e t f o r t f u lw i t h d y n a m i c a l l y c o m p l e x e v e n t s a n d w i t h a t t u n e m e n t s t o p r o -

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

H o w d o e s s h i f t i n g o c c u r ? . I t r e l i e s u p o n t h e a t t e n d e r ' s u s e o f

t i m e t r a n s f o r m a t i o n s . F o r m a l l y , l e t a p r i m e d i n t e r v a l , A T n , r e -

f le c t t h e a t t e n d in g r h y t h m t h a t b e c o m e s a t t u n e d t o l ev e l A T n in

t h e e v e n t . F o c a l a t t e n d i n g r e f l e c ts t h e p h a s e - l o c k i n g o f "I n w i t h

A T 'n , i n w h i c h A T n = A T ' n f o r a s u b s e t o f le v e ls . T h e p h r a s e

using t ime r e f e r s t o a r e l i a n c e o n a n e x t r a c t e d t i m e r u l e ( e . g .,

C ; ) t o s h i f t a t t e n d i n g e n e r g y f r o m o n e l e v e l t o a n o t h e r . A n y a t -

t e n d i n g l e v el , A T ' n m a y t h e r e f o r e b e a f o c a l l e v e l i f i t g a i n s e n -

e r g y . A f o c a l le v e l i s r e l a t e d t o a r e f e r e n t p e r i o d b y a t i m e r u l e ,

( C ~) n -j . T h i s i s e v i d e n t i n t h e f o l lo w i n g r e c u r s i v e f o r m u l a :

A T n = A T A C ~ ) - j ( w h e r e I n - J l < 5 ) . ( 2 )

T o t h e e x t e n t t h a t C ~ a n d T ~ a r e g o o d e s t i m a t e s o f C ~ a n d A T j i n

t h e e v e n t , t h e n A T " = A T n .

P e o p l e c a n r a r e l y v e r b a l iz e u s e o f a r h y t h m g e n e r a t o r ( C ~) ,

n o r c a n t h e y r e p o r t f o c a l t i m e l e v e l s ( A T 'n ; J o n e s , 1 9 8 l a ) . F o c a l

a t t e n d i n g i s a t a c i t , h o w - t o s k i l l t h a t i s i m p l i c i t ly a c q u i r e d ( R e -

b e r , K a s s i n , L e w i s , & C a n t o r , 1 9 8 0 ) .

A t t e n t i o n a l S h i f t s

A n i m p o r t a n t a s p e c t o f s k il le d a t te n d i n g a n d e x p e r t is e i s

f l e x ib i l it y ( e .g . , G e n t n e r , 1 9 8 7 ; K e e l e & H a w k i n s , 1 9 8 2 ) . F l e x i -

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

r e f e r e n t l e v e l t o m a n y o t h e r e v e n t l ev e l s. F o r e x a m p l e , i n t h e

e v e n t o f F i g u r e 3 a , a s k il l e d a t te n d e r c a n u s e r a t i o t i m e i n v a r i -

a n t s t o f l e x i b l y t a r g e t m u l t i p l e t i m e l e v e ls , m o v i n g e f f o r t le s s l y

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

i s a t t e n d i n g o v e r m e l o d i c p h r a s e s ( e . g. , 4 a n d 8 b e a t s ) b u t m u s t

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

m o r e a t t e n d i n g e n e r g y o v e r th i s l e v e l ( e .g . , 1 6 b e a t s ) o r e v e n t h e

e n t i r e e v e n t sp a n b y r e l y i n g o n E q u a t i o n 2 . I n s h o r t, a t t u n e m e n t

s h i ft s a ll o w o n e t o s e le c ti v el y " e x a m i n e " s t ri n g s o f n o t e s m a r k -

i n g a g i v e n h i e r a r c h i c a l l e v e l.

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

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

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

( J o n e s , 1 9 8 6 ; s e e a l s o C u t t in g , 1 9 8 2 ). D e p e n d i n g o n t h e t a s k , ap e r s o n c a n r e l y o n h i g h o r l o w f o c a l le v e l s t o a t t u n e t o e v e n t

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

g u i s h tw o g e n e r a l k in d s o f a t t u n e m e n t s . Future-orientedattend.i n g i n v o l v e s a g l o b a l f o c a l a t t e n d i n g o v e r t i m e p e r i o d s h i g h e r

t h a n t h e r e f e r e n t l e v e l ( n > j ) , w h e r e a s analytic attending directsa t t e n d i n g e n e r g i e s t o r e l a t iv e l y lo w l e v e ls in a t e m p o r a l h i e r a r -

c h y ( n < j ) . T h u s , f u t u r e - o r i e n t e d a t te n d i n g m a y s u p p o r t o n e ' s

a b i l i ty t o fo l lo w c o n v e r s a t i o n a l t u r n - t a k i n g b e t w e e n t w o s p e a k -

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

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

e n t t e m p o r a l p e r s p e c ti v e s o f t h e s a m e e v e n t .

T h e s e a t t e n d i n g m o d e s i n v o l v e d if f e r e n t r e g io n s i n a c o n t i n -

u u m o f n e s t e d t i m e l e v el s , b u t w i t h t h e f o l l o w i n g t w o q u a l i f i c a -

t i o n s : ( a ) t h a t t h e y y i e l d d i f fe r e n t t e m p o r a l p e r s p e c t i v e s o n t h e

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

e v e n t ( h i g h e r f o r f u t u r e - o r i e n t e d , l o w e r f o r a n a l y t i c ), a n d ( b )

t h a t t h e y m a y s u p p o r t s e l e c ti v e ly d i f f e r e n t s o r t s o f a c t iv i t ie s , d e -

p e n d i n g o n t a s k g o a l s . T h a t i s , f u t u r e - o r i e n t e d a t t e n d i n g i s p a r -

t i cu l a r ly f u n c t i o n a l w h e n l o n g e r t e r m p r e p a r a t o r y a t te n d i n g

a n d r e a l t im e e x t r a p o l a t i o n s o f a n u n f o l d i n g e v e n t a r e i n v o l v e d .A f u t u r e - o r i e n t e d e x t r a p o l a t i o n i s t e r m e d a n expectancy. A n a -

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

t i v it i e s a r e i n v o l v e d . B e c a u s e r e l e v a n t f o c a l p e r i o d s a r e u s u a l l y

l es s th a n t h a t o f th e r e f e r e n t p e r i o d , e x p e c t a n c i e s a s s u c h a r e

n o t s u p p o r t e d , a l t h o u g h a t t e n d i n g t o l o c a l d et a il a n d g r o u p i n g

w i t h r e s p e c t to t h e r e f e r e n t s p a n i s .

F i g u r e 4 i l lu s t r a t e s t h a t b o t h a t t e n d i n g m o d e s a r e p o s s i b l e i n

a c o h e r e n t e v e n t. T h e y a r e s h o w n h e r e w i t h d i f f er e n t r e fe r e n t

l ev e ls ( f o r c o m p a r i s o n p u r p o s e s , b o t h a r e s t a n d a r d i z e d w i t h r e -

s p e c t t o th e s a m e b e a t p e r i o d ) . I n F i g u r e 4 a , f u t u r e - o r i e n t e d

a t t e n d i n g i n v o l v e s s h i f ts up t o s e v e r a l p o t e n t i a l f o c a l l e v e l s

h i g h e r t h a n t h e r e f e r e n t , w h i c h h e r e i s a t w o b e a t p e r i o d ( n =

j = 1 ). T h e A T 3 f o c a l l e v e l r e c e i v e s m o s t a t t e n d i n g e n e r g y( C ; n - j = 2 2 ), s o t h a t f u t u r e t o n a l o n s e t s s e p a r a t e d b y 8 b e a t s a r e

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

( v i a C~ = 2 4 ) . F u t u r e - o r i e n t e d a t te n d i n g o c c u r s h e r e b e c a u s e

C t = 2 m a y b e e x t r a c t e d a n d u s e d r e c u r s i v el y a s C ~ ( w h e r e

C ; = C , ) .

I n F i g u r e 4 b , t h e r e f e r e n t l e v el b e c o m e s f o u r b e a t s ( n = j =

2 ) i n o r d e r t o i l lu s t r a t e a n a l y t i c a t te n d i n g . W i t h t h i s a t t e n d i n g

m o d e , e n e r g y c a n b e s h i f te d down to the l ev e l o f a d j a c e n t i t e m s

o r p u l se s ( A T 0) f r o m A T 2 . T h u s , w h e n s o m e o n e a t t e n d s a n a l y t i-

c a ll y , a t t e n d i n g i s f o c u s e d d o w n w a r d t o c o v e r f in e c h a n g e s t h a t

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

e n t p e r i o d ) . S u c h a n a c t i v it y m i g h t c o r r e s p o n d , f o r in s t a n c e , t o

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

o f f ou r . I t c a n b e e f f o r tf u l a n d w i ll b e m o r e c o m m o n i n e a r l y

s t a g e s o f l e a r n i n g ~

C o n s t r a in t s o n A t t u n e m e n t s a n d A t t u n e m e n t S h i f t s

A p e r s o n ' s g o a l s d e t e r m i n e t i m e l e v e ls m o s t r e l e v a n t f o r a t -

t u n e m e n t . B u t t h e c a tc h i s t h a t a lt h o u g h a t t u n e m e n t s t o a n

e v e n t c a n s h i f t t o a c h i e v e d i f f e r e n t g o a l s , t h e e v e n t ' s d y n a m i c

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

p l i sh e d . I n p a r t i c u l a r , a t t u n e m e n t s h i f t s a r e l e s s l ik e l y in e v e n t s

o f lo w t e m p o r a l c o h e r e n c e . T h i s i d e a i s f o r m a l i z e d a s a c o n -

s t r a in t o n a t t u n e m e n t c o n f e r r e d b y t h e e v e n t ' s r a t i o ti m e p r o p -

e r t i e s ( r a t i o c o m p l e x i t y c o n s t r a i n t ) . O t h e r c o n s t r a i n t s o n a t -

t u n e m e n t e x i s t b u t t h e s e c o n c e r n t h e a t t e n d e r 's i n h e r e n t a b i l i tyt o s h i f t a t t e n d i n g ( d o m i n a n c e r e g i o n c o n s t r a i n t s ) .

R a t i o C o m p l e x i t y C o n s tr a i n ts

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

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

T h e c o m p l e m e n t o f t h is b i a s r e p r e s e n t s r a t io c o m p l e x i t y c o n -

s t r a i n ts . W i t h l e s s c o h e r e n t e v e n t s , a t t e n d i n g b e c o m e s l e s s f l e x -

i b l e ( a t l e a s t i n it i a ll y ) b e c a u s e t h e r a t i o , Ctn, is c o m p l e x . A t t e n d -

i n g is c o n f in e d t o o n e o r t w o t e m p o r a l l e v e ls i n w h i c h b i a s e s f o r

s i m p l e a n d c o n s t a n t r a t i o s m a y b e r e a l iz e d . I n s h o r t, a n a l y t i c

a t t e n d i n g i s m o r e l ik e ly w i th m a n y n o n h i e r a r c h i c a l e v e n t s .

T o i ll u s t r a te , c o n s i d e r t h e w a y s o f l i s te n i n g e n c o u r a g e d b y



47 2 MAR l RIESS JONES AND MARILYN BOLTZ

Figure 4. Futur e-ori ented (a) and analy tic attendin g (b) as shifts of attending energy from a given referencelevel (ATe, o r AT2, respectively) to higher (future-oriented) or lower (analytic) tim e levels. (Theoretically,

dominance region constraints are a factor in both, but they are shown here only for future-oriented attend-ing as decreasing energy [thinn er lines] associated w ith mo re rem ote tim e levels.)

m e lod ie s o f Figures 2 and 3 . Al though fu tu re -or ien ted a t t end-

ing i s m ore ap t to o ccur wi th those m e lod ie s shown in F igures

2a and 3a, where C, = C; = 2 faci l i ta tes ant ic ipa t ions of melod ic

phras ing , ana ly t i c a t tend ing i s m ore l ike ly wi th those o f F igures

2d, 2f , or 3c , in w hich a con stant Ct is diff icul t to specify. In th e

la t ter , analyt ic a t tending involves focusing on a success ion of

ind iv idua l i t em s because these nonhie ra rch ica l pa t t e rns invo lve

h igh ly com plex an d va r iab le t im e ra t ios . In o the r words , when

the big pic ture in t ime is not c lear , people focus on the small

p ic tu re .

F ina lly , ra t io cons t ra in t s sum m ar ize peop le ' s re sponse to the

dyna m ic com plex i ty o f env i ronm enta l even t s. At tende rs have

biases for s imple t i me sy mmetr ies , and th is affects the ease with

which t hey can achieve certa in go als that d epend, respect ively,

on fu tu re -o r ien ted o r ana ly t i c a t t end ing .

Dominance Region Constraints

A dom inance reg ion ref l ect s na tu ra l a t t end ing l im i t s tha t a re

independen t o f ra t io -com plex i ty cons t ra in ts ( s ee Equa t ion 2 ) .




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

s h i f t a t t e n d i n g e n e r g i e s s o f a r b e f o r e t h e c o n n e c t i o n b e t w e e n a n

e s t a b l i s h e d r e f e r e n t a n d a r e m o t e f o c a l le v e l b r e a k s .

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

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

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

n e i g h b o r i n g t i m e l e v el s ( a r e l a t e d c o n c e p t i s t h e s e r i a l i n t e g r a -t i o n r e g i o n ; J o n e s , 1 9 7 6) . 12 F o r e x a m p l e , i n m u s i c a l c o m p o s i -

t i o n s i n w h i c h m a n y r e l a t e d t im e l e ve l s a p p e a r , th e d o m i n a n c e

r e g i o n s u g g e st s t h a t a t t e n d i n g s h i f t s f r o m a r e f e r e n t t o r e m o t e

l e v e l s a r e u n l i k e l y ; l i s t e n e r s c a n n o t a c c u r a t e l y a n t i c i p a t e t h e

l e n g th o f a s y m p h o n y f r o m i t s te m p o . ( A s i m i l a r n o t i o n i s tac-tus, a p e r c e p t u a l l y d o m i n a n t s u b s e t o f t im e l e ve l s s u r r o u n d i n g

t h e m u s i c a l b e a t ; L e r d a h l & J a c k e n d o ff , 1 9 8 3 ). D o m i n a n c e r e -

g i o n t i m e l e v e ls ( A T b to A T s ) a r e s u g g e s t e d b y p o t e n t i a l f o c a l

l e v e ls s h o w n i n F i g u r e 4 a . T h e k e y n o t i o n i s t h a t a t t u n e m e n t s

s h i f ts e x c e e d i n g [ n - J l o f 4 o r 5 b e c o m e i n c r e a s i n g l y di f fi c u lt .

D o m i n a n c e r e g io n l i m i t s a r e r e l at i v e n o t a b s o l u t e t im e l i m i t s

i n t h a t t h e y a r e e x p r e s s e d i n t e r m s o f h i e r a r c h i c a l l e v e ls ( e x p o -

n e n t s o f C ~ ) . A t t u n e m e n t s a r e r e l a t i v e t o a n e v e n t ' s c h a r a c t e r i s -t i c re f e r e n t p e r i o d , m e a n i n g t h a t o n e c a n p o t e n t i a l l y a t t e n d o v e r

a l i m i t e d s e t o f r e l a t e d t i m e l e v el s , r e g a r d l e s s o f t h e i r a b s o l u t e

t i m e v a l u e s . B u t n o t e t h a t i f a t te n d e r s a r e s t r o n g l y b i a s e d i n

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

s t r a i n t s w i l l s e e m l i k e a b s o l u t e o n e s . C o n c r e t e ly , t h i s m e a n s t h a t

p e r c e i v e d c o h e r e n c e c a n b e a f f e c t e d b y a p a t t e r n ' s r a t e o r d u r a -

t i o n .

F ai l e d A t tune m e nt s

G i v e n t h e p r e c e d i n g d i sc u s s io n o f a t t u n e m e n t c o n s t r a in t s , i t

f o l lo w s t h a t a t t u n e m e n t s c a n f a i l . A f a i l e d a t t u n e m e n t i s a n

a s y n c h r o n y b e t w e e n s o m e a t t e n d i n g r h y t h m ( AT 'n ) a n d t h e r e l e -

v a n t f o c a l le v e l o f a n e v e n t ( A T n ) . T h e n a t u r e a n d c o n s e q u e n c e s

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

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

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

a s a t e m p o r a l c o n t r a s t b a s e d o n f u t u r e - o r i e n te d a t t e n d in g . I n

h i g h ly c o m p l e x e v e n ts , m a n y a s y n c h r o n i e s a p p e a r a n d t h e s e

f o r ce a t t u n e m e n t r e f i n e m e n t s b a s e d o n a n a l y t ic a t t en d i n g .

t o f f e r s on , 1976 ) . 13 He r e , we p r opos e t ha t c e r t a i n c on t r a s t s c a n

i n f lu e n c e j u d g m e n t s a b o u t e v e n ts w h e n t h e g o a l i s t i m e e s t i m a -

t i on .

R e f in ing A t tune m e nt s a nd A naly t ic A t t e nd ing

C o m p l e x e v e n t s c o n t a i n m a n y i r r e g u la r i ti e s , a n d s o t h e y i n -e v i t a b l y i n v i t e m a n y f a i l e d a t t u n e m e n t s . I n t h e f a c e o f th i s , r e -

d o u b t a b l e a t t e n d e r s m a y t u r n t o r e f i n i n g a t t e n d i n g s k i l ls d e -

p e n d i n g o n t h e n a t u r e o f t h e t a s k . I n d e e d , i f t h e e v e n t i s b a s e d

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

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

w i t h n o n h i e r a r c h i c a l e v e n ts i n w h i c h n o i n v a r i a n t t i m e r u l e e x -

i s t s , s uc h s k i l l a c qu i s i t i o n i s l e ss li ke l y . Fo r i n s t a nc e , t he pa t t e r n

o f F i g u r e 2 f a f f o r d s li t t l e o p p o r t u n i t y f o r f l e x i b le a t t e n d i n g , e i -

t h e r i n i t i a l l y o r w i t h p r a c t i c e . H e r e , r a t i o c o n s t r a i n t s o n a t t e n d -

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

t i m e l e v e ls w h e r e t h e y m a y s u p p o r t v a r i o u s g o a l d i r e c t e d a c t iv -

i t ies .

