CHA,PTER 8

Musical timeMari Ri~ss Jones

THIS chapter presentsperspectives on percep­tion of metre and rhythm, with a focus ondynamicattendingtheory(DAT). Threemajor

sections address, respectively, metre perception,rhythm perception,and the roleoftime markers.

Metre perceptionIntuitively, metre perception refers to a listener'ssensitivity to musical timing regularities, evidentwhen 'keeping time' by tapping in synchronywith musical tones. Sometimes tones are clearlyaccented and contribute to metrichierarchies, assuggested in Figure 8.1(a). Here, an idealizedhierarchy features accents that are increasinglystronger (i.e. more salient; thicker bars) on non­adjacent tones separated by increasingly longer

time spans. Metric hierarchies comprise over­lapping (i.e., embedded) time spans; they can bedistinguished from time spans between succes­sive tones (i.e., serial spans). Whereas metricspans reflect temporal embeddings (Figure8.1(a)), serial spans invite rhythmic grouping(Figure 8.1(b)). Conventional wisdom holdsthat metre and rhythm are distinct time struc­tures, engaging different perceptual processes.In this chapter I question this dichotomy.

Let's begin with metre perception. First, weshould differentiate metric information in a vis­ual score from that which meets a listener's ears.A typical (Western) score spells out two hierar­chical time spans: a measure and its subdivisions.Thus, a notated 4/4 metric signature defines themeasure as a time level evenly subdivided into

Metrical(a) hierarchy

Embedded time spans

I I\.1~1600 ms---ll

11-800 ms-tl I

j I

Rhythmic ---+ ~ • ~ _ ~ _ ~ • ~ _ _ • ~ _ _ _ 1~ •• _ ~ _ ~ • ~ _ _ • ~ _ _ _

sequence ~ ~ ~

~i~Serial time spans (lOis)

Grouped(b) figures

LJJ

J

Time

L-J U L-J LJt..... l \. J

\.... /

Fig. 8.1 Metric hierarchy, with embedding time spans (a); and rhythmic groups with serial (lOis) timespans (b).

82 . CHAPTER 8 Musical time Metre perception . 83

Fig. 8.2 Four patterns from Povel and Essens (1985). Grouping accents are »: clock ticks are 0;negative clock evidence, s, is *.

»»> > >

4·1 •I . . III •1111 •••I

> > > > > >

3. II.1 ••IIIII •I•••I

positive evidence model (P), weighting clockticks coinciding with, accents; and a hybridmodel (H), weighting both positive and nega­tive evidence. Musicians and non-musicianstapped to metrical sequences, indexed by C, P,and H. The Hybrid model best predicted musi­cians' behaviour, whereas Povel's C index bestpredicted non-musicians' performance. Thus,non-musicians appear to be affected by clockviolations, consistent with Povel and Essensmodel, whereas musicians draw strength fromconfirmations as well as clock violations.

Patel et ale (2005) found that tapping to iso­chronous patterns at a fixed beat period of 800ms was less variable with isochronous subdivi­sions of this period than with non-isochronous(rhythmic) ones. Although consistent with clockpredictions, other findings involving subdivi­sions by 2 or 4 were more difficult for the clockmodel. These data converge with others (Essens1986) to suggest that listeners rely on relation­ships among multiple time levels. Indeed, evenvery young children appear to use multiple timelevels to differentiate duple from triple metrecategories (Phillips-Silver and Trainor 2005;Trehub and Hannon 2006;Bergesonand Trehub2006), although reports of children's preferencefor duple metre (2:1 ratios) (Drake 1993) werenot confirmed.

Dynamic attending theory and themetric binding hypothesisDynamic attending theory (DAT) addresses Tn­the-moment' expectancies in listening. Its rele­vance to metre perception is discussed in thissection, where I propose a new hypothesis: themetricbindinghypothesis.

Entrainment is a biological process that real­izes adaptive synchrony of internal attendingoscillationswith an external event. Different eventtimescales correspond to marked (i.e., accented)metric levels(Figures8.1,8.3). Time spans withina metric level can elicit a corresponding neuraloscillation, which has a persisting internal perio­dicity (Pi), manifest as a temporal expectancy. It'tunes into' recurrent time spans at a given levelby adjusting its phase in response to temporalexpectancy violations (<\» at that level.

Various DAT models share four assumptions(Large 1994; McAuley1995; Largeand Kolen 1995;

(1)C =W's+ u

The W (W > 1.0) weights the number of clockticks falling on a silence, s (stars in Figure 8.2)and u is the number of ticks on unaccented ele­ments. Thus, for pattern 1, s = 0 and u = 0whereas for pattern 2, s =2 and u =O.For bothpatterns, C is low reflecting strong metricalpatterns.

The second stage features symbolic memorycodes which are more economical for metricthan for non-metric patterns. For non-metricpatterns, codes reflect grouping properties (cf.Figure 8.2). Thus, although the non-metric pat­tern 3 lacks a good clock fit, its five groups pro­duce nominal codes of Short or Long lOIs, orsymbols of group sizes:2-1-5-1-1. These codesreflect nominal segmentations, not interval timerelationships. Others propose different codingstrategies (e.g. Lerdahl and Jackendoff 1983;Temperley 2001).

