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2005 BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIAALL RIGHTS RESERVED .

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Address correspondence to Peter Keller, Department of Cognitive Psychology,University of Finance and Management, Warsaw, ul. Pawia 55, 01-030 Warsaw, Poland.(e-ma il: [email protected])

ISSN: 0730-7829, electronic ISSN: 1533-8312. Please direct all requests for permissionto photocopy or reproduce article content to University of California Presss Rights andPermissions website, at w w w.ucpress.edu/journa ls/right s.htm.

M usic PerceptionSummer 2005, Vol. 22, No. 4, 629661

Musical Meter in Attention to Multipart Rhythm

P E T E R E . K E L L E R

MARCS Auditory Laborator ies, University of Western Sydney, Sydney, Australia& Universit y of Finance and M anagement, Warsaw, Poland

D E N I S K . B U R N H A M

MARCS Auditory Laborator ies, University of Western Sydney, Sydney, Australia

Performing in musical ensembles can be viewed as a dual task thatrequires simultaneous attention to a high priority target auditory pat-tern (e.g., a performers own part) and either (a) another part in the

ensemble or (b) the aggrega te texture that results w hen all part s are inte-grated. The current study tested the hypothesis that metric frameworks(rhythmic schemas) promote the efficient allocation of attentionalresources in such multipar t musical cont exts. Experiment 1 employed arecognition memory paradigm to investigate the effects of attending tometrical versus nonmetrical target patterns upon the perception ofaggrega te patterns in w hich they w ere embedded. Experiment 2 requiredmetrical and nonmetrical target patterns to be reproduced while memo-rizing different, concurrently presented metrical pa tterns tha t w ere alsosubsequently reproduced. Both experiments included conditions inwhich the different patterns within the multipart structure werematched or mismatched in terms of best-fitting meter. Results indicatethat dual-task performance was best in matched-metrical conditions,intermediat e in mismatched-metrical conditions, and w orst in nonmetri-cal conditions. This suggests that metric fra mewo rks may f acilitate com-plex musical interactions by enabling efficient allocation of attentionalresources.

Received June 1, 2003, accepted Ja nuary 7, 2005

M USIC is often complex, with multiple patterns sounding concurrentlyacross the different instrumental parts within an ensemble. In suchmultipart textures, parts a re usually differentiated by a number of fa ctors,including rhythm. This article focuses on how musicians contend with


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rhythmic complexity during multipart musical interactions. The centralclaim is tha t metric frameworkstha t is, cognitive/motor schemas tha tguide rhythmic perception and actionenable efficient allocation ofattentional resources and thereby facilitate the performance and percep-

tion of multipart music.

Metric Frameworks

Metric frameworks consist of multiple levels of pulsation that are gen-erated w ithin an individua l during music performa nce or listening. In theirsimplest form, metric hierarchies are made up of beat-level and bar-levelpulsations that are nested in ratios such as 4:1 (quadruple meter) or 3:1(triple meter). Pulsations at the beat levelwhich are often reflected infoot ta pping w hile performing or listening to musicare thought to play

a dominant role in rhythmic organization by serving as a referent levelof periodicity (Jones & Boltz, 1989; Pa rncutt, 1994). H igher level bar pul-sations allow a person to group beat-level pulsations into units that canbe used to measure the length of musical phrases (e.g., a 4-bar phrase) orlarger musical sections (e.g., the 12-bar chord cycle typical in Bluesmusic).

The degree to which a rhythm pattern is interpretable within a metricfra mework is one determinant of its complexity (G ab rielsson, 1993;Pressing, 1997; Shmulevich & Povel, 2000). In metrical patterns, theplacement o f individua l pat tern elements a nd the accents (i.e., salient loca-tions in pattern structure) associated with these elements imply periodic

metric divisions. This is illustrated in the left panel of Figure 1, whichshows notated examples of metrical and nonmetrical patterns. In Figure1, elements in the patterns labeled A and B are positioned so as to suggestperiods belonging to a quadruple and triple meter, respectively.Furthermore, the periodic elements that demarcate metric barsandhence occur at points where beat- and bar-level impulses coincide in thepatterns labeled A and Bwould most likely be perceived as accented(even though they are physically identical) because they are followed byrelatively long silent intervals (see Povel & Okkerman, 1981). Metricalambiguity ca n a rise w hen a patt ern contains evidence of periodicities tha tare consistent w ith more tha n one fra mewo rk. Even so, it is generally the

case that a metrical pattern will fit best within a particular frameworkusually the framework that maximizes the number of pattern elements,and minimizes the silences, tha t co incide with metric pulsations (McAuley& Semple, 1999; Povel & Essens, 1985). For example, although the pat-tern (labeled G ) show n in the bott om right pa nel of Figure 1 fits w ithinquadruple and triple frameworks, the quadruple fit is better. (This was

Peter E. Keller & Denis K. Burnha m630


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Fig.

1.Exampleso

frhythmp

atterns.QuadrupleandtriplepatternsarenotatedinA

andB,

respectively,withbeatandbar-level

metricpulsa-

tionsdepictedbelo

w

asdots.

A

nonmetricalpatternisn

otatedinC,withanunderlying49-unitgrid(eachunit!

150ms).

Multi

partpatterns,

inwhichthequadr

uple,

triple,

andnonmetricalpatterns

(fromA,

B,

andC)serveastargetintegrantpatterns,arenotatedinD,

E,

andF,

respec-

tively.

Theaggrega

tepatternthatresultswhentargetan

dcomplementaryintegrantpatterns

arecombinedisshowninG.

Notethatx,

o,

andveachrepresentasoundonset(withadifferentinstrumentaltimbreforeachletter),

and-representstheabsenceofasoundonset.


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determined empirically; see Experiment 1, Stimuli and Appara tus section. )N onmetri cal patternslack (explicit and implicit) periodicity and do notencourage metric framework generation. Because of their structural irreg-ularity, nonmetrical patterns are more complex than metrical patterns

composed of the same number of elements (see the pattern labeled C inFigure 1).

Numerous empirical studies have demonstrated that recognition mem-ory and reproduction accuracy are superior for metrical patterns com-pared with nonmetrical patterns (e.g., Bharucha & Pryor, 1986; Essens,1995; Franks & Canic, 1991; Povel & Essens, 1985). Furthermore, met-rical patterns are recognized poorly and judged to be complex when theyare interpreted according to a meter other than the one that they fit best.This result has been demonstrated in studies where recognition tests andcomplexity judgments were carried out on patterns that were presented inthe presence of periodic auditory markers that were either consistent or

inconsistent w ith the patt erns best-fitt ing meter (e.g., Keller, 2001a; Povel& Essens, 1985). On the basis of such findings, it has been argued thatmetric frameworks facilitate both the efficient processing and representa-tion of rhythm (Keller, 1999).

With regard to real-time processing, metric frameworks provideexpectancy schemes that guide attention to important locations in a pat-terns structure (D esain, 1992; G jerdingen, 1989; Jo nes, 1990; Jo nes &Boltz, 1989; Jones & Yee, 1997; Large & Jones, 1999; Yee, Holleran, &Jones, 1994). Based on these expectancies, an individual will automatical-ly invest more attentional resources at strong metric locations (e.g., thebeginning of bars a nd beats) than a t w eak locations (e.g., betw een

beats). This results in efficient processing because, in music, pattern ele-ments are statistically more likely to occur at strong locations (Palmer &Krumhansl, 1990; Palmer & Pfordresher, 2003).

M etric framew orks also facilita te the representationof rhythm patternsin memory by providing a grid-like template for organizing pattern ele-ments w ith respect to their position relative to one another in time (Essens& Povel, 1985; Handel, 1998; Palmer & Krumhansl, 1990; Palmer &Pfordresher, 2003; Parncutt, 1994). Representations based on metric hier-archies are efficient in the sense that if elements from each particular met-ric level are connected in memory, then temporal information is effective-ly chunked in a manner tha t highlights the relationship betw een nona dja-

cent elements (Martin, 1972; Palmer & Pfordresher, 2003; Palmer & vande Sande, 1995). Efficient processing and representation are jointlyimporta nt because musical interactions, for performers and listeners alike,involve monitoring a dyna mically unfolding a uditory event w hile retriev-ing information from memory to guide ones participation in the event.Here we investigate whether the processing and representational efficien-cy associated with metric frameworks is beneficial specifically in the con-



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text of multipart rhythmic interactions, wherein attentional resourcesmust be allocated to separa te instrumental parts.