S u m m a r y o f P a rt 2

D y n a m i c a t t e n d i n g r e f l e ct s t h e a t t e n d e r ' s t a c i t u s e o f a n

e v e n t 's d y n a m i c s t r u c t u r e . I t r e l ie s o n t h e p a r t i c u l a r n a t u r e o f

t h e e v e n t ' s t e m p o r a l i n v a r i a n t s ( e . g . , i n g e s t u r e s , m u s i c ,

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

i t s d y n a m i c c o m p l e x i t y . B e c a u s e e n v i r o n m e n t a l e v e n t s d i ff e r i n

c o h e r e n c e , t h e y o f f er t h e r h y t h m i c a l a t t e n d e r d i f f e re n t w a y s t o

s e l e c ti v e l y s y n c h r o n i z e w i t h o n e o r m o r e n e s t e d t i m e l e v e l( s )

( f o c a l a t te n d i n g ) t o a c h i e v e s p e c i fi c g o a l s . T h i s p a r t i c i p a t o r y

a t t e n d i n g i s t e r m e d a t t u n e m e n t a n d i s t e m p o r a l l y s e le c ti v e. A t -

t u n e m e n t i n v o lv e s e n t r a i n m e n t t o a r e f e r e n t t i m e p e r i o d a n d

s e l ec t iv e f o c a l a t t e n d i n g t o s o m e t i m e l e v e l. A t t u n e m e n t s a r e

f l e x i b l e . Th e y c a n s h i f t ove r f oc a l l e ve l s t o r e f l e c t e i t he r f u t u r eo r i e n t e d o r a n a l y t i c a t t e n d i n g . H o w e v e r , t h i s f l e x i b i li t y i s l i m -

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

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

a n a t t u n e m e n t s h i f t . C o n s e q u e n t l y , f u t u r e - o r i e n t e d a t t e n d i n g

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

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

Te mpo ra l C ont ras t and F uture -Or ie n t ed A t t e nd ing

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

f i n d i n g t o y o u r s u r p r i s e t h a t t h e r e ' s a d i s c r e p a n c y . T h i s i s w h a t

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

a h i e r a r c h i c a l o n e . T h e m e l o d y o f F i g u r e 3 b d o e s t h is . I n it i a l ly ,i t s u p p o r t s f u t u r e - o r i e n t e d a t t e n d i n g , b u t a s w e s a w e a r l ie r , i t

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

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

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

( i .e . , C ~ = 2 ) , w h i c h d o e s n o t o c c u r . T h e d i f f e re n c e b e t w e e n o b -

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

a n a s y n c h r o n y t h a t i s e x p e r i e n c e d a s a t e m p o r a l c o n t r a s t :

ATn - A T ' n . W e a s s u m e t h a t t e m p o r a l c o n t r a s t d e t e r m i n e s

o n e ' s r e s p o n s e ( e . g . , s u r p r i s e ) t o s y s t e m a t i c a d d i t i v e c h a n g e s

( a s y m m e t r i e s ) t h a t p l a y a g a i n s t t i m e s y m m e t r i e s . I n s h o r t , i t i s

c o n t r a s ts o f v a r i o u s so r t s t h a t f u n c t i o n t o c o m m u n i c a t e r h y t h -

m i c s t y l e s, e m o t i o n , a n d t i m e c h a n g e . A n d s o m e t h i n g a k i n t o

t e m p o r a l c o n t r a s t m a y f u n c t io n i n t i m e d i s c r i m i n a t i o n ( K r i s -

~2 The serial integration region addressed th e way in w hich tem pora lorder s preserved in world events throug h relationships between prop er-

ties of markers a t different t im e levels. Fo r exam ple, if at level n, the

pi tch change over tha t level - -namely , AP, - - i s d ispropor t ionate lygrea tfor the corresponding t ime chang e--namely , A Tn-- then the pa t tern wi l lhave low tem poral coherence. A consequence is the breakdown of syn-

chronous a t tending and loss of one ' s abi l i ty o o rder th ings in t ime. Thisis evident in phenomena such as auditory pattern streaming (Jones,1976). The serial integration region, thus, is bounded by extrem e pitch/

time (APn/ATn) ratios. I t is conta ined in the dom inance region, whichis bounded by ext reme t ime/ t im e (ATn/ATj where In - J l = 4 or 5)ratios. In th is art icle we focus only on constraints affecting t ime levels,that is, dominan ce region constraints.

~ Temporal cont ras t and lawful pa t terns of tempo ral cont ras ts servespecial communicative functions in music. Jones (1987a)has suggestedthat these additive t ime changes arise from a horizon tal com pone nt in-t roduced in to a per former ' s product ion pat terns , a componen t tha t cor -responds to velocity pattern s of gestures. In other contexts, singular con-trasts defined earlier, have been postu lated to affect t im e discrim inatio n

(Kristofferson, 1977).



474 MAR1 RIESS JONES AND MARILYN BOLTZ

ages focusing over lower time levels is more likely with less co-

herent events. Finally, attunement failures can lead to temporal

contrast, namely the deviation of expected from observed focal

levels.

Part 3: Dyna mic Attending and Time Estimations

The conceptual framework of Part 2 has implications for at-

tending in various contexts. Part 3 develops these with respect

to time estimation. Solutions posed with regard to the filled in-

terval effect (Part 1) are seen as consequences o f constraints on

a general attending activity imposed by these tasks. One goal of

Part 3 is to model time estimation behaviors in comparative

judgment and production tasks using general assumptions of

dynamic attending.

Typically, a time estimation task requires assessment of one

or several time intervals. In light of Part 2, this creates a puzzle:

If people attend rhythmically, by relying tacitly on ratio time

transforms, then how do they come to explicitly judge time in-

tervals as such? Society and our own schedules require that we

judge time as intervals, and we often comply with more or less

accuracy. How is this puzzle resolved?

One resolution plays on the idea that interval time estimates

encourage selective attending over higher order time spans that

relate beginnings and endings of udged events. Clearly, this at-

tending has a basis in relative time. Yet, the interval time esti-

mate is not necessarily an easily achieved goal. The perspective

of Part 2 suggests three assumptions about the way rhythmical

attenders approach such tasks: (a) They use relative time to

achieve task goals. (b) Ease of goal achievement depends on

event structure, notably on the way dynamic complexity con-

strains flexible attending (i.e., future-oriented and analytic). (c)

Time estimates themselves depend on tacit use of resultant fo-

cal levels and because awareness o f these levels is poor, timeestimates are liable to be biased by attunement failures (tempo-

ral contrast and attunement refinements).

According to the first assumption, interval time requests en-

courage attenders to target attending over one or more higher

time levels (future-oriented attending). In the second assump-

tion, their success depends on event complexity. Future-ori-

ented attending is easier to achieve in comparative time judg-

ments about simpler time structures. Here, expectancies about

ending times of standard and comparison events are fairly

effortless. Finally, according to the third assumption, if an at -

tunement failure occurs, then it creates a temporal contrast,

and this, in turn, is apt to tacitly bias time judgments especially

if ending times are involved. That is, people respond to the pres-ence or absence of expectancy violations, not to absolute values

of expected intervals. This scenario predicts that people can

correctly judge intervals whenever a comparison event truly

ends before (or after) some expected ending time (given by the

standard). By the same token, it predicts that people will err in

judging truly identical intervals if one (or both) event(s) hap-

pens to violate expectancies about event endings (a filled inter-

val effect). This occurs whenever expectancies based on embed-ded, not total, time periods lead to contrasts that implicate an

event's ending. If these embeddings make an event's ending

seem too early or too late, then time judgments can be tacitly

distorted. Contrasts do not occur with expectancy confirma-

tions nor when either the expected or observed time period is

absent. But when they do occur and impinge on ending times,

then biased t ime estimates can result. In sum, one way rhythmi-

cal attenders cope with time intervals depends on fnture-ori-

ented attending and temporal contrast.

If attenders don't succeed in attending over higher time levels,

then analytic attending occurs. In this case, although interval

time estimates remain influenced by the way information fillsto-be-judged time intervals, biasing can take a different form.

Particularly if events are incoherent, whenever task goals bring

into play memory-oriented strategies, attending will be focused

over lower time levels. People may engage in counting, grouping,

associative labeling, and so on, in order to impose some struc-

ture on the event, and all o f these activities direct attending to

relationships among adjacent items. Consequently, if time esti-

mates are required they will be biased by these activities and

specifically by differences in focal levels used to attend to the

events involved. For example, if two complex tunes of equal

duration are filled with different numbers oftones, then the one

with more tones will usually involve a denser temporal spacing.

If people count tones, then attunements to the denser sequence

will be based on lower focal attending. However, awareness of

focal time levels is poor. Thus, whenever people tacitly (and er-

roneously) infer that focal levels used to attend to each tune

are the same and that the one with more tones is longer, then

judgment errors will appear (a filled interval effect). Again, such

mistakes arise from the attenders' lack of awareness of differ-

ences in focal levels actually used. In sum, a second way in

which rhythmical attenders cope with intervals of time involves

focal time level differences based upon analytic attending.

In short, Part 2 suggests a broad dichotomy for the way rhyth-

mical attenders interact with temporally coherent and nonco-

herent events, and ultimately this explains how they may arrive

at interval time estimates. Independent evidence for this dis-

tinction comes from Povel and Essens (1985), who found thatreproductions of hierarchical audi tory sequences involve a reli-

ance on higher order time relations, whereas those of nonhierar-

chical sequences involve the use of mnemonic strategies such

as count ing (see also Bamberger, cited in Povel & Essens, 1985;

Hamilton & Hockey, 1974; Jackson, 1985; Maser, 1983). This

distinction offers a way of explaining the notorious variability

found in time estimation studies. It suggests that duration esti-

mates of the same event will vary with attending mode.

Finally, although this framework relies on new constructs

such as future-oriented and analytic attending, the analytic at-

tending mode does incorporate notions underlying contempo-

rary time models. It differs in linking the mnemonic activities

suggested by current time models to a rhythmic base and todifferences in focal time levels. Thus, it suggests that although

attending to events filled with more information may involve

more effort (Underwood & Swain, 1973) or complexity

(Ornstein, 1969) or changes (Block, 1978), finally the decisive

factors involve temporal levels of attending.

Time Estimation in Judgment Tasks: A Contrast Model

A contrast model formalizes the proposal that time judg-

ments are biased by the style of attunement failure (temporal

contrast or mnemonic refinements) associated with a given at-

tending mode (future-oriented or analytic). Two parameters o f

this model reflect contrast and mnemonic activities, respec-



D Y N A M I C A T F E N D IN G 4 7 5

t iv e ly . A th i rd p a ra m e te r , a c o h e re n c e w e ig h t , d e t e rm in e s th e

l ik e l ih o o d o f e ith e r a t t e n d in g m o d e . I t r e f l e c ts r a t io c o m p le x i ty

c o n s t r a i n ts ( P a r t 2 ) a n d s o s u m m a r i z e s t h e i m p a c t o f d y n a m i c

c o m p l e x i t y o n a t te n d i n g .

I n c o m p a r a t i v e d u r a t i o n t a sk s , t h e t e m p o r a l c o n t r a s t b i a si n g

t im e e s t im a te s i s a p a i rw i s e o n e b a s e d o n e x p e c ta n c y v io l a t io n s

in b o t h e v e n t s ; fo r p a i r i i t i s d e n o te d b y th e p a ra m e te r , D E / .T h e m n e m o n i c d i f f e r en c e p a r a m e t e r i s b a s e d o n d i f f e re n c es i n

a n a ly t i c a t t e n d in g l ev e ls o v e r b o th e v e n t s ; i t is d e n o te d D M / .

H e re , w e a p p ly th e m o d e l t o f i ll ed t im e in t e rv a l s t h a t a re e q u a l

in d u ra t io n b u t e x te n s io n s to u n e q u a l i n t e rv a l s a re s t r a ig h t fo r -

w a r d a n d g i v e n in t h e A p p e n d i x . T h u s , f o r a n y p a i r w i s e j u d g -

m e n t , i , w e a s s u m e t h a t t w o k i n d s o f r a n d o m v a r ia b l e s ex i st

th a t a re d i s t r ib u te d , r es pe ct iv e ly , a s N (D E / , ~ i2 ) a n d N (D M i ,

aMi2), in w hic h aEi2 = aM2 = o ' i 2 .

F o rm a l ly , t h e C o n t ra s t M o d e l d i f f e re n ti a l ly w e ig h t s t e m p o ra l

c o n t r a s t, D E / , a n d m n e m o n i c d i f f er e n ce s , D M i , b y t h e p r o b a -

b i l i t y o f fu tu re -o r i e n te d , W / , a n d a n a ly t i c a t t e n d in g , 1 - W /

( 0 < W / < 1 .0 0) . T h i s lo g i c l e a ds t o a b i n a r y m i x t u r e m o d e l i n g

o f th e tw o a t t e n d in g s t a t e s (T o w n s e n d & A s h b y , 1 9 83 ). L e t D ~

b e t h e e x p e c t e d v a l u e o f a t h e o r e ti c a l d i s t r ib u t i o n o f d u r a t i o n

e s t im a te s th a t r e s u l t s f ro m a b in a ry w e ig h t in g o f t h e tw o s t a t es :

D i = W I D E / + (1 - W i ) D M i . ( 3)

T h e p r e d i c t e d a v e r ag e o f sc a l ed d u r a t i o n j u d g m e n t s , J D / , i s a

m o n o t o n i c f u n c t i o n , f , o f D / . F o r s i m p li c it y , f i s a s s u m e d t o b e

l in e a r w i th s c a l e p a ra m e te r s a a n d b . T h e in t e rc e p t p a ra m e te r ,

b , r e f le c t s r e s p o n s e s c a l e c a t e g o ry ; i f b i s t h e s c o re fo r a n u l l

d i f fe r e n ce j u d g m e n t , t h e n a v e ra g e j u d g e d t i m e m a g n i t u d e s i n a

ra t in g t a s k a re a s fo l lo w s :

J D i = f [ D i ] , ( 4)

a n dJ D / = a [ W / D E i + (1 - W / ) D M / ] + b . ( 5)

J u d g m e n t b i a s i s g iv e n b y th e p o in t o f su b je c t iv e e q u a l i ty ,

P S E / , a n d i s g a u g e d fo r t h e c a s e in w h ic h tw o in t e rv a l s h a v e

i d e n ti c a l to t a l d u r a t io n s . F r o m E q u a t i o n 5 , t h e c o n t r a s t m o d e l

p re d ic t s P S E /a s fo l lo w s :

P S E i = J D i - b = a [ W i D E i + ( 1 - W / ) D M / ] . ( 6 )

T h e p r e d i c t e d v a r i a n c e o f o b s er v e d d u r a t i o n j u d g m e n t s i s de -

r i v ed f r o m a s s u m p t i o n s r e g a r d i n g m o m e n t s o f h e w e i g h te d d is -

t r ib u t io n s . T h i s i s S D ~2 f o r j u d g m e n t s o f e v e n t( s ) i :

S D i2 = a 2 [Wi( l - W i X D E i - D M i) 2 + a i2] . (7 )

E q u a t i o n s 5 - 7 r e f le c t p re d i c t io n s o f t h e c o n t r a s t m o d e l . T h e y

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

o f th e w e i g h t i ng p a r am e t e r , W / , a n d t h e t w o a t t e n d i n g m o d e

p a r a m e t e r s , D E / , a n d D M i .

P arame te rs and The i r E s t ima t ion

T h e W / w e i g h t i s s en s it iv e t o e n v i r o n m e n t a l s t r u c t u r e,

w h e r e a s t h e D E~ a n d D M / a t t e n d i n g p a r a m e t e r s r e fl e ct t h e r e -

s p e ct i ve i m p a c t s o f a t t e n d i n g m o d e o n t i m e e s ti m a t e s. P a r a m e -

t e r d e t e r m i n a t i o n s r e s t o n t h e a t t u n e m e n t c o n s t r a i n t s d e s cr i b e d

in P a r t 2 . In p a r t i c u la r , fo l lo w in g th e d o m in a n c e r e g io n c o n -

s t r ai n t , w e a s s u m e t h a t e m b e d d e d p e r i o d s p la y a n i m p o r t a n t

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

j u d g m e n t s . A n d w i t h r e s p e c t t o r a t i o c o m p l e x i t y , w e a s s u m e

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

o v e r b o th e v e n t s . We n o w i l l u s t ra t e p a ra m e te r d e t e r m in a t io n

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

F ig u re 3 to f il l s t a n d a rd a n d c o m p a r i s o n t im e in t e rv a l s .