Evidence for metric encoding

Povel and Essens required people to reproducemany metric and non-metric sequences.Consistent with clock model predictions, besttemporal accuracy occurred with metricalsequences. Since 1985, this model has stimu­lated much research on metric encoding.However, conflicting reports surround its impli­cations that highly metrical patterns elicit bettertemporal acuity (Handel 1992; Ross andHoutsma 1994; Handel 1998). Hebert andCuddy (2002) found that both a metric frame(metrical sequences) and the presence of arhythmic figure (non-metrical sequences) bene­fit time-change detection.

Much research on synchronized tappingappeals to motor control theory (see Repp 2005for review). However, few (e.g. Palmer andPfordresher 2003) consider metre perception.Some empirical examinations of synchronizedand reproduction tapping do directly addressclock model assumptions (e.g. McAuley andSemple 1999; Patel et al. 2005). McAuley andSemple questioned whether clock inductiondepends only on negative, i.e., counter-evidence(i.e., ticks at unaccented times). They formu­lated alternativeversions of Equation 1,creating a

namely the clock with fewest violations, i.e.,least counter-evidence, C, where:

LLSSLSSSL or 1-1-3-4-1

SLLSSSSL L or _2-1-5-1-1

Possible Nominal Codes

An encoding theoryPoveland Essens(1985)proposed that metre per­ception is governed by an internal clock.Metricalsequences, containing regular accents, readilyinduce a 'good' clock and lead to efficient encod­ing of serial time intervals, whereas non-metricalsequences,with irregularaccents,do not. Examplesof metrical and non-metrical monotonesequences, involving various inter-onset timeintervals (Iols), appear in Figures 8.1 and 8.2.Grouping accents (> ) putatively occur on:

1 isolated tones;

2 the second tone of a two-tone group; and

3 initial and final tones in groups of three ormore tones (Povel and Okkerman 1981).

This clock model has two stages. The firststage entails matching accents with internalclock ticks (i.e.,beats). The best clock maximizesaccent isochrony via minimizing mismatches(clock violations). Strong metric patterns (pat­terns 1 and 2, Figure 8.2), have accents (» thatcoincide entirely with ticks (0) of the best clock,

SSSSLSLLL or 5-2-1-1-1

SSLLSSLSLor 3-1-3-2-1

(1981) showed that metrical context modulateslisteners preferences for 2:1 serial time ratios.Next, I describe theory and research surround­ing two current psychological theories of metreperception, an encoding theory and a dynamicattending theory (DAT).

Strong Metrical Rhythms

> > > > > >

1. 11111 •• 11.1.1 ••• 1o 0 0 0 0

Weak (non) Metrical Rhythms

> > > > > > >

2. III. I.111 ••II •••I000000000

* *

four quarter notes (a 4:1 embedded time ratio,Figure8.1(a)),whereasatriple (3/4) metre impliesa subdivision of three (a 3:1 ratio).

Yet, given an unfamiliar melody, a listeneroften does not 'know' its designated metre; peo­ple don't have scored bar lines in their heads. Tounderstand metre perception in sound patterns,we must consider that listeners may infer severalmetric time levels. From this, challenging issuesarise. For instance, listeners may selectivelyinternalize aspects of a metric hierarchy byengaging a series of internal beats at one or moretime levels.Stronger beats might be felt at pointsin a sound pattern where multiple objectiveaccents align. Further, if an internal beat patternpersists, then beats are also felt at times where noobjective accents exist, i.e., 'subjective accents'.Also, different listeners may focus upon differ­ent internal beat patterns as a referent level (tac­tus). In short, to understand metre perception,we must discover factors in sound patterns andin listeners that bias people to hear a pattern'stime structure in a particular way.

Contemporary research on musical timebegan with classic work of Fraisse (1963), whofocused on rhythmic groupings. He proposedthat listeners rely on favoured serial time ratiosto segment groups. Preferred ratios approxi­mated 1:1 for within-group time spans and 2:1for between-group serial time ratios. However,metric issues entered the picture when Povel

84 . CHAPTER 8 Musical time Metre perception . 85

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

...... /AAAAAAA""""""'AAAM". P1= 200 ms

Attentionalfocus

~Nar~w -I focus \

steady narrowing of an attentional pulse aboutan expected phase point: <I> =O. This entails con­tinuous phase adjustments to minimize differ­ences between momentarily expected phasesand observed tone onsets. The goal is an attrac­tor, defined by phase coincidence (synchrony),of expected and observed .time points. Onceattuned, an entrained oscillation persists toextrapolate beats (attentional pulses), each beatrealizing an anticipated region in time (insert).

Metre perception is described with morecomplex models; at least two oscillations,entraining at different metric levels, are neces­sary (see Figure 8.3) (Large and Jones 1999;Large and Palmer 2002). Moreover, these oscil­lations can interact. To illustrate, consider pat­tern 2 (Figure 8.2). This rhythm differs from therhythm of Figure 8.3 in containing lower orderlOIs that elicit oscillations with periods: 200,400, 600, 800 ms. That is, three oscillator peri­ods (200, 400, 800 ms) nest neatly with highermetric levels (400, 800 ms, 1600 ms), but onedoes not (600 ms). Nevertheless,the metric bind­ing hypothesis assumes internal entrainments

Phase (oi)

Time

Isochronous rhythm

_----A (~t)r , ,--A-,

I I I I I rJ I ~JI I

hypothesis implies that: 'Oscillators that aligntogether, bind together.'

Once acquired, metric clusters grant trainedlisteners attentional flexibilityto activate oscilla­tors for unmarked metric levels (Palmer andKrumhansl 1990) and to flexibly shift focalattending to different marked levels. In fact,Jones and Boltz (1989) proposed two attendingmodes, future-oriented and analytic attending,to reflect focal attending to higher and lowertime levels, respectively.

