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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 ttending and Responses to Tim e

Mari Riess Jones Marilyn oltz

Oh 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 events

affords different attending mod es. Future-oriented attending supports anticipatory behaviors and

occurs 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 attending

supports other activities (e.g., grouping, counting), and if it occurs with events of low temporal

coherence, then time judgm ents dep end o n the attending levels involved. A weighted contrast m odel

describes over-and underestimations of event durations. The model applies to comparative duration

judgm 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 other

traditional 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 t h 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 b y Gran t BN S-8204811 from the Na-

tional Science Foundation an d by a fellowship from the N etherlands

Institute for Advanced Study awarded to the senior author (I 986-1987).

The authors tha nk C hris Antons, D avid Buffer , Walter Johnson, G ary

Kidd, Kerri Marsh, Elizabeth Maxshburn, John Michon, Mitch Pratt,

Ken Pugh , Jackie Ralston, an d W ithe r wan Vreden. Special thanks axe

due to Steve Handel an d two anony mo us reviewers for their excellent

comm ents o n an earlier version of this article.

Correspondence concerning this article should be addressed to Marl

Riess Jones Department of Psychology,The Ohio State University, 142

Townshend Hall, Columbus, Ohio 432 I0.

459

in te r v a l e f fe c 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 en 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 e i r d u ra t i o n s . T h e g e n e r al f r a 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 ime in te r v a l s a s we l l a s t e m p o r a l e x t r a p o la -

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 i s 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 I ss u e 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 e

m 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 hypothesis

t 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 ff e re n 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 to r a ge s p a c e i n m e m o r y : T h e c e n tr 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

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46 M RI RIESS JONES ND M RILYN BOLTZ

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

experienc e lengthens (Ornste 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

def in i t ions of s t imulus com plexi ty (e .g . , num ber of angles

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 lus

c 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 t

du 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 t ime e s t i -

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

re po r t e d those m a ske d by a h igh - in te ns i ty no i se ( i. e. , r e qu i r 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 Model

A nothe r c ha ll enge 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 iz e 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 t o 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 typ ing sty le of 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 e m e rge f rom the l i t e ratu re a s a w ho le. A n in t e rva l de f ine d

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 fam il ia r i ty (e .g. , Avant & L ym an, 1975, vs. Devan e , 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.

Schiffm an & Bobko , 1974) .

Some confl ic t ing f indings may be due to methodologica l

differences. 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 th e 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 l is ts , t he a m oun t o f ba c kg roun d 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 on be ha v io r i s 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 iz e 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 ., Deuts ch & F eroe , 1981; Leeuw enberg , 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 a nsw e re d . C om ple x i ty de t e rmina n t s o f a tt e n t iona 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 nd in tona t ion , a nd ye t w e don ' t know w h ic h k ind o r how muc 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 (Orn ste 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 .

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D Y N A M I C A T T EN D I NG

46

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 p a t t er n 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 re 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 t h i s c o n t r i b u t es 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 e c 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 i gh 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 how 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 r e n ce ,

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

th e y s h o u ld o c c u r . T h u s , fu tu re -o r i e n te d a t t e n d in g e x p lo i t s

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 io n o f e x p e c t e d e n d i n g ti m e s . W h e n t w o e v e n ts 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 ll c o 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 se

e 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 il l ed w i th m o re i t e m s to b e lo n 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 r e -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 di 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 a ly t i c) 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 objects

and experimental m aterials as stimuli In protest to implications regard-

ing the impoverished nature o f such materials, some recent approaches

have adopted the term

event

o refer to ecologicallyvalid objects under-

going physical motio n or change (Gibson, 1966, 1979). Ou r framework

reflects both notions in that an event refers to any environmental object

or 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).

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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 n t s t h 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 tu 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 e

m e a n s in e v e n t s a n d t o 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 en t s t r u c t u re , 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 ty

o r f low 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 , M c 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 81 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 re n c e ) t o n o n a r b i t r a r y ( h i g h c o he r 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 s

r e l at e d t o t e m p o r a l p r e d i c t ab i l i ty 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 e ct i on s . T h e i s s u e o f la w -

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 r v in 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 th i s , i n tu rn , i s n e s t e d in a n 8 0 0 -m s p e r io d ,

a s i n F i g u r e I a , t h e n o n e o f t h 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 ) r e f le c t 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 are

formed 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 logarithmically

defined as a frequency ratio: A f f = .05946. A m ajor diatonic scale,

beginning on th e keynote or tonic, has the followingsequence of whole

steps and half-steps: w, w, s, w, w, w, s. Thus, th e m ost fam iliar m ajor

diatonic scale is C m ajor, in wh ich suoeessive pitch classes of CDE F-

GA BC a re separated by w, w, s, w, w, w, s. In this scale, successivepitch

classes 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). Some

important harmonic relationships within each scale include a major

third (e.g., C-E in C-major scale), which corresponds to the pitch

changes 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 the

note (G) th at defines a perfect fifth above the tonic (C ). Together the

notes C-E-G form the tonic triad chord in C m ajor.

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

46

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 4

o 8 3

- - 1,600ms ~

1 6 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 a t

m t L F R F

O n e C y c l e

[

Cat RF RF

RH RF

F e e ~ ~ I . ~ . ;

LH I

LF 1 I

Rid m I

RF I

T i m e (ms) ~ ,

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 k ey of C major. The to nic

[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

of f ground

Leve l (n )

4

5

2

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 show.