The Weighting Parameter, W~

T h e W / p a r a m e t e r i s i d e n t i f i e d w i t h c o n d i t i o n s t h a t d e t e r -

m i n e w h e t h e r o n e u s e s a n a ly t i c o r f u t u r e - o r ie n t e d a t t e n d i n g f o r

t i m e e s t i m a t i on . T h e m o s t i m p o r t a n t o f t h e se i s t h e t e m p o r a l

c o h e r e n c e o f t h e e v e n ts t o b e j u d g e d . T h u s , a s s u m e t h a t h i e r a r-

c h i c a l (H ) a n d n o n h i e r a r c h i c a l ( N H ) m e l o d i e s fi ll s t a n d a r d a n d

c o m p a r i s o n in t e r v al s a s s h o w n i n F i g u r e 5 ( H - N H o r N H -

H ) . T e m p o r a l c o h e r e n c e i s g r e a t e r w h e n H m e l o d i e s a r e i n -

v o lv e d a n d a l s o w h e n th e y fu n c t io n a s s t a n d a rd s . In th e s e c a s e s,

d y n a m i c c o m p l e x i t y i s l o w a n d h e n c e W / s h o u l d b e h i g h . T h u s ,

W / i s h ig h w h e n C t , fo r s it u a t io n i is a n in v a r i a n t a n d lo w in t e g e r

r a t io . I n o t h e r w o r d s , e s t im a t e s o f W / , ' ~ / , s h o u l d b e h i g h e r

w i th ( a ) H e v e n t s ( th a n N H o n e s ) , a n d (b ) p a i rw i s e c o m p a r i s o n so f t h e f o r m H - N H ( t h a n N H - H ) . F in a ll y , i n s t r u c ti o n s a n d

t a s k d e m a n d s ( g o a l / f u n c ti o n ) c a n a l s o a f fe c t W ~ b y d e t e r m i n i n g

th e l i k e l ih o o d o f a g iv e n a t t e n d in g m o d e. 14

A t t e nd ing Mo de P arame te rs

In p r in c ip l e , a l th o u g h e i th e r a t t e n d in g m o d e i s p o s s ib l e fo r a

g iv e n e v e n t , t h e y a re n o t e q u a l ly l ik e ly . F u r th e rm o re , b e c a u s e

e a c h m o d e i s a ss o c ia t e d w i t h i ts o w n b r a n d o f a t t u n e m e n t f ai l-

u re , d i f f e re n t t im e e s t im a te s c a n o c c u r fo r t h e s a m e s i tu a t io n .

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

p e o p le a t t e n d in f lu e n c e s th e i r t im e e s t im a te s . W e s h o w th i s u s -

ing two me lod ie s fi ll ing iden t ica l t im e in te rva ls .

Estimation o f DE~. I f p e o pl e a t t e n d i n f u t u r e - o r i e n te d w a y sto e v e n t s o f F ig u re 5 , t h eX w i l l b e b i a s e d b y a p a i rw i s e c o n t ra s t ,

D E / . E s t i m a t e s o f D E ~ ( D E / ) a r e b a s e d o n i n d i v id u a l t e m p o r a l

c o n t ra s t s i n e a c h e v e n t . In d iv id u a l a n d p a i rw i s e c o n t ra s t s a t a n y

lev el c a n b e p o s i t i v e , n e g a t iv e , o r z e ro . I f c o n t ra s t s i n v o lv e th e

to t a l t im e l e v el o f e a c h e v e n t, t h e n t ru ly u n e q u a l t im e in t e rv a l s

o b ta in ( s e e A p p e n d ix ) . B u t i f t h e y a r i s e f ro m t im e l e ve ls e m b e d -

d e d w i t h i n e v e n ts o f e q u a l d u r a t i o n , a s s h o w n i n F i g u r e 5 , t h e n

c o n t r a s t s b a s e d o n f i n a l e m b e d d e d p e r i o d s d e t e r m i n e D E ~ .

T h u s , D E ~ i s a d i f f e re n c e o f f in a l c o n t ra s t s , A T 0 - AT~o, fr om

e a c h o f j p a t t e rn s ( [ j = 1 , 2 ] le v e l s u b s c r ip t s s u p p re ss e d ) . T h i s

p a r a m e t e r r e fl e ct s a c o m p a r a b i l i t y o f e x p e c t a n c y v i o l a t i o n s

a c ro s s b o th p a t t e rn s :

DE i = (A Ta - AT,2) - (AT/ , - AT,-1) . (8 )

14 Com parative judgm ent tasks hav e traditionally been distinguishedin terms of prospective and retrospective designs. Such d e s i g n differ-

ences can also influence Wj. In prospective tasks, people are told tocom pare the durations o f wo forthcoming intervals leading to a greaterchance o f future-oriented attending. In retrospective tasks, people en-gage in incidental activities dur ing two tim e span s ot~en based on ana -lytic attending; later they learn they m ust compare durations. T his vari-

able contributes to divergence n the literature in that differential resultsbetween task type sometimes occur (e .g. , Block, George, & R eed, 1980;S. W. Brown, 1985; Hicks, Miller, & K insbourne, 1976). We believe thismixture of results comes from interactions of instructions w ith eventcoherence.



47 6 MA RI RI ESS J ONES AN D MARI LYN BOLTZ

a ) H

STANDARD)AT ,

A T ; = = 8 b e a t s

( A T I I - A T l l l } = 0

A

NH

(COMPARISON). _ _ , 8 + 8 + 1 0 - - -

,~ ,T i : , = " - - ' - -~ - ' ~ : ~ .b r

~ E

A T i 2 = 6 b e a t s

( T i 2 - Z ~ T ~ a ) = ( 6 - 8 . 6 7 ) = - 2 . 6 7

D E I = ( A T ~ z - A T ' I z ) -O = - 2 . 6 7 ( N e g a t i v e C o n t r a s t )

b )NH H

(STANDARD) (COMPARISON)I 8 + 8 + 1 0 I ~ T I I 2 = 8 b e a t s

I Z X T , , = - - T- - = s . 6 7 J ,

I I~ - k ~ -~ l, _ L -~ _ k o _ i . . . . . . . . . . . . . . . . ° , ~ ' l , _ o _ ~'~ l, L ° _ h _ L o _~-~_L o _ ~

A T i l = 6 b e a t s A T i 2 = 8 b e a t s

( A T I I - A T I ; I ) = ( 8 . 6 7 - 6 ) = 2 . 6 7 ( A T i ~ , - A T / 1 2 ) = 0

A

D E I = O - ( A T i i - A T ' i i ) = + 2 . 6 " / ' ( P o s i ti v e C o n t r a s t )

Figure 5. Abstra cted t ime stru ctures for two events, a hierarchica l (H) and a nonhierarchical (NH ) one, to

be judged in a comparative t im e estimation task. (This event pair i produc es two different kinds of tempo ralcontrast , D Ei, depending on event order. In (a) the H me lody is the stand ard and the N H is the com parisonyielding a negative contrast . In (b) the NH is the stand ard and the H is the com parison, yielding a posit ive

contrast . These t im e structure repres ent the melodies of Figure 6. Smaller dots represent a comm on be atperio d and larger dots signify superord inate t ime period s of phrases m arked by S accents. Expected ending

t ime i s denoted by E. )

E q u a t i o n 8 s i m p l i f i e s w h e n e v e r a n e x p e c t a n c y a b o u t o n e p a t -

t e r n e n d i n g i s c o n f i r m e d b e c a u s e t h a t c o n t r a s t b e c o m e s z e r o .

T h u s , i f t h e f i r st p a t t e r n ( j = 1 ) o f p a i r i c o n f i r m s a n e x p e c t e d

e n d i n g t i m e , t h e n A T h = A T , a n d

DE i = ATi2 - - ATe2. (9)

D i f f e r e n t d e g r e e s a n d k i n d s o f p a i r w i s e c o n t r a s t s a r e g i v e n b y

E q u a t i o n s 8 - 9 . F o r e x a m p l e , s t r o n g e x p e c t a n c i e s o v e r t h e H -

N H a r r a n g e m e n t ( F i g u r e 5 a ) s h o ul d a p p e a r b e c a u s e C~ = 2 a n d

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

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

t h e c o m p a r i s o n f o r f o c a l p e r i o d s o f 8 b e a t s o r m o r e ( i .e . , A T ' a

i s t h e a v e r ag e d u r a t i o n o f p r e c e d i n g p h r a s e s i n t h e c o m p a r i s o n :AT ' n = ( 8 + 8 + 10 ) / 3 = 8 . 67 be a t s ) . Th i s e xp e c t a nc y i s u l t i -

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

t o o e a r l y ( a ft e r 6 b e a t s ), y i e l d i n g a n e g a t i v e p a i r w i s e c o n t r a s t o f

I ) E i = - 2 . 6 7 b e a t s ( E q u a t i o n 9 ) . R e v e r si n g t h e o r d e r o f H a n d

N H e v e n t s ( F i g u r e 5 b ) l e a d s t o a p o s i t iv e p a i r w i s e c o n t r a s t o f

t h e s a m e m a g n i t u d e ( I ) E i = 2 . 6 7) . M o r e g e n e r al l y , E q u a t i o n s

8 - 9 i n d i c a te t h a t t h e m a g n i t u d e a n d d i r e c t io n o f a n y p a i r w i s e

c o n t r a s t d e p e n d o n d i s c r e p a n c ie s b et w e e n o b s e r v e d a n d e x -

p e c t e d e n d i n g s w i t h i n b o t h p a t t e r n s .

Est ima t ion o f DM~. I f p e o p l e a t t e n d a n a l y t i c a l l y t o t h e s e

s a m e e v e n t s , th e y a r e b i a s e d b y D M ~ . T h i s m a y a p p l y i f p e o p l e

r e s o r t t o c o u n ti n g A lo w e r o r d e r f e a t u r e s w i t h i n e a c h e v e n t . E s t i -

m a t e s o f D M ~ ( D M ~ ) w i l l n o t n e c e s s a r i l y a g r e e w i t h c o n t r a s t

e s t i m a t e s ( I ~ E i ). I f D M i i s b a s e d o n a c o u n t i n g s t ra t e g y , t h e n

l e t N l i a n d N 2~ d e n o t e , r e s p e c t iv e l y , t h e n u m b e r o f i t e m s ,

c h u n k s , o r b e a t s t h a t a r e c o u n t e d w i t h i n t h e i t h p a i r o f st a n d a r d

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

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

e l s a r e t h e s a m e f o r b o t h e v e n t s; t h i s c o m m o n f o c a l le v e l i s d e -

n o t e d b y A ~ ( s u p p r e s s i n g l e v e l s u b s c r i p t s ). T h u s , D M i i s e s t i -

m a t e d b y

D M i = A T ~ ( N 2 i - N I i ) . ( 10 )

F o r e x a m p l e , i f a t t e n d i n g i s c o n f i n e d t o t h e r e f e r e n t l e v el ,

t h e n D M i i s e s t i m a t e d f r o m d i f f e re n c e s i n t h e n u m b e r o f b e a t s

c o u n t e d i n e a c h e v e n t . I n t h e e v e n ts o f F i g u r e 5 a a n d 5 b , t h e

a s s u m p t i o n o f e q u i v al e n t f o ca l p e r i o d s i s c o r re c t a n d s o c o r -r e c t ly y i e ld s D M ~= 0 , b e c a u s e N 1 = N 2 ~ . B u t , w h e n e v e r b e a t s

( o r o t h e r a t t e n d e d - t o i n f o r m a t i o n ) m a r k o u t d i f f e re n t N 1~ a n d

N 2 ~ v a l u e s , t h i s a s s u m p t i o n i s i n c o r r e c t . C o n s e q u e n t l y , t i m e

d i s t o r t i o n s a r e p r e d i c t e d ( f i l le d d u r a t i o n e f fe c t) . S u p p o r t i n g e v i -

d e n c e f o r E q u a t i o n 1 0 a p p l i e d t o b e a t c o u n t i n g i s f o u n d i n s t u d -

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

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

t o t a l n u m b e r s o f b e a t s ( N 1 : ~ N 2 ) ; B o l t z , 1 9 8 5 ) . 15

15 Boltz (1985) found th at w hen two melodies are identica l in d ura-t ion , as well as in num ber of ones and n umber of pause-def ined chunks ,they are nonetheless judge d to differ in du ration a s a function o f thenumb er o f d i fferent beats , w i th those conta in ing more beats judged to

be longer.



DYNAMIC ATTENDING 47 7

In sum, attending mode parameters can assume different val-

ues for the same pair o f events. Furthermore, either parameter

can yield over- or underestimations of a given interval. The de-

gree to which one or another parameter estimate holds sway

depends on its relative weight (Equations 5-7). Temporal con-trast effects will predominate if future-oriented attending oc-

curs (high W~), whereas mnemonic differences will predomi-

nate i f analytic attending occurs (low W~). In general, this leads

to predictions that variability and disagreements in time esti-

mates are to be expected. Explanatory orderliness comes only

with reference to event st ructure and dynamic attending.

Contrast Model Predictions

The Contrast Model predicts that judgment accuracy (Equa-

tion 5), average bias (Equation 6), and variance (Equation 7)

will vary systematically with model parameters. Among its im-

portant predictions are the following: (a) Time estimates will bebiased in magnitude and direction by values of contrast (DEi).

(b) Biasing effects of a given contrast will increase directly with

temporal coherence, namely with increments in Wi. (c) Esti-

mates o f Wi will be a function ofpairwise coherence, as indexed

by Ct,, such that XfCiwill be high whenever a pair contains H

patterns and especially when these serve as standards (ratio

complexity constraints). (d) Judgment variability should de-

crease with increasing predominance o f one attending mode (as

Wi --* 1.0 or 0.0).Numerous other predictions can be deduced from Equations

5-10. Some concern effects of mnemonic strategies (DM~),

which should be most pronounced when Wj is low. Others con-

cern range effects arising from dominance region constraints.

Finally, additional parameter influences on judgment variance

can be anticipated from Equation 7.

These same equations also generate corresponding predic-

tions about judgment accuracy and discriminations o f unequal

time intervals. These appear in the Appendix where related

models such as Kristofferson's (1977) real time criterion model

are considered. Systematic departures from Weber's function

are predicted by the Contrast Model as a function of task, at-

tending mode, skill, and event structure. However, our focus

here and in Part 4 is on the case of equal time intervals and in

particular on the first several predictions previously outlined.

Time Estimation in Production Tasks: Expectancies

The Contrast Model only applies to comparative judgment

situations. But time estimation has also been studied in tempo-

ral reproduction and production tasks (cf . Allan, 1979; Baker,

1962; Bartlett & Bartlett, 1959; Johnson, 1986; D. N. Lee,

1980). In reproduction, subjects recall a time span by overtly

marking its beginning and end. In production, a specified span(e.g., 1 s) is constructed. A variant o f the latter involves timed

extrapolations in which part of an interval is presented and the

appropriate remaining time must be produced. Analyses of re-

production and production tasks are beyond the scope of this

article. However, temporal extrapolations are relevant because

they directly involve expectancies.

Temporal extrapolations require an individual to use the pre-

ceding context to indicate (overtly) when an event should end in

real time. Thus, they have potential for revealing expectancies

because only the initial part of an event occurs and one must

covertly continue it. Attending that controls performance oc-

curs in the absence of the event itself; only "pure" expectanciesremain.

Predictions based on expectancies rely on Equation 2. As-

suming that a referent period, ATj and a rhythmic generator,

C't, are supplied by the preceding context, Equation 2 suggests

the existence of sets of nested expectancies. Let AT" be the value

of that focal period most relevant to a particular task. Produced

and extrapolated times reflect such expectancies, and these can

be predicted from average values of AT, within the relevant

event. Thus, focal periods of 8 beat phrases within a musical

event allow estimation of the extrapolated completion time,

providing, of course, that the listener uses expectancies to time

extrapolations. By contrast, analytic attending should not pro-

duce extrapolation times that are systematically related to anevent's higher order time periods.

Summary of Part 3

Time estimation in judgment and production tasks involves

dynamic attending over various levels of structure within events

that fill time intervals. According to the Contrast Model, means

and variances of comparative duration judgments are deter-

mined by the likelihood o f different attending modes (future-

oriented, analytic) and their related potentials for attunement

failure (temporal contrast, mnemonic activity). Over- and un-

derestimates can occur with either future-oriented or analytic

attending, with the nature and extent o f biasing depending on

event structure, its complexity, and attending mode itself. Ac-

cording to the production model, extrapolations involve only

use of event structure. Thus, it predicts that produced time esti-

mates will be systematically affected by expectancies but not by

temporal contrast. Together, both models reinforce new defini-

tions of complexity and, at the same time, suggest some reasons

for seemingly diverse experimental findings regarding nontem-

poral information and time estimation.

Part 4: Time Judgments and Productions

Two experiments address issues raised by the Contrast Modeland other models presented in Par t 1. Together, they also ex-

plore the relation between time judgment and production tasks.

The first experiment tests the hypothesis that temporal contrast

affects judgments of identical time intervals (Boltz, 1985). The

second uses a production task to provide converging evidence

that temporal contrast arises from temporal expectancies about

event endings. 16 In both, events are melodies based on simple

folk tunes.

16 Experiment 1 is one of several from Marilyn Boltz's(1985) disser-tation. Experiment 2 and the Contrast Model were conceived by MariRiess Jones.



478 M A R l R I E SS JO N E S A N D M A R I L Y N B O LT Z

o )

b )

E X C E R P T F R O M " T H E R E ' S M U S I C I N T H E A I R " B Y G E O R G E R O O T

H OBSERVED T IME PERIODS A T i j

8 BEATS 8 BEATS 8 BEATS 8 BEATS

t ~ ~ I I I I I I I. . . . . j [ . ' , , . . . . . . . . . . , _ , % , ~:

- . . = J : ' , - ~ : : - - . . . . . . . . # ~ . . . . . - - ' , - ' ',..~ ', ( 8 + 8 + 8 ) • 0 B E A TS, . , , ( ~ ) _ _ . ( : , ) . ; . ( ; ) _ ( .~ , ) - . ( : ) B

EXPEC TED TIME PERIODS AT~j

N H E A R L Y T i j O B S ER V ED T IM E P ER IO D S A T i j

B BEATS 8 BEATS 6 BEATS I0 BEATS

I I If ~ . I I T 1 1 : 1 ,"72 ' ' ' ' ' ': , ~ . ~ . , , . ~ , ~ - , . ' , ~ ; ; , ; , ~ . . . . . . . . . . ; ,

: ' ' 3 c : - - - : _ - - : - ~ ' ~ : : = - ' ~ - _ - - = ' q = . . . . ; - - - - ' I -- : ( 8 + B + 6 ) 2 . 6 7 B EA TS( ~ , ) - - " ( ; ,) " ( ~ ' ) - - " ( : ) ~ E " ( ; ) ,o ~ •

N H L A T E OBSERVED T I M E PERIODS AT i j

8 BEATS S BEATS I0 BEATS 6 BEATS

I I I I I I I I. . . ~ , ~ ' . ~ , . , . ~ . L _ I . . I . , . , . , , . , , _ , '~ . _ ~ l ~ ,,t J l . . . . . . . . . . . . . . .

