Psychological ReviewVOLUME 89 I"iUMBER 2 MARCH I98?

Rhythm and Timing in Skill

L. H. ShafferUniversity of Exeter, Exeter, England

The conccpt rrf rhythm pt-rints to diversc phenonlcnil in skilled pcrlormance. Atheoretical frame sufficiently general to deal with these is presented, togethcrwith data from a variety of skills. It is argued that a motor system, responsiblefor movernent production, can produce movements that realize given time-scalesand hence can act as a timekeeper. In contexts rcquiring ternporal coordination,a more abstract.tirnekeeper, or clock, can provide temporal re ferences for a motorsystern or several motor subsystems; this enables complex timing such as is foundin musical performance. Skilled movement is teleological in the sense that it aimsat targets in space aqd time. Its timing is based on an internal schedule of motorevents*the targets o[ rnov€ment-not rnovement onsets: The motor system ar-ranges the latter on considerarions of movcment economy or expre$siveness"Tapping, handwriting, typing, playing music, and speech are examined as in-stances of skills having a near-miss periodicity.

"Skilled pe rforrnance i.s rhythmical." Likemany apparent truisms this one is weakenedby ambiguity, in this casc in the meaning olrhythm. If we ask whet is common betweenthe rhythms of speech, playing tennis, andpla;"ing music, we find that it refers to dif-ferent properties of tinne series, relevant invarying degrees to the different skills, Amongthese are properties of temporal patte rn, pe-riodicit,v*, stress, expressiun, and quality ofmovement. The purpcse here is to developa theoretical frame for rhythm that can en-ccmpass this variety af pl'lenomena.

We can illustrate the different senses ofrhythm by taking music as a paradigm ofserial-structured forms. Excluding some oftblk music and a handful of modern f'ree-form cornpcsitions, the timing in a piece ol

This rcscarch wus supported by Grant HR 4671 fromthe Scrcial Science Rescarch Csuncil. The papcr arosefrom discussions with Csrol Fowler, Scott h.elso, PeterN'lacNeilage, Don l\iorman, Dave Rumeihart, DickSchrnidt, Saul Sternberg" Ewart Thomas. and manyot,hers. lt is just possible th;rt none of thern agree withany of the idcas prescnted here.

Rcqucsts for reprints shouid trc sent to L. ]1. Shaffer,De partment of Psychoiog)', University of Exeter, ExeterEX1 -tQJ, England"

music is based on the fixed interval of a re-current beal. This is specified in writlenrnusic; the beat is easrv to identify in a conl-petent performance; and a listener can danceor clap in time with it. The beat usually sup-ports two othe r rh1'thmic structures: cne ismeter, a recurren[ group of beats in wlrichcertain beats are more salient, or stronger,than others; the othe r is a ternporal patte rnr:btained by joining antl subdividing be at in-tervals to create a series of note and pausedurations. Temparal patte rns are con-structed by producing rhythmic figures andthen transforrning them in ways that sim-plify, ornarnent, expand, contract, or invertthe original version, embedding the resultsin a variety of contexts. Thus the ge nerativegrarnmar of these patterns is typicall,v morecomplex than those describcd by Simon( 197?) and Greeno and Simon ( l9?.1). Theterm rhythm has often been used indiffer-enlly to rsler to the beat, the rneter, or thetemporal pattern of music"

The strong beats in the meter provide fo-cal points toward which rnusicatl,v importanteve nls tend to grevitate { Lerdahl & Jack-endoflf. 1977). Hence the-v tend to receive

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il0 L. H. SHAFTER

stress in perforrnance so that a listener caninterpret ttre mete r and clap more vigorouslyon the strong |eats. The stress rhythrns ofrnusic, however, seldorn remain withia therneter, and rhythmic interest is obtained byoccasicnally displacing stress from a strongto a weak beat {Forte, I979}.

Jackendoff and Le rdahl t t{ote I ) haveexamined the possibility of a deep paratrlelbetween music and speech by showing thatthe abstract structures r:fl saiience in musicand speech produce sirnilar graphs. Theirst,ructural analysis of prosodic stress followsthe work of Liberman and Prince ( 1977 j andSe lkirk { 1980). What is of inte rest here isthat the stress rhyttrms of spee*tr may fiotilormally be associated with a me ter: Stressgroups may not form isoctrronous intervals{ Lehiste, 1977}, and the tcmp:ral patternsof speech, summarized by Klatt ( I 97 6), maynot contain a periadic beet. Speech can, ofcourse, acquire a regular beat in ccrtain con-texts; it is pcssible to count in regular time,recite verse, and perforrn song-speech as inthe music of Schoenberg. Conversely, rrru-sicians can depart from regular timing inplaying music, and in Romantic music tlreyrnay piay with something approaching therhythrnic freedom of spee*h. Thus, if thereis a difference between music and speech itis normetiv*, and l#e expect to find that theability to irnpose a beat as a supcrordinatetiming constraint is- to some extent, inde-pendent af the performailce mediurn.

To a musician an important se nse ofrhythrn is the expressive use of tirning inperformance" This enrails a judicicus Ese ofrubato, or temps variatiofi, to give the beatan elastic quality, and of playing off the beat,leading or lagging it, when it is provided byan accorTrpanirnent- A musician who playssquarely on an inftexible beat definitely hasnot "go[ rhythm. "

One mors sense of rhythm, and perhapsthe only oile that applies to ball games andother cpisodic a*tivities, is the qualiry ofmovernsnt, which in the skilled performergives thr appearance of be ing unhurried,fluent, and avoiding abrupt acceleratians.Thus. a the*ry of rhythrn h*s to distinguishbct.ween tlre timing of motor eysnts, such asn:aking eontact with a bail. striking a, note

on a keybaard, or producing ph*nation r:f aspeech sound, and the kinematics of thernovements that lead to thern. Motor eventsare the successive gaals of movement. Theyca$ be reFresented in models of timing &soccurring at discrete moments in time, buta theory of rhythm has ts take account afthe underlying continuity of movement.

The praduction of rhythm in general ismade possible by the preparatioil of move-ments and their caordination { Lashley, 195 t;Leonard, 19531 Poultsn, I957; Shaffer,198 I ). tfr/ithout preparation performance isa series of discr€te reactions to external rv-ents. Ttre developmrnt of motor skill can betraced as the progress from reaetive move-ment to movement ftuency, coupled with aftexibility in tailoring actian to the detailsof an infinite vuriety of contingencies.

The properties of rluency and flexibilityin skilled perforrfiance lead us to a tlreoryof motor programming, whose major com-ponents are a perfcrrnancf, gramrnar and a

control systern. A perforfilirn{:e grammar isa collection of generat,ive rules for creatingsyntactic strings relevant to *fi infinile va-rie ty of actions in a certain domain, togetherwith rules for translating symbols in thesestrings first into the coffirnands for rnove*ments and then into the movfrilents them-se lver. Liberrnan t I9?0) described suctr agrammar in sLrowing that the linguist'sgrarnmar must be supplemented by rules fortranslating phonologicai strings into speech.A motor program is a set *f grarnmaticalrepresentations of inte*ded action con-structed, by a coiltrol systcrn, &s a hierarcLryof abstractions, terminating in motor output.In serial performance these representationsurdergo continual renewai as the action uo-fohjs.