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

A c c e n t s o f t h e f i rs t C 4 ) a n d s i x t h G 4 )

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 i n 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 context

and 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 serial

structure.

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Hierarchical rhythmic) T ime St ructures

Level (n)

ATI~

AT ~

O • • • •

• . : • : • : •

:

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

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

~ n

C = ~ T ~ . I = 2

A T n

C t = ~ T n _ I = 3

A T n

C t = = 2

A T n - I

f o r n > I

d

No n-Hierarchical T ime St ructures

~T

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 r a r c h i c 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 rs t Ha l f

C t = 2

S e c o n d H a l f

C 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 )

• = A c c e n t e d

( l i g h t o n )

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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 ( 34 ) i n 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 .

Coupled accents are

i n f a c t t y p i c a l l y s t ro 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 nd o f f , 1983 ; M a 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 l s.

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 s f o r m 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 y

r 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 it i a ll 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 el .

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 in t e g er . 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 re 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 n

a s k ) . T h i s c h a n g e e s s e n t i a l l y 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 on s i s t e n t l y r e l a t e d by C t = 2 .

A l l o f t h e s e 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 group (e.g., Ha hn Jones, 1981; Cox eter Greitzer, 1967). For a

more genera l t rea tment in te rm s o f t ime t ransformat ions tha t speci fy

the logar i thmic spi ra l , see Hah n 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 ertain

markers, beat periods, and rh ythm ic figures may facil i tate meter identi-

fication on the par t of an attender (Essens Povel, 1985; Longnet-Hig-

gins Lee, 1982, 1984). These issues involve attending and detection

of temp oral invaria nts and are considered in a later 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 e

irregular one of low coherence in (f) that is nonhierarchical. The la tter represents a tem pora l pattern of

lights, in on [O] or off [O] posit ions, from a judged dura tion study by P oynte r and Ho ma [ 1983]. In all

pattern 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-~.)

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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

simul taneously recurrent per iodici t ies that form a noninteger

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 nd

t r inary t ime st ructures are involved, each ident i f ied 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 F igure 2c: Both display a h ighe r level b inary t im e 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 that i s in i tial ly h ierarchical . However, th i s re gular i ty o f

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 ore

comp l ex t ime r a t i o i s t hus needed t o fo rm al i ze th i s s t ruc t u 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 Equa t ion 1). Dynamical ly , they

are m ore com pl ex because r a t i o and add i t ive t i 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 t ion o f t empo ra 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 i s coherence wi ll 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 im e 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 t h f ixed per iods and phase l ock i ng i n wh i ch marker s o f

these periods are often specified by dist inctive directional

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 ic in terplay of comp lex, co-occ urr ing body gestures.

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 co rresponding veloci ty d i f ferences associated wi th

on-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 .

Of course, any systemat ic pat terning in t ime lends predict -

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 al so means

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 t

definit ion.

Musical Structure

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 Music) and David Butler (Ohio State Department of Mu-

sic) for com men ts on an earlier version of this sec tion. Any interpreta-

tive errors, howeve~are the authors'.

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

and 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 in g s o f t e n c o r re s p o n d to c e r t a in p i t c h e s a s s o c ia t e d w i th a

to n a l s y s t e m (D o w l in g H a rw o o d , 19 8 5 ; P i s to n , 19 7 8) . 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 e

m 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 Kessle 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 e

re 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 and

tempo. Meter

p 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 s

f 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 e st 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 ( se e F o o t n o t e 9 ) . I n s h o r t , t he 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 ies ; L e rd a h l J a c k e n d o f f , 1 9 83 ) , b u t i n fo r m 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 s

d 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 se s .

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

p a c e s ( e. g. , l a rg o , a l l e g ro ) . F o r e x a m p le , a l l o th e r t h in g s b e in g

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 is 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 t u 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 prevailing

tonality and grammatical con siderations (H. Brow n, 1988; Krum hansl,

1979; Krum hansi Kessler, 1982)but on temporal context provided by

rhythm (M onahan Carterette , 1985) and temporal order (e .g. , various

notes identifying intervals such as tritone; H. Brown Butler, 1981;

Butler Brow n, 1984, Kidd, 1984). Finally, temporal ordering of har-

mon ically significant pitches, as in Figure 3 , can establish, via implied

harmony, 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 also

affect coherence in tonal melodies by creating con flicting tonalities and

inappropriate 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. This

idea, although compatible with ou r general approach, should n ot be

confused with more traditional definitions of tempi (e .g., Kronm an

Sundherg). In produced sound oatterns, i t is quite possible tha t charac-

teristic tem pi follow Clynes' exposition, a notion th at reinforces our

approach, rather th an contradicting it.

9 Sternberg. Knoll, Zukofsky (1978) used a psychopliysical ask to

study 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,

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  68 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 time ra t i o s i n p roduc e d rhy 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 te n a c c u ra t e ly p rodu c 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 ime

c 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 la ys t e mpor a l c ohe re nc e by the w a y

i t c ombine s s t ruc tu ra l a nd me t r i c t im e s t ruc tu re s . Se pa ra t ely ,

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.

O b je ct ive ly , m os t c ohe re nc e a ppe a r s i n F igu re 3a in w h ic h 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 ts ) 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 . Th 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 i se c re a t e d by de v ia n t ph ra se 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 re

tha 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