EXPEC TED TIME PERIODS

A T I j

NH E A R L Y - h OBSERVED 3 :I M E PERIODS Z ~T ij

6 BEATS 8 BEATS 8 BEATS I0 BEATS

i - O n . , I I I I I I I Id ) . . 1 _ , . j ; . . , , , r -q , . ; _ , i J , J J f l

EXPECTED T IM E PER I ODS AT i j

F I NAL CONT RAST IN PAT T ERN i j : l

OBSERVED ( A T I J ) - EXPECTED ( A T i J )

e )

6 ( 8 + 8 + 1 0 ) • - 2 . 6 7 B EA TS3

I 0 ( 6 + 8 + 8 ) = 2 . 6 7 BE AT S3

NH LATE-h OBSERVED T IME PERIODS AT i j9 BEATS 8 BEATS 8 BEATS 7 BEATS

t ~ ~ I I I I I I I I

I~,.~. _ . ; ~ , " A ; . . ; - % " - ~ ' . . . I J r - ~ . ' , " A ' ~ . . . . . . . ~ - - . . I I

iO

EXPECTED T ,.E PER,ODS IL ~ T i j

7 - ( 9 + 8 + 8 ) = - I . 3 3 B EA TS3

F i gu re 6. Exc e rp t f r o m a f o l k t u n e i n G m aj or i n w h i c h r e la t ive d u r a t i on s o f p h r ase s ( m e t e r c on s t an t ) ar e

var ied. ((a) H i s t h e or i g i n a l e xce r p t; ( b ) t h r ou gh ( e ) ar e t e m p or a l var i a t i on s t h at ad j u s t r e l a ti ve d u r at i on s

of s t ru c t ur a l p h r ase s m ar k e d e i th e r b y c ou p l e d t an d h ac c e n t s (b , c ) or by h ac c e n t s a l on e (d, e). SinBle

p at te r n c on t r as t s ar c b ase d on ob se r ve d m i n u s e xp e c t e d t i m e s w h e r e e xp e c t e d t i m e s , i n t u r n , ar e b ase d on

c on t e xt u a l l y gove r n e d e xp e c t an c i e s ab o u t f i n a l p h r ase d u r at i on s . )

Ex per im ent 1 : Judgments o f M el od i c Du ra t i ons

T h e f ir st s t u d y a s s e s s e s p r e d i c t io n s o f v a r i o u s t i m e e s t i m a t i o n

m o d e l s , i n c lu d i n g t h e C o n t r a s t M o d e l , i n c o m p a r a t i v e j u d g -

m e n t ta s k s . M o d e r a te l y s k i l l e d l i s t e n e r s ju d g e d th e r e l a ti v e d u -

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

p a i rs o f m e l o d i c p a t t e r n s, t h e ir t i m e s t r u c t u r e w a s m a n i p u l a t e dt o v a r y ( a ) t e m p o r a l c o n t r a s t t h r o u g h c o n f i r m a t i o n a n d v i o l a -

t i o n of e x p e c t a n c i e s an d ( b ) d e g re e o f t e m p o r a l c o h e r e n c e

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

M e l o d i es w i t h i n a p a ir a l w a ys in v o l v e d a c o m m o n f o l k tu n e

b a s e d o n t h e s a m e ( d u p l e ) m e te r. H o w e v e ~ o n e o f t h e t w o r u n e s




c ou ld d i f fe r r e la t i ve t o t he o the r i n t he t im ing o f i ts m e lod ic

p h r a s e s t r u ct u r e. O n e t u n e a n d f o u r t e m p o r a l v a r i a ti o n s a p p e a r

in F igu re 6 . The o r ig ina l t une (F igu re 6a ) ha s a h i e ra rc h ic a l

fo rm w he re ha rmon ic a c c e n t s c o r re spond ing to t on i c t r i a d

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

longed du ra t ions . The se jo in t a c c e n t s func t ione d a s s t ruc tu ra l

ma rke r s o f me lod ic ph ra se e nd ings (C one , 1968 ; K ra me r , 1982 ;Todd , 1985 ) . W i th in e a c h H tune , s t ruc tu ra l a c c e n t s alw a ys r e -

c u r r e d a f te r a n i n v a r i a n t n u m b e r o f b e a t s a n d w e r e p r e d ic t e d t o

p rom ote t e mp ora l e xpe c t a nc ie s a bou t ph ra se a nd e ve n t e nd ings

tha t a re r e l i a b ly c on f i rme d . A l l va r i a ti ons o f a n H tune in t ro -

duc e d a dd i t i ve t ime c ha nge s t h rough t iming mod i f i c a t ions o f

s t ruc tu ra l a c c e n t s . In pa r t i c u l a r , a l l va r i a n t s w e re N H tune s

c on ta in ing c on t ra s t s o f spec if ic ma gn i tude a nd d i re c tion . Some

( NI -I e~ y a n d N ~ y . h ) w e r e d e s ig n e d t o p r o m o t e t e m p o r a l ex -

pec tanc ies for ear ly endings, and in these , m elodic phra sing was

in i t ia lly regular so tha t foca l t ime per iods were , on the average ,

shorte r th an the f ina l one . Others (NHla t¢ and NHat~.h) were

s imi l a r ly de signe d, bu t w i th t he a im o f p romo t ing e xpe c t a nc i e s

for la te endings; thus, in i t ia l phrases had foca l per iods tha twere , on the average , longer than the f ina l one .

Te m pora l c ohe re nc e w a s va r i e d ove r a n e ve n t pa i r i n se ve ra l

w a y s- -a l l r e l a t e d to t he ove ra ll de g re e o f t e mp ora l r e gu la r i t y i n

mu sica l phrasing ( i .e . , not m eter ; , Par t 2) . Both the presen ce of

a s imp le (H ) t ime s t ruc tu re a nd i t s r e l a t i ve p l a c e me n t i n t he

e ve n t pa i r ( e ve n t o rde r ) w e re va r ie d . A th i rd po te n t i a l sou rc e o f

c ohe re nc e invo lve d the c l a r i t y o f foc a l per iods . The p rom i -

ne nc e o f s t ruc tu ra l ph ra s ing w a s va r i e d th rough the c oup l ing

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

c on t ra s t e f fe c ts shou ld be e nha nc e d in e ve n t s w i th c oup le d a c -

cents (NI-L~ y and NH~.~ melodies) , re la t ive to those w i th less

p rom ine n t , de c oup le d a c c en t s (NI-I~ay.ha n d NHlate-hmelodies) .

A l though the t e mp ora l a c c e n t s o f the se me lod ie s do r e c u r w i th

inva r i a n t t ime p e r iods (he nc e the y a re h i e ra rc h ic a l) , t e mp ora l

c on t ra s t a r i se s f rom ha rmon ic a c c e n t s t ha t a ppe a r e i t he r t oo

e a r ly o r t oo l a t e . The e x t e n t t o w h ic h suc h ma n ipu la t ions o f

t ime ma rke r s a re , i n f a c t , pe rc e ive d by l i s te ne r s w a s va l ida te d

in a n inde pe nde n t r a t i ng s tudy in w h ic h a d i f f e re n t g roup o f

ski l led l i s teners were asked to judge accen tua t ion pa t te r ns in a l l

me lodies (see Meth od sec tion).

M o d e l P re d i c t io n s

T h e C o n t r a s t M o d e l

T h e C o n t r a s t M o d e l a s s u m e s t h a t a t te n d i n g m o d e a n d e n v i -

ronm e n ta l s t ruc tu re j o in t ly in f lue nce t ime judgme n t s . Tho sep re d ic t ions f rom Pa r t 3 i nvo lve ( a ) a t t e nd ing mod e a nd t e m po-

ra l contrast , (b) a t tending an d m nem on ic ac tiv ity , and (c ) envi-

r o n m e n t a l s t r u c t u r e a n d t e m p o r a l c o h e re n c e.

Future-oriented attending and temporal contrast. Th e t e m -

po ra l c on t ra s t pa ra m e te r , D Ee, i s o f p r ima ry in t e res t . Fo r a pa i r

o f e qu iva le n t i n t e rval s , t ime judgm e n t s shou ld d i f fe r f rom

e qua l i t y a s a func t ion o f t he ma g n i tude a nd s ign o f D E~, a ssum -

ing mo dera te to h igh va lues of i t s weight, W~ (Equ at ion 6) . In

th i s study , pa irw i se c on t ra s ts r a nge f rom mi n im a in some H -

H p a i r s t o ma x im a in some N H - N H pa i r s ( e.g. , N I - l~ ly -

N H h ~ ) .

Analytic attending and mnem onic activity. The D M~ va lue s

a re e s t ima te d a c c o rd ing to a ssume d mne mon ic s t r a t e gy . A l -

though nume rous s t r a t e g i e s a re poss ib l e ( se e P re d ic t ions o f

A l t e rna t ive The o r i e s a he a d ) , fo r pu rpose s o f e va lua t ing the

C on t ra s t M ode l , w e a ssume a be a t c oun t ing s t r a t e gy in w h ic h

I) M i = O.

Environmental structure and temporal coherence. Eve n t c o -

he re nc e invo lves t he t e mpo ra l r e gu la r i t y o f ma rke d t im e l e ve ls

e mb e dde d w i th in t he e ve n t pai r. B e c a use the c ohe re nc e w e igh t,W i , r e f le c t s r a t i o c om ple x i ty c ons t ra in ts o n C tn , W l shou ld be

h ighe r w i th pa i r s i nc lud ing H e ve n t s a nd w i th t hose tha t be g in

with H tunes ( i .e . , H - NH ). Theore t ica l ly , accent decoupl ing

c a n a l so a f fe c t c ohe re nc e by re nde r ing e i t he r ha rmon ic o r t e m -

pora l regular i t ies less not iceable . The W; parameter g ives

g re a t e r w e igh t t o p ro mine n t ly m a rke d c on t ra s t s .

P re d ic t io n s o f A l te rn a t i v e T h e o r i e s

A l te rna tive t he o r i e s a re me m ory o r i e n t e d in na tu re a nd ba se

p r e d ic t io n s a b o u t j u d g m e n t b i a s o n m e m o r y c o d e c o m p l e x it y .

With regard to melodies, spec i f ic predic t ions re ly heavi ly on

mus ic a l c od ing the o ry , w h ic h a ssum e s tha t c ode c o mple x i ty de -p e n d s o n t h e n u m b e r o f p i t ch r u l e c h a n g es a n d t h e n u m b e r o f

encod ed chu nks (e .g ., Deutsc h & Feroe , 1981; see Jones, 1985,

for a review). Com plexi ty i s g iven by the resul t ing co de length

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

doe s no t i nvo lve e xpec t a nc ie s . N one the l e ss , a c c o rd ing to t ime

e s t ima t ion mode l s i n Pa r t 1 , e nc od ing c om ple x i ty c a n va ry in

the se me lod ie s. Th i s l e a ds t o t h re e t e s t a b le m ode l s o f t ime judg -

m e n t .

Null model. A nu l l m ode l p re d ic t s no t im e d i f f ere nc e s a mo ng

me lod ie s , be c a use in a ll me lod ic pa i r s (H a nd N H ) the num be r

o f t one s, c hu nks (de s ignate d by t e m pora l a c c e n ts ) , p i tc he s , a nd

p i t c h ru l e c ha nge s a re e qua te d . B y the se c ri t e ri a , t he non te m po-

ra l i n fo rm a t ion th a t f il ls bo th t ime in t e rva l s is e qua lly c omple x .

Thus , one in t e rp re t a t i on o f t he s to ra ge s iz e hypo the s i s

(Ornste in , 1969), a t tent iona l e ffor t mo dels (e .g. , Un derw ood &

Swain, 1973), and a contex t change mod el (e.g ., B lock, 1978)

i s t ha t no m e m ory c ode o r s t r a t e gy d i ff e re nce s e x is t t o a f fe c t

du ra t ion judgme n t s .

Chunk model. A c h u n k m o d e l c a n a l so b e g e n e r at e d f r o m

the s to ra ge si z e hypo the s is . I t p re d i c t s t ha t N H me lod ie s shou ld

se e m longe r t ha n H me lod ie s be c a use the fo rm e r c on ta in

c hunks (ph ra se s ) o f d i f f e re n t le ng ths a nd thus a re mo re c om -

plex .

Change model. A c ha nge mode l i n i t s s tr i c te s t fo rm (a s r e -

v i e w e d in B loc k , in p re ss ) i s some w ha t d i ff i cu l t t o a d a p t t o mu -

sica l pa t te rn s becau se i t i s not a lways c lear which types o f s t ruc-

tura l chang e pro mo te changes in processing stra tegy. However,be c a use a c c e n t s r e f l e c t c on te x tua l c ha nge , t he mo s t p l a us ib l e

p re d ic t ions c e n ter on the i r pa r s ing po te n ti a l . The N H me lod ie s

shou ld be m ore c om ple x tha n H me lod ie s , a nd i t i s a l so p la us i -

b l e t ha t N H me lod ie s w i th de c oup le d a cc e n t s shou ld se e m lon -

gest of a ll . The idea is tha t no nhierarch ica l m elodies genera l ly

d i sp l a y more unp re d ic t a b l e c ha nge s t ha n h i e ra rc h ic a l one s ,

w he re a s N H - h me lod ie s spe ci fy s ti ll mo re c on te x tua l cha nge

be c a use c hunk s a re de f ine d by e i t he r h o r t a c c e n t s . I f pe op le

e nc ode u s ing bo th ha rmon ic a nd t e mpora l a c c e n t s , t he n in

N H - h me lod ie s , t he i r s tr a t e g ie s w i ll unde rgo m os t c ha nge s ,

perh aps even ones asso c ia ted wi th confl ic t ing tona l i t ies a r is ing

f rom de e oup le d a c c e n t s.

In sum , t he C on t ra s t M ode l r e li e s on a dyn a mic in t e rp re t a -



4 8 0 M A R l R I ES S J O N E S A N D M A R I L Y N B O L T Z

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

c o n t r a s t a n d t e m p o r a l c o h e r e n c e . A l t e r n a ti v e m o d e l s r e l y u p o n

d i f f er e n t i n t e rp r e t a t i o n s o f c o m p l e x i t y t o p r e d i c t j u d g m e n t b i -

a s e s d u e o n l y t o m e m o r y c o d e s .

M e t h o d

D e s i g n

The des ign was a 5 X 5 X 3 × 2 m ixed fac to r ial . F ive t ime s t ruc tu res

(H , NHearly, NHl~t~,NI-l~ly.~, NH~te-h) existed for ea ch pattern, yielding

25 pairs (5 × 5) of to-be-judg ed melodies ( i = 1, 25). Thre e folk-tune

instances were used with in each level. Cou nterba lance order (1, 2) was

the single between-subjects ' factor. A total o f 16 subjects, each w ith at

leas t 4 yea rs o f mus ica l exper ience wi th in the pas t 6 yea rs, were ran -

dom ly ass igned to on e o f the two coun te rba lance o rders.

S t i m u l u s M a t e r i a l s

Pattern construction. All o f the pa t te rns cons is ted o f compute r -gener -

ated s quare waves of equivale nt loudness levels. They w ere based onadap ted excerp ts (leng ths rang ing f rom 34 to 37 no tes ) f rom th ree fo lk

tunes . Al l spanned four me lod ic phrases tha t covered in tac t themat ic

s ta temen ts and tha t w ere comp le ted by the tune ' s end ing , wh ich in a l l

cases was the ton ic (F igure 6a i s an exempla r ) . Al though H tunes cou ld

be in different keys, all were scored in a dup le m eter, wh ere the SOA for

= 300 ms . In add i t ion , a l l H tun es con ta ined (a ) coup led s t ruc tu ra l

accents o f elongated note s ( t) and stable pitches (h), and (b) an inv aria m

num ber o f beats (e .g . , 8) betwe en these accents. Oth er structur al details

com mo n to a l l H and NH pa t te rns were as fo l lows: (a ) Al l con ta ined the

same n um ber o f bea ts. (b ) "Keyn ess" o f a ll me lod ies was ensured by

inclusion o f certain key-specific m usical intervals (cf . H. Brow n & But-

ler , 1981) and by init iating each with a lengthened tonic. (c) Structural

accen ts (h, 0 a lone de f ined the re levan t ( s t ruc tu ra l ) t ime h ie ra rchy ; no

me tric stresses rein forced the m etric t im e hierarchy. (d) h accents always

cor responded to the ton ic , dominan t o r med ian t o f the estab l i shed key(Krum hans l & Kess le r , 1982); in two H ins tances (and the i r NH var ia -

tions), this req uired changes in a few scored h accen ts for greater phrase

emphas is . (e ) In th ree o f the f ive t ime s t ruc tu res , h and t accen ts were

coup led (i .e . , H, N H~riy, NHj~t~). (f) In th e two rem aining c onditio ns

(NH ,dy.h, NHl, t~.h), h and t acce nts were decoupled, separate d in t i me

by _+k = 300 ms . In NH, , ]y .h, h accen ts occur red on no tes imm edia te ly

prio r to t accents, ther eby shortenin g the f irst phrase in these tunes; in

NHl~t,.h , the h accents followed t accents, thereby lengthening this

phrase . Cor respond ing f ina l t ime pe r iods were 10 and 7 bea ts fo r the

two tunes . In decoup led s t ruc tu res, on ly h accen ts marked nonh ie ra r -

chical t ime levels; t accents remained str ictly hierarchical. Thus,

NH~ay.h and NHl, t~.h corresp onded to NH~dy and NHl~t~ n weaken ing

tempo ra l coherence v ia h markers, bu t they co r responded to H tunes

wi th regard to t markers . They a re te rm ed H-type melodies.