Grarnrnars are usuaily considered as sys-tems for generating strings of symbals orcategorial elements. A perlcrmailce grrm-rnar conl.ains a level of rules that map syrn-bcls into continuous variables, such as force,rate, and directian. If a nnctor command isa syrnbotr specif,ving the targets of a rrrove-rnent {VtacNeilage, i 970}. then the rules atthe ierminul lcvel are c$rnpr:t,ational algc-rithms deterrnining the trajectories af iimbsa*d articulators.

RHYTHM AND TIMING IN SKILL ut

Movement Timing

A suitable starting point for a theory ofmotor rhythrn is the observation that skilledmovement can be contin uous ove r large timespans. Although it is conyenient to talk ofa succession of movements, it is more ac-curate to describe performance as a sequenceof moter events produced by moveme nts thatevolve fluently from one anothe r. Also,movements in different limbs and articula-tors can overlap in time in the productionof successive motor events, If the motor ev-ents are fixed in time as well as space byrequirements external to the move mentsthemselves, as in playing music, for instance,then movements have to be structured aroundttrese fixed points.

The proposition that a rnovement has a

temporal goal as its reference point is fun*damental to the present thesis" It is markedlydifferent in ernphasis frorn an assumptionthat movements are triggered at the timesuf motor events ( Kozhcvnikov & Chistovich,l*{ote ?; Shaffe r, 197 6, 198 1; Wing & Kris-toffersor, 1973)" The proposition carries animportant corollary: The motor systern re-sponsible for constructing movements cantranslate a given time interval, or equivalentinformation, such as that derived from visualstimulus ffow (Lee, 1980), into a movementtrajectory having that duration. Hence, themotor system can act as a timekeeper, te-alizing a time scale in a movement tra.iec-tory, The data frorn some recent st udies arerelevant to these proposais.

A minimum condition for a motor systemto act as a tirnekeeper is that the time courseol a movement trajectory be reproducible.Cooke ( 1980) has shown, lor step trackingbetrveen two fixeci points, that the phase -plane plots ol individual movements, relatinglirnb velocity to position, superimpose on oneanother u'ith very little variance. The-v alsohave the smooth unirnodal shape of a bal-listic moyement. He also obtained a linearrelationstrip between peak velocity and theunrptitudc of sinrple rcaching movcnlsnts,when there was no specified distance or timeItlr ttre movement. blovement time was notinvariant; but the result raises the possibilitythat tirning cen be a deterrnining parilmeter

of movement; and this can be examined inphase-plane plots of step tracking paced bya metronome, with duration and arnplitudeas controlled variables.

This was indirectly studied by Kelso, Sou-thard, and Goodman t 1979) by looking atconcurrent movernents made with both handsto targets differing in size and distance frornthe resting position. In rnaking single move-ments the times to initiate and complete a

movement varied with target size or move-ment arnplitude. In the combined condition,with the instruction to complete both rnove-rnents as quickly as possible, where one hada large close target and the other a smalldistant target, the trands tended to start andarrive together, having to produce differentvelocity trajectories to do so. Also, the ve-locity curves were smooth and reached theirpeaks at the same tirne. This indicates thattirning parame ters were involved in themovements and that it was easier to preparethe combined movernents if the parameterstook the same values for each limb. In thiscase the lirnb making a large movement toa srnall target preernpted the timing fon bothlimbs.

Timing as a goal af performance can be-come more impcrtant in serial than in singlemovernents. Schmidt { 1980) reports a studyin which a lever had to be moved to a spec-ified endpoint in a given amount of time. Onoccasional trials and without warning themass of ttre lever was changed. For a sinrplernovement to target, the endpoint of rnove-rnent was unaffected by the ctrange but itstiming altered: in making a serial movement,to t,Lre target and back to the start position,movement, time was unaffected, but the e nd-point of movement altered. The priorit-v ofattaining the spatial and temporal compo-ne nts of the target thus differed between theconditions.

A motor e vent can usually be give n a

multivariate description, but not all the vari-ables rnay have been set in programming themovement. Playing a note on the piano inthe context of a piece of music entails amovernent to & certain location on the ke,v-board, timing the movement of st,riking thekey, and controliing both the intensity andmanner of strike, the last affecting the qual-

ity of legato or staccato by suslaining pres-sure on the key or rebculnding fr$rn it" AIIthese v4riables are rnusically important andso sh*uld be programmed. In a Iess stringe ntcontexto some variables rnay be allowed toinhe rir yalues from carlier move rnents ortake default values to simplify the sompu-tatian of movement trajectory. The evidencefrom Schmidt's exprirnent shows that bothlocation and timing variables wers pro-gramrned, but only onc or the other, de *

pending orl the rrrovement, \.{i as protectedfrom input distsrtion.

ltr/e cail suppose that the tcrnporal rhythmof a performance, if it is reproducible, is ttrerealization of a schedule in a rnotor prograrn.The variable specified in rhe sclredule *eedilor itself be time; it can be any yariable th*thas a, definite timing concomitant within amode of computation af the motor system.Stress leve I or movsme nt amplitude canserve if thcy do not already have to varyorthogonally wittr timing.

Given a schedule, the motor system canproduce a moyrrnent to the next temporaltarget, taking a previaus target as a rsfer-ence point ior the rnsveffient trajectory. Inrep€titive tapping with one tingcr. the pre-vious tap provides the reference paint for thenext one. \Hhen tapping with two fingers inalternation, the ffiovement for ttre next tapcan start on ttre penultirnate tap. and thereis & choice of taking timing i'eference fromthat moment or frtlm the rnr*rent of theprevious tap r:n tlre altcrnate rrnger. In typ*ing iCentner. Grutlin" & Cunws], N*tc 3,tand piano playing. using all I0 hngrrs inirregular s*quencc, a tinger can move tr:-wai'ds its next ke), at ilny timc f*llowing irslast use. Howevgr the mom{:nt ,;f. ons€t ofnl$vement ts a sprtial targst mitt' n*t he there f crence poin t f rnrn wh ich ir is t imed rorcuch lhc target. Thc reieren*c point canoceur fairly late in rhe trajectury if there ise xtensive coartie ul;rtion oF rnovsrnents, inwhicir cas€ it should hc Flos$ible t* detecr achange of acceleration in the trajectorl* asa rnovement changes frorn '*ballpark" timingto refereacs tirning.