Specialized entrainment models

Several DAT models formalize oscillator behav­iours for different tasks; typically, a single oscil­lation exhibits three components: period; pulse,and phase. Some tasks rely on a single oscilla­tion model, others on multiple oscillations.

The simplest oscillator model appears inFigure 8.4 entraining to an isochronous event(Large and Jones 1999). This single oscillationcarries a concentration of attending energy, anattentional pulse. With rhythmically simpleevents, an oscillator's 'tuning' is reflected in a

P3= 800 ms

P2= 400 ms

3 Resonance (i.e., relatedness) among oscillatorperiods.Figure 8.3 illustrates how metric clusters

form. As a rhythmic pattern unfolds, it succes­sively activates neural oscillations with periods(Pi) matching each of the lower-level lOIs.Initially recurrent l'Ols, in this case, elicit anoscillation with a period of 200 ms, which isstrongly coupled to these lOIs. However, thisrhythm subsequently awakens oscillations withperiods of 400 and 800 ms due to serial lOIs thatfollow. Oscillations of periods 400 and 800 msfind added support mainly from higherevent time spans between non-adjacent tones.This analysis shows how rhythm and metreco-constrain oscillation activities. Once active,co-occurring internal oscillations mutuallyentrain.

I propose that, over time, internal entrain­ment leads to cluster binding and the formationof a persisting metric form (here duple metre).This is a mechanism for bootstrapping learningbased on pattern relationships. It is constrainedby binding principles such that learning is facili­tated not only by longer total times of oscillatorco-activity (e.g., Hebbian learning), but alsoby strong resonance and phase relationsamong active oscillations. The metric binding

rrr ...."'800m~

MUltiple Neural Oscillations

Metrical level markers

1h--1600 mS---I1

Large and Jones 1999). First, neural oscillationsare self-sustaining; they persist over time, extrap­olating the induced beat. Second, an oscillator'sintrinsic period exhibits stability; a perturbationfrom an ill-timed tone only briefly disrupts astable oscillation, which returns to its intrinsicperiod. Third, entraining oscillations exhibitadaptivity, the flip side of stability; an oscillatorresponds appropriately to event-generatedexpectancy violations by adjusting phase andperiod. Fourth, multiple related oscillations areactivated by multiple time levels within metricand rhythmic events.

The metric binding hypothesis expands theseassumptions. It adds learning principlesto addresstraining and enculturation that contribute to lis­teners' familiaritywith metric categories.It holds:whenever twoormoreneural oscillations aresimul­taneouslyactive, overtime their internalentrain­ments lead to binding and formation of a metriccluster. A metric cluster comprises sets of co-oc­curring oscillations with interrelationships thatpersist due to acquired internal bindings.Entrainments among internal oscillations pro­mote binding, which strengthens as a function of:

1 Duration of co-occurring oscillatory activity.

2 Phase coincidences, and,

Widefocus

"""~

"" IMUltiple simultaneously-active oscillations bind as a function of: 1. Duration of simultaneous activity2. Intrinsic period ratios (pilpj)3. Coincidence of pulse peaks

A Metric Cluster

Serial lOis: 200, 200, 400, 400, 400, 400, 200, 200, 800, ...

Fig. 8.3 MUltiple metric levels entrain corresponding neural oscillations. Rhythm (serial lOis) alsoactivates oscillations. This figure illustrates metric binding hypothesis principles.

Fig. 8.4 A single oscillator entrains to an isochronous rhythm. Basic components are period, pulse(insert) and phase.

86 . CHAPTER 8 Musical time

among active oscillations lead to common met­ric percepts for different rhythms. Bindingamong oscillations depends not only on theduration of joint oscillator activities, but also onresonance relations among these oscillations,namely period and phase relationships. Thus,for pattern 2, although the oscillator with an ill­fitting period (e.g., 600 ms), is initially active, itdies out due to poor resonance. The winningmetric cluster for pattern 2 turns out to be iden­tical to the metric cluster for the differentrhythm of Figure 8.3. This analysis predicts thatthe 600 ms 101 (pattern 2, Figure 8.2) will beperceptually distorted to (fit' the duple metreframe common to both rhythms. More gener­ally, metric binding in multi-oscillator systemsexplains how various rhythmic instances areperceived as members of a common metriccategory.

The mathematics of multi-oscillator systemsis complex. Nevertheless, resonance propertiesrequire some mention. When two oscillationsareactive, their periods form embedding ratios(e.g., 1:1, 2:1, 3:1, 1:2, 2:3; 3:2 etc.) that gaugeoverall stability of their interaction. Embeddingratios specify resonance states (i.e., attractors)that have different degrees of stability; this, inturn, predicts differential lasting qualities ofmetric clusters (Large and Kolen 1995; cf.London 2004). For instance, clusters based onduple metre ratios are predicted to be morestable than those based on complex ratios.

Finally, it is common to distinguish metreperception from rhythm perception, in that itreflects an acquired skill, whereas rhythm per­ception is attributed to innate Gestalt principles(Bregman 1990; Handel 1989). DAT does notincorporate this dichotomy. Rather, dynamicalproperties offer biological springboards that dif­ferentially constrain the learning of metric ver­sus rhythmic time structures. DAT implies thatunlearned biological responses (neural oscilla­tions) are fundamental to time perception,whether metric or rhythmic. These biologicaldispositions (oscillatory entrainments) initiallyfacilitate attending to event structure via acti­vated oscillations. Next, stability differencesamong simultaneously active oscillations lead todifferential learning of metric patterns versusnon-metric and rhythmic patterns given themetric binding hypothesis.