Pattern structure validation: Ratin g stud y. To assess the psychological

va l id i ty o f accen t man ipu la t ions in these excerpts, an independen t

g roup o f 18 mus ica lly tra ined l i s teners were asked to ra te a l l m e lod ies

(us ing a 10-po in t scale ) on two d imens ions . For a d im ens ion o f accen t

t iming , sub jec ts judged w he ther a melo dy ' s tempora l accen ts seemed

w e ll t i m e d ~ u r r i n g w h e n e x p e c t e d - - o r w h e th e r t h ey se e m e d i ll -

t i m e d ~ o e c u r r i n g e a r li e r o r l a t er t h a n e x p e c t e d . T h e s e c o n d d im e n s i o n

was one o f ha rmo nic appropr ia teness . Here , sub jec ts judged whe ther

tempora l accen ts seemed appropr ia te to the melody ' s key and whe ther

they occur red on tona l ly appropr ia te p i tches . As an t ic ipa ted , accen ts

wi th in the h ie ra rch ica l me lod ies were cons ide red to be the mos t we l l

t imed (M = 3 .10) and tona l ly appropr ia te (M = 3 .09). Fu r the rmore , a l l

th ree H ins tances were judged to b e h igh ly appropr ia te , ha rm onica l ly ,

with no significant tun e differences (F < 1.0), thus in dicating that acce nt

phras ing and h -p lus - t coup l ing in H vers ions o f the adap ted excerp ts

T a b l e 1

Me an J u dge d D ur a t ion Ra t ings fo r P a t t er n Pa i r s

in Ex pe r im e n t 1 a s a Func tion o f Me lod ic

Tim e Struc ture (Bol tz , 1985)

S t a n d ar d C o m p a r i s o n m e l o d y ( j = 2 )m e l o d y

( j r 1 ) 1 2 3 4 5

1. H 4.04o) 4.60o) 3.51o) 4 . 7 8 o ~ 3.22~)2 . NI- I~ ly.h 3 . 50 (2 ) 3 .99 ~3~ 3 .610) 4 .510) 3 .590)3. NHla~h 4 .6 4~ 2 ) 4 . 5 5 ( 3 ) 4 . 0 2 ( 3 ) 4 .6 7o ) 3 .6 6 (3 ~4 . N I " ~ y 3 . 4 8 ( 2) 4 . 0 5 ( 4) 3 .8 3t 4 4 . 0 7 ( 4 ) 3. 5 2 ( 4 )

5 . N HI ~ 4 .51(2) 4 .22 t4 4 .1 2( 4 ) 4 .66 o~ 4 .03 t4

Note. A va lue o f 4 ind ica tes equ iva len t du ra t ion ; va lues le ss than 4 ind i -ca te tha t the com par ison was judged shor te r . Nu mb ers in pa ren thesesind ica te ass igned coherence g roup o f F igure 7. H = h ie ra rch ica l ; NH =nonh ie ra rch ica l ; h = ha rm onic accents.

were tona l ly mean ingfu l to l i steners . With respec t to va r ia t ions on H

tunes , those wi th coup led tem pora l and h a rm onic accen ts tha t dev ia tedin tempo ra l regu la r i ty (NH~ay , N Hate) w ere ra ted the leas t we l l . t imed

(M = 6.22, M = 6.11, respectively) b ut only slightly less appro priate

to the m elody ' s key (M = 4 .09 ; M = 4 .02). A se t o f Tukey pos t hoe

comparisons confirmed that these ratings significantly differed from

those o f tb e H melody (p < .01 ) . The H- type melod ies , namely those

wi th regu la r ly recur r ing temp ora l accen ts bu t deeoup led ha rm onic ones

(NI- I~rly.h, NH]a~h) , d id indeed seem m ore w e l l t imed than the ~ y

and NHl , te tunes (M = 4 .85 , M = 4 .56). A s p red ic ted , the i r ha rm onic

accen t ing was deemed less appropr ia te (M = 6 .02 ; M = 6 .38). T hese

ra t ings d i f fe red signi fican tly f rom those o f bo th H and o the r NH melo -

dies (p < .01).

Overall , these results suggest that l is teners found H versions of folk-

t u n e e x c e r p t s t o h a v e ap p r o p r i a te h a r m o n i c a n d t e m p o r a l a e c e m u a -

t ions . These tunes conf i rm ex pec ta t ions tha t the co r rec t p i tch accen ts

coup led wi th tem pora l ones occur in the r igh t spots . B u t l i steners a l soc lea r ly d isce rn t accen t regu la r i ty o f H- type tunes . Dev ia t ions f rom

these regu la r i tie s resu l t in accen ts tha t a re pe rce ived as occur r ing re la -

tively early or late .

P r o c e d u r e

Subjec ts l i s tened over A K G (M ode l K240) headphon es to 150 ran -

dom ized pa i r s o f me lod ies (25 pa i r s fo r each o f th ree songs wi th one

repe t i t ion each), each pa i r s igna led by a l - s warn ing tone . Melod ies

wi th in each pa i r a lways spanned the same to ta l du ra t ion (10.3 s ).

Sub jec ts were asked to comp are the to ta l du ra t ions o f two melod ies

wi th in a pa i r (and to rem ove wa tches). They then hea rd a l l pa i r s o f me lo -

d ies and ind ica ted on a 7 -po in t sca le whe ther the second melody seem ed

longer than , shor te r than , o r the sam e dura t ion as the f i r s t - -ve ry short( 1 , very ong (7), same (4), the null response score.

R e s u l t s a n d D i s c u s s i o n

M e a n d u r a t i o n j u d g m e n t s f o r t h e 2 5 p a i r w i s e c o n d i ti o n s a r e

s h o w n i n T a b l e 1 . V a l u e s le s s t h a n 4 . 0 0 i n d i c a t e t h a t t h e s e c o n d

p a t t e r n o f a p a i r s e e m e d s h o r t e r ; v a l u e s g r e a t e r t h a n 4 . 0 0 i n d i -

c a t e t h a t i t s e e m e d l o ng e r .

B a s i c F i n d i n g s

D u r a t i o n j u d g m e n t s d i f f er e d s ig n i f ic a n t ly a s a f u n c t i o n o f in -

f o r m a t i o n f i ll i ng b o t h p e r i o d s, i n s p i t e o f th e f a c t t h a t n o d u r a -

t i o n a l d i f f e r e n c e s r e a l l y e x i s t e d . A v e r a g e a b s o l u t e d e v i a t i o n s



D Y N A M I C A T T E N D I N G

T a b l e 2

Predicted and Signed Bias Values (PSEi) ofFour Models

4 8 1

APSE ~ p r ed i c t i ons

A l t e r n a t iv e m o d e l s

N u l l C h u n k C h a n ge

M e l o d ic p a i r D M * P S Ei D M * P S Ei D M * P S Ei

C o n t r a s t m o d e l O b s e r v e d d a t a

AD~Mi D"Ei PSEi P S E i

G r o u p 1 : H i g h c o h e r e n c e

VVI = 0 W, = 0 VV, = 0

H - H 0 0 0 0 0 0

N - NHlate 0 0 + + + +H - NI - l ~ r l y 0 0 + + + +

H - NHl a t~- -h 0 0 + + + + + +

H - N H ~ y . , 0 0 + + + + + +

SD I

W ~ = . 8 9

0 0 0 .040 - 2 . 6 7 - . 7 2 - . 7 8

0 2 .67 .72 .780 - 1 . 3 3 - . 3 5 - . 4 90 2 .67 .72 .60

.204 .273

G r o u p 2 : M e d i u m c o h e r en c e

~¢~=0 fv~=0 ~v2=0

NH ~t~ - H 0 0 . . . .NI-Ic~y - H 0 0 . . . .

N H ~ h - H 0 0 . . . .N H ~ y . h - H 0 0 . . . .

S D 2

~V = .70

0 2.67 .56 .51

0 - 2 . 6 7 - . 5 6 - . 5 20 1.33 .28 .64

0 - 2 . 6 7 - . 5 6 - . 5 0

.334 .375

G r o u p 3 : M e d i u m c o h e re n c e

~V 3 = 0 W 3 = 0 W 3 = 0

N H t ~ h - N f t . a y 0 0 0 0 - -

NH|ate-h - NHcaay-h 0 0 0 0 0 0

NHla~h - - N H I ~ t e 0 0 0 0 - -

N H l a t ~ . n - N H l ~ h 0 0 0 0 0 0

N H ~ a r ly . h - N H e ~ y 0 0 0 0 - - - -

N H ~y .h - NH~aay.h 0 0 0 0 0 0

N I ' ~ r l y .h - NI'-Ilate 0 0 0 0 - -

NHl~t, - NH ear l y 0 0 0 0 0 0

S D 3

~ t 3 = . 4 0

0 4 .00 .48 .67

0 4.00 .48 .55

0 - 1 . 3 3 - . 1 6 - . 3 40 0 0 .020 0 0 .510 0 0 - .0 10 - 5 . 3 4 - . 6 4 - . 4 1

0 5 .34 .64 .66

.489 .334

G r o u p 4 : L o w c o h e re n c e

fv,=o ~v,=o fv,=o

NI -I ~ ,ty - N H ~ h 0 0 0 0 + +N I " l ~ , . h - N H a ~ h 0 0 0 0 0 0

N O l a t e - N H l a t e - h 0 0 0 0 + +

NHta~ - N Hat~ 0 0 0 0 0 0

NH ~ay - NH,~dy.h 0 0 0 0 + +NI"~ ,ty - NH,~.ty 0 0 0 0 0 0

NHi,tc - NH= dy.h 0 0 0 0 + +NH,.~y - NHh,~ 0 0 0 0 0 0

SD 4

' ~ 4 = .2 2

0 - 4 . 0 0 - . 2 6 - . 1 7

0 - 4 . 0 0 - . 2 6 - . 3 90 1.33 .08 .12

0 0 0 .03

0 0 0 .050 0 0 .070 5 .34 .35 .220 - 5 . 3 4 - . 3 5 - . 4 8

.422 .373

Note.H = h i e r a r c h i c a l; N H = n o n h i e r a r c h i c a l ; h = h a r m o n i c a c c e n ts .

f r o m a n u l l d i f f e r e n c e ( 4 . 0 ) t o o k o n a m a x i m u m v a l u e o f 0 . 7 8 ,

w h i c h r e p r e s e n t s a 2 2 % u n i d i r e c t i o n a l s h i f t o n t h e r a t i n g sc a l e.

O v e r a ll , t h e i n t e r a c t i o n o f t i m e s t r u c t u r e a s s o c i a t e d w i t h t h e

f ir s t a n d s e c o n d p a t t e r n s w a s s i g n i f i c a n t b e y o n d t h e . 0 0 0 1 l e ve l ,

F ( 1 6 , 2 2 4 ) = 1 3 . 6 7 , MSe = 0 . 0 8 8 .

T h e n a t u r e o f t h i s i n t e r a c t io n s u p p o r t s t h e C o n t r a s t M o d e l

p r e d i ct i o n s. P e o p le j u d g e d p a t t e r n s t h a t s e e m e d t o e n d " t o o

s o o n " t o b e s h o r t a n d t h o s e t h a t s e e m e d t o e n d " l a t e " t o b e

l o n g. P o s t h o c a n a l y s e s ( T u k e y ) v e r i f i e d t h e s e f i n d i n g s : (a ) T y p e

o f c o n t r a s t p r o d u c e d s i g n i f i c a n t d i f f e re n c e s ( p < . 01 ) b e t w e e n




pairs wi th ea r ly ve rsus la te end ings (e .g . , NI-I~a , NHla~) . (b )

M a g n i t u d e o f p a ir w i s e c o n t r a s t p r o d u c e d p r e d i c t e d d i f f er e n ce s

in th a t n e g l ig ibl e c o n t ra s t e f f e c ts a p p e a re d in p a i r s w i th e q u iv a -

l e n t s ing le p a t t e rn c o n t ra s t s ( e .g ., N I - ~ y w i th N I -~ ,~ y ) a n d in

p a i r s w i th n o c o n t ra s t s ( e. g. , H - H ) . P a i r s w i th n o n z e ro c o n -

t ras ts , however , y ie lded sys temat ic d i f fe rences . (c ) Pred ic ted

d i f f e ren c e s a s a fu n c t io n o f t e m p o ra l c o h e re n c e w e re s ig n i fi -c a n t , w i t h t e m p o r a l c o n t r a s t h a v i n g a g r e a t e r i m p a c t i n p a i r s

c o n ta in in g a n H m e lo d y (p < . 01 ). (d ) E f fec t s o f c o n t ra s t w e re

s ig n i f ic a n t ly l e ss fo r p a i r s c o n ta in in g a m e lo d y w i th d e c o u p le d

a c c e n t s (p < . 01 ) . ( e ) T e m p o ra l o rd e r e f f e c t s w e re s ig n i f i c a n t i n

t h a t a g iv e n c o n t r a s t h a d m o r e i m p a c t w h e n e v e r a n H ( p < . 0 1)

o r H - ty p e ( i. e. , N H h ) m e lo d y (p < . 0 5 ) fu n c t io n e d a s a s t a n d a rd .

( f ) O v e ra l l , t h e s e f in d in g s w e re ro b u s t i n g e n e ra l i z in g a c ro s s a l l

t h re e m e lo d ic in s t a n c e s (F = 1 .0 fo r m e lo d ic in s t a n c e ) a n d to

1 2 o f t h e 1 6 s u b je c t s i n v o lv e d (4 s u b je c ts t e n d e d to s h o w s t ro n g

c o n t ra s t e f f e c ts o n ly in H a n d n o t i n H - ty p e m e lo d ie s ) .

Model Predictions: Contrast Model Versus Alternatives

S e v e ra l s im p l i fy in g a s s u m p t io n s a re in t ro d u c e d to f a c i l i t a t e

p r e d i c ti o n s a b o u t j u d g m e n t m e a n s ( f r o m E q u a t i o n s 5 - 6 ) a n d

v a r i a n c e ( E q u a t io n 7 ) a s a f u n c t i o n o f c o n t r a s t a n d t e m p o r a l

c o h e re n c e .

1 . T o e v a lu a t e th e C o n t r a s t M o d e l , t h e l i ne a r f u n c t i o n f w i t h

s lo p e a a n d in t e rc e p t b = 4 ( th e n u l l r e s p o n s e ) r e l a t e s th e r e -

s p o n s e sc a le ( 1 - 7 ) t o b i a s p r e d ic t i o n s o f t h e m o d e l . F r o m E q u a -

t io n 6 :

P S E i = J D ; - 4 = a [W iD E i + (1 - W i )D M~ ] . (1 1 )

2 . T o ev a l u at e th e C o n t r a s t M o d e l , a t te n d i n g m o d e p a r a m e -

t e r s i n E q u a t io n 1 1 a re e s t im a te d u s in g E q u a t io n s 8 a n d 1 0 . T h e

D E ~ e s t im a te s (E q u a t io n 8 ) a re b a s e d o n th e a s s u m p t io n th a t

s k i ll e d a t t e n d e r s c a n u s e h ig h e r o rd e r fo c a l p e r io d s o f m u s ic a l

p h r a se s , a n a s s u m p t i o n s u p p o r t e d b y t h e r a t i n g ta s k d a t a r e -

p o r t e d i n t h e M e t h o d s e c ti o n . T h e D M i e s ti m a t e s ( E q u a t i o n 1 0)

a re b a s e d o n th e a s s u m p t io n th a t l i s te n e r s m a y a l t e rn a tiv e ly r e ly

o n th e r e fe re n t l e v e l a n d c o u n t b e a t p e r io d s . T h i s a s s u m p t io n

i s s u p p o r t e d n o t o n ly b y r e s e a rc h d e s c r ib e d e a r l i e r (B o l tz , 1 9 8 5 ;

a l s o F o o tn o te 1 5 ), b u t b y th e p re s e n t d a t a . T h a t i s , u n d e r th i s

s t r a t e g y , D Mj = 0 , a n d w e s h o w th a t a l t e rn a t iv e m o d e l s b a s e d

o n D M~ ~ 0 a re n o t a p p ro p r i a t e fo r t h e p re s e n t t a s k (T a b le 2 ).

H e re , D M~ i s w e ig h te d b y 1 - W i . T h i s y i e ld s th e m o s t c o n s e r -

v a t iv e t e s t o f th e c o n t r a s t m o d e l b y r e in fo rc in g th e t ru e (n u l l )

t im e d i f f e ren c e a n d fo rc in g c o n t ra s t a lo n e to b i a s ju d g m e n t s .

3 . E a c h o f t h e 2 5 m e l o d i c p a i rs w a s a ss i g n ed t o o n e o f f o u r

(k = 1 , 2 , 3 , 4 ) e x p e r im e n ta l ly d e s ig n a te d g ro u p s p re d ic t e d tod i f f e r i n t e m p o ra l c o h e re n c e , a s s h o w n in F ig u re 7 . P a i r s w e re

c a t e g o r iz e d a c c o r d i n g t o w h e t h e r t h e y c o n t a i n e d a n H o r H -

t y p e m e l o d y a n d w h e t h e r t hi s m e l o d y w a s t h e s t a n d a rd . T h u s ,

e v e n t p a i r s in G r o u p s 1 a n d 2 h a v e t h e s a m e a b s o l u te a m o u n t

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

(G ro u p 1 ) o r a s a c o m p a r i s o n (G ro u p 2 ) . S im i l a r ly , p a i r s i n

G r o u p s 3 a n d 4 i n v o l v e o n l y N H m e l o d i es , in w h i c h a n H - t y p e

p a t t e r n i s t h e s t a n d a r d ( G r o u p 3 ) o r c o m p a r i s o n ( G r o u p 4 ) .