Subsequeilces *f movcrnents rnsy bec+meorganized as a group if the,y occur lrcque ntlyor havs a short tirne scalc. We can thus tlrinkol a cornpsund movemenl,-trajectrlr,r*, which

L. H. SHAFFER

includes thc rnovernents for $evrral m*tarevenls, launchrd lrom & cornmsn referencopoint and articulated on an intcrnsl su'hed-ule . [n this ca$e ttre motor program canspecify the onset of the first event snd leavethe motor system to compute the internalsctredu le .

In surnmary, we have outlined a theoryof motor skill in which movements have theteleological propsrty of anticiparing rargetsin space and time and can be ffuently co-ordinated to realize tr given sclredule. It isassurncd that the motcr system prducingtfre msve rnents has the computational rr*sources to act as a timekeeper by c*ntrollingthe time scale of rnovement trejectories andcan construct trajectories producing morcthan orie evsnt.

It has been supposed that motar com-mands in afi output buf,fer are serially ac-tivated on an internal schedule { Kozhevni-kav & Chistovich, l.,lote ?; MacKal', l97l;Straffur, 1976)" T,his is reasonable if motortiming is relateci t* m*vement onsets bur nsrif it is reiated to rn$vement targets. To en-able anticipatory moveme nt a representationof event sequencs would have to be trilns-forn'led to cne crdered in tsrms of mouerne*tonset, wittr the undesirable cansequence tlratefTective timing control wculd psss ro theinesse ntial variahie { rrroyeille nt r:nset } ratl:*rthan to the essentiaX variable (cvent onset).

\il'ith the ilcru prl'posal the motor systemhas to be given a perspeetive l:n the outputstring of the n:ot*r Fregram tc snabl* ir tsanti*ipate rrrlverrent requirements. It cl***hieuc tl'tis hS,seilnning ttre string in ad-vance oi prod uctian to obtain tlre rele va ntin fornraticn, Such a $can can serve seve ralpurposes: (a) It allows the motor systrm t,;anticiFat€ movemenr t&rgsts and tt) ;.rdd ;lur-iliary inf*rnrarion relevrnt to the back-gro$nd conditicns for move ment. such as therfgulatian ol breathing in speech t Lade-foged, 1967) or the postural adjustmcnl pre-paratory to ruising a limb { Bele nkii, Gurfin-ke I, & Pal'rsev, 196?); i b) it allor*'s them$tor syslem lo group rnotor comrnands tt)Construct r.;ornpound rnovement trajectories:antl ic) it allows lhe motcr sy$tsm ro inter-pre t e xpressive inforrnation ranging over a

sequence of moverncnts.Apart frorn matters of timi*g, the scan

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RHYTHM AND TIMING IN SKILL I rl

concept can account for certain prope rtiesof speech errcrs. The displaced phonemesand phonetic features in spoonerisrns tendto move to similar phone tic contexts( Fromkin, l97l ), or suctr errors are trig-gered by the conflicting rhythm.s ol phonemeor feature alternation in tongue twisters(Clark & Clark, Lg77; Schourup, 1973). Aprior scan of the output string. picking upcontext information. cen cont'use this withorder information and create an orderingambiguity in the translation from comrnandsto rnoveme rrt (cf. Shattuck-Hufnagel, 1979).

The rnotivations for the assumpt.ions madehere should become clearer in the lollowingsect,ions, when we discuss particular skills.

Clock Reference

The function of tinrckceping mi.ry* be dis-tributed in the neuromotor systern ratherthan be the property' of a single subsystem.A time interval may be realized in a move-ment trajectory or constructed at r moreabstract ie vei. A tirnekeepe r at the latterlevel can be called a clock: It can servc toptovide temporal ref'erence points for move-menls and hence coordinate rnovements inindependent motor subsrlstems. The case fora clock can be made from the performanceof tapping in time with a me t,ronome, eithertapping in synchrony with it or tepping thecontinuation of its series whe n it stops ( Mi-chon, lr{ote .1; Stevens, 1886; Wing & Kris-toffe rson, I 97 3 ).

S"vnchronic tapping is achieved if a move-ment can be found having the same periodas the metronome and then, starting in syn-chrony with the metronom€, iterating on thismovernent. To abtain s.v*nchron)' in the firstplace, the perforrner rnust construct an in-ternal modrl of thc beat interval and com-pute a movement lhat leads to a tap on thenext beat. He re are the ingredients of dis-tributed timing: an internal model that byrecyciing can act as r clock and a rnotorsystem that cerl construct a rnovement hav-ing r given pcriod.

Let us eKarnine the possibiiity ol pe rform-ing synchronic tapping without the use of a

clock. Like Michon we shatl for this purposetake it for grented that pe riormers can startin time r+'ith the metronorne. They* produce

a series of tapping movements, each aimingat the duration of the rnetronome period, buthaving a random error of production. In ef-fect they act as a stochastic metronome inparallel with the external one. If tappingcycles are serially indexed, the n ovtr a seriesof taps the asynchrony between metronomebeat and its indexed tap will describe a ran-dom walk about zero, its starting point. Butasynchrony is additive and so its varianceincreases linearly with the nurnber of cycles;he nce in a prolonged performance the asyn-chronv can become indefinite ly lar*qe, thoughits expected value is zero.

As e way of improving synchrony, theperformer ma!' adopt one of two tactics. Thefirst uses feedback information of the pre-vious asynchrony to regulate the next move-ment interval. In the nth tapping cycle, acantlidate intcrvul. I'n, drawn from a fixeddistribution, is modified by adding a pro-portion. d, of the asynchrony on the previoustap. en - t.The actual tap interval is t,hen

ln: I'n- chon- lr -l <O <0.

It can be shorvn that as the feedback coef-ficiefrt, e, approeches * 1 the variance of thetapping interval increases. Conversely, thevariance of asynchrony decreases to anasymptote, the variance of a single tap in-terval" Thus, synclrrony error can be tradedagainst variability ol the tapping inte rvei.

Alternatively the pe rforme r may timeeach tap from the previous metronome beat,hence eliminating the possibility of a cu-mulative drift, out of synchron)'. Then, if themetrcnome period is C and a movernent in-terval re ferred to a beat is I', the intervelbctweentaps n and n + lis

In: C+ I'r- {'n-t.

If the successive I'ere iniependent vari-ables, the variance of I is twice the varianceof I'; also the se rial covariance at a lag ofone ti.e., between adjacent intervals) is mi-nus the variance of I', whereas covariancesat greater lags are zero i Wing &. Kristoi-ferson, 1973). r.

These two tectics are equivaicnt il 'b =- I in th* irrst tactic. hecause thrs degree oifeedtrack eftectivcly cancels the ilreviousesynchrony. lvtichon (Iriote 4) comment-*d

I l4 L. H. SHAFFER

on the equivatence but faited ts recognizethe distinct tactics. They lead to the samfoutcome but they entail vrry different com*putations, because with sne tactic there isno need tS compute and then subtract theprcvious synchr$ny error- Note that thesetactics depend ofi ail intimate cauptring be-tween mctronome beats and tapping move-ments, such that information derived froma sensory input cafi be used to affect the timecour$s *f a 6svefflcnt alrcady in progress.Thus it seems that they put performance inthe domain of reactive rather than preparedmovement and $$ de ny th* pcssibilrty ofmovcment fluency.