Attention to Multipart Musical Patterns

In multipart rhythmic textures, such as those that characterize poly-phonic (contrapuntal or chordal) music, separate parts articulate differentrhythm patterns concurrently. These contrast with single-part rhythmictextures, in which either there is only one part (monophony), or multipleparts articulate the same rhythm (homophony). In Kellers (1999, 2001b)terminology, each part in a multipart texture is called an int egrant patt ern(see Figure 1D, 1E, 1F), and the structure that emerges when these partsare combined is called an aggregate patt ern(see Figure 1G ). M ultiparttextures afford four main attending modes: selective attention, divided

at tention, nonprioritized integrat ive attention, a nd prioritized integrativeattention. Selective attending(SA) occurs when the individual focusesat tention on a part icular integrant pa ttern and ignores other integrant pa t-terns. Standard divi ded att enti on(DA) involves attending simultaneouslyto several integrant pa tterns w ithout necessarily integrat ing them. On theother ha nd, nonpr ior it ized integrative attending(NPIA) involves combin-ing all integrant patt erns and focusing on the emergent a ggregate pattern.Note that NPIA differs from DA in the sense that it necessarily involvesrecognizing the relationship between the features of perceptually distinctstreams of informat ion, rather that simply being a mat ter of spread ingattention across such streams (Jones & Yee, 1993). SA, DA, and NPIA

have been studied in musical contexts (e.g., C raw ley, Acker-M ills, Pa store,& Weil, 2002; Jana ta , Tillmann, & Bha rucha, 2002; Satoh , Takeda,Nagata, Hatazawa, & Kuzuhara, 2001).

Prior it ized in tegrati ve attending(PIA) is a hybrid of SA and NPIA. Itinvolves simultaneously attending to a high priority ta rget integrantpattern (e.g., the part that carries the melody, or a performers own partin a musical ensemble) andthe aggregate structure that results when allintegrant patterns are combined. Thus, PIA can be viewed as a dual taskto the extent that it requires attentional resources to be divided between(a) producing and/or tra cking the target integra nt pa ttern and (b) group-ing together the elements of all integrant patterns to derive the aggregate

(Keller, 2001b). For present purposes, it is assumed that, during PIA,attending to the target integrant pattern is the primary task and attendingto the aggregate pattern is the secondary task (as would certainly be thecase in ensemble performance). Dual task demands also arise during DAwhen attention is divided between the integrant patterns in a multiparttexture made up of only two parts. It is important to note that PIA is aform o f D A, albeit one w here it is necessaryto a ttend to t he interrelation-

Attention to M ultipart Rhythm 633


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ship between two (or more) integrant patterns. Such integration is not anecessary condition with standard DA.

The current study a ddresses the dual ta sk demands of bo th PIA and D Ain the context of multipart musical rhythm. H ow ever, the ma in focus is on

PIA because it seems to correspond more closely than standard DA to thegoa ls of ensemble performa nce: To produce an a ggregat e pattern tha tpresents a coherent and cohesive musical entity (see Keller, 2001b).

The Dual-Task Demands of PIA

In dual-task situations generally, it is typical to observe a trade-offw herein performance on t he secondary ta sk suffers as the difficulty of theprimary task is increased (see Wickens, 1980). This trade-off has beendemonstrated in numerous studies investigating standard DA (see Damos,

1991, a nd P ashler, 1998, for review s), a nd w e assume that a similar trad e-off occurs with PIA in the context of multipart music. Thus, aggregatepattern perception should become less accurate as the rhythmic complex-ity of the target integrant pattern is increased. Specifically, aggregate per-ception should be compromised when target integrant patterns are non-metrical relat ive to w hen they are metrical. Such a finding w ould be con-sistent with the notion that attending to a nonmetrical target integrantpatt ern places great er demands on resources than a ttending to a metricaltarget integrant, and therefore produces greater interference to aggregatepattern perception. Thus, metric frameworks may promote the efficientprocessing of the target integrant and thereby free attentional resources

for the task of processing the aggregate. In a sense, this idea is related toM ichons (1985, p. 29) more general claim tha t the process of synchro niz-ing ones biologically based rhythms with periodicities implied by an envi-ronmental event enables the individual to function with a certain degreeof independence from the event, in effect granting t he freedom to doother things in between the instants at which perfect coincidence is cru-cial. H ow ever, it is unlikely tha t th is type of independence is sufficient foroptimal dual-task performance in the case of PIA, as the two tasks areinextricably linked through an overlap in stimuli: The target integrant pat-tern is itself part of the aggregate pattern. This overlap suggests that itmight be useful to consider the degree to which the tasks of attending to

the target integrant a nd the aggregate are compatiblew ith one anot her, inaddition to the complexity o f the ta rget integrant itself.

In the domain of dual-task research, two concurrent tasks are consid-ered to be compatible to t he extent tha t some dimension or a spect of o nestimulus can be used to predict a dimension or aspect of the second stim-ulus (D amos, 1991, p. 105). In t he context of multipart musical rhythm,



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dual-task compatibility varies as a function of how well the target inte-grant and the aggregate pattern can be accommodated within the samemetric framework (Keller, 1999, 2001b). This conception of compatibili-ty allows multipart patterns to be classified as illustrated in the top right

panel of Figure 1. Each of t he three multipart pat terns show n here (labeledD, E, and F) consists of a target integrant pattern and a complementaryintegrant patt ern that combine to form the same aggregate patt ern, which,w hen isolatedsee the pattern labeled G in the botto m right pa nel ofFigure 1is metrically a mbiguous but best fits a quad ruple meter. The let-ters x, o, and v in the Figure correspond to sounds that differ in instru-mental timbre.

The manipulation of interest occurs in the target integrant patterns,w hich w e constructed so a s to fit either a quadruple (patt ern D ) or a triple(pattern E) meter (i.e., these patterns house an implicit underlying beat,with pattern elements occurring either every four or three beats, respec-

tively), or to be nonmetrical (pattern F) in structure (i.e., there is noimplicit beat ). The complementary integrant pa tterns w ere then construct-ed by placing elements around the elements of each target integrant pat-tern in a manner that gave rise to the same aggregate pattern in all threecases. Thus, the metric identity (quadruple, triple, or nonmetrical) of theta rget integrant patt ern changes across the three multipart pa tterns to pro-duce three levels of multipart rhythmic compatibility relative to the aggre-gate pattern. In pattern D in Figure 1, the target integrant and aggregatepatt erns both best f it a quadruple meter and are hence highly compat ible.Compat ibility is lower in pat tern E, w here the target integrantif consid-ered in isolationis triple meter whereas the aggregate, although metri-

cally ambiguous, best fits a quadruple meter. Compatibility is lowest inpattern F, where a nonmetrical target integrant meshes with its comple-mentary integrant to yield the metrical aggregate. Although the patternsshown in Figure 1 are obviously contrived (they correspond to a subset ofthe experimental stimuli described below ), there are plenty o f exa mples ofreal multipart music in which integrant patterns yield different metricinterpretations depending on whether they are presented in isolation or incombination with other integrant patterns (e.g., see Yeston, 1976).

PIA should benefit from compatibility between target integrant andaggregate aspects of multipart patterns because, as in compatible dual-ta sk situat ions generally, a common mental set, processing ro utine, o r

timing mechanism can b e activated in service of the tw o ta sks (Wickens,1991, p. 23). Metric frameworks may provide such a common mechanismduring multipart rhythmic interactions. Although this hypothesis has notpreviously been tested in the context of PIA (i.e., by ma nipulating compa t-ibility between a target integrant and aggregate pattern, as in the presentstudy), it has been shown that attention can be divided more effectively



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betw een separa te integrant patt erns w hen they are temporally compatiblewith one another than when they are incompatible. For example, Kleinand Jones (1996) required listeners to detect subtle timbre cha nges in con-current high- and low-frequency tone sequences that were either compat-

ible or incompatible (i.e., the ratio between periods marked by theisochronous high-tone sequences and those implied by the nonisochro-nous low-tone sequences was simple or complex, respectively). When lis-teners were instructed to respond to changes in the high sequence and toignore the low sequence (SA), detection was better with incompatible thanwith compatible sequences. However, when listeners were instructed torespond to changes in both sequences (which may be interpreted either asDA or NPIA),1 detection w as best w ith compa tible sequences. Together,these findings suggest that incompatibility between integrant patternsfa vors SA to individual part s, w hereas compat ibility betw een integrantswhich presumably allows them to be processed according to a single

schemein fact encourages attention to be cast across parts in the multi-part texture.