I n t e r p r e ta t i o n s o f th i s p a r a m e t e r l e a d t o t h e e x p e c t a ti o n t h a t

W i > V¢2 > ~r3 > ~V4 for VCk- N ote tha t th is p a r t i t i on in g ha s

b e e n s im p l i f ie d a t t h e e x p e n s e o f i g n o r in g c o h e re n c e e f f e c t s d u e

t o m a r k e r p r o m i n e n c e . F o r e x am p l e , G r o u p 1 i n c lu d e s b o t h

H - N I - I , a y a n d H - N I - ~ r t y . h . I f m a r k e r p r o m i n e n c e i s, i n f a c t ,

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

f it s o f t h e C o n t ra s t M o d e l .

P r e d i c ti o n s o f t h e C o n t r a s t M o d e l a r e s u m m a r i z e d i n T a b l e s

2 a n d 3 . A p r io r i e s t im a te s o f D M~ a n d D E ~ a re in c o lu m n s 8

a n d 9 o f T a b le 2 , r e s pe c t iv ely ; t h e fo u r W k (a b o v e th e s e c o l -

u m n s ) a r e e s t i m a t e d f r o m t h e d a t a . P r e l i m i n a r y m o d e l f it s i n d i -

c a t e d t h a t t h e c o m m o n v a r i a n c e o f d i ff e r en c e s co r es , o~ , w a se x t re m e ly s m a l l , a n d s o i t w a s f ix e d a t z e ro . T h u s , f i ve p a ra m e -

t e r s w e re e s t im a te d f ro m th e d a ta : fo u r W k a n d a s c a l e f a c to r , a.

Mo d e l f it s, u s in g E q u a t io n 1 1 , w e re b a s e d o n a n o n l in e a r l e a s t

s q u a re s c u rv e - f i t t i n g t e c h n iq u e ( N O N L I N ) , w h i c h m i n i m i z e d e r-

ro r s b e tw e e n p re d ic t e d a n d o b s e rv e d s c o re s, t 7 B e s t - f it t i n g Wk

a re in T a b le 2 ; ~ w a s . 3 0 3 . T h i s v e r s io n o f t h e c o n t ra s t m o d e l

a c c o u n t s fo r 8 8 % o f th e v a r i a n c e (R 2 ).

A l s o in T a b le 2 a re p re d ic t e d a n d o b s e rv e d v a lu e s o f P S E~

(c o lu m n s 1 0 a n d 1 1 , r e s p e ct iv e ly ) a n d S ' D k (p o o le d fo r t h e k th

g r o u p ) f o r th e C o n t r a s t M o d e l , a l o n g w i t h p r e d i c t i o n s o f o t h e r

m o d e l s . I s P re d ic t io n s o f a l l m o d e l s d e r iv e f ro m E q u a t io n 6 .

H o w ev er , t h o s e o f t h e C o n t r a s t M o d e l a r e b a s e d o n n o n z e r o

e s t im a t e s o f W k (a n d l - W k ) , w h e re a s th o s e o f a U o t h e r m o d e l sa s s u m e W k = 0 . In t e rm s o f E q u a t io n 6 , w h e n Wk ----0 , e ffec ts

o f c o n t r a s t a r e e l i m i n a t e d a n d m e m o r y e f fe c ts a r e m a x i m a l

[ (1 - Wk ) = 1 .0 ] . T h e m e m o ry p a ra m e te r fo r a l t e rn at iv e m o d e l s

i s d e n o t e d D M * , b e c a u s e i t d if f er s c o n c e p tu a l l y f r o m D M ~ o f

t h e C o n t r a s t M o d e l a n d a l so b e c a u s e m o s t m o d e l s y i el d o n l y

o rd in a l a s s e s s m e n t s o f m e m o r y d i f fe re n c e s. T h e s e a re in c o l -

u m n s 2 , 4, a n d 6 . C o r r e s p o n d i n g d i r e c t i o n a l p r ed i c t i o ns o f b i a s

(g re a t e r o r le s s t h a n ) fo r a ll m e lo d ic p a i r s a re s h o w n in c o l u m n s

3 , 5, a n d 7 fo r t h e N u l l , C h u n k , a n d C h a n g e Mo d e l s , r e s p e c -

tively.

A s u m m a r y o f d ir e c t io n a l ( + , - ) p r e d i c t i o n a c c u r a c y o v er

th e fo u r m o d e l s (o f T a b le 2 ) a p p e a r s in T a b le 3 . T h e s e in d ic a t e

th a t t h e C o n t ra s t M o d e l f a re s b e s t , p re d ic t in g 2 4 o f h e 2 5 p o s s i -

b l e d i r e c t io n a l d i f f e re n c e s in t im e ju d g m e n t s . T h e C h a n g e

M o d e l i s n e x t w i th l I o f t h e P SE ~ s in th e c o r re c t d i r e c t io n . In

o th e r r e s p e c t s , t h e C o n t ra s t Mo d e l a l s o p ro v e s su p e r io r . I t c o r -

r e ~ l y p r e d i c ts ( a ) h i g h es t t e m p o r a l c o h e r e n c e f o r G r o u p l

(Wi = . 8 4 ) a n d lo w e s t c o h e re n c e fo r G ro u p 4 (W4 = . 22 ), (b )

m a x i m a l t e m p o r a l c o n t r a s t e ff e ct s w i t h l e a s t t e m p o r a l u n c e r -

t a in ty , n a m e ly in G ro u p 1 , ( c ) g re a t e r c o n t ra s t e f f e c ts fo r a h i e r -

a r c h i c a l o r H - t y p e s t a n d a r d ( G r o u p s I a n d 3 ) t h a n w i t h a n N H

s t a n d a r d ( G r o u p s 2 a n d 4 ) b e c a u s e W t > W 2 a n d W 3 > W 4 ,

a n d (d ) l e a s t v a r i a b i l it y in G ro u p 1 in w h ic h " ~/~ i s h ig h e s t .

T h e C o n t r a s t M o d e l y i e ld s a p r of i l e t h a t i s m o r e a c c u r a t e a n d

in fo rm a t iv e th a n a l t e rn a t iv e s . H o w e v e r , i t d o e s n o t a c c o m m o -

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

equa l ly we l l , and i ts fa i lu res a re ins t ruc t ive . I t desc r ibes pe rfo r-m a n c e b e t t e r i n m e l o d i c p a i rs t h a t h a v e c le a r ly m a r k e d f o c a l

t im e p e r io d s ( i .e ., i n p a i r s w i th c o u p le d a c c e n t s ) . In f a c t , w h e n

s ig n i f i ca n t m o d e l d e v ia t io n s d o o c c u r , i t is i n m e lo d ie s w i th de-

coupled a c c e n t s . T h e s e p a t t e rn s p re s e n t l e s s o b v io u s v io l a t io n s

17 NONLIN Ohio State S cience Package) operates on a least squares

algorithm developed by M arquardt (1963), which is basically an inter-polation between N ewton-Raphson and gradient m ethods.

,8 The PSE i predictions o f he Contrast M odel (column 10) are basedon Equation 11 and variance predictions on Equation 7 (with ~ = .303).Th e D~Mi and D"Et calculations (Tab le 2, columns 9, 8) axe based o nEquations 10 and 8 , respectively. See text f or DM, calculations of Null,Chunk, and Change Models.



DYNAMIC ATTENDING

F O U R C O H E R E N C E G R O U PS

H-type Melody

Standard Comparison

483

Simple

H Me lody

P r e s e n c e

/

\A b s e n c e .

G R O U P I

I = H i g h R h y t h m i c C o h e r e n c e

H - N H

GROUP 5

:5 = M e d i u m Rhythmic Coherence

NHh-NH

GROUP 2

2 = M e d i u m Rhythmic Coherence

NH-H

G R O U P 4

4 = L o w R h y t h m i c C o h e r e n c e

N H - N H h

Figure 7.Four coherence groups of he 25 pairs of melodies used in Experiment 1: Groups 1, 2, 3, and 4.

of expectancies, and so this is not surprising. Although better

model fits can be obtained with additional Wk estimates, effects

of accentuation are nevertheless clear. We consider this applica-

tion o f the Contrast Model to be largely illustrative and take

these discrepancies to underscore the broader theoretical point

that the way in which nontemporal information marks time lev-

els is important.

Experiment 2: Productions of Melodic Durations

A second study was designed to confirm that people actuallyexpect patterns to end at particular times. Converging evidence

for the psychological reality o f expectancies is provided by a

product ion task. A new group oflisteners heard the same melo-

dies, without the final three tones, and produced probable end-

ing times with a button press. Thus, pure expectancies were

made overt via extrapolated productions of the final focal pe-

riod.

Some songs, such as NHeady, should encourage anticipations

for early endings by virtue o f their shorter focal time periods.

A~cording to Equation 2, these melodies should lead to shorter

final production times. Other songs, such as NH~te, should gen-

erate expectancies about late endings and thus yield longer re-

sponse times to completion. These predictions derive not fromthe Contrast Model, but from Equation 2 for timed produc-

tions.Of interest is the reciprocity between produced time and

Table 3

Summary of PSEi Predictions or Four Duration Models

Alternative modelsNo. of Contrast

predictions NuH Chunk Change Model

Total correct 6 10 11 24Total possible 25 25 25 25

judged time. This involves the prediction that the pattern of

produced times will be opposite to the pattern of udged times

predicted (and observed) by the Contrast Model. In Exper iment

1, for example, NH~tc patterns were predicted to be judged

shorter than others, and they were. Here, the claim is i f those

duration judgments were based on temporal contrasts involv-

in_g expectancies, then people will expect these same patterns

to last relatively longer and this expectation will be evident in

production. The converse, of course, should be true for NHe~y

melodies.

Finally, the three alternative models do not predict a recipro-

cal pattern of results because none incorporates expectancies.

Indeed, memory models taken literally are no t particularly con-

ducive to extrapolated times because time estimates are based

on previously stored information. However, assuming that pro-

ductions for a melody are governed by its code complexity, al-

ternative models all imply that the pat tern o f produced times

will be similar to judged times for the various H and NH tunes.

Thus, either no differences in produced times should arise (Null

Model) or NH melodies should yield longer produced times

(Chunk and Change Models).

MethodDesign

A 5 × 3 × 2 mixed factorial nvolvedcrossing he five ypes ofaccent/timing patterns (H, NI-I~y, NH,.~, NI-I~y.h, NHa~.h) with threedifferent songs (used in Experiment 1). Two counterbalance ordersformed the single between-subjects factor, 9 subjects, each with at least4 years of recent musical experience, were assigned o each counterbal-ance order.

Stimulus Materials

Stimulus materials were identical to those of Experiment 1, except

that the final three tones were omitted from each melody. Three ran-



4 8 4 M A R l R IE S S J O NE S A N D M A R I L Y N B O L TZ

T a b l e 4Results of Extrapolation Study (Experiment 2)

Condi t ions of melodic t ime s t ruc ture

Me asure H N I- ~ ly NHearly.h NHlat~ NHlate./~

Mdn ext rapola t ion ime(in ms) 1154 899 1173 1209 1305

Mdn accuracy score( in ms ) - 4 6 - 301 - 27 + 309 + 105

M no . of judged miss ingbea ts 2.67 1.59 2.56 3.11 3.24

Note.Entrie s in each row reflect , respectively, one o f three dependent measures use d in E xperim ent 2 toindicate expectancies abo ut m usical endings for five melo dic conditions. Median extrapo lation t ime formissing notes (row 1) and its accuracy (row 2; negative sign indicates anticipation) are given along with themean num ber of beats judge d missing (row 3). H = hierarchical; N H = nonhierarchical; h = harm onicaccents.

dom ized blocks, each with 15 melodies, occu rred within two counter-

balance orders.

Procedure

Subjects perfo rmed two tasks. The first involved extrapolations; the

second requi red udgments of the num ber of miss ing notes.Production. Recorded instru ctions told subjects to (a) l isten to in-

complete melodies whose final (1 to 5) notes, including the closingtonic, were missing, and (b) indicate when a m elody should end if miss-in_gnotes were played in real t ime. Fou r practice tr ials clarified he p ro-

cedure.On each trial , a 1-s warning tone (5000 hz) preced ed a melod y by

2 s. When the last note o f a melod y was signaled by a pane l l ight, sub-jec ts cover tly cont inued the tun e and indica ted i ts t rue ending t ime b y

a butto n press. This extinguished the signal l ight, and the n ext tr ial be-

gan. This phase lasted 40 m in.Judgments of missing tones. Recorded in structions told subjects to

judge, in writ ing, how ma ny n otes were missing from ea ch melody. Sub-jects then heard the same 15 experim ental melodies, now randomized

according to one o f two schedules. On each o f 15 trials, a 5000-hz w arn-ing tone preceded the m elody by 2 s; after the melody, subjects had 5 s

to respond.

Results and Discussion

T a b l e 4 p r e s e n t s t h e r e s u l t s i n w h i c h a v e r a g e s a r e b a s e d o n

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

b o t h o f w h i c h a g a i n p r o d u c e d n e g l i g i b le e f fe c ts ( F < 1 .0 0 ).

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

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

a r e i n t h e f i rs t ro w o f T a b l e 4 . M e a n d i f f e re n c e s w e r e s i g n i f i ca n t ,

F ( 4 , 64 ) = 7 . 48 , MSe = 5 4 , 724 . 97 , p < . 0001 , a n d r e f l e c t e xpe c -

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

p r e d i c t e d t o g e n e r a t e e x p e c t a n c i e s f o r l a t e e n d i n g s ( N H l a t e ,

NHl at e- h) , a nd t he s ho r t e s t t i me s oc c u r r e d f o r NI- Ie ar ly une s . A l -

t hou gh NHl at e wa s s i gn i f i c a n t l y l onge r t ha n NH~a rl y ( p < . 01 ,

Schef l~) , th is w as n ot t ru e of NHl~te-h versu s NI-I~r~y.h . 10 < p <

. 0 5) , a l th o u g h d i f f e re n c e s h e r e w e r e i n t h e p r e d i c t e d d i r e c t i o n .

A c c u r a c y s c o r es ( in m s ) a p p e a r i n t h e s e c o n d r o w o f T a b l e 4 a n d

r e fl e ct t e m p o r a l d i s c r e p a n c i e s b e t w e e n p r o d u c e d a n d o b s e r v e d

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

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

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

p l e d s t r u c t u r a l a c c e n t s , N H ~ r ~ y v e r s u s N H l a te , y i e l d g r e a t e rd i f f e r en c e s t h a n o n e s w i t h l e s s p r o m i n e n t ( i .e . , d e c o u p l e d a c -

c e n t s ) ma r k i ngs , NHe a dy - h ver sus NHlate-h. P e o p l e a r e r e l a t iv e l y

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

t h e y a r e a l s o a c c u r a t e w i t h N I ~ a y _ h m e l o d i e s . O n e r e a s o n f o r

t h i s m a y b e t h a t i n t h o s e N H m e l o d i e s w i t h d e c o u p l e d a c c e n ts ,

t e m p o r a l a c c e n t u a t i o n r e m a i n s h i e r a rc h i c a l. I f p e o p le i g n o r e

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

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

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

F i n a l l y , t h e a v e r a g e n u m b e r o f m i s s i n g b e a t s r e p o r t e d b y l i s -

t e n e r s ( r o w 3 , T a b l e 4) c o n v e r g e s w i t h t i m e m e a s u r e s . I n a l l i m -

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

p r o f i l e d if f e r e n c e s e x i s t a n d t h e s e g e n e r a l i z e a c r o s s t h e m a j o r i t yo f s u b j e c t s u s e d i n t h i s s t u dy .

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

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

a t e e x p e c t a n c i e s a b o u t m u s i c a l en d i n g s . M o r e r e c e n t w o r k r e l y -

i n g o n d if f e r e n t m e l o d i e s a n d t a s k r e q u i r e m e n t s c o n f i r m s th e s e

r e s u l t s ( Va n Vr e de n , B o l t z , & J one s , 1989 ) . Toge the r , s uc h f i nd -

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

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

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

j u d g m e n t s ( E x p e r i m e n t 1 ), s u p p o r t s t h e i d e a t h a t t e m p o r a l

c o n t r a s t i s b a s e d o n l i s t e n e r s ' e x t r a p o l a t i o n s ( t e m p o r a l e x p e c -

t a nc i e s ) .

General Discussion

T o g e th e r, E x p e r i m e n t s 1 a n d 2 s u g g e s t t h a t d u r a t i o n j u d g -

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

m o n a c t i v i t y . R e l a t e d c o n c l u s i o n s h a v e b e e n d r a w n b y o t h e r s

u s i n g d i f f e re n t s t i m u l u s m a t e r i a l s ( K e e l e , P o k o r n y , C o r c o s , &

I v r y , 1 9 8 5; K r i s t o f f e r s o n , 1 9 8 4 ). O u r e x p l a n a t i o n c e n t e r s o n t h e

r o l e o f e x p e c t a n c i e s i n e x t r a p o l a t i o n s a n d i n s e l e c ti v e a t t u n e -

m e n t s i n d u r a t i o n j u d g m e n t s . E q u a t i o n 2 , w h i c h d e s c r ib e s ex -

t r a p o l a ti o n s , a n d E q u a t i o n s 5 - 6 , w h i c h d e s c r i b e j u d g m e n t s , t o -

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

t h e t w o t a s k s .

A p r i m a r y a i m o f E x p e r i m e n t s 1 a n d 2 w a s t o a p p r o x i m a t e

a n a t u r a l c o n t e x t i n w h i c h f u t u r e - o r i e n t e d a t te n d i n g w o u l d a p -



DYNAMIC ATTENDING 485

pear. Folk tunes, particularly coherent ones, fit the stimulus re-

quirements. Reliance on moderately skilled musical listeners

further ensured a possibility of future-oriented attending and

simplified estimation of DE~. Although both constraints limit

experimental generality, they succeeded in demonstrating the

existence of future-or iented attending. These findings suggest

that when skilled attenders interact with relatively coherenttime patterns, temporal expectancies will arise and durat ion

judgments can be biased by temporal contrast. Related influ-

ences of temporal contrast have been reported in other contexts

as well (Kidd, in press; Kristofferson, 1977; Lehiste, 1975,

1977).