The situation changes if the performer cafiutilize an internal clock, :iup€rordinate to themotor system. McGill (1962) dev*lopd aclock model to characterize the time seriesof intervals that ffuctuate randomly but havean underlying periodicity. free of temporaldrift. He assurned a deternninate clock gen*erating pulses with a fixed period, C, eachpulse triggering a response with a random,independeat delay, d. The interval. I, be-tureen successive responses is then a randomvariable whose ntl: value is

Ina C+ dn* d"*,.This rnode! gives a good account of ttre tirnecharacteristics of the pulse train in a nervefiber whex it fires. I{owevcr, the as$urTrption*f a determinate clock is too strong for psy*ehalogical theories. Accordingly, Wing andKristoffers*n t l9?3), in a dcscriptic* of re-petitive tapping. weakrned the assumptionlo one of a stochastic clock, but re tained thefcrm of tlre model, which led tlrern to rep-r*s*n{, the tapping rfiovemer}t a$ a rs$ponsetriggered with rardtlm delay b,v a clockpulse. This model has been successful in de-scribing properries *f the time series of mo*tor events in continuaticn tapping" that is,t*pping the continuat ion tlf a pcrior3ic met-ronorn€ series. and it has led to int*restingextensions *f the task and the rncdcl {Vor-he rg & Harnbuch. 1978; \!'ing, 1977,r e$Ob ).

If we wish to retain a constructive role oftiming far the motor systsilt, this ran beachieved in a variant r:f McGiil's model thatgives it the form of rhe second tactic for sy,'n-

cl'lr*nic tapping, but substitute$ afi internal

stoctrastic clock for the metronome. BecauseC is *ow a random variable, the earlicrexpression bec*mes

I, = f" + I'n- I'n-t.

Assuming i*dependence betw*cn the c*n-struct variablss, the yarianc$*csvarianceproperties of I can be simply described interrns of the variances of C and I':

Yar C + iVat I', k - 0

-Varl', k:10, k> I,

Covo ! :

where k is the serial lag between covariateintervals so that ccvariance at a lag of zerois just ttre variaRss. This rnodel gives thesame description of tirning among motorevents as the ll/ing- Kristofferson ( I 9?3 )modetr, but it interprets the motor c$rnpone *t'Jiffere ntly.

Before evaluating these proposals weshould reffect that the only point of using aclock [o control rnovrms*t timins is t]:at itcan rninimize ternporal drift between sepa-rate streams of events that ha're to be co-ordinated" The clock s$rves this purpose ifand only if it cafl grnerate time intervalswith a lower order of variance than the rnc-tor system can.

The advantage of having a clack san beseen in the context of musicians playing to-gether. In rnusical groups one musician u$u-ally aets as leader, or timekesper, for tlreothers, and so wr can consider the perfar-mance of a duet withcut losing generality.T;*pically each player piays a part with itsown teffiporal rhythrn $s rhat betw*en thsmthey prduce notes at Cifferent points intime. Their rhythms are based on a commonbeat and meter, but these are only scca.sioil*allv mede explicit in the perf*rmances,iJrnce, thc second player can derive timinginformation from the leader only on an ir-regular basis. flven if rhe beat and rnet*rwere made explicit rncre regularly in theleeder's performance, attempting to followits stochastic vagarics wauld distort therh3'thm *i the s**ond player" Thus, snsembieplaf ing appears to de pend oil thc playe rsheing able to generate t;-ieir timgke€piirg iaFarall*l, cnch using ilrr inte rnal ctock. Cf

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RHYTHM AND TIMING TN SKILL 115

course, even the clocks will drift apart overtime, but if the variances of clock intervalsare srnall enough, the drift can remain withinthe bounds of perceptual acceptability overlong stretches of the rnusic, and feedbackcorrect,ion, at the level of bringing one ciockinto synchrony with the other, can be de-ferred to suitable boundaries in the rnusic.

The proposed clock model can equallyscrve as a model of synchronic or contin-uation tapping. All that diffe rs betweenthese conditions is that in synchronic tappingthe performer has ttrs opportunity to detectdrift between his clock and the metronomeand so can apply occasional correction. Theadvantage of the proposed model over thatof Wing-Kristofferson is that the proposedmodel opens the theory to the domain ofmovement kinematics and allows us to con-sider how movements as well as motor eventsare serially structured. It also has the ad-vantagc of showing htliv cxpressive tin:ingcan be introduced in the tapping task. If aperformer can use a clock to model the met-ronome beat and can separately time move-ments in relation to clock pulses, then tre hasttre option to tap ahead of or behind the beat.Musicians frequently mcve in and out of anaccompanying beat in a cont,roltred wa), andpianists c;tn go one step further by lettingone hand play in and out of time with theother (Shaffer, l98l)"

Yorberg and Hambuch ( 1978) have con-side red t,heoretical exte nsions of clock timingin wtrich a hierarchy of clocks is used to gen-erate temporal structures, such as may occurin musical performance. This will be takenup below; the existing evidence suggrsts thatthe timing hierarchy of'a clock and a motorsystem are su{ficient to account ior musicalpe rforrnance (SUaffer, 198 1 ).

I.{ear-M iss Periodicity

Many serial skills seern to have lhe prop-erty of being ncarly periodic, at some lcvclof performance unit, with some skiils beingnearer than others. In skills that ailow rupidperformancs, pertraps the strongcst motivefor periodicity is that it creates an iterativeprocessing cycle that cen facilitate the con-trol of motor output. It can also help to reg-ulate the accelerations in movement :rnd so

reduce the energy dissipated in performance;and at another level it may simplify the com-putation of successive movement trajectoriesif a basic timing parameter can be propa-gated over a sequence of cornputations. Incomrnunicative acts it can provide a bound-ary cue for segmenting the rnessage signal(Martin, 1972). In music it is a structuralproperty of rhythrn, and it allows temporalcoordination among players.

These skills can be classified on two fac-tors. The first raises the distinction of whetheran underlying periodicity is based on a clockor on a nominal specification given to themotor system by the motor program. In ei-ther ca$e it is assumed that a timekeeper,clock or motor system, has a way to con-struct a required time interval. The secondfactor considers whether departure frorn pe-riodicity is merely stochastic, that is, randomerror, or includes a structured component;if the latter whether this component is in-troduced at the syntactic or ttre logistic levelo[ constructing motor output. The logisticlevel is concerned with rnovement prcduc-tion, and so the last distinction is related tothat of basic rhythms and their expressive,or quasi-expressive, rnodulations.