Evidence for OAT

Evidence associated with various entrainmentmodels of metre perception derives from bothbehavioral and biological sources.

Behaviouralassessments of DAT

Experimental research often concerns responsesto timing of metrically regular and irregularcontexts. The most rigorous tests involve thresh­old judgements of timing and categorical timejudgements (see Jones 2004 for a review).

Single oscillator entrainment models predictthat lower-order serial lOIs of monotonerhythms are important, a finding confirmed byDemany and Semal (2002). These models alsocorrectly predict that, in judging time intervals,listeners will distort unexpected time intervals tofitwith a contextually expected beat span (Barnesand Jones 2000). Other entrainment models,which involve biologically preferred periods(McAuley 1995), also find support McAuleyet al. (2006). Two oscillator entrainment models,used to describe metre perception, assume thatone oscillation entrains to a higher metric level,marked by more salient accents, while anotheroscillation, with a shorter period, entrains toembedded event time spans, marked by less sali­ent accents. Such a model was shown to correctlypredict that greater metric regularity (within andbetween trials) enhances temporal acuity (Jonesand Yee 1997;Largeand Jones 1999).

Acuity thresholds are affected by tempo.London (2004) argued that such acuity limitsaffect metre identification, biasing listenerstoward particular metres at certain tempi.Effectively, a perceived tactus corresponds to alower metrical level in relatively slow patternsbut a higher one in faster patterns (Handel andOshinsky 1981;Parncutt 1994;Duke 1989).

McAuley et al. (2006) found that the limits oftempo perception (e.g. Weber's Law) dependupon entrainment constraints expressed byentrainment regions. An entrainment region is arange of tempi, surrounding a preferred eventrate, that corresponds to good entrainment.Both the location and width of these regionswere found to shift with age: children wereshown to prefer narrow entrainment regions,surrounding a fast event rate (active oscillationswith briefperiods), whereas elderly listeners had

broader entrainment regions centered on slowerevents (active oscillations with longer periods).Thus, perceived metre may modulate not onlywith tempo but also with age.AlsoseeDrake andBotte (1993), Miller and McAuley (2005), Jonesand McAuley (2005), and Parncutt (1994).

Biological assessments of DAT

Neurophysiological findings buttress entrain­ment theory (see Zanto et al. 2006). Consistentwith DAT, electroencephalography (EEG)reveals neural oscillations that synchronize toperiodic auditory stimuli in the musical range,i.e. 2 Hz (Will and Berg 2007).

Using event-related potentials (ERPs),Brochard et al. (2003) were the first to verify thepresence of subjective accents, i.e., internalizedbeat patterns (Fraisse 1963; Woodrow 1932).They found ERP activity in the parietal cortex ofnon-musicians that reflected duple metreexpectancies (see also Besson and Faita 1995;Janata 2001). Often ERP signal frequencies(0-10 Hz) reveal relatively long latency brainresponses (e.g.,P300),which may reflecta synthe­sis of higher frequency oscillations (Makeig et al.2004). Indeed, fronto-cortical ERP recordingsrevealed two kinds of high frequency activities(Snyder and Large 2005):

1 An induced periodic response, in the Beta/Gamma range (20-30Hz), prior to onsets ofmetrically expected tones;

2 A phase-locked evoked Gamma (30-60 Hz)response following tone onsets.

These findings confirm DAT distinctionsbetween expectancies (oscillator period) andexpectancy violations (phase corrections)(Ianata 2001; Zanto et ale 2005).

A common question is: (Are internal oscilla­tions purely event driven?' (Iverson et al. 2006).

Both behavioural and neurophysiological stud­ies suggest the answer is (No'. Combined manip­ulations of event structure with task andinstructions (imagery, attentional set) suggestthat event structure plays a role in facilitating orinhibiting listeners' compliance with instruc­tions (Palmer and Krumhansl1990; Klein andJones 1996; Janata and Grafton 2003; Snyderand Large 2005; Iverson et al. 2006). Clearly,people rely upon both guided imagination andevent structure to shape metricexpectancies.

Rhythm· 87

RhythmRhythm is a serial figure based on an arrange­ment of discrete time intervals. It contrasts withmetre, which is based upon embedded timeintervals. In this section, I outline current limitson our understanding of rhythm perception.

Theoretical backgroundMany contemporary approaches to rhythm per­ception assume that it is psychologicallydistinctfrom metre perception (Figure 8.1(b) versusFigure 8.i(a)). Rhythm perception is assumedto depend upon temporal grouping principles,given by Gestalt rules of proximity, similarity,continuity, etc. In turn, Gestalt theory holdsthat rhythm perception is innate, based upon anautomatic, primitive, universal process that isgoverned by hard-wired, domain-free, groupingprinciples. Thus, rhythm perception is consid­ered inherently different from metre perception,which is viewed as an acquired skill, reflectingdomain-specific musical rules.