Aims of the Current Study

Tw o experiments are reported in the current a rticle. The aim o f t he firstexperiment was to investigate whether temporal compatibility betweenta rget integrant a nd a ggregate aspects of multipart patt erns affects abilityto engage in PIA. This was tested b y using a d ual-task pa rad igm in w hichmusically trained participants were required to memorize, and subse-

quently recognize, both the target integrant aspect and the aggregateaspect of multipart patterns (such as those shown in Figure 1D, E, and F).When target integrant and aggregate patterns are matched in terms ofbest-fitting meter, the structural boundaries between bar-level units coin-cide, and hence a common metric framework provides an appropriatescheme for processing and representing both aspects of the multipart pat-tern. Moreover, the fact that both the target integrant and the aggregateshare an underlying beat structure, w hich a ffords synchronization, shouldprove advantageous. It was hypothesized that attending to the target inte-grant would produce minimal interference to aggregate perception undersuch circumstances. H ow ever, w hen a nonmetrical t arget integrant patt ern

is embedded w ithin a metrical a ggregate patt ern, structural incompatibil-ity is relatively high. Aggregate perception is expected to be impoverishedunder such circumstances because attending to the aperiodic structure ofthe target integrant may (at least) divert a proportion of resources from


1. Klein and Jones (1996, p. 36) refer to this as a divided attention condition but theirinstructions specified to integratehigh and low tones to form a unified rhythm.


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the task of encoding the aggregate pattern or (at worst) enlist processingroutines that tota lly preclude metric framew ork generation, thus distract-ing the attender from the periodicity underlying the aggregate. In any case,resource allocation should become effortful and not conducive to PIA

when target integrant patterns are nonmetrical. Finally, when the targetintegrant and aggregate patterns are mismatched in meter, they share acommon underlying beat structure, but their structural bar-level bound-aries are in conflict. If it is assumed that only one metric framework canbe generated a t a time, t hen, in such situat ions, the aggregate patt ern ma ybe processed and represented relatively inefficiently according to theframework belonging to the target integrant. The second experimentexamined similar issues in the context of a pattern reproduction taskrequiring D A.

Experiment 1

Experiment 1 employed a recognition memory paradigm designed tosimulate the PIA demands that arise in many instances of listening toensemble music. We focus exclusively on individuals who have experienceat musical ensemble performa nce in this a rticle. In each experimental tr ial,listeners are first exposed t o a multipart patt ern composed of a ta rget inte-grant pattern and a complementary integrant pattern, and then they areimmediately tested for recognition memory of either the target integrantor the aggregate structure (made up of the sum of the target and comple-mentary integrant patterns). Following each single presentation of the

multipart exposure pattern, listeners are required to rate how confidentthey are that correct and incorrect memory test patterns are the same as,or different from, either the target integrant o r the aggregate aspect of theexposure pattern (see Figure 2). Whether memory is tested for the targetintegrant or the aggregate pattern is varied randomly from trial to trial,and participants are cued only after the exposure item has ended as towhich type of memory test will occur. We assume that engaging in PIA is


Fig. 2. Diagram depicting the contents of a single trial from Experiment 1. First, a multi-part exposure item is presented, during w hich PIA is required. This is follow ed by a recog-nition test phase, w herein either an integrant o r a ggregate test item is presented, a nd fina l-ly a scale appears for the listener to m ake a same/different confidence rating o f the t estitem.


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Fig.

3.Quadruple,

triple,

andnonmetricaltargetintegrantpatternsand(metricallyamb

iguous)aggregatepatternsfrom1

2rhythms

ets.

Rhythmicfiguresareindicatedbyellipsesinthequa

drupleintegrantpatternfromR

hythmS

etI.Assignmentofrhythms

etsto

thesixlev-

elsofthebetwe

en-groupfactor(seeExperiment1,D

esignandProcedure)isindicatedin

thecolumnsheadedGroup.


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consists of nine elements (i.e., sound events) that are clustered throughout the pattern toform fo ur to five rhythmic figures, tha t is, isolated elements or short runs of (tw o orthree) elements (see Handel, 1992, 1998; Hbert & Cuddy, 2002). (These figures havebeen highlighted in the Q uad ruple target integrant pa ttern nota ted in Figure 3.) Targetintegrant patterns from different rhythm sets are distinguishable on the basis of their con-

stituent rhythm ic figures and /or t he seria l ord er in which these figures occur. Tar get inte-grant patterns within each rhythm set consist of identical rhythmic figures, but the posi-tioning o f t hese figures relative to an underlying 49-unit grid varies such tha t figure-finalelements occur periodically in qua druple and triple patterns and aperiodically in nonmetri-cal patterns. Specifically, the final element of each successive rhythmic figure is placed at(a) grid unit 1, 17, 33, a nd 49 (i.e., every 16 units) in qua druple patterns, (b) grid unit 1,13, 25, 37, and 49 (i.e., every 12 units) in triple patterns, and (c) grid unit 1, 15, 28, 40,and 49 (irregularly) in nonmetrical pat terns. These arra ngements w ere intended to encour-age the perception of quadruple meter, triple meter, and nonmetrical structure when pat-terns are presented at a rate corresponding to a grid-unit duration of 150 ms. At this rate,the beat-level period in the metrical pat terns spans four grid units (corresponding to a beatduration of 600 ms, which is within the range of 400900 ms at which pulse salience isthought to be maximal; see Fraisse, 1982; Parncutt, 1994). This leads to three bar-levelperiods (each spanning 16 grid units) in quadruple patterns and four bar-level periods(each spanning 12 grid units) in triple pat terns, given tha t the overall length of a ll patternsis 49 grid units (and the 49th unit serves merely to allow all patterns to end with an ele-ment). Keller (2001a) has demonstra ted the perceptual va lidity of the ab ove classificat ionof ta rget integrant pat terns as qua druple, triple, and nonmetrical in a series of experimentswith participants that varied in terms of musical experience.

Importa ntly, the target aggrega te pattern in each rhythm set has the potential to con-ta in each of the three tar get integrant patt erns belonging to its set. That is, if a ta rgetaggregate was presented simultaneously with one of its related target integrants, then atno point w ould a sound in the target integrant coincide with a silence in the aggregat e. Thenumber of elements in aggregate patterns varies across rhythm sets (although overalllength is a consta nt 49 grid units), ranging fro m 21 to 28, w ith an a verage of abo ut 25 ele-ments. Although all aggregate patterns are metrically ambiguous (they have the potentialto contain either a quadruple or a triple target integrant, and hence can be accommodat-ed by either a quadruple or triple metric framework), a pilot experiment (Keller, 2001a)involving judgments made by musical experts confirmed that they best fit a quadruple

meter. Specifically, fo ur professional musicians w ere required to rat e the aggregat e patternsfrom each rhythm set twiceon a goodness-of-fit scale. One rating measured how well thepatt erns are perceived to fit a q uadr uple meter, a nd the o ther measured t riple fit (the orderin which ratings were made was counterbalanced). For each aggregate pattern, the musi-cians were unanimous in giving a q uad ruple rat ing that w as higherindicating better fitthan the corresponding triple rating.

Each rhythm set contains three multipart exposure itemsmatched-metrical, mis-matched-metrical, and nonmetricalin which a quadruple aggregate structure houseseither a quadruple, a triple, or a nonmetrical target integrant pattern, respectively.Specifically, multipart exposure items w ere derived b y com bining each o f t he three targetintegrant patterns from a given rhythm set with a complementary integrant pattern so asto yield the aggregate pattern from that set. These complementary integrant patternswhich are not notated in Figure 3simply consist of the elements that are necessary toproduce the relevant a ggregate pat tern (as in Figures 1D , 1E, a nd 1F).