The present results are difficult to explain in terms of con-

temporary models that emphasize memory for accumulated

amounts of nontemporal information. For example, in Experi-

ment 1 the Null Model predicts that all melodies should be

judged equal in duration because the number of tones and pitch

changes are identical. And yet some were judged longer (i.e.,

NH~,ly, NH~rly-h) and others shorter (i.e., NHt~t~, NHlate-h).

Differences in number of chunks or in changing accent patterns

(Chunk, Change Models) also cannot account for these effects.

Although melodies o f a pair can differ in relative timing of cer-

tain accents, even models addressed to rhythmic chunking have

difficulties because they fail to acknowledge that accent patterns

incite dynamic and preparatory attending.

The Contras t Model weights the influence of contrast so that

over- or underestimates of durations due to contrast are most

evident in coherent events in which future-oriented attending

occurs more often. I t turns out that in event pairs with low tem-

poral coherence (e.g., some NH-NH pairs), estimates of tempo-

ral contras t could be quite high. Yet, according to this model,

these DE`. values should not have proportional impact on judg-

ments, and they do not. According to the Contrast Model, ex-

pectancies are less likely and analytic attending with beat-counting strategies are more likely in judging these tunes. As a

result, tendencies to correctly judge two events as identical in

total duration are reinforced. Of course, in other cases, if events

differ in number of beat periods, then tendencies to over- or

underestimate duration will emerge (see Boltz, 1985). Thus,

both attending modes may have been used in the present stud-

ies, a possibility supported by the fact that greater variability

also appears in judgments involving pairs with moderate to low

coherence.

Finally, although the overall emphasis here has been on DE~,

in principle the DM~ parameter lends itself to several interpre-

tations. As with DE,-, this parameter can reflect the way some-

one uses time at any of several different levels (e.g., chunks orgroups of beats). That is, people will not always rely on beat

count ing; they may analytically attend over other levels, levels

that correspond to things other than beats. Part 1 indicates that

amount of information (defined in various ways) does seem to

bias time judgments in certain contexts. The present study and

the Contrast Model suggest some reasons for these seemingly

conflicting findings on the filled duration effect: The way infor-

mation fills an interval to mark different time levels and the way

a person attends to this information can affect time estimates.

In short, memory-oriented approaches to duration judgment

must be supplemented, and the Contrast Model illustrates one

way to do this. It incorporates some version of a memory-based

model through the concept of analytic attending. It does so by

expressing the idea that effortful memory activities and expec-

tancies are stimulated by different contexts, ones at opposite

ends of the structural coherence continuum.

S u m m a r y o f P a rt 4

A reciprocal pattern of findings emerged from two experi-ments involving comparative duration judgments (Experiment

1) and timed productions (Experiment 2) in which attending

mode and temporal coherence were varied. Experiment 1 find-

ings support the Contrast Model's proposition that duration

judgments are a funct ion of weighting attending mode parame-

ters (temporal contrast, mnemonic differences) by degree of co-

herence. Experiment 2 findings suggest that contrast itself de-

pends on temporal expectancies about musical endings.

Part 5: Conclusions

In this article we derived illustrative models of time judgment

and production from a general theoretical framework in whichboth attending mode and event coherence figure. These models

have some potential for explaining ways in which rhythmical

attenders who use relative time nonetheless estimate intervals

of time in different tasks. They also address divergent findings

surrounding the filled interval effect. In Part 5, we conclude

with general observations about the theoretical framework that

relate to issues of generality, biological bases of attending, and

philosophical views of time.

Theore t ical General ity." I s a Rh yth m ic

Approach Warranted?

The assumption of inherent rhythmicity in both the environ-ment and the attender is a basic one. Because its claim to gener-

ality can be questioned, let us be clear about what it does and

does not mean. It means that temporal patterning exists in envi-

ronmental energy patterns and in the structure of attending over

time. It does not mean that these patternings are immediately

obvious, necessarily simple, or rigidly fixed. Indeed, the main

point of our earlier discussion of environmental structure was

to illustrate that formalization of time s tructure is a challenging

goal, one demanding careful identification of functional time

markers, marker couplings/strength, and various time transfor-

mations. The very success of another, quite different approach

to rhythmicity, fourier analysis, should discourage ideas that in-

herent periodicities of events and attending activities can be su-perficially discerned.

At the level of the Contrast Model, the relative impac t of sim-

pie and complex rhythmicities is expressed through attentional

weights that assume a continuum of dynamic environmental

complexity. It posits conditions in which evidence of simple

rhythmicities will appear, and clearly these are not ubiquitous.

Temporally incoherent events do exist. Our claim is simply that

ready attunements to such complex events will fail in particular

and sometimes meaningful (e.g., contrast) ways, given the na-

ture of rhythmic attending. In this sense, the approach has

greater generality than those time estimation models cited in

Part 1 that focus largely on events with low temporal coherence.

Interestingly, it achieves this by reconceiving the elusive con-




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

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

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

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

th i s m ig h t o c c u r h a s b e e n i l l u s tr a t e d in P a r t s 3 a n d 4 u s in g m u -

s i ca l e v en t s . P e rh a p s th e C o n t ra s t M o d e l w i l l n o t g e n e ra l i z e to

c o m p a ra b le , n o n m u s ic a l s i t u a t io n s in v o lv in g s k il l e d a t t e n d e r s.A l th o u g h th i s r e s t r i c t io n r e m a in s a p o s s ib i l i t y , w e th in k s o m e

fo rm a l i z a t io n o f c o n s t ru c t s s u c h a s ex p e c ta n c y , c o n t ra s t , a n d

a n a ly t i c a t t e n d in g w i l l b e u s e fu l fo r fu tu re m o d e l s . U l t im a te ly ,

t h e v a l u e o f a f u n d a m e n t a l a s s u m p t i o n i s f o u n d i n i t s p o t e n -

t i a l fo r s t im u la t in g e x p la n a t io n s o f d iv e r s e p sy c h o lo g ic a l

p h e n o m e n a .

Biological Clocks Versus a Rh yth m ic

Attending Perspect ive

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

w h e n c o n s id e re d w i th r e s p e c t t o th e a t t e nd e r , im p ly a b io lo g ic a l

f o u n d a t i o n f o r a t t u n e m e n t s . T h e b i a s t o w a r d a b i o l o g ic a l u n -

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

fo r t h e in h e re n t rh y t h m ic i ty o f a n im a te b e in g s (e .g ., K e l s o e t

al., 1985).

W i th r e g a rd to th e o r i e s o f t im e e s t im a t io n , h o w ev e r, b io lo g i -

c a l ly b a s e d th e o r i e s h a v e b e c o m e u n fa s h io n a b le . O rn s t e in

(1 9 6 9 ) w a s m o s t e x p l i c it i n p o in t in g to l im i t a t io n s o f b io lo g ic a l

c h r o no m e t e rs : " A l th o u g h p s y c h o l o g i s t s . . , h a ve a tt e m p t e d t o

s t u d y t im e e x p e r i en c e t h e r e h a s b e e n a m a z e o f p o s t u la t e d p o s -

s ib le m e c h a n i sm s p r o p o se d f o r t i m e. O n e m a j o r r e a s o n . . . [i s

t h a t ] . . , t i m e h a s b e e n t r e at e d a s . . . s e n so r y p r o c es s " ( p. 3 4) .

O rn s t e in (1 9 6 9 ) c o r re c t ly c r i t i c i z e d e a r l i e r a p p ro a c h e s fo r

th e i r d i s a g re e m e n t o n a s p e c i f i c t im e b a s e . H o w e ve r, h i s a l t e rn a -

t ive s to ra g e s i z e h y p o th e s i s r e s t s o n e q u a l ly c o n fu s in g g u id e l in es

c o n c e r n i n g c o m p l e x it y , o n e s t h a t d o n o t r e l ia b l y p r e d i c t t i m eju d g m e n t s . N e v e r th e le ss , b e c a u s e o u r a p p r o a c h e n v i s io n s a b io -

lo g ic a l b a s i s, i t i s u s e fu l t o d i s t in g u i s h th e w a y t im e i s c o n c e iv e d

h e re f ro m th e w a y i t is v i e w e d in m o d e l s o f a s t r i c t b io lo g ic a l

c lo c k .

S t r i c t ly s p e a k in g , a c lo c k i s a t im e k e e p e r th a t a b s t r a c t s a n

a b s o lu te in t e rv a l f ro m th e t im e d im e n s io n to s e rv e a s a f ix e d

in te rv a l t im e b a s e . I ts a p p e a l i n t im e e s t im a t io n o f t e n in v o lv e s

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

th a t t h e in t e rv a l t im e b a s e s h o r t e n s o r l e n g th e n s w i th , fo r e x a m -

p le , d ru g s o r b o re d o m . N e v e r th e le s s, a s a b io lo g ic a l m e t r i c t h e

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

s t ru c tu re o f p a r t i c u la r e v e n t s b e c a u s e th e c lo c k in t e rv a l i n d i s -

c r i m i n a t e l y m e a s u r e s b o t h a r b i t r a r y a n d n o n a r b i t r a r y t i m e p e -r io d s . F o r e x a m p le , a 5 - ra in in t e rv a l i s a rb i t r a ry w h e n d e f in e d

o n l y b y c l oc k n u m b e r s , b u t n o t w h e n i t c o i n c i d e s w i t h t h e b e -

g i n n i n g a n d e n d o f a b i r d ' s s o n g a c h i l d ' s g a m e , o r a c o n v e r sa -

t io n . Y e t s u c h d i s tin c t io n s a re i r r e l e v a n t fo r a c lo c k m o d e l t h a t

e x c lu siv e ly c o u n t s e l a p s e d t im e . F u r th e rm o re , t h e c h o ic e o f a

s in g le t im e in t e rv a l a s a c lo c k i t s e l f i s a p ro b le m , a s O rn s t e in

(1 9 6 9 ) n o te d . F o r a c lo c k m o d e l t o b e s e n s i t i v e to n e s t e d t im e

p e r io d s , t h e re m u s t b e p o s tu l a t e s r e fe r r in g to c lo c k s w i th in

c lo c k s , a s w e l l a s a m a s te r c lo c k th a t s o m e h o w c o n t ro l s a n d

m o n i to r s t h e i r i n t e ra c t io n s . F in a l ly , e a c h c lo c k m u s t b e in t e l l i-

g e n t : i t m u s t " k n o w " h o w to id e n t i fy i t s s a l i e n t m a rk e r s , t h o s e

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

u l a r i n t e rv a ls . M o s t p s y c h o lo g ic a l v er s io n s o f c lo c k m o d e l s b e -

g in a s s im p le o n e s th a t d o n o t d i r e c t ly r e f l e c t e i th e r r e la t iv e t im e

(e. g. , t im e r a t io s , t im e c o n t ra s t s ) o r s t ru c tu ra l m a rk in g s . C o n s e -

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

e x p la n a t io n s o f s p e c ia l g o a l -d i r e c t e d t e m p o ra l s e n s i ti v i ti e s a re

re q u i re d . F o r e x a m p le , t h e ro l e s o f e x p e c ta n c y v io l a t io n s a n d

te m p o ra l c o n t ra s t a s w e l l a s t h o s e o f f le x ib le a n d /o r e f fo r t fu l

a t t e n d in g r e m a in d i f f i c u l t t o in c o rp o ra t e in to c lo c k m o d e l s . In -s t e a d , c lo c k m o d e l s e n c o u ra g e a s e a rc h fo r a c e n t r a l t im in g

m e c h a n i s m ( m a s t e r c lo c k ) t h a t m o n i t o r s a b s o lu t e i n t e rv a l s a n d

fo r p s y c h o lo g ic a l t im e l im i t s t h a t a re in t e rv a l i n n a tu re . T h e s e

a re d u b io u s u n d e r t a k in g s in l i g h t o f c u r re n t d a t a ( e. g. , Jo n e s ,

1 9 7 6 ; K o le r s & B rew s te r, 1 9 8 5 ; v a n N o o rd e n , 1 9 7 1 ) a n d th e

a r g u m e n t s s u p p l i ed h e r e o n t h e r e l at i o n al n a t u r e o f t im i n g a n d

te m p o ra l l im i t s (e .g ., d o m in a n c e r e g io n ; s e e F o o tn o te 1 2 ).

In o u r v i e w , th e b io lo g ic a l b a s i s fo r r e s p o n s e s to e v e n t t im e

t a k es t h e f o r m o f a t t u n e m e n t r h y t h m s t h a t s e le c ti v el y e n t r a in ,

th a t s h i f t o v e r n e s t e d l e ve ls , a n d e v e n tu a l ly a re s h a p e d b y th e

e v e n t i ts el f. A t t e n d in g i s b a s e d d i r e c t ly o n r e l a tiv e t im e , a n d th i s

r e s u l t s i n t e m p o ra l f l e x ib il i ty in w h ic h n e i th e r t h e r e fe re n t t im e

b a s e n o r fo c a l a t t e n d in g l e v el s a re r ig id ly f ix e d . T h u s , v a r io u s

a ro u s a l e f f e c ts c a n a l s o b e a d d re s s e d w i th in th i s t h e o ry v i a r e fe r -

e n t l ev e l s h if ts . B u t t h e m a j o r a d v a n t a g e o f h e c u r r e n t a p p r o a c h

o v e r s t r i c t c lo c k m o d e l s i s fo u n d in i t s p re d ic t io n s c o n c e rn in g

fo c a l a t t e n d in g s r e l a t iv e to s o m e re fe re n t l e ve l. F o r in s t a n c e , e x -

p e c ta n c ie s a n d t e m p o ra l c o n t ra s t d e r iv e d i r e c t ly f ro m a n a ly s e s

o f d y n a m i c i n t e r a c t i o n s o f a n a t t e n d e r w i t h p a t t er n i n g s o f e n v i -

ro n m e n ta l s t ru c tu re . In e f fe c t, t h e s t ru c tu re o f a t e m p o ra l l y c o -

h e re n t e v e n t c a n fu n c t io n a s a n a tu ra l t im e k e e p e r fo r th e a t -

t e n de r . In s t e a d o f a c lo c k - t im e d w o r ld , t h e a t t e n d e r r e s p o n d s to

a d y n a m i c e v e n t - t im e d w o r l d i n w h i c h t i m e j u d g m e n t s d e p e n d

o n a n e v e n t ' s c h a r a c te r i s ti c t i m i n g a n d o n h o w i t s s t r u c t u r e c o n -

f i rm s o r d i s c o n f i rm s s o m e e x p e c te d c o u r s e . O f c o u r s e , t h is s o r t

o f a t t e n d in g i s le s s li k e ly w i th in c o h e re n t e v e n ts . In th i s c a s e

p e o p l e m a y r e s o r t t o a n a l y t i c a t te n d i n g o r a n e v e n m o r e p r a c t i-c a l s t ra t e g y : T h e y m a y c h e c k th e i r w a tc h e s . In f a c t , w e p re d ic t

th a t p e o p le w i l l r e fe r t o e x te rn a l t im e k e e p e r s m o re f r e q u e n t ly

in r e l a tiv e ly u n s t ru c tu re d s i tu a t io n s .

In p ro p o s in g th a t d y n a m ic e v e n t s a f fo rd d i f f e re n t , b io lo g i -

c a l ly b a s e d a t t e n t io n a l p e r s p e c tiv e s ( e. g. , fu tu re -o r i e n te d v s . a n -

a ly t ic ) , w e a l so r a i s e o th e r i s s u e s w i th r e g a rd to a t t e n d in g . O u r

e x p e r i m e n t a l f o c u s h a s b e e n o n t i m e e s t i m a t io n , b u t t h e c o n -

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

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

c e rn e d w i th a t t e n d in g o v e r t im e . A s a c o n s e q u e n c e , t h is a p -

p ro a c h h a s g re a t e r a p p l i c a b i l i t y to p a t t e rn s o f s p e e ch , m u s ic ,

d a n c e , a n d s o o n , i n w h i c h t h e c o n c e p t o f a t t u n e m e n t l ev el s

m a y b e f ru i t fu l ( Jo n e s , 1 9 86 ). I t i n t r o d u c e s th e p o s s ib i l it y th a tp e o p le r e ly d i r e c t ly o n e v e n t s t ru c tu re to a c h ie v e d i f f ere n t t e m -

p o ra l p e r s p e c tiv e s fo r d i f f e re n t g o a l s. T h e s e p e r s p e c tiv e s c a n r e -

s u l t i n d i f f e re n t e s t im a te s o f re l a t iv e d u ra t io n in t im e e s t im a -

t i o n . D y n a m i c c o m p l e x i t y e n t e r s i n t o q u a l i f y h o w o n e u s e s

e v e n t s t ru c tu re t o a c h ie v e th e r e q u i s i t e p e rs p e c tiv e . B u t i n o th e r

s i tu a t io n s a n d g o a l s , a t t e n d in g p e r s p e c t iv e s a n d c o m p le x i ty m a y

y ie ld a l t e rn a t iv e m o d e l s . F u r th e rm o re , b y l i n k in g d i f f e re n t a t -

t e n t io n a l p e r s p e c t iv e s to d i s t in c t iv e t im e l e v e l s w i th in e a c h

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

t ro u b le s c e r t a in a t t e n t io n a l t h e o r i e s ( s e e J o h n s to n & D a rk ,

1 9 86 ) . F in a l ly th e n , t h i s a p p ro a c h in c o r p o ra t e s r e s p o n s iv e n e s s

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

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




m a t i o n t h a t w e r e m e n t i o n e d i n P a r t 1 . I n s u m , t h e c o n s t r u c t o f

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

m a t i o n c a n s e l e c t iv e l y c o n t r o l a t t e n d i n g i n t i m e a n d a l s o a ff o r d

p o t e n t i a l r e f e r e n t l e v e ls f r o m w h i c h o t h e r a s p e c t s o f t h e e n v i -

r o n m e n t c a n b e a t t e n d ed .