The classic dichotomy of rhythm and metreperception is appealing for several reasons. First,it captures an experiential difference betweenserial (rhythmic) and embedded (metric) timestructures. Second, reliance on Gestalt princi­ples leads to coarse codingof serial time spanswhich correctly captures listeners' often fuzzypercepts of rhythmic time spans. Bythis account,the rhythmic figure of 400-200-200 ms inviteslax encoding of proximal tones as (groups', seg­mented by non-proximal tones (i.e., groups of 1versus 3 tones; cf. Figure 8.2). Nominal codes oftime intervals as either short (proximal) or long(non-proximal) yield a coarse rhythmic code,such as long-short-short for this figure. Third,nominal codes often accurately predict percep­tual confusions among rhythms. For instance,the 400-200-200 ms figure has the same nomi­nal code (long-short-short) as 500-100-200ms, leading to observed confusions of suchrhythms. In sum, Gestalt rules are intuitivelycompelling and coarse temporal groupings,nominally encoded, offer explanatory value.

In spite of the appeal of Gestalt theory, arhythmic/metre dichotomy cloaks pitfalls. First,because Gestalt principles are hard-wired, thisapproach denies that listeners may blend innate

88 . CHAPTER 8 Musical timeMaking time and accent salience . 89

Fig. 8.5 Upper JAS example: aligned melodic (MA) and duration accents (TA) lead to a duple metreJAS pattern. Lower: misaligned accent sequences form a polyrhythmic JAS-based duple (MA) andtriple (TA) patterns.

Simple .. _~o • 0 • 0 • 0 • 0 • 0 •

i . i . i . i . i . • .

• Temporal (TA) accents

o Melodic (MA) accents

..---.. A igher-Ievel time span

.. - - • A lower-level time span

Both duple metre:

Embedded ratio 2:1

~ Duple-plus-triple metre:

• Embedded ratio 3:2

o

•

A large relative intensity change in a musicalsequence is more attention-getting, i.e.,more sali­ent, than a small one. Thus, to compare accents ofdifferent types (i.e., dimensions) as effectivemarkers of metre, it is important to equate themfor salience.

Dynamic attending theory assumes thataccents arise from local serial changes (Jones1987). This broadens the definition of phenom­enal accents of Lerdahl and Jackendoff (1983).Operationally, the salience of an accented toneincreases with the:

1 Magnitude of its local serial change along adimension of variation;

2 Number of simultaneous accents on it (i.e., allelse equal;two co-occurring serial changes arestronger than one);

3 Surrounding variability (melodic, rhythmic,etc.) in global serial context (Ellisand Jones inpress).

In DAT, various accent types mark time spansof both rhythm and metre. Further, if the per­ceptual impact of an accent, i.e. its salience,turns on the magnitude of a local serial change,then different accent types (pitch, time, etc.) canhave equivalent salience. This idea is formalizedin the concept of joint accent structure (JAS)(Jones 1987). A JAS reflects a temporal collabo­ration of different (salient) accent types that

• 0 •

•••

Complex

i : ~

Theoretical backgroundThe dichotomy of rhythm and metre perceptionholds implications for understanding accents astime markers. Sometimes accents are drawninto this dichotomy through the assumptionthat codes for metre and rhythm are processedindependently and/or stored in respectivelysep­arate modules. Thus, metric versus rhythmicaccents may be distinguished by linking them,respectively, with different physical dimensions(e.g., time, intensity, pitch etc.). For instance, insome views metre is considered to be marked byintensity accents whereas rhythm is marked byduration accents. A related hypothesis holdsthat rhythm and metre percepts are not onlydichotomous, but that both are independent ofmelodic features, e.g., pitch accents.

Complicating discussions of independenceversus dependence of metre, rhythm and mel­ody is the practice of differentiating musicalaccents a priori by dimensionality alone, e.g., asintensity, time, or pitch accents. This practiceraises certain dilemmas. Consider this: if anaccent effectively (calls' attention to a point intime, then logically accents cannot be solelydefined by their dimensions. Rather, accentsmust be contextually defined because they onlyoccur in serial contexts. An accent gains its poweras a serial change, regardless of dimension.

sufficiently large (Hebert and Cuddy 2002) or ifpatterns occur repeatedly (Handel 1992).Although poorly understood, listeners do learn todifferentiate confusable rhythms having similarGestalt grouping codes.

An important difference between DAT andGestalt accounts is the latter's emphasis onnominal coding of rhythmic time spans. Bycontrast, DAT features roles for both interval(tempo) and ratio (metre/rhythm) time rela­tionships. Critically, even in brief rhythmicsequences, listeners are sensitive to rhythmiccategories with special serial time ratios (e.g.,1:1, 2:1) (e.g., Desain and Honing 2003). Usingonly two time intervals, incremental lengthen­ing of the first interval (relative to the second)between serial ratios of 1:1 and 2:1 (and viceversa) revealed preferences for the simpleranchoring ratios, consistent with Praisse's ideas.Not to be overlooked is research showing metricpriming of such rhythms (Povel 1981; Clarke1987; ten Hoopen et al. 2006)

Related findings accompany a time-shrinkingphenomenon (Nakajima et al. 1992; Sasaki et ale2002; Nakajima et al. 2004). Using brief two­interval patterns, Nakijima and his colleaguesfind that when a long time interval follows ashort one, listeners underestimate it, revealing agravitation to a preferred serial time ratio of 1:1.However, reversal of the two intervals fails toelicit time expansion. Generally, research ontime distortions suggests that perception ofrhythmic figures is influenced by stability ofcertain serial time ratios: 1:1, 2:1, 1:2.Interestingly, brain activities, measured by func­tional magnetic resonance imaging (fMRI), alsoappear to depend upon the simpler time ratiosproduced by listeners (i.e., stable anchoringratios) and not stimulus ratios (Sakai et ale1999).