Hundwriting

Handwriting is a good exarnple ol a skillhaving a near-miss periodicity. Hoilerbach( 1979) describes a robot arm whose basicproduction is drawing a sine y/ave on a writ-ing surface. Handwriting is obtained bymodulating the amplitude of the ve rticalcomponent, producing the oscillation, andinde pendengly modulating the le ft-to-rightdisplacement. With suitable choices of mod-ulation parametetrs, the robot arm begins tomirnic the different trandwriting of humanindividuals. '$/ing ( 1978, 1980a) has re-ported some preliminary results on ttre timecourse of human handwriting. I n cursivewriiing the letters e and I are similar loopsdiffering only in amplitude: Their produc-tion times within a word arc not the sarne,but they are relatively rnore alike than theiramplitudes. Thus there appearu to be an un-Cerlying pcri*diciti nrudulated by fast,rrsaffecring letter shape. An anall'sis of timingacross iette rs showed ihat there was no con-

il6 L. H. SHATTIR

sistent *sgativc covariatian betwee n adja*cent lett*rs. which suggests that the undsr*lying peridicity is nominally $pecified ratherttran elack *rient*d, Thsse studies did nctconsider a ealligraphic csrnpanent, illodu-lati*g prrsssr€ cn ihe writing surfaee to *f*fect li*e thickne$$, which may in turr: affecttinring.

Typing

Gsrest { t956} studi*d typists at differentlevels of proficie **y and faund that the $r*r*skilled tlre typisl the rnorc nearly her typingrr'a$ peridic. In an i*tensive study *f a typistwhose spe*d was ab*ve I *0 words psr *rin*utn, $haffer { }973} *bserved a regularity i*her timing that led ta the co*jecturs that itwa$ clock *rie*ted. But it was alsc tbserv*dthat w*rds typed on diff*rent mcasis*s pr*-served t*mp*ral prafiles sver the $equsncc*f inter-key }ate*ci*s. These propertiss oftirning t+f,rs ssparatetry *xamined by $o*-strucling special texts t'ar typing {Shaffer.r e?8 ).

One kind af text was designed to test acl*ck m+del af timing. For th* purpos* *fusir"lg s*rial *avari*fiec te*hniques, it wasdesirabl* tr; make the timing *f {novernc*ttransiti*ns &s *niform as possible: erccord*ingly the texts corrtained *nly words thatcat*il*d strict al[*r*ati*n betw*e* hands inthc norr$al c*xventions of typing {teadingt* phrases like '.authe *tic divisar,'n n'fiexdish

pau*it_v,.' etc. ). The typist was faster *nd l:*rtiming *ven less varis"blc with these tsxts;also the serial c*variii{ts* b*tw**{r silccessiv*int*r-key in tervals was negative, as a *l*ckmcdel re{+uires, and the correlatia* $s{T?c-tirn*s dppr*actred the the*retical lirnit *t'*t/r for a d*tsrrninate cl*ck.

TI"re atlr*r ki*d of text wils +3*signed toexarnin* whether timing pr*filcs wcrc rs-ducible to sffccts of rnovernent transiticn rri*v*lvcd factsrs beycnd {}re irnmcdiats t rsrr*siti*n. In particular, wc werf i*t*resled inttre passible anticipations of right csrltcxt.Acc+rdingly, texts wers c**structed fromsets ,;f wards sharing thc first fhre* lett*rs,distributirrg wcrds frr:n: different $sts overa text, and in s*mc tsxls alternati*g thesewards witfu th* t* frx the kft csr:tc.{t" Thclatencies, thet is, intsry;lls t* s*set, i* typing

th* first thre* lettsrs sf words were the crit*ical variabls$. It *'as f*r"rnd that the palt*rfiof latency in these l*tters was affccted bythe csr:ti*uatiar of the letter $equence, dem-on$trating extensive anticipati**.

Rumethart and Ncrman i f-iate 5 ) haverun a c*rnputer simulation of skilled typing-which atternpts t$ accsu*t for anti*ipat*rytiming as a sccond;rry consequence of antic-ipatory msvement" In the m*del e?ery rnsl$rco#Imard in an outpul buffer rec*ives a par-tial activati*n, the arncunt decr*asing sfiavsragr r+ith its *rdinal remote**ss from thecurrent eve*t. A movem**t to prsss a k*ywith s c*rtai* fingcr can implicate the lr*ndso that the pasiticn *f thc hand at afiy rtrr*-rnent is th* vsctsr res*ltant of ,r number *fwe ighted rnoverns*t te*dexci*s. Not onlymay tlr* h*nds mcvs but u*cor*rnitted frn*gfrrs may also more tawards th*ir next keysso t hat there is extensivc coarticulatian, Thelatcncy sf typi*g ihe next letter depends $rIthe surreilt pasiti** *f the hand and relevantfingerr; beeause ha*d pcsition is affected b3"

m*verxfnt tendencie* t*rrards letters to b*trvp*d- the*e can inff*en*e th* iate*cy +f the*ext keypress.

This model has ma*y inter*sting proper*t,ies- but a countsrex*mpl* frorn S}:af!*rt 19?8 ) sh*ws that it gives ail in*d*guareacccunt *f l*t*ncv p*tte rn. Th* f*ll*wingcontrast shuws the averagie latencies. in mil-Iiseconds, of typi*S the s*queflc*s w&fg andwhirr:.

whig 109 I:1 153 l*3whim tl{J 155 95 ISd

Th* prcceding wr:rd in ra*h case was th€,and se wc ses tlie anticipat*ry rffect of g arrn ixr the sequencf, 'r+'&r'. $n the keyb*ard l#*nd T are +Jn thc lcfi hasd , h* i, end ,?r arfl*n the middle, t$p, ;rnd b*tt.:m rsl,vso t*-speetiveiy, of the right hand,. I* whig ha*dp*siti** should mak* t slightty slower thanh: in whim the opposi*g pulls af i and ntsh*utrd rnak* h *lightty fastEr than in w*ig:th* dow*ward pull *f rt sh*uld r*ake I muchslower than in w&fg rnd lhe rernaining tra**sition t* rn shsuld m*ke thi* y€ry slow. Ther*l;ltive latencies *i * and I betwesn tl:+ twowor*s go merk*rll3' against the predicticns.

?his a*d *ther statistically significart csc*trasts lr**: the datil suggest that the typist

RHYTHM AND TIMING IN SKILL 117

used definite tactics to negotiats transition$equences. The inverted slowing between kand f preceding ffi suggests that these within-hand letters were typed as part of a group,coordinated in a compound movernent tra-jectory. We have still to discover tht rulesgove rning such groupings, but the consis*tency of word-timing profiles leads us to sup-pose that they fornE a logistic component ofa performance grarnmar.