Memory test stimuli consisted of target and distracter integrant items and target anddistracter aggregate items. The target integrant patterns presented in isolation served astarget integrant test items. There are three distracter integrant items for each of the threetarget integrant patterns (quadruple, triple, and nonmetrical) within each rhythm set.Distracter integrant test items were created by temporally displacing either one or tworhythmic figures forward in time by two grid units relative to their position in the targetintegrant pa tterns. The second rhy thmic figure w as shifted in early-change distracter itemsso that the temporal deviation was located in the initial half of the pattern; the third rhyth-



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mic figure was shifted in late-change distracter items, resulting in a temporal deviation inthe final half of the patt ern; and the second an d third rhythm ic figures w ere bot h adva ncedin both-change distracter items, resulting in a large chunk of the target pattern being dis-placed (see Figure 4).

There are also one target and three distracter aggregate test items per rhythm set (see

Figure 4). The ta rget aggrega te item is a single-part version of the aggregat e pattern fro mthe rhythm set. The three distracter aggregate items were created by first partitioning thetar get aggregate patt ern into three groups (A, B, and C ) of 16 grid units in accorda nce w ithits quadruple structure. Then the order in which these three groups occurred was variedfor each distracter item: BAC in early-change distracters, ACB in late-change distracters,and CBA in both-change distracters. Thus, the quadruple structure implied by targetaggregate patterns is preserved in distracter aggregate items, but the serial order of bar-level groups of elements varies.

Thus, altogether, the stimulus pool consists of 36 multipart exposure items (matched-metrical, mismatched-metrical, and nonmetrical items from t he 12 rhythm sets), 36 ta rget,early-, late-, and both-change distracter integrant test items (three each per rhythm set),and 12 target, early-, late-, and both-change distracter aggregate test items (one each perrhythm set). In multipart exposure items, the target integrant pattern was articulated by aconga drum sound and the complementary integrant pa ttern wa s articulated by a cowb ellsound. Integrant test items were articulated by a conga drum sound and aggregate testitems were articulated by a snare drum sound. (We used different instrumental timbresmainly to avoid potential confusion about whether integrant or aggregate memory wasbeing tested, but also to allow us to examine how well listeners are able to abstract theaggregate structure from two interleaved integrant patterns). All sounds were taken from


Fig. 4. Target a nd distra cter versions of integrant a nd a ggregate test items from a singlerhythm set. Bra ckets indicate regions where the structure of d istracter items deviates fromtar get structure.


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an archive in Sample C ell (a sa mple player/editor d eveloped by Digidesign). O ther a ppa-rat us consisted of AKG K270 headphones and M AX (Version 3.5) softw are running on aMacintosh IIvx computer.

Design

Multipart rhythmic structure (matched metrical; mismatched metrical; nonmetrical)w as varied w ithin participants. In addition, a between-group factor w ith six values (Group1-6) wa s included for control purposes; specifically, to allow multipart r hythmic structureto be treated as a within-group factor without individual participants encountering thesame aggregate pattern in more than one experimental block (see Procedure for moreinformation). Participants were allocated randomly to the six groups in equal numbers.The dependent variable was recognition accuracy for integrant and aggregate test items(see D ata Transfo rmat ion a nd Analysis).

Procedure

Par ticipants w ere tested individually a t the computer in a small sound-at tenuated cham-ber, and sounds were presented over headphones at a comfortable loudness level. Each

participant first completed a training session consisting of (a) a computer-based tutorialaimed a t establishing whether the participant could d etect the types of cha nges tha t distin-guished ta rget and distracter test items, and (b) an exercise tha t provided d etailed instruc-tions and an opportunity to pra ctice the task in one experimental blo ck (using stimuli fromeither the matched-metrical, mismatched-metrical, nonmetrical multipart rhythmic struc-ture condition; randomly assigned on a participant-by-participant basis). This was fol-low ed by a test session consisting of six blockstwo for each multipart rhythmic structurecondition (matched metrical; mismatched metrical; nonmetrical) with block order ran-domized. The identity of the rhythm sets from which stimuli were drawn for use in theseblocks was determined by the group to which the participant had been allocated. Each ofthe six groups accounted for the three types of structure with different combinations oftarget integrant patterns (quadruple, triple, or nonmetrical) and aggregate patterns, withthe constraint t hat all possible integrant/aggrega te combinat ions w ere exhausted acro ssgroups. The assignment o f rhy thm sets to groups is show n in Figure 3. Thus, each part ic-

ipant encountered target integrant and aggregate patterns from two different rhythm setsin each of the three multipart rhythmic structure conditions, with rhythm sets and condi-tions being combined differently for participants in different groups.

The task involved a series of trials, wherein each trial consisted of an exposure phasein which a multipart exposure item was presented once, and a recognition memory testphase in w hich a single test item w as presented. Each o f six experimenta l blocks contained10 such trials, acro ss which the sam e multipart exposure item w as presented. To gua rdagainst metricality carryover effects (maintaining metric pulsations from one block to thenext), pattern presentation rate was varied from block to block by choosing between threegrid-unit dura tions: 129, 150, and 179 ms. These values were chosen to encourage the per-ception o f bea t-level periods (516, 600, and 716 ms) based on gro ups of fo ur grid units inmetrical patterns. The task took approximately 1 hour to complete.

To initia te a t rial, t he participant depressed the space bar on t he computer keyboard. Theparticipant was required to listen to the multipart exposure item that ensued, and simultane-ously to memorize the target integrant, or part, pattern (played by the conga drum), and

the aggregate, or w hole, pattern that resulted from combining the target (conga drum) andcomplementary (cowbell) integrant patterns. Instructions specified that both aspects of thetask, that is, memorizing the target integrant and memorizing the aggregate pattern, wereequally important: Hence, PIA was required. One second after the exposure item ended,either the wo rds PART TEST or WHO LE TEST appeared on t he computer screen.When PART TEST appeared, a target or distracter integrant test item (played by the congadrum) was presented 3 s later. When WHOLE TEST appeared, a target or distracter aggre-gate test item (played by the snare drum) was presented after a 3-s silent interval.



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After the test item, a six-point rating scale automatically appeared on the computerscreen, with points labeled from left to right very sure different, moderat ely sure dif-ferent, not very sure different, not very sure same, moderately sure same, verysure same. The participant w as required to rat e (by clicking on the scale) the degree tow hich they w ere confident that t he integrant or a ggregate test item wa s the same as, or dif-

ferent from, the target integrant or aggregate pattern, respectively. Information aboutw hether memory w ould be tested for the target integrant o r aggregate pattern w as w ith-held until aft er the exposure item had been presented in o rder to encourage the participantto attend simultaneously to integrant and aggregate aspects of the multipart pattern. Thefirst four trials of every block contained a target integrant, a both-change distracter inte-grant, a target aggregate, and a both-change distracter aggregate test item (presented inrandom order for each participant). Each of the remaining six trials within a block con-tained either a target, an early-change distracter, or a late-change distracter integrant testitem, or a target, an early-change distracter, or a late-change distracter aggregate test item(in random order). Thus, three integrant test items (one target plus two distracters) andthree aggregate test items (one ta rget plus two distracters) were presented in ra ndom orderacross the last six trials of each block. The random ized presenta tion ord er of test items w asintended to ensure that in each trail within a block the listener was unable to predict reli-ably w hether memory w ould be tested for t he target integrant pa ttern or the aggregate pat-tern. Thus, w e assume tha t listeners w ere forced to engage in PIA in each tr ial.

Data Transformation and Analysis

To separa te sensitivity from response bias (i.e., a tendency to fa vor same or differ-ent rat ings), same/different confidence rat ings for integrant and aggrega te test items w ereconverted to d' and c' scores (see Macmillan & Creelman, 1991) after collapsing acrossthe three levels of confidence w ithin the same and the different category. O nly ratingsfrom t he final six trials of ea ch experimental blockwhich comprised target, early-changedistracter, and late-change distracter integrant and aggregate test itemswere thus con-verted. (Earlier trialswith t arget a nd b oth-change distra cter itemsserved to fa miliarizethe participant w ith the multipart exposure item.) Early-change and la te-change distracterswere collapsed for the computation of d'and c'. Analyses of variance (ANOVAs) wereconducted for the d' and c' scores, with the criterion for statistical significance set at " =.05. The G reenhouse-G eisser correction w as a pplied w hen the value of the degrees of free-

dom numerator exceeded 1.