Marking time and accentsalienceAll time patterns exist because accents markconstituent time spans. Accents (call attention'to onsets of time spans. In this section I focusupon the neglected issue of accentsalience (fordifferent perspectives, see Krumhansl 2000;Clarke 1999).

with acquired responses to time structures. Forinstance, the two confusable rhythms (above)may be eventually differentiated as listenersacquire sensitivity to different temporal nestingproperties. Second, by denying a role for learn­ing' this approach discourages research on thistopic. Indeed, Gestalt rules are often mistakenfor final explanations when they are simply use­ful descriptions of phenomena that requireexplanation. Third, this dichotomy renders itdifficult or impossible to address rhythmicpriming of metre and vice versa.

DAT assumes that learning builds upon innateoscillatory brain activities. It offers a potentialfor explaining both metre and rhythm percep­tion based on entrainment constraints associatedwith their respective time properties. Perceptuallearning (i.e. the metric binding hypothesis)depends upon entrainments of innate oscilla­tions elicited by an event's time spans. Althoughmultiple time spans occur in both metric andnon-metric rhythms (cf. Figure 8.1), they pro­mote different learning paths. Relationshipsamong saliently marked embedded time spansare typically orderly and aligned to highlightconsistent ratio time relationships in metric pat­terns, whereas in rhythmic figures, time spansfrom grouping accents can offer unruly, mis­aligned, embeddings (especially in non-metricpatterns) that obscure higher level temporal reg­ularities. Because of this, metric patterns pro­mote quicker binding of oscillators acrossembedded time levelsthan do rhythmic patterns.Rhythmic figures that lack consistent higher-or­der time spans cannot support effectiveentrain­ment of higher level oscillators; instead, looselyconnected oscillations among 101 resolve togroup segmentations. It follows that DAT canaddress rhythmic priming of metre and viceversa (Desain and Honing 2003) . Nevertheless,despite its potential no DAT task model has for­malized these ideas to rigorously explain serialsegmentation in rhythmic patterns. In this regardDAT and Gestalt approaches share incompleteexplanations of rhythm perception.

Empirical evidence on rhythmperceptionListeners can distinguish among theoreticallyconfusable rhythms if timing differences are

90 . CHAPTER 8 Musical time

outline a common, higher order, time structure.As shown in Figure 8.5, structural interdepend­ence of melodic (pitch change) and rhythmic(duration changes) accents is inherent in that ametric structure emerges from time spansmarked by both melodic and rhythmic accents.One configuration reflects a simple combina­tion of melodic accent and rhythmic accentsequences (duple metre embedding ratios of 2:1)where both melodic (MA) and temporal (TA)accents align; in the other, a more complex JAScombination results in misaligned accents(polyrhythmic ratios of 3:2). According to ametric binding hypothesis, the former is themore stable due to its resonance properties.Nevertheless, as experimental compositions,both JAS patterns reflect interdependence ofmelodic, rhythmic and metric structures.

Experimental evidence onmarking timeExperimental evidence offers mixed support forhypotheses about perception of musical eventscontaining melodic and temporal accents. Somefavours a hypothesis that melody, rhythm andmetre are perceived independently, whereasother evidence favours a perceptual dependencyhypothesis. Such issues remain unresolved.

Research which relies upon established com­positions is consistent with the idea that melodyand metre are perceptually independent. Forinstance, listeners' inferred beats indicate a reli­ance on rhythmic (duration) over melodicaccents (Snyder and Krumhansl2001; Hannonet ala 2004). Hence, Huron and Royal (1996)question the effectiveness of melodic accents formarking metre. Yet evidence for this conclusionremains inconclusive. In part, this is because thesalience of various accents is unknown, and inpart it is because such correlational evidenceprecludes causal inferences. Furthermore, otherevidence, based on experimental compositions,favours the alternative view. In these, melodic(pitch) and rhythmic (temporal) accents togetherappeared to determine listeners' sense of metre(Boltz and Jones 1986; Pfordresher 2003).

A resolution ofthis issue depends upon insur­ing comparable salience across accent types. Forexample, in specified musical contexts we mustgauge whether a three semitone pitch leap

(melodic accent) is equal in salience to length­ening tone duration by 5 per cent or by 15 percent (rhythm accents). Overall variability ofsur­rounding melodic and rhythmic contexts mustalso be controlled.

A few studies have controlled accent salience.Windsor (1993) calibrated intensity accents,and confirmed that larger serial changes inintensity yielded clearer metric identifications.Ellis and Jones (in press) used melodic (MA)and temporal (TA) accents ofcalibrated equiva­lence in various sequences to create nine differ­ent JAS patterns; to appear in Figure 8.5 (i.e.,2:1 duple; 3:2 polyrhythm). Different JAS con­ditions combined duple and triple accent pat­terns in aligned (e.g., duple for TA and MA) andmisaligned (e.g., duple TA and triple MA) ways.Listeners rated the metric clarity of all patterns.Results appear in Figure 8.6. In JAS patternswith aligned MAs and TAs, time spans shouldactivate multiple aligned oscillations (for dupleor triple metre), and thus here DAT correctlypredicts stable metric clusters and high metricclarity. By contrast, in misaligned JASpatterns,with irregular high-level time spans, DAT cor­rectly predicts lower clarity.