S o m e P h i l o s o p h ic a l I m p l i c a t io n s

F i n a ll y , so m e o f o u r d i s t in c t i o n s i n e v i ta b l y i n v i te c o m p a r i s o n

w i t h B e r g s o n ' s ( 1 9 4 4 , 1 9 5 0 ) n o t i o n o f " l i v e d " t i m e v e r s u s

" m e a s u r e d " t i m e . I n r e a c t i n g t o K a n t ' s ( 1 90 0 ) c l a i m t h a t t i m e

i s a n i n t e r n a l i n t u i t i o n t h a t a l l o w s s e p a r a t i o n s o f o b j e c t r e p r e -

s e n t a t i o n s o n a n i n f i n i t e t i m e l i n e ( i. e ., " i n r e l a t i o n s o f t i m e " ;

K a n t , 1 9 0 0, p p . 2 8 - 3 1 ) , B e r g s o n ( 1 95 0 ) a r g u e d t h a t

Ka nt ' s grea t mis take was to v iew t ime as a homogeneous m edium.He did no t not ice tha t rea l dura t ion i s made up of mom ents ins ideone another, and tha t when i t seems to assume the form of a hom o-geneous whole, i t is because i t gets expressed in space. (p. 232)

F o r B e r g s o n, n o n h o m o g e n e i t y c h a r a c t e r iz e s e x p e r i e n c e d t i m eb e c a u s e t h i n g s e x p e r i e n c e d f i r st a l w a y s a f f e ct ( i n t e r p e n e t r a t e )

t h i n g s e x p e r i e n c e d s u b s e q u e n t l y i n t i m e ; t h i s i r r e v e r s i b i l i ty d e -

s c r i b e s t i m e i n t e r v a l s a s w e l iv e t h r o u g h t h e m . I t i s n o t c a p t u r e d

b y t h e e x p r e s s i o n o f a t i m e l i n e ( J o n e s , 1 9 8 7 b ).

C l e a r ly , o u r c o n c e p t s o f t e m p o r a l n e s t in g , a t t u n e m e n t s , e x -

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

t i m e . B u t B e r g s o n a n d K a n t p r e s e n t e s s e n t i a ll y p h e n o m e n o l o g i -

c a l a p p r o a c h e s i n t h a t b o t h a s s u m e t h a t o n l y p r iv a t e ly e x p er i -

e n c e d t i m e i s r e a l , b e c a u s e t h e t i m e o f e x t e r n a l o b j e c t s is c o n -

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

t e r v a l i n c h a r a c t e r , a n d o p e r a t e s i n a n a b s o l u t e f a s h i o n ( s ee , e .g . ,

B e r g s o n ' s , 1 9 6 5 , r e p l y t o E i n s t e i n ) . B y c o n t r a s t , o u r s i s n o t a

p h e n o m e n o l o g i c a l a c c o u n t . N o r d o w e c o n c e iv e o f t i m e i n t e r -v a ls in a b s o l u t e t e rm s . W e a s s u m e t h a t b o t h t h e e n v i r o n m e n t

a n d i t s o rg a n i s m s e x h i b i t t e m p o r a l p a t t e r n in g s t h a t a r e r e c i p r o -

c a l l y r e l a t e d a n d s h a r e d d u r i n g a t t e n d i n g a c t i v i t ie s . T h e i n t e r -

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

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

l a t e d e v e n t c h an g e s . I n o r d e r t o i n t e r a c t , b o t h m u s t e x i s t.

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A p p e n d i x

J u d g i n g O b j e c t i v e ly U n e q u a l T i m e I n t e r v a l s

Con tras t Mode l p red ic t ions app ly to m ean accuracy and v a r iab i l i ty

(d isc r imina t ion) o f du ra t ion judgm ents abou t even ts tha t do d i f fer in

dura t ion . Le t th is d i f fe rence fo r pa i r i be deno ted by At1. Fo l lowing con-

ven t ion in th is f ield , le t AT re fe r to the to ta l du ra t ion o f the s tandard

and AT + Ah tha t o f the com par ison . In mos t se tt ings, At ,- va r ies in

magn i tude and d i rec t ion over the se t o f ( standard p lus compar ison)

pa i r s based on a cons tan t s tandard AT va lue .Con t ras t Mode l app l ica t ions a re d i rec t : (a ) DE~, based on the assum p-

t ion tha t expec tanc ies a ssoc ia ted wi th the s tandard (AT) , a re ca r r ied

over to the com par ison (A T + At /) ; DE~ p rov ides one es t ima te o f each

t rue t im e d if fe rence, Ah . (b ) DMi, based on ana ly t ic a t tend ing and foca l

leve l d i ffe rences be tween s tandard and compar ison , p rov ides ano ther

es t ima te o f At i fo r the sam e i . (c) The tw o es t ima tes , DEi and DM i, a re

weighted, respectively, following Equations 5 -7, b y W~ o deter min e the

l ike l ihood o f fu tu re -o r ien ted and ana ly t ic a t tend ing .

Resu l t ing p red ic t ions ind ica te tha t non tem pora l in fo rm at ion f i ll ing

two d i f fe ren t t ime in te rva ls can enhan ce o r degrade dura t ion judgm ent

accuracy and d isc r imina t ion depend ing on even t s t ruc tu re and a t tend-

ing mode . These p red ic t ions a re ou t l ined la te r in the A ppend ix a long

wi th spec ial adap ta t ions fo r de te rmin ing m ode l pa ramete rs when em pty

t ime in te rva ls a re invo lved .

M e a n J u d g m e n t P r e d i ct i on s

Equa t ion 5 app l ies unchanged , wi th m ode l pa ramete r e s t ima tes g iven

by Equa t ions 8 -10 fo r two f i lled t im e in te rva ls . The foca l levels o f re le -

vance he re invo lve to ta l du ra t ion (o f s tandard and com par ison) ; these

d e t e r m i n e D E i a n d D M j . F o r D E . e x p e c t e d t i m e i s d e t e r m i n e d b y t h e

to ta l du ra t ion o f the s tandard , whereas fo r DM~ the assump t ion o f a

com mo n foca l leve l suppor t ing , fo r example , coun t ing , remains un-changed (and , in th is case, may be a co r rec t a ssumpt ion) .

Equa t ion 5 y ie lds many p red ic t ions abou t judgment accuracy : (a )

The magn i tude a nd d i rec t ion o f a t rue t im e d i f fe rence wi l l sys temat i -

cally affect average (rated) judg me nts a bou t this difference. (b) If e ither

D E i o r D M / y i e l d s a g o o d e s t im a t e o f A t . t h e n p e r f o r m a n c e i s i m p r o v e d

when th is e s t ima te ge ts more we igh t (W` .) and degraded when i t does

no t . I f bo th DE/andD M /are good es t ima tes o f At ,, then accuracy wi l l

be h igh and unaf fec ted by va r ia t ions in W~! Other p red ic t ions re la te to

e f fec ts o fa t tun eme nt cons t ra in ts and p rac t ice and can be deduced f rom

Equa t ion 5 .

E m p t y T i m e I n te r va l s

Si lences a re a lways judged wi th in a la rge r tempo ra l con tex t . T hus ,

adap ta t ions o f Equa t ion 5 to judgm ents o f em pty in te rva ls requ i re tha t




(a ) the tempora l coh erence pa rame te r re f lec ts the con tex t p rov ided by

the succession o f n te rva l markers , fo r example , in a su r round ing p hrase

(prose, m usical) or in an ex perim ental session (psyehophysical setting),

(b ) DEj remains t ied to expec tanc ies abou t to ta l even t du ra t ions ,

whereas DM~ re f lec ts d i f fe rences due to coun t ing , tapp ing , and o the r

tempora l ly based ac t iv i t ie s in wh ich a pe rson engages and uses to subd i -

v ide some emp ty t im e pe r iod , and (c) the re fe ren t leve l i s de te rmined

by the mos t f requen t , p rominen t ly marked t ime con tex tua l pe r iod .

Given th is , p red ic t ions abou t em pty in te rva l judgments fo l low f rom

Equa t ions 5 -6 . As be fo re , these sugges t tha t a t tend ing m ode and te mpo -

ra l con tex t shou ld a f fec t judgm ent ac curacy and b ias .

The ro le o f tempora l con t ras t in the la t te r p red ic t ions is remin iscen t

of Kxistofferson 's (1977, 1984) real t ime crite rion in his mod eling of

dura t ion jud gmen ts o f empty in te rvals . However , the re a re s ign i f ican t

d i ffe rences . O ne i s tha t the rea l - t ime c r i te r ion m ode l addresses on ly

speeded respond ing in two cho ice udgm ent ta sks ( long and shor t) . Tha t

ta sk encourages and the m ode l dep ic ts re spond ing on ly to the re la t ive

tempo ra l o rde r o f expec ted ve rsus obse rved end ing times . The Con tras t

Mode l app l ies to com para t ive t ime in te rva l e s t ima tes o f expec ted ve rsus

obse rved end ing t imes . A second i s tha t ne i the r a t tend ing mode s and

tempora l coherence a re found in the rea l - t ime c r i te r ion mode l . A d i -

ch o t omou sa t tend ing mode l has a l so been p resen ted by Thomas andCan tor (1978) for em pty an d fi l led intervals. However, i t applies only to

dura t ions le ss than 100 ms , and a l though the mod e l does cons ide r e f fec ts

due to d i f fe ren t amo un ts o f in fo rmat ion , i t canno t address con t ras t

e f fec ts a r i s ing f rom tempo ra l expec tanc ies. Concep tua l ly , i t s pa ramete rs

differ.

Variance and Time Discrimination Predictions

When Equa t ion 7 (va r iance p red ic t ion ) invo lves DE~ and DM ; pa -

ramete rs , bo th o f wh ich es t ima te the d i f fe rence in to ta l t im e o f the two

in te rva ls ( i. e. , At i ), i t can be used to make p red ic t ions abou t t ime-d is -

crim ina tion per form ance in a classic psychophysieal context. Th at is , if

At i va lues abou t som e AT a re smal l , t emp ora l th resho ld i ssues a r i se .

Conven t iona l ly , t ime d isc r imina t ion th resho lds ( JNDs) a re es t ima ted

f rom the s tandard d ev ia t ion o f obse rved judgm ents over the even t pa i r s( i ) a ssoc ia ted wi th a g iven s tandard in te rva l , AT , namely SD(AT) . A

cr i t ica l des ign cons t ra in t i s tha t the At~ va lues fo rm a ba lanced se t fo r

each AT, so tha t the i r sum (over s tandard /com par ison pa i r s ) is ze ro .

Thus , to adap t Equa t ion 7 to express SD(AT) , pa ramete rs DEi, D M i ,

and W~ mus t be averaged over appropr ia te even t pa i r s i hav ing a com-

mon A T Tak ing the square roo t :

JN D = SD(AT ) = [a2 [W(1 - WX DE - DM ) 2 + 02] ]1 /2. (A1)

In th is fo rm, d ise r iminab i l i ty i s a func t ion o f temp ora l coherence

(W), attent ional estim ates (DE, DM ) o f the average At~ value (i .e . , At =

0), and a n average base erro r variance, o-2 (for either f i l led and em pty

in te rva ls g iven p rev ious assumpt ions). Thus , the d isc r iminab i l i ty func-

t ion re la t ing JN D to AT can take d i f fe ren t fo rms , wi th some a t va r iance

wi th Weber ' s Law fo r t ime d isc r imina t ion . Equa t ion AI a lso p red ic ts

tha t non tem pora l in fo rma t ion f i l l ing two d i f fe ren t in te rva ls can a f fec t

the i r d isc r iminab i l ity . Bo th p red ic t ions m us t be jus t i f ied .

Weber ' s Law ho lds tha t a tempo ra l JN D is a cons tan t p ropor t ion o f

AT. I t i s suppor ted i f SD(AT) i s a cons tan t p ropor t ion o f AT fo r a ll AT ,

imply ing a l inea r re la t ion be tween JND and AT. Weber ' s Law is no t

compa t ib le wi th Equa t ion A 1 because i t does no t p red ic t d isc r iminab i l -

i ty to va ry as a func t ion o fa t tend ing mode , coherence , con tex t , p rac t ice ,

and so on . N one the less , Equa t ion A 1 i s wor th exp lo r ing , g iven tha t l i t t l eempir ic a l suppor t ex is t s fo r a s imple ve rs ion o f Weber ' s Law (e .~ , A l lan ,

1979; Dive nyi & Danner, 1977; Getty, 1976; Halper n & Darw in, 1982;

Kr is to f fe rson , 1976 ; Povel , 1977) . Al though te mpo ra l d isc r iminab i l i ty

is good over a range o f ime in te rva ls (50-2 ,000 ms) , JND s a re no t l inea r

func t ions o f A T as p red ic ted by W eber ' s Law. In fac t , the d ise r iminab i l -

Skilled attending and JND invariance with A T. Thresho ld invar iance

i s p r e d i c te d b y E q u a t i o n A I i f ( D E - D M ) 2 = 0 . T h i s o c c u rs i f p e o p l e

reliably estimate the tru e t im e differences, Ati , regardless of attending

mode . Tha t i s , because DE~ and DM i each es t ima te At i va lues, the i r

sums (over i ) , l ike those o f At i va lues themse lves , wi l l be ze ro i f a l l a re

good es t ima tes . Because sk i l led a t tend ing i s f lex ib le a t tend ing, e i the r o f

the two a t tend ing m odes m ay be used to a r r ive a t the co r rec t At i e s t i -

m a t e s. I f D E = D M = 0 , E q u a ti o n A I b e c o m e s

SD(A T) = (a202) /2 . (A2)

The 02 i s the (average) va r iance o f d i f fe rence d is t ribu t ions and wi th

skilled observers i ts constan cy is reasonable. Th erefore , a202 = Vr, a

va r iance compo nen t th a t i s independen t o f s t imulus dura t ions (Ge tty ,

1975).

Some predictions are as follows: (a) Asymptotically , thresholds are

invar ian t wi th AT . (b ) Given a f ixed (moda l ) re fe ren t pe r iod , dom inance

reg ion cons t ra in ts im ply range l imi ts to p red ic ted th resho ld invar iance

( i. e. , invar iance ob ta ins on ly wi th in l im i t ing AT va lues, wi th JN Ds in -

c reas ing mono ton ica l ly wi th la rge r AT va lues , ones ou ts ide the do mi-

nance reg ion range) . (c ) Var ia tions in tempo ra l coherence do no t a f fec t

asymp to t ic pe r fo rmance ( i .e ., W[ I - W] van ishes ! ). Al though some

supp ort ex ists for these first two predictio ns (Kristofferson, 1980, 1984),no eva lua t ions ex is t fo r the th i rd p red ic t ion .

Unskilled attending and monotonically increasing JNDs. Fol lowing

E q u a t i o n A 1 , a m o n o t o n i c f u n c t i o n o c c ur s i f t h e t e r m ( D E - D M )2

0 and inc reases wi th A T T h is i s p red ic ted wi th unsk i l led judges and /o r

a wide range o f AT va lues ( see a t tunem ent cons t ra in ts , P a r t 2 ) . In such

cases, regardless of attending mo de, un reliable estim ates of At~ occur,

lead ing to nonzero average es t ima tes o f bo th DE and DM (see mean

judgments ) . In genera l , (D E - DM ) 2 shou ld inc rease wi th AT because

(a ) [At /[ inc reases p ropor t iona te ly wi th AT , and (b ) domin ance reg ion

cons t ra in ts imply tha t d ispa r i t ie s be tween expec ted and ob se rved t imes

wi l l inc rease as the la t te r exceed the dom inance reg ion .

Finally , Equation A1 leads to Getty 's (1975) generalized version of

Weber ' s Law, i fW and 02 a re invar ian t wi th changes in AT Thus , i f AT

are cons t ra ined in range and wi thou t sys temat ic sequen t ia l pa t te rn ing

wi th in a session, then w e assume k 2 = W(I - W) and Vr = a202. Wh en-ever a2 (DE - DM ) 2 approx im ates AT 2, then Equ ation A 1 yields

S D ( A T ) = [k2(AT2 - I- V r ) ] 1 / 2. (A3)

Pred ic t ions regard ing sk i ll l eve l and AT range have some su ppor t

(Kristofferson, 1980, 1984). With respect to tem por al coheren ce (W),

a t leas t wi th d isc r imina t ions o f empty in te rvals , the re la tive t iming o f

markers o f d i f fe ren tia l p rominence wi th in an ex per imen ta l sess ion

(context) s ignificantly affects perfo rma nce (e .g~, Abel, 1972a, 1972b;

Dive nyi & Sachs, 1978; Penner, 1976). In sum, th e predicte d discrimi -

nab i l i ty func t ion takes d i f fe ren t fo rms depend ing on the way Con tras t

Mode l pa ramete rs re f lec t a t tend ing sk i ll , t a sk cons t ra in ts , in s t ruc t ions ,

and con tex t .

Nontemporal InformationWith in two d i f fe ren t in te rva ls , non tempora l in fo rmat ion can a f fec t

d isc r iminab i l i ty accord ing to Equa t ion A 1 . Al though th is p red ic t ion

crea tes apparen t p rob lems fo r the Con t ras t Mode l because e f fec ts o f

n o n t e m p o r a l i n f o r m a t i o n o n j u d g m e n t s a b o u t e q u a l t i m e i n t e r v al s h av e

no t been re l iab ly repor ted fo r t ime d isc r imina t ions (Al lan , 1979 ;

Woods, Sorkin, & Boggs, 1979), i t is resolved in Equations A1-A2.

These equa t ions p red ic t tha t such e f fec ts do n o t a lways occur and more -

over , tha t when non tem pora l in fo rm at ion does a f fec t th resho ld pe r fo r -

mance , i t wi l l e i the r enhance o r degrade pe r fo rman ce depend ing upo n

a t tend ing mode .

R e c e i v e d M a y 3 1 , 1 9 8 8

Documents

(Boltz; Jones, 1989) Dynamic Attending and Responses to Time