RESULTS

Recognition scores (d') for integrant and aggregate test items inmatched-metrical, mismatched-metrical and nonmetrical conditions areshown in Figure 5.2 High scores indicate high sensitivity to changes fromexposure to test. Response bias scores (c') are reported later.

To determine w hether listeners were in fact engaging in PIA, w e exa m-ined whether recognition accuracy for target integrant and aggregate pat-terns was reliably greater than chance by comparing listeners d' scores

aga inst zero in separa te ttests. These tests revealed better than chance per-formance both for integrant patterns (M d' = 0.78), t(23) = 2.78, p< .01,and for aggregate patterns (M d' = 1.94), t(23) = 7.89, p< .001. Finding


2. The error bar on the rightlabeled 2*SErepresents double the standard error ofthe mean. The standard error was computed in the manner suggested by Loftus andMasson (1994) for repeated-measures designs.


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that aggregate recognition was better than chance is particularly impor-tant because indicates that listeners were able to abstract the aggregatestructure from two interleaved integrant patterns. We would not haveobtained this result if listeners had simply divided their attention betweenthe target and the complementary integrant patterns without integratingthem (because the aggregate test items were presented in a single instru-

mental timbre). Similarly, recognition accuracy for target integrant pat-terns would not have been better than chance if listeners were focusingexclusively on the aggregate structure (pure NPIA). Thus, we concludethat the listeners were most likely engaging in PIA.

A preliminary ANOVA on the d' scores revealed that the between-group fa ctor ha d no significant effect on recognition, F(5, 18) = 1.34, p>.2, so we collapsed across this factor for the main analysis. The mainanalysis examined the effects of multipart rhythmic structure on recogni-tion at both the target integrant and the aggregate textural levels in a 3(matched-metrical, mismatched-metrical, nonmetrical) 2 (integrant,aggregat e) ANO VA. This ana lysis revealed significant ma in effects of mul-

tipart rhythmic structure, F(2, 46) = 4.98, p< .02, and textural level, F(1,23) = 11.12, p< .01, but no significant interaction between these factors,F(2, 46) < 1.

The effect of multipart rhythmic structure w as unpacked by using tw oplanned orthogonal contrasts that are based on the predictions stated inthe introduction to the current experiment. The first contrast compared


Fig. 5. Recognition accuracy (mean d') for target integrant and aggregate patterns inmatched-metrical, mismatched-metrical, and nonmetrical conditions in Experiment 1.(The error bar on the rightlabeled 2*SErepresents double the standa rd error; see foot-note 2.)


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recognition accuracy between the matched-metrical condition and thenonmetrical condition. In a ccorda nce with o ur main prediction, t he recog-nition of ta rget and integrant a nd a ggregate patterns w as reliably better inthe matched-metrical condition than in the nonmetrical condition, F(1,

23) = 6.79, p< .02. The second contra st tested our more tenta tive predic-tion that recognition accuracy in the mismatched-metrical conditionw ould be intermediate to accuracy in the ma tched-metrical condition a ndthe nonmetrical condition. This contrast compared accuracy scores fromthe mismatched-metrical condition with the average of the accuracy scoresfrom the matched-metrical and nonmetrical conditions combined. In sup-port of our second prediction, accuracy scores from the mismatched-met-rical condition were intermediate: They were not significantly differentfrom the average of the accuracy scores from the matched-metrical andnonmetrical conditions combined, F(1, 23) = 0.52, p> .4. This resultseems to support a null hypothesis, which raises the question of whether

our test had sufficient sta tistical pow er. O ur ana lysis indicates that it did:For the main effect of multipart rhythmic structure, partial #2 (a measureof effect size) wa s .17 and o bserved pow er wa s .77 (w hich is around con-ventionally accepted levels).

The main effect of textural levelindicating that recognition wasgenerally better for aggregate patterns than for target integrant pat-ternsmay be due to (a) participants treating aggregate recognition asthe primary dua l-ta sk component, a nd/or (b) the types of cha nges fromtarget to distracter items being easier to detect in the case of aggregatetest items (w herein the serial ord er of f igural groups w as chan ged) tha nintegrant test items (wherein the time interval between figural groups

was changed, while the order of these groups remained the same). Itwas not a purpose of the current study to distinguish between thesealternatives.

The fact that textural level did not interact with multipart rhythmicstructure indicates that the effects of multipart rhyt hmic structure w erecommensurat e at bo th the ta rget integrant level and the aggregat e levelof multipart texture. (A significant interaction between multipartrhythmic structure and textural level would have justified analyzingaccuracy scores for integrant test items and aggregate test items sepa-rately.)

The c' scoresrepresenting response biaswere analyzed in an analo-

gous fashion to t he d' scores. Neither the preliminary ANO VA (testing fo reffects of group) nor the main ANOVA (testing for effects of multipartrhythmic structure and textural level) on c' scores revealed any statistical-ly significant effects, ps > .3. Furthermore, a ttest revealed that c' scores(M = -0.09) were not reliab ly different f rom zero, w hich indicates thatresponse biases were negligible, t(23) = 1.09, p> .2.



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DISCUSSION

The current results indicate that the dual task of simultaneously mem-orizing the target integrant a nd a ggregate aspects of a multipart patt erna task that we assume requires PIAcan be performed more accuratelywhen the target integrant pattern and the aggregate pattern fit within thesame metric framework than when the target integrant pattern is non-metrical. Furthermore, such dual-task performance is of intermediateaccuracy when the target integrant and aggregate patterns do not fit wellw ithin the same metric framew ork. Thus, at tentional resource allocationis enhanced, and PIA proceeds most efficiently, when metric frameworkgeneration is encouraged by multipart rhythmic structure, though thesebenefits appear to be affected by whether or not the target integrant pat-tern and the aggregate pattern are compatible in terms of best-fittingmeter.

The results for the mismatched conditionwhich was included in thestudy for exploratory reasonsare particularly interesting because theyprovide behavioral evidence that the incompatibility between metric bar-level periodicities produces a degree of rhythmic complexity that liessomewhere between the complexity of metrically compatible patterns andnonmetrical patterns. This incompatibility can be considered to be analo-gous to the conflicting pulses underlying polyrhythms, wherein isochro-nous integrant patterns divide the same overall time period into temporalunits that combine to form inharmonic ratios such as 2:3 and 3:4 (e.g.,H andel, 1984; Jones, J aga cinski, Yee, Floyd, & Klapp, 1995; Klapp, H ill,Tyler, M ar tin, Ja gacinski, & Jones, 1985), a lthough t he incompa tibilitylies at the beat level rather than the bar level in polyrhythm.

M etric incompat ibility betw een ta rget integrant a nd a ggregate patternsis one possible explanation for the intermediate performance accuracyobserved in the mismatched-metrical condition. However, the mere factthat we used triple target integrant patterns in this condition may havealso played a role. Triple meter is less common than binary (duple andquadruple) meters in Western music (Lerdahl & Jackendoff, 1983), andthere exists evidence that rhythm perception and production are poorerwith triple patterns than with patterns fitting a binary meter (Drake,1993; Fraisse, 1982; Smith & Cuddy, 1989). We circumvented this issuein Experiment 2 by testing professional percussionists, for whom triplemetric structures should not be problematic. However, the main aim of

Experiment 2 was to investigate whether the benefits of matched-metricalta rget integrant/aggregate relat ions over nonmetrica l integrant /aggregaterelations found in the current experiment generalize to a dual task withdifferent behavioral (reproduction ra ther than recognition) and a ttention-al (DA rat her than P IA) demands.