These findings reveal the importance ofcalibrating accent salience. Melodic and rhyth­mic accents, of comparable salience, lead to JAS

High 3 Melodic accents (MA)

-- Duple-- Triple

~2-t-----------__--I.t:«SUo.t:1):E

Low 0 -'------------__--l

Duple Triple

Temporal accents (TA)

Fig. 8.6 Metric clarity ratings of average

listeners. Melodic (MAs, dark lines) and temporal(TAs, light lines) accent patterns are either

aligned (e.g., circles) or mis-aligned (squares)(Ellis and Jones in press).

patterns of different complexity when combinedwith embedding ratios of2: 1versus 3:2.Listeners'ratings of these patterns supports the hypothesisthat percepts of melody, rhythm and metre arenot independent.

SummaryThis chapter selectively reviews psychologicalresearch on perception of metre and rhythm. Itsfocus is upon the dynamics of attending to pat­terns in time. It considers how event timing, asoutlined by salient accents in metre, rhythm, andeven melodic structures, may guide attending intime, bootstrap learning, and influence timeperception.

AcknowledgementsThe author is grateful for the assistance ofRobert Ellis.

ReferencesBarnes R and Jones MR (2000) Expectancy, attention, and

time. Cognitive Psychology, 41, 254-311.Bergeson TR and Trehub SE (2006) Infants' perception of

rhythmic patterns. MusicPerception, 23, 345-360.Besson M and Faita F (1995) An event-related potential

(ERP) study ofmusical expectancy: comparison ofmusicians with nonmusicians. Journal of ExperimentalPsychology: Human Perception and Performance, 21,1278-1296.

Boltz M and Jones MR (1986) Does rule recursion makemelodies easier to reproduce? If not, what does?Cognitive Psychology, 18, 389-431.

Bregman A (1990) Auditory scene analysis. MIT Press,Cambridge, MA.

Brochard R, Abecasis D, Potter D, Ragot R and Drake C(2003) The 'ticktock' ofour internal eleeledirect brainevidence of subjective accents in isochronous sequences.Psychological Science, 14, 362-366.

Clarke EF (1987) Levels of structure in the organizationof musical time. Contemporary MusicReview,2,211-238.

Clarke EF (1999) Rhythm and timing in music. InD Deutsch) ed., The psychology of music) 473-500.Academic Press, New York.

Demany Land Semal C (2002) Limits of rhythmperception. QJExpPsychol A, 55, 643-657.

Desain P and Honing H (2003) The formation of rhythmiccategories and metric priming. Perception, 32, 341-365.

Drake C (1993) Reproduction of musical rhythms bychildren, adult musicians and adult nonmusicians.Perception and Psychophysics, 53, 25-33.

References' 91

Drake C and Botte M (1993) Tempo sensitivity in auditorysequences: evidence for a multiple-look modeLPerception and Psychophysics, 54, 277-286.

Duke RA (1989)Musicians' perception ofbeat inmonotonic stimuli. Journalof Research in MusicEducation, 37, 61-71.

Ellis RJ and Jones MR (in press) The role of accent salienceand joint accent structure in meter perception. Journalof Experimental Psychology: Human Perception andPerformance.

Essens PJ (1986) Hierarchical organization oftemporalpatterns. Perception and Psychophysics, 40,69-73.

Fraisse P (1963) Thepsychology of time. Harper and Row,New York.

Handel S (1989) Listening: an introduction to theperceptionof auditoryevents. MIT Press, Cambridge, MA.

Handel S (1992) The differentiation of rhythmic structure.Perception and Psychophysics, 52, 497-507.

Handel S (1998) The interplay between metric and figuralorganization. Journal of Experimental Psychology:Human Perception and Performance, 24,1546-1561.

Handel S and Oshinsky JS (1981) The meter of syncopatedauditory patterns. Perception and Psychophysics,30,1-9.

Hannon EE, Snyder JS, Eerola T and Krumhansl CL (2004)The role ofmelodic and temporal cues in perceivingmusical meter. Journal of Experimental Psychology:Human Perception and Performance, 30, 956-974.

Hebert S and Cuddy LL (2002) Detection ofmetricstructure in auditory figural' patterns. PerceptPsychophys, 64, 909-918. ~'~

Huron D and Royal M (1993). What is melodic accent?Converging evidence from musicalpractice. MusicPerception,13,489-516.

Iverson JR, Repp BH and Patel AD (2006) Metricalinterpretation modulatesbrainresponses to rhythmicsequences. The Neuroscience Institute, San Diego, CA.

Ianata P (2001) Brain electrical activity evoked by mentalformation of auditory expectations and images. BrainTopogr, 13, 169-193.

Ianata P and Grafton ST (2003) Swinging in the brain:shared neural substrates for behaviors related tosequencing and music. Nat Neurosci, 6, 682--687.

Jones MR (1987). Dynamic pattern structure in music:recent theory and research. Perception and Psychophysics,41,621--634.

Jones MR (2004) Attention and timing. In JG Neuhoff, ed.,Ecological psychoacoustics, 45-89. Academic Press, SanDiego, CA.

Jones MR and Boltz M (1989) Dynamic attending andresponses to time. Psychological Review, 96, 459-491.

Jones MR and Mcauley JD (2005) Time judgments inglobal temporal contexts. Percept Psychophys, 67,398-417.

Jones MR and Yee W (1997) Sensitivity to time change: therole of context and skill. Journal of ExperimentalPerception and Psychophysics, 32, 693-709.

Klein JM and Jones MR (1996) Effects of attentional setand rhythmic complexity on attending. Perception andPsychophysics, 58, 34-46.

92 . CHAPTER 8 Musical time

Krumhansl CL (2000) Rhythm and pitch in musiccognition. Psychological Bulletin,126, 159-179.