How should ttre iwo results on timing betheoretically cornbincd? Let us supposc that,in fast typing a clock providcs a periadicity,and departures fr*rn periodicity arise frarnthe piay ol logistic rules over group$ of let-ters. Th*n either the logistic rules arrangea timing pattern that moves away from andreturns to ttre sequence of invariant clockpulses, in the man{}er of a musician makingan excursion from the beat, or the clock ral*is itself modulated by those rules. Shaffer( 198 1 ) suggested th* latter to draw ou[ aresemblance between th* latency patterns intyping and m usical rubato. An alte rnativeassurnption is that normal typing may notu$e a ciock, but clock timing can be adoptedas an exctic opt,ion if it is rsquired or if thetext induces a high degree of regularit,y inlhe movcmEnt ssqu*nce, as on "'alternation"texts.

The idea that tirning patterns move awayfrorn and return to an unyarying clock pulscis diffrcutt to test in its general form" andgoing back to tl're data we find no obvioussupport for it, The idea of a liexible clockhas been tested using cross-covariance anal-ysis t Yorbe rg & Hambuch, 1978 ). Thistschnique, applicabl* to sequencss with un-equal intervals, correlates pairs ol intervalsovrr the rcplications of a sequencc. A finoresynoptic test is obtainsri by using analysisof variance (Shaffer, 1980, 1981 ), in whichca$e negat,ive covilriation leads to f ratiusin rhe lcft tail of the f' distributir:n ( Waine r.1973). Xn effect ii gsneralizes a test for cc-variance used by K*:zhevnikov and Chistov-ich (Note 2).

Taking lhe datt use d to cxarnine te mporalpattcrn, 29 analyses *f variancs u/e re carriedout r:n lette r latencies Gver whotre words.Only half the F retios were less than I andtheir mean was 1.03. This fails Io supporta clock modei. S*r'nc o[ the f ra[ios wfre

nevertheless so small, the smallest be ing . 14,

that the temporal patterns were reexaminedin these extreme cases. They indicated some-thing other than random fluctuation on anunderlying pattern: It appears that the typistsometimes vacillated betwe*n two patterns,changing a slow-fast pattern into a fast*slowpattern for a pair of letter;. Sometirnes thetwo letters were not even adjacent.

S/e are led to conclude that normal fasttyping has only a nominally specified peri-odicity, Ttris is moduiated by contingencies*f move mcnt transition, and for some ofthese contingencies there are logistic rulesgrouping rnovements into cornpound trajec-torie s.

M usic PerJormofice

Because music has a beat and a metetr,there is rsason to expect its performance tobe contrCIlled by clbck timing. As a" prelirn-inary to studying this, Vorberg and Ham-buch ( 19?8) have looked at metrical tapping,using the data [a test n:odels of concat,enatedor hierarchic ctrock structures.

A variety of timing structurss can be ob-tained by as$e{nbling in different ways twobasic methods of timing a rhythrnic Sroupaf two be at intervals. One wey is to generatethe intsryals in concatenatisn; the other isto genflrate ttre group interval and its firstbeat interval, whictr thus determines the $ec'ond interval. These concatenated and hier-arch ic groups hal'f; dilfere nt variance-co*variance properties, which are inherited bythe larger structures that assennble them.

Ctrock intervals" f, and their derived beatinte rvals, 8, and als* their variances anci

covariancss, are related in the followingwa,v$ {Yorberg & Hambuch, l9?8}. Let Cibe an independent clock interYal {i : 1 or2) and 8i be a derived beat interval' Thenin a concatenation group

var

or,ll;, c,.

C*v ^B,, .8i.. r : 0^.

ln a hierarchic grouP C: gsnrrates the groupintervatr and Cr the interval between the firstend second beats. I*{*nce,

I IS L. H- SHATTER

B, s C*, Bt s Cr * C,;

Yar ,, :

Y*r C1,

Yar Bz = Var fr + Var fi;Cov SrBz * *Yar fr, Cov 828, : S.

The last expressi*n is of & covari*nc* e{ro$sa grsup b*undary. These sxprf,ssions de-scribe abstract timing structure*; the tirningprope rties of cbservable r*otor *v*nts can beobtained by adding ass*mpti*ns ab*ut therelationship bctlrr**t: a beat and irs csrrs-sp*nding ffiotor evsnt,

These ideas sf stru*tur* wfrs used t* sfi-alyzr twe pia*o p*rf*rffiacccs of a Bach fu-gui' *btained in succ*ssion frcm th* samepia*isr {Shaffer, l ps } }. The fugue wa$ infaur vaices, and so ths pianist had to playfour mcl*dic lines at oncf. Hach rnelody \rasa series *f r:otes **d rests varying in dura-tior, and these durations at afiy rnorne ntwere independ*nt e*rsss voice$. Playing ttrefour v*ic*s in c+ardi*atia* whilc maintai*-i*g tlrsir rhythmic and n:e ladic ind*pen-denc* secrns f*asible **1y if thc perf*rrr*rcan u$€ a eloek, sr cl*ck structure, 1* g*n-erate an abstraet fireter and play the nctesin relation t* this. A covaria*ce a*aly,sis per*f*rmed on the data suppcrted this co*jec-lur*. It app*ilrs that a cl*ck was used tocsastruct ttre halt--b*at intervals gf the rritJ-sic, *hich ,:+incid*d with ihc most frequentnote duration: The cross-covariafices be-twee* adjac*r:t int*rvals w*re nssative, andthe pilttern *l covaria*ce indieared that theintcrvals \i/er* gener*ted in cortcate nati**rath*i than in a l'rierarchy. *rr th* *t,herhand. gi:* **variailce between lhe durati**s*f sh*rt notfs that divided a fuaif-beat i*tcr-val fev*rsd * hi*rarchic structur*, supp*rl-ing th* idc:l thlt the miltt:r sy$tflm con-structed a c*tfip*und rTrtlvt:ffi*r:t trajectoryt$ pr*duc* shqlrt nr:t*s"

Ar:*thrr f*ature $t'ils rl'rat the timing *fsu*rsssive rn*tricsl units af tlre n:usic variedrlvcr the pe rfarm&ilcs. This variatio* rvilsreplicated in the two performailces andth*ref*rs reprcsc*t*d *xpre$sive rathrr ihsfirand*m variatir;n" Here \#c must suppo$ethat sxpr*ssive information in a {notor pro*grer$ w&$ used ts rnodutrate thc block rete-In tl:* nature of CIur assumpti** that tire

mot*r systern uses clock pulses as ternporalrsfe rence poi*ts, it is nsc*ss ery that bothIev*ls *f tirneke$Fer* clock and mot*r sys*tsrfi, should receive the exprcssive infcrma*tion $s that tl,ey can negotiats changes intennp* without becoming radically sut afphas*.