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Experiment 2

Experiment 2 employed a pattern reproduction paradigm to simulateDA during ensemble performance. The reproduction task involves arhythmic canon w herein the lead part is presented by computer and t heperformer is required to follow this lead by reproducing it at a lag inter-val. The lead par t a lw ays consists of a model antecedent/consequent pa irof patt erns, w here the consequent follow s the antecedent immediately andboth have the same overall duration (see Figure 6). In fact, the antecedentand consequent patterns were adapted from the rhythm sets used inExperiment 1: Antecedent patterns were identical in structure to the tar-get integrant patterns, and consequent patterns were identical to the tar-get aggregate patterns (see Figure 3). The participants task is to beginreproducing the a ntecedent/consequent pa ir at the point w hen the conse-quent pattern begins in the computerized lead part. This produces a situ-ation where the performer is required to (a) memorize the antecedent pat-tern, (b) memorize the model consequent pattern while reproducing theantecedent pattern, and (c) reproduce the consequent pattern.

The temporal relationship between antecedent and consequent patternswas manipulated to produce three multipart rhythmic structure condi-tions that correspond to those examined in Experiment 1: (a) matchedmetricalantecedent and consequent patterns best fit a quadruple meter;(b) mismatched metricalantecedent and consequent patterns best fit dif-ferent meters (triple and quadruple, respectively); (c) nonmetricaltheantecedent pattern is nonmetrical, whereas the consequent pattern is met-rical (quadruple). Our main prediction was that reproduction accuracyfor antecedent and consequent patterns should be better in the matched-metrical condition tha n in the no nmetrical condition.

Several possible informative outcomes can be distinguished with regardto how performance in the mismatched-metrical condition relates to per-formance in the matched-metrical and nonmetrical conditions. First, per-


Fig. 6. The rhyth mic cano n ta sk used in Experiment 2. The mod el ant ecedent/consequentpattern (presented by computer) is reproduced by the participant at a lag interval. DA isrequired during the section of the canon where computer and the performer overlap (i.e.,consequent model a ccompanies antecedent r eproduction).


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formance accuracy in the mismatched-metrical condition could be inter-mediate to accuracy in the metrical and nonmetrical conditions both forantecedent and consequent patterns (similar to the result for integrant andaggregate patterns in Experiment 1). This outcome would indicate that

metric incompat ibility and/or t riple structure present pro blems for pa rtic-ipants. Second, performance in the mismatched-metrical condition couldbe better than intermediate to performance in the metrical and nonmetri-cal conditions both for antecedent and consequent patterns. This wouldindicate that neither metric incompatibility nor triple structure are prob-lematic. Third, there could be a dissociation between performance in themismatched-metrical condition relative to performance in the metricaland nonmetrical conditions for antecedent and consequent patterns. Onepossibility is that performance in the mismatched-metrical conditioncould be intermediate to performance in the matched-metrical and non-metrical conditions for consequent patterns, but not for antecedent pat-

terns. This would indicate that triple structure per se is not problematic(i.e., triple antecedent patterns can be reproduced with better than inter-mediate a ccuracy), suggesting t ha t incompa tible antecedent/consequentmetric structure is the problematic factor (i.e., quadruple consequentreproduction accuracy is intermediate when antecedent patterns aretriple). The only remaining alternativethat is, performance in the mis-matched-metrical condition is intermediate to performance in thematched-metrical a nd nonmetrical conditions fo r a ntecedent patt erns, b utnot for consequent patternscould be interpreted similarly.

Note that although the current rhythmic canon paradigm presents adual taskreproducing the antecedent pattern while memorizing the con-

sequentit does not require PIA: Accurate performance is, in principle,achievable by simply dividingones attention between the two task com-ponents. In the context of ensemble performance, such a strategy wouldamount to attending simultaneously to ones own part and another musi-cians part without necessarily integrating the two. Nevertheless, the cog-nitive processes underlying attention to both parts are not entirely inde-pendent under such circumstances (cf. Klein & Jones, 1996). Theseprocesses must be linked to gether, o r time-locked, in ord er to f or t he part sto remain synchronized, which is necessary for performance in ensemblesand the current experimental task alike. In the case of synchronizationwith a computerized performance, this time-locking is most likely

achieved by the same processesphase correction and period correc-tionthat enable sensorimotor synchronization with an auditorymetronome (Large & Jones, 1999; Mates, 1994; Pressing, 1999; Repp,2001, Repp & Keller, 2004; Vorberg & Wing, 1996). However, theseprocesses are augmented in the current task by the need to abstract a beat-and bar-level periodicity from the nonisochronous computerized pattern(see Snyder & Krumhansl, 2001).



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METHOD

Participants

Participants were 12 professional percussionists (2052 years old). All had extensiveexperience as performers in symphony orchestras and smaller ensembles specializing incontemporary music.

Stimuli and Apparatus

The stimulus patterns used as an tecedent and consequent pa tterns were dra w n from thesame 12 rhythm sets used in Experiment 1. The tar get integrant pa tterns from each rhy thmsetlabeled Qua druple, Triple, and Nonmetrical in Table 1served a s antecedentpatt erns and the Aggregat e patt erns served a s consequent pa tterns. The entire stimuluspool consisted of (a) 12 quadruple antecedent patterns, (b) 12 triple antecedent patterns,(c) 12 nonmetrical ant ecedent pat terns, and (d) 12 consequent patt erns, each b est fitt ing aqua druple meter. These patterns w ere concat enated to form stimulus items in w hich a con-sequent pattern follows each antecedent pattern immediately (i.e., the final element of an

antecedent is treated as the first element of the consequent). Thus, three stimulus itemsw ere ad apted f rom each rhyt hm set. Across items from a set, the same consequent patternis preceded by either a q uad ruple, a triple, or a nonmetrical a ntecedent pat tern, correspon-ding to the three multipart rhythmic structure conditions. All patterns were presented atthe same rate: grid unit duration = 150 ms.

Apparatus included (a) a PowerBook 5300cs Macintosh computer, (b) MAX (version3.0) softw are, (c) a R oland M T-32 sound mod ule, (d) a Ro land SPD-11 MID I percussionpad, and (e) a Creative SBS-300 loudspeaker.

Design

As in Experiment 1, multipart rhythmic structure (matched metrical; mismatched met-rical; nonmetrical) w as varied within part icipant s, and a betw een-group facto r (G roup 1-6) that determined the assignment of rhythm sets to multipart rhythmic structure condi-

tions was included for control purposes. The dependent variable was reproduction accu-racy for antecedent and consequent patterns (see Data Collection and Analysis).

Procedure

Each participant was tested at his or her private residence. After written and verbalinstructions were given, the participant completed t hree blocks of pra ctice trials (one blockper multipart rhythmic structure condition), followed by six blocks of test trials (twoblocks per multipart rhyt hmic structure conditio n). Thus, in the test trials, each pa rticipantencountered two different antecedent and consequent patterns in each of the three multi-part rhythmic structure conditions, with the patterns and conditions being combined dif-ferently for participants from the six different groups. Each block consisted of two phas-es: A familiarization phase and a test phase.

In the famil iari zatio n phase, the participant was given the opportunity to gain famil-

iarity with the antecedent pattern that was to be featured in the test phase of the cur-rent block. Clicking with the mouse on a virtual button on the computer screen trig-gered one presenta tion of the ant ecedent pat tern, wh ich wa s articulated by a sna re drumsound emanating from the loudspeaker positioned directly in front of the participant.The participant w as instructed to listen to t he antecedent patt ern as many t imes as w ererequired in order to memorize it. The number of times that the participant chose to lis-ten to the antecedent pattern was recorded by the computer as a measure of auditoryinspection tim e, which is a crude behavioral index of pattern complexity (see Povel &Essens, 1985).



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The test phaseconsisted of three identical performance trials, each initiat ed bydepressing the spaceba r on the computer keyboard . The task in each performa nce trial w asbased on a rhythmic canon, wherein the computer presented the lead part and the partic-ipant f ollow ed. The lead part s consisted of ant ecedent/consequent pairs of patt erns artic-ulated by a snare drum sound (with a MIDI velocity value of 96). In each pair, the conse-

quent pattern followed the antecedent pattern immediately. The transition from theantecedent to the consequent pattern was not signaled explicitly, but should have beenassisted by familiarity with the antecedent pattern.