Large EW (1994) Dynamic representation of musicalstructure. Unpublished doctoral dissertation. Ohio StateUniversity, Columbus.

Large EW and Jones MR (1999) The dynamics ofattending: how people track time-varying events.Psychological Review,106, 119-159.

Large EW and Kolen J (1995) Resonance and theperception of musical meter. Connection Science, 6,177-208.

Large EW and Palmer C (2002) Perceiving temporalregularity in music. Cognitive Science, 26, 1-37.

Lerdahl F and JackendoffR (1983) A generative theoryoftonalmusic.MIT Press, Cambridge, MA.

London JM (2004) Hearingin time:psychological aspects ofmusicalmeter.Oxford University Press, New York.

Makeig S, Debener S, Onton J and Delorme A (2004)Mining event-related brain dynamics. TrendsCognSci,8,204-210.

Mcauley JD (1995) Perception of timephase: towardanadaptiveoscillator modelof rhythmicpatternprocessing.Indiana University Press, Bloomington, IN.

Mcauley JD and Semple P (1999) The effect of tempo andmusical experience on perceived beat. AustralianJournalof Psychology, 51, 176-187.

Mcauley JD, Jones MR, Holub S, Johnston HM and MillerNS (2006) The time of our lives: life span developmentof timing and event tracking. JExpPsychol Gen,135,348-367.

Miller NS and Mcauley JD (2005) Tempo sensitivity inisochronous tone sequences: the multiple-look modelrevisited. Percept Psychophys, 67, 1150-1160.

Nakajima Y, Ten Hoopen G, Hilkhuysen G and Sasaki T(1992) Time-shrinking: a discontinuity in theperception of auditory temporal patterns. PerceptPsychophys, 51, 504-507.

Nakajima Y, Ten Hoopen G, Sasaki T, Yamamoto K,Kadota M, Simons M and Suetomi D (2004) Time­shrinking: the process of unilateral temporalassimilation. Perception, 33, 1061-1079.

Palmer C and Krumhansl CL (1990) Mentalrepresentations for musical meter. Journal ofExperimental Psychology: Human Perception andPerformance, 16, 728-741.

Palmer C and Pfordresher PQ (2003) Incrementalplanning in sequence production. Psychol Rev, 110,683-712.

Parncutt R (1994) A perceptual model of pulse salienceand metrical accent in musical rhythms. MusicPerception, 11, 409-464.

Patel AD, Iversen JR, Chen Y and Repp BH (2005) Theinfluence of metricality and modality onsynchronization with a beat. ExpBrainRes,163,226-238.

Pfordresher PQ (2003) The role of melodic and rhythmicaccents in musical structure. MusicPerception, 20,431-464.

Phillips-Silver J and Trainor LJ (2005) Feeling the beat:movement influences infant rhythm perception. Science,308, 1430.

Povel D-J and Essens P (1985) Perception of temporalpatterns. MusicPerception, 2, 411-440.

Povel D-J (1981) Internal representation of simpletemporal patterns. Journal of Experimental Psychology:Human Perception and Performance, 7, 3-18.

Povel DJ and Okkerman H (1981) Accents in equitonesequences. Percept Psychophys, 30, 565-72.

Repp BH (2005) Sensorimotor synchronization: a reviewof the tapping literature. Psychon BullRev, 12, 969-992.

Ross J and Houtsma AJ (1994) Discrimination of auditorytemporal patterns. Percept Psychophys, 56, 19-26.

Sakai K, Hikosaka 0, Miyauchi S, Takino R, Tamada T,Iwata NK and Nielsen M (1999) Neural representationof a rhythm depends on its interval ratio. Journal ofNeuroscience, 19, 10074-10081.

Sasaki T, Suetomi D, Nakajima Y and Ten Hoopen G(2002) Time-shrinking, its propagation, and Gestaltprinciples. Percept Psychophys, 64,919-931.

Snyder JS and Krumhansl CL (2001) Tapping to ragtime:cues to pulse finding. MusicPerception, 18,455-489.

Snyder JS and Large EW (2005) Gamma-band activityreflects the metric structure of rhythmic tone sequences.Cognitive BrainResearch, 24, 117-126.

Temperley D (2001) The cognition of basic musicalstructures. MIT Press, Cambridge, MA.

Ten Hoopen G, Nakajima Y, Remin G, Massier, B,Rhebergen K and Holleman W (2006) Time-shrinkingand categorical temporal ratio perception: evidence fora 1:1 temporal category. MusicPerception, 24, 1-22.

Trehub SE and Hannon EE (2006) Infant musicperception: domain-general or domain-specificmechanisms? Cognition, 100,73-99.

Will U and Berg E (2007). Brain wave synchronization andentrainment to periodic acoustic stimuli. NeuroscienceLetters,424,55-60.

Windsor WL (1993) Dynamic accents and categoricalperception of metre. Psychology of Music,21, 127-140.

WoodrowH (1932) The effects of rate of sequence uponthe accuracy of synchronization. JournalExperimentalPsychology, 15, 357-379.

Zanto TP, Large EW, Fuchs A and Kelso JAS (2005)Gamma-band responses to perturbed auditorysequences: evidence for synchronization of perceptualprocesses. MusicPerception, 22, 535-552.

Zanot TP, Snyder JS and Large EW (2006) Neuralcorrelates of rhythmic expectancy. Advancesin Cognitive

Psychology, 2, 221-231.