Alsa r*portcd with the Bach fuguc werestudi*s of perfcrmarrses of a Chopi* *tudyand a Bartsk dance, played by diffsrent pi*arrists. These illustrats the mastery *f dif-fere*t kinds *f rlrythrrric complexity in ryllr-sical prf*rffrafics, Thc Ch*pin study was rnexercise in playing the palyrhythm *f thre*agairrst, four, the right hand playing threeequal n*tes in s beat int*rval while the leftharrd played four. I* the perform&$ce it wasplayed with a free us* *f rubat* and withone hand moving off and back *nto the beat.Yct it was p*ssible to show by mappins thetirning *f *ne hand *nt* tlrc *ther that u*derthe twc kinds of *xpr*ssive deforraatisn *ftiming the two *rands prsservcd a prspsr Br*ittrm*tic division *f s roffirnan beat istervalinto thres a*d fs*r parts.

Th* corTrputatia*al dernands *f such aperf*rmance i*dicate the rlse of a hi*rarchyof timekeepers: a ffexible elock ts tims ttrsbeats and tir*ekcep€rs in the rn$tor subsys-leffis, sile far eaeh hand, to ff$nstruct theapprspriate subdivisi**s *f the beat arrd *l*iotry one hand to m{}Ye off the beat.

The rhythrnic i*tercst of the Bart*k da*ceis that it has a ffifter of three bcats u*equatrin le*gth. rr:ade up *l eight equal **tcsgrcuped three, thr*e, end two. fo{uch *f thelinr* sne hand h*d tr) play chords on thebeats while the othe r play*d thc fi*t*s. Agai*usi*g e*varia*cs in*tha*l* tiJ analyze tir* psr-f*rrnanc*, it rvas faund that the hand pla,v-i*gnotes *sed a clock. and t};eref$re carried thebeat. urhile the h*nd ptray*ing ch*rds w:rs al*lowcd to msve *ff rhe bcat.

In sh*rt, therc is evidence in piano per*f*rmance of a cl*ck rryhcss rat* carl be ex-pressively varird. A motor system can prs*duce c$rnpound rnsvsrnent trajectcries thatsubdivid* clock i*te rvals a*d can urlder-sficot sr sversl:oat cl*ek r*f*renc&s in a csrr*trollcd way"

Sr's have incide*tally shawn that skilledpianists have greater hand i*d*p*ud**cr andcan make rft*rs eomplex uss *f timi*g than

RHYTHM AND TIMINC IN SKILL il9

was observed by Kelso et al. ( 1979). In gen-erail, with prolonged practice the skilled per-forrner goes progressivcly beyond the pro-cessing constraints that limit ttre unskil.ledperson. Hence, we have argued that manyproblems of skilled performance cannot bestudied within the conventional paradigmsof introducing subjects to arbitrary labora-tory tasks (Shaffer, 198 I ). There are, forinstance, no counterparts of expressive tim-ing in unskilled performance. The impor-tance of studying speech in skills researchis that almost every adult is a relativelyskilled exponent of this complex activity.

S peech

In English speech there are rwo units thatmay plausibly have an underlying periodic-ity: the stress group and the syllable, bothof which are contentious entities in linguistictheory. The major proponents of the ideattrat speech production uses an abstractclock were Kozhevnikov and Chistovich( llote ?), who thought ol it as a rhythrngenerator. Fowler ( 1980, Note 6) has criti-cized such a theory on the grounds that itunderestirnates the tirne keeping ability ofthe rnotor system.

Kozhevnikov and Chistovich found nega-tive covariation betwee n t,he durations ofsuccessive phoneme segments and betweensuccessive syllables. The results are repli-cable but there are rsasons for resisting theinference of a clock {Ohala, Note 7). Oneof these arises from the difficulty of locatingthe boundaries of speech units from a phys-ical record. Ttre infer*nce of a clock dependson being,able to show, through a covarianceanalysis of time series, ttrat there is an un-derlying time interval more stable than theone rneasured. If the observed interval con-tains measurement error, this can induce anegative covariance as an artifact and socreate the illusion of hierarchic timing.

Another source of doubt arises from thernethod of obtaining data. Kozhevnikov andChistovich had subjects repeat the sentence-'Tanya topila banyu" 100 times in succcs-sion. in such a situation the speaker may fallinto a rhythmic rnode of speech that assumesclock timing" Thus, as in the typing of al-ternation texts, the task may" induce clock

timing, but it does not follow that ttris is thenormal mode of speech.

The problern of inadrrertently inducingclock timing in speech can be partly over-come by distributing the repetitions of targetphrases in time or by embedding them inlarger texts. The problem of measuring in-tervals separated by fuzzy boundaries ismore intractable and may restrict the scopeof covariance analysis as a test of clock tim-ing. Rather than attempt to refine methodsfor testing a clock concept it may be betterto finesse the problern and question whetherthe concept is relevant to a skill in rvhich aclock scrves no useful purpose. If timing isa prinrary variable in speech production, itsspecification can be interpreted directly bythe motor system. W'e have argued that thebasic role of an abstract clock is to providea basis for coordination, and this is not a

requirement of normal speech; people are notrequired to speak in unisoo, except in formalchants and church litanies.

If people repeatedly hear a recording ofa spoken sentence and are then asked to tapin time wit,h the rhythm. they readily do so,and they tend to interpret ttre instruction bytapping in time with the onsets of stressedvowels (Allen, 1972). Further, if they areasked to listen to recorded speech to detectirregularities in its rhythm, this task is easierif the speech has bee n distorted to affect theinterval between the onset of stressed vowels(Huggins, 1972). If the distortion prolongsone segment and shortens another, then thetwo changes may go unnoticed if they leavethe stress interval relatively unchanged. Thuswe learn that stress rhythm is the percep-tually dominant, rhythm in speech, at leastin languages such as English, and that theinterval between stressed syllables may carr,vdefinite timing expecta[ions.

A hypothesis, arising from Pike ( t l+S;,that stress groups in English are temporallyregular, is easily falsified by measurement,wtrich shows that the stress intervals in asingle discourse may vary fivefold in mag-nitude (Lehiste, 1977). A weaker hypothe-sis-that stress tirning is re gulated in ttredirection of isochrony-is too weak to ac-count for Huggins's result. An alternativestrong hvpothesis is that there are linguisticrules structuring degrees of stress over an

r20 L. H. SHAFFER

utterance, and what the listener detects inthe distorted recording is a violation of stresspatterning detcrrnined by this structurc. Lib-erman and Prince (197?) have shown trowa relative*prorninence rule , actiilg recur-sively a* a*ierarchy of binary syntactic con-stituents, can construct such a stress patternover the sequencc of syllables in a phrase orsentence. Ttreir theory may need modifyingto take account of the prosodic freedom ofsentencc stress assignment in making 5o-mantic and pragmatic distinctions ( Bolingcr"1972; Cutler & fsard, t 980]. The importantpoint is that speaker and listener can orientto the syllables of major stress, using stresspattern rather than duratioil as the prirnaryvariable of speech timirrg. Duration tras a

more definite role in the pragmatic use ofpausing, used to its greatest effect by actorsand comedians, and as a cue to the syntactic$tructure of e$ utterailce {Cooper, 1980;Huggins, l9?8; Lindblorn & Rapp, Note I ).