In each perform ance trial, the participant w as required to begin reproducing the (fam il-iar) antecedent pattern (by tapping with a pair of drum sticks on the percussion pad) atthe point when the consequent pattern began. While reproducing the antecedent pattern,it was necessary for the participant to attempt to memorize the consequent pattern thatwas being presented concurrently by the computer, in order to reproduce the consequentimmediately after their reproduction of the antecedent. Each strike of the percussion padproduced a single cowbell sound (with a fixed MIDI velocity value of 118).

Data Collection and Analysis

To m easure reproduction accuracy, the percussion pad w as sa mpled every 150 ms,

starting 50 ms before the beginning of each model (i.e., computer-presented) consequentpatt ern. Sampling units w ere thus offset by -50 ms relative to grid units underlying modelconsequent patterns in order to allow for anticipations of the veridical position of patternelements. (In fact, informal pilot tests had revealed thatwhen tapping nonisochronousrhythms with drumsticksdelays were more common than anticipations, which is con-trary to what is usual when the task is to produce isochronous finger taps in synchronywith a metronome; see Aschersleben, 2002). If a tap occurred during one of the 150-mssampling units, a 1 w as recorded; otherw ise a 0 w as recorded. The resultant string ofbinary code for each performance trial represents the participants reproduction of a sin-gle antecedent/conseq uent pair o f pa tterns. We parsed each d ata string into ant ecedent a ndconsequent sections according to features such as rhyth mic figures and tota l number of ele-ments, in order to take into account errors involving phase-shifted consequent reproduc-tions (e.g., early or la te entries due to erroneous antecedent timing). Such errors a ffected,on a verage, 14% of m atched-metrical tria ls, 14% of m ismatched-metrical trials, a nd 68%of nonmetrical trials. Phi coefficientsa measure of the correlation between two dichoto-

mous variableswere calculated (a) between the binary code version of each antecedentpattern reproduction and a similarly coded version of the relevant model antecedent pat-tern and (b) between the coded version of each consequent pattern reproduction and therelevant coded model consequent.3 These correlations were used as an index of perform-ance a ccuracy.4

Correlations between antecedent models and reproductions, and consequent modelsand reproductions, were converted to Fisher z' scores and then analyzed in an ANOVA


3. The coded version of each model antecedent and consequent pattern was appendedw ith a string of 15 0 s to increase the number of grid units so tha t it mat ched the num-ber of sampling units in the antecedent and consequent reproduction codes (which wasincreased by a corresponding amount of units to accommodate potential errors thatresulted in the lengthening of pattern reproductions). Although these appended zeros

increase the absolute value of th e phi coefficients slightly, they do not a ffect how the coef-ficients from different multipart rhythmic structure conditions compare relative to oneanother.

4. An alternat ive w ould have been to employ the Unix diff comma nd (see Finney,1997). This w ould ha ve been useful for identifying diff erent t ypes of errors (e.g., commis-sions vs. omissions) and their location in patt ern structure. H ow ever, fo r present purpos-es, we were more interested in a global measure of accuracy, and hence correlations wereconsidered to be an appropriate index.


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est in the current study (e.g., the difference in the number of elements inantecedent and consequent pa tterns, the fa ct tha t only the ant ecedent pat -terns were encountered during familiarization phases, and the fact thatantecedent reproduction was paced by the ongoing model consequent,

while consequent reproduction was unpaced). The effects of multipartrhythmic structure and the interaction between multipart rhythmic struc-ture and part of the canon are more remarkable.

The effect of multipart rhythmic structure on reproduction accuracy forantecedent and consequent patterns was unpacked by using two plannedorthogonal contrasts (following the logic from Experiment 1). The firstcontrast compared reproduction accuracy between the matched-metricalcondition and the nonmetrical condition. In accordance with our mainprediction, the reproduction of antecedent and consequent patterns wasreliably better in the matched-metrical condition than in the nonmetricalcondition, F(1, 11) = 41.55, p< .001. Furthermore, there was a significant

interaction between part of the canon and the effect of matched-metricalversus nonmetrical structure, F(1, 11) = 34.76, p< .001, indicating thatthe advantage of the matched-metrical condition over the nonmetricalcondition was more pronounced for antecedent patterns than for conse-quent patterns. This may reflect the fact that rhythmic complexity wasmanipulated directly in the case of antecedent patterns (wherein physicalpattern structure was varied), but only indirectly in the case of consequent


Fig. 7. Reproduction accuracy (mean phi coefficients) for antecedent and consequent pat-terns in matched-metrical, mismatched-metrical, and nonmetrical conditions in Experiment2. (The error bar on the rightlabeled 2*SErepresents double the standard error; seefootnote 2.)


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patt erns (w herein physical pa ttern structure w as held constant in order toallow us to examine the subjective effects of producing metrical versusnonmetrical antecedent patterns on the concurrent perception of a conse-quent pat tern). To check w hether the effect of ma tched-metrical versus

nonmetrical structure was present for both parts of the canon, we ana-lyzed t he antecedent a nd consequent reproduction a ccuracy dat a separa te-ly. The results of this analysis confirmed that the advantage of matched-metrical over nonmetrical structure was present for both parts of thecanon: antecedent, F(1, 11) = 44.67, p< .001; consequent, F(1, 11) =10.39, p< .01.

The second contrast examined whether antecedent and consequentreproduction accuracy in the mismatched-metrical condition was interme-diate to accuracy in the matched-metrical condition and the nonmetricalcondition. This contrast compared accuracy scores from the mismatched-metrical condition with the average of the accuracy scores from the

matched-metrical and nonmetrical conditions combined, revealing thatreproduction accuracy in the mismatched-metrical condition was, onaverage, bett er t han intermediateto accuracy in the matched-metrical andthe nonmetrical condition, F(1, 11) = 9.86, p< .01. H ow ever, there was asignificant interaction between this effect and part of the canon, F(1, 11)= 15.75, p< .01, perhaps suggesting that performance was better thanintermediate for antecedent patterns, but not for consequent patterns (seeFigure 7). To test this, w e ana lyzed the antecedent a nd consequent repro-duction accuracy data separately for the second contrast.

The ana lysis of a ntecedent reproduction da ta revealed t hat accuracy inthe mismatched-metrical condition was indeed better than intermediate to

accuracy in the matched-metrical and the nonmetrical condition, F(1, 11)= 15.46, p< .01. This result, taken together with the finding that audito-ry inspection time for triple antecedent patterns was relatively low, sug-gests thatas expectedparticipants had little trouble with triple struc-ture. Important ly, ho w ever, t he ana lysis of consequent reproduction d atarevealed that accuracy in the mismatched-metrical condition was interme-diate to accuracy in the ma tched-metrical a nd t he nonmetrical condition,that is, a ccuracy in t he mismat ched-metrical condition w as not significant -ly different from average accuracy in the matched-metrical and nonmetri-cal conditions combined, F(1, 11) = 0.02, p> .8. (For the main effect ofmultipart rhythmic structure, partia l #2 was .7 and observed power was 1).

DISCUSSION

The current results indicate that the dual task of simultaneously repro-ducing a rhythm pattern (the antecedent) while memorizing a concurrent-ly presented pattern with different rhythm (the consequent)a task thatrequires DAcan be performed more accurately w hen the tw o pa tterns fit



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DAwas best when the antecedent and consequent patterns werematched in meter and poorest when the antecedent was nonmetrical.However, a dissociation was observed when the antecedent and conse-quent were metrically mismatched (triple and quadruple, respectively):

Reproduction accuracy w as intermediate to accuracy in the ma tched-met-rical and nonmetrical conditions in the case of consequent patterns, butbetter than intermediate for antecedent patterns. This outcome suggeststha t the ab ility to engage in DA w as a ffected more by antecedent/conse-quent metric compatibility (quad ruple/quad ruple vs. t riple/quadruple)tha n by t he metric identity of t he antecedent patt erns per se (quadruple vs.triple). Thus, the results of Experiments 1 and 2 provide converging evi-dence that our conception of metric compatibility is psychologically valid.

On the w hole, t he results of Experiments 1 and 2 suggest tha t P IA andDA proceed efficiently so long as the target integrant pattern and theaggregate pattern (in PIA) or the two integrant patterns (in DA) share the

same underlying metric structure. As mentioned at the start of this article,past studies have shown that the process of synchronizing ones biologi-cally based rhythms with such hierarchical structure facilitates recognitionand reproduction of rhythm. The current study extends that finding to adual-ta sk context, carrying t he implication that synchronization providesa common mechanism that assists performa nce on both tasks that involvePIA (target integrant and aggregate processing) and t asks that involve DA(processing multiple integrant patterns). There are several ways in whichsynchronization may be beneficial. First, it may serve to time-lock theindividuals cognitive/motor system to the pattern and t hen, follow ing thisform of calibration, it may form the basis for expectancies that delineate

attentional trajectories (Jones, 1990; Large & Jones, 1999) for processingupcoming events at bot h the ta rget integrant and the aggregate level dur-ing PIA, or for processing events in two separate integrant streams duringDA. Thus, in the context of ensemble listening (Experiment 1), internalpulsations provide a common timing mechanism that can be used to pre-dict events at both levels of multipart structure. In ensemble performance(Experiment 2), th is mechanism a dditiona lly guides the process of retriev-ing from memory the performance plans used in producing a target inte-grant pattern (see Drake & Palmer, 2000; Palmer, 1997; Palmer &Pfordresher, 2003). Broadly speaking, the current findings are consistentw ith the hypothesis tha t metric frameworks serve as cognitive/motor

schemas that promote efficient attentional resource allocation during PIAand D A.

However, when the target integrant pattern does not have an underly-ing metric structure (i.e., it is nonmetrical), ability to engage in PIA andD A is impaired even when the aggregate pattern, or a secondary integrantpattern, does have such structure. The decrement in performance going



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from (matched) metrical to nonmetrical conditions ob served here providesempirical evidence tha t processing nonmetrical structure is costly in termsof attentional resources. Whether these costs arise directly or indirectlyremains uncertain. Indirect costs might occur if, even though one is suc-

cessful at synchronizing with the periodicities underlying the aggregatepattern (in PIA) or the secondary integrant pattern (in DA), measuring thecomplex structure of the nonmetrical t arget integrant aga inst this regularstructure were to divert resources from the task of encoding the aggregate,or secondary integrant, pattern. Specifically, when elements in the targetintegrant pattern cannot be reliably predicted or produced, the process ofgrouping together target and complementary integrant elementsor evensimply attending to a second integrant patternmay encounter interfer-ence. Alternatively, direct costs would arise if processing nonmetricalstructure actually disrupts synchronization with the periodicities underly-ing the aggregate or secondary integrant, and thus precludes metric frame-

work generation. Indeed, such disruption may occur because the process-ing of nonmetrical patterns involves strategies such as counting the num-ber of elements w ithin figura l groups, estima ting the time interval betw eenthese groups, and employing mnemonic devices (Bamberger, 1980;Handel, 1992; Hbert & Cuddy, 2002; Smith, Cuddy, & Upitis, 1994).Although counting elements in figural groups may be a relatively auto-matic process (when the number is small), time estimation and the use ofmnemonics are generally effortful (Hasher & Zacks, 1979; Jackson,1985) and, t o t he extent tha t t hey channel at tention to aperiodic structur-al boundaries within the pattern, incompatible with the extraction ofbeat- and bar-level periodicities. Note that the foregoing is consistent with

more general interference-based explanations of dual-task decrements,w hich posit tha t performance degrada tion is a consequence of the disrup-tion of processingsynchronization in the current caserather thanscarcity of resources per se (see Neumann, 1996; Wickens, 1989, 1991).During PIA and DA, the disruption of synchronization would preventtime-locking between the attender and the external pattern, leading to asituation where target integrant and aggregate processing become inde-pendent, mutually interfering, tasks.

Several noteworthy issues remain unanswered by the current study.These relate mainly to the mechanisms that underlie PIA, which is a modeof a ttending about w hich little is know n. O ne issue concerns w hether ta r-

get and complementary integrant patterns are processed in parallel, byswitching, or b y a mixture of these tw o stra tegies during PIA. Para llel pro-cessing involves distributing a ttention cont inuously acro ss elements in tar-get and complementary integrant patterns in a graded fashion, with moreweight given to target elements, whereas switching involves shifting atten-tion back and forth between target and complementary elements. Thesetypes of strategy have been studied in the context of DA in nonmusical



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ta sks (see M ora y, 1969; Pashler, 1998; Wickens, 1991). To the ext ent thatthe results of such research generalize to musical ta sks, the choice of strat -egy is most likely context dependent, for example, switching may be opti-mal when target and complementary integrant patterns are rhythmically

differentiated, o r interleaved (as w as the case in Experiment 1), w here-as pa rallel processing may be more appropriate w hen target a nd comple-mentary integrants a re in rhythmic unison. Attenders may even a dopt dif-ferent strategies during the course of a pattern. Finally, it may be the casetha t if sw itching occurs, it is achieved w ith great er success in metrical con-ditions: The predictability of metric structure may grant listeners the lati-tude to shift a ttention freely betw een ta rget and complementa ry pat terns.

The preceding issues concerning sw itching versus para llel processingcould be investigated in future research by examining the effects of pres-entation rate on ability to engage in PIA and DA.5 If listeners employ aswitching strategy, then aggregate perception should be better at slow

rates than at fast rates because there is more time to shift attentionbetween target and complementary elements; however, if parallel process-ing is used, then aggregate perception should either be unaffected by rate,or become most difficult at slow rates due to increased memory load.Precedent for such work has been set in studies addressing the distinctionbetween integrated and parallel processes in the perception and produc-tion of polyrhythms (e.g., Handel, 1984; Jones et al., 1995; Klapp et al.,1985; Krampe, Kliegel, Mayr, Engbert, & Vorberg, 2000; Pressing,Summers, & Magill, 1996; Summers, Rosenbaum, Burns, & Ford, 1993).

Another potentially interesting issue concerns how PIA is affected bythe degree to which integrant patterns are differentiated in terms of tim-

bre and pitch range (see Keller, 2001b). These factors would be expectedto b e influential to the extent tha t they play a role in aud itory stream seg-regation (see Bregman, 1990; Brochard, Drake, Botte, & McAdams,1999; van Noorden, 1975). Earlier research has demonstrated that widepitch separation between integrant patternswhich encourages each inte-grant pattern to be perceived as an independent perceptual streamfacil-itates selective att ending (SA) to a ta rget integrant w hereas na rrow sepa-rationwhich encourages the separate integrants to be perceived as a sin-gle streamencourages nonprioritized integrative attending (NPIA) to theaggregate (Jones et al., 1995). Therefore, during PIA, pitch separationshould influence both how w ell the target integrant can be segregated and

how w ell target a nd complementary pa tterns can be combined to perceivethe aggregate. Similarly, in DA, segregation should be easier with widepitch separa tion and integrat ion should be easier with na rrow separa tion.Furthermore, pitch separation might influence whether a switching or


5. Although presentation rate was varied randomly between blocks in the currentExperiment 1, this variation was not systematic enough to justify analysis.


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parallel processing strategy is adopted because streaming is more con-ducive to switching whereas integrated percepts favor parallel processing(Jones, 1976; Michon & Jackson, 1984). Analogous effects should occurwith timbre, as it has been shown that auditory stream segregation is

af fected by the perceived similarity o f integrant pa tterns in terms of instru-mental sound (Iverson, 1995).

A final topic that may be fruitful to explore concerns the neural mech-anisms underlying PIA. R ecent brain ima ging studies have show n tha t t hedegree to which the various cortical areas implicated in attentive listeningto music are activat ed differs for NPIA/D A and SA (Jana ta et al., 2002;Satoh et al., 2001). For example, Satoh et al. (2001) found differences incortical activation based on whether the task for listeners was to detectminor chords in four-part Bruckner motets (NPIA) or to detect tonic ordominant tones in just the alto part of the motets (SA). This raises thequestion whether PIA produces an activation profile that is distinct from

the profiles associated with NPIA and SA. That is, would Satoh et al.(2001) have found further differences in cortical activation if they hadrequired their listeners to perform both detection tasks simultaneously, orwould it simply be the case that both the NPIA and the SA profile arisetogether? Either w ay, bra in imaging techniques may yield clues about thenature of the attentional resourcesa traditionally rather amorphousconceptinvolved in PIA.6

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