Stress is a variable acting on syllablesrather than on phonernfs. It affects the tirn-ing or intensity of all ttre phcneme$ in a syl-lable, although, as with speech rate, it affectsthe vowel rnore than ttre cofisonants (Klatt,I 9?6 ). Turning to ttre timing of phonernicsegrneRts, a case can be rnade that the rulesgoverning segmental timing are based on thesyllable or its demisyllabies.

Segment duration is context dependent.Some of the dependencies can be stated byphonatactic rules, for instance, the effect onvowel duration of whether the following con*sonanl is voiced sr unvoiced; others requirerules going be yond immediate adjac*ncy,such as those affecting consonant durationin conssnant clusters (Klatt, 1976), Thereis no loss in generative power in stating theseas rules acting on units suctt as demisylla*bles. Fudge ( 1969) identities the nTajar di-vision of a syll*ble into its initial consonantcluster and its rhyme, containing the nuclearvowe I and a consonantal c,:da. Fujimurat l9?9) obtains ii gain in descriptive powerby separating the postvocalic consonants intothose belonging lo the core syllable and theiraffixes. The gain in stating phcnologicalrules oR such units is tlrat it becornes rsia-tively easy for thc motor system costrollingspeech to compute compound movement tra-jectories tarticulatory g*stures) for syllabicgroup$ containing one or more syllables.

The question arises whether the syllablchas a nominally specified periodicity. [n sup*port of periodicity is the observation thatadding consonants to increase the sizs t:f a

syllable has the Elfect of compressing seg-

mental durations t Lindblom & Rapp- NotcI ). The effect doe s not produc€ an invariantsyll:lble duration but it may indicatc a reg-ulation of duratian. Another considerationis thilt sprch appears to have a definite rate:In order to perceive stress variation and theslowing at syntactic boundaries as prosodicvariables rather than as fluctuations in rate.there may need to be some underlying pe-riodicity that these variables modulate.Howevcr we have not tak*n account, for in-stance, of the way in which pitch contourrnay affsct the p€rception of stress or ratc.

Two further points on speech tirning arebrieffy discussed hers. They are raised byFowler {1930, }{ote 6}, but the treatmenthere is different. The relative timing of vsw-els and consonants changes with stress lcvelor speech rate. Fowler attempts to aicountfor tlris by supposing that vowels and con-sonants are produced by parallel but soor-dinated articulatari subsystems. This doesnot achieve the desircd result, however, be-cause it predicts either that o*e strcam ofsegme n[s, vowe ls or consona.ilts, shoulde hange wittroul the ottrer ( being parallel)or that both streams should change propor-tionally {being cooreiinated). In the presentttreory a syllable is produced by a compoundarticulatory gesture. Its fiajectory is com-puted to conyey an internal rhythrn of soundappropriate to the language or dialect whenthe syllable is uttered in citation form:Ciranging stress level or speech rate carr aLfect the trajectory *nd ia doing so alter theinternal rhythrn. Thus we are supposing thatwithin-syllable rtrythrn is coded in terms ofrnovsrrrenr and that duration itself is not aprirnary variable even at this level of sp,eech.Recalling the earlier argurncnt about sched-utres, this is not inconsistent with the ideathat speech has a ncminally specified peri-cdicity.

Alteration of internal rhyttrm in the syl-lable is not the only symptorn of stress orrale change" Speaking at a t-aster rate orreducing stress also affecrs vowe I color, rnov-ing it towards the neutral schwa. In thc limittire vowel is deiete{i so tlrat governor be-

RHYTHM AND TIMIhIG IN SKILL l2l

comes guvnor. Under the pressures of rapidspeech and casual style , several syllablesmay be compressed in an articulatory tra-jectory, as in "watctia gonna do?"

Fowler allorvs syllable boundaries to bedefined by vowel succession and attempts toaccount for both timing and coarticulationphenomena in terms of the superposition ofconsonantal gesturcs L)n the continuous ges-ture of vowel production. This fails to ac-count lor the coarticulation of consonantsand for coarticulation across syllable bound-aries; it does not consider the timing of post-vocalic consonants or show why syllable du-ration is affected by the size of the consonantclusters. In this paper rve have separated thefactors affecting movernent timing, anci hencecoarticulation, from those goueining eventtimingi the main purpose being to allowmovemcnts to anticipate their temporal goals.Sonne aspects of co'articulation have imme-diate acoustic consequences (Kent & IvIin-ifie, 1977 ), and so their tinning must be com-puted in a compound articulatory gesture.For example, the velurn must be lowered inpreparation for a nasal stop consonant, andthe timing of its lowering and return has tolimit the spread of nasality to adjacent pho-netic segments. On tlre other hand, rnanyforms of coarticulation have no important,acoustic consequences and their timing canbe arranged to satisfy factors such as move-ment economics, Lip rounding in prepara-tion for a vowel may have no effect on pre-ceCing consonants, and it has been observedto anticipate the vor+'el by as many as sirinterve ning se gments { Benguerel &. Cowan,1974): This goes beyond economy require-rnents, but it rnay be se rving as a visuallyexpressive gest,ure.

Reference f{otes

l" Jackcndofl R., & Le rdahl, F, A deep paralle! be-tween music and languag*. Unpublished manuscript,Indiana lJniversity Lingui:;tics Club, 1980.

2. Kozhevnikov, V. A.. & Chisrovich, L. A. Speech:Aniculation and perception {Publication No. 30541).Washington, D.C.: U.S. Department of Commerce,r 965

3. Gcntner, D. R., Grudin, J., &, Conway, E. Ftngermovem*nts in *anscription typing (Occasional Pa-per No" 4). La .lolla, Calii.: Center lor Hurnan ln-formation Pracessing, I 980.

4. Michon, J" A. Timing in t€mporal *acking. Socs-tcrberg, The Netherlands: Irrstitute for Perception,RVO-TNO, t967.

5. Rumclhart, D. E., & Norman, D. A. Siaulating askilled typist: A study af skilled cognitive-motorWrformance (Report No. 102). La Jolla, Calif.: Cen-tcr for Human Information Processing, 1981.

6. Fowler, C. A. Timing control in speech production.Unpublishcd manuscript, indiana Unive rsity Lin-guistics Club, 1977 .

7. Ohala, J. J" Aspects d the cantrol and productionof speecrt (UCLA Working Papers in Phonetics, No.l5). Unpublished manuscript, University of Califor-nia, Los Ange les, 1970.

8. Lindblorr, 8., & Rapp, K. Sonre iemporal regular-ities of spoken Swedrilr tPublication No. 2l ). Uni-versity of Stockholm, Sweden, lnstitute of Linguis-tics, l9?3.

References

Allen, G. D. The location of rhyttrmic beats in English:An experimrntal study I . Language end Speech,1972, I 5, 72- 100.

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Received April I 3, I98 I

R*vision received September I , 198 I r