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Influences of metrical structure and groupingon the kinematics of rhythmic finger tapping

Bruno H. Repp and Elliot L. Saltzman1

Haskins Laboratories, New Haven, CT, and 1Boston University

Unpublished manuscript, February 9, 2002

Bruno H. ReppHaskins Laboratories270 Crown StreetNew Haven, CT 06511-6695

Tel. (203) 865-6163, ext. 236FAX (203) 865-8963e-mail: [email protected]

Repp & Saltzman: Meter and grouping 2

Abstract

We investigated whether metrical accentuation has obligatory effects on

the kinematics of rhythmic finger tapping. Auditory rhythmic patterns were

repeated cyclically, and participants first synchronized with each pattern and

then reproduced it 10 times on a MIDI keyboard, which yielded measures of the

timing and velocities of key depression and release. Experiment 1 used strongly

and weakly metrical patterns from Povel and Essens (1985). Experiment 2 varied

metrical structure independently of grouping structure by adding an explicit

beat in different phases to rhythmic patterns. Strongly metrical sequences were

produced with more precise and less variable timing (Exp. 1), and syncopation

had some unexpected effects on timing (Exp. 2). However, metrically accented

taps were similar in most respects to unaccented taps; only key release velocities

tended to be faster for accented taps (Exp. 2). By contrast, grouping structure had

strong effects on all movement parameters. The results suggest that, unlike

rhythmic grouping, metrical structure (and metrical accentuation in particular) is

not necessarily reflected in action.


INTRODUCTION

The distinction between grouping and meter is fundamental to music

(Clarke, 1985; Lerdahl & Jackendoff, 1983) and other rhythmic activities such as

speech. The term rhythm has been used with different connotations in the

literature, sometimes synonymous with meter. We employ it here to mean a

sequence of acoustic events with a nonrandom temporal structure and with

event inter-onset intervals (IOIs) between about 100 and 2000 ms (see, e.g.,

Fraisse, 1982; Wittman & Pöppel, 1999-2000). Grouping refers to the organization

of successive events into larger units according to principles of temporal

proximity and acoustic similarity. Meter refers to regular recurrences

(periodicities) of accented events, as defined below. For both grouping and

meter, relevant properties of the physical signal engage perceptual and cognitive

processes that give rise to a structural representation in a person’s mind.

Both groups and meter often have several nested hierarchical levels, as is

illustrated schematically in Figure 1. The figure shows two rhythmic patterns

from the set used by Povel and Essens (1985). Each “x” stands for the onset of a

sound, whereas each dash stands for the absence of such an onset in a grid of 16

equally spaced time points. Each pattern is repeated cyclically. Since the sounds

are all identical, their grouping is determined by temporal proximity alone.

Three hierarchical levels of grouping are indicated by the horizontal lines above

each pattern. At the lowest level, only adjacent sounds are grouped together. At

the next level, sounds separated by a short interval (a single dash) are grouped

together as well, and at the third level sounds separated by longer intervals (two


dashes) are combined into a single large group which is separated from the next,

identical group by the longest interval in the pattern (three dashes). The lowest

level is always perceptually salient, unless the tempo is so slow that no

perceptual grouping occurs at all (Fraisse, 1982). The perceptual reality of higher

levels depends on tempo: The faster the tempo, the more salient the larger

groups will be (e.g., Handel, 1993). At the tempo at which Povel and Essens

(1985) presented their sequences (200 ms per element), all three levels in the

grouping hierarchy tend to be perceptually salient.

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Insert Figure 1 here

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Three hierarchical metrical levels are indicated by the vertical lines below

the patterns in Figure 1. The lowest level (drawn closest to the pattern)

represents the “metrical grid” or fastest periodicity in the patterns. The higher

metrical levels (lower down in the figure) represent periodicities that are 2 and 4

times slower. How many levels are cognitively represented and which level is

most salient—variously called the tactus (e.g., Parncutt, 1994), beat (e.g.,

McAuley & Semple, 1999), referent level (Jones & Boltz, 1989), or clock (Povel &

Essens, 1985)—again depends on tempo (Parncutt, 1994) and also on individual

perceptual-motor and cognitive capacities, which may be enhanced by musical

training (Drake, 1998; Drake, Jones, & Baruch, 2000). With a metrical grid spacing

of 200 ms, the tactus in strongly metrical Povel-Essens patterns (such as shown in

Fig. 1A) tends to be perceived at the 800-ms level. The lower levels function as

subdivisions of the tactus. Levels higher than the tactus are possible but need not

be considered here.


Perception of a beat is induced or facilitated when temporal regularity is

conveyed by accented events in a sequence (Povel & Essens, 1985). Usually,

accents arise from physical differences such as greater intensity, longer duration,

different pitch, or sharper attack. However, events can also be perceived as

accented merely because they occur in the initial or final position of a group

(Povel & Okkerman, 1981), because of auditory processing advantages that these

positions convey (Todd, 1994). Such sounds tend to be perceived as more intense

than neighboring sounds even if there is no actual difference in intensity (Povel

& Okkerman, 1981). In Figure 1, accented events are marked by a wedge above

the “x”. The lowest level of the grouping hierarchy is assumed to apply. Thus,

the initial and final events in the longest group, the final event in a two-event

group, and single events are all considered accented.1

The two patterns shown in Figure 1 have the same number of accented

events but differ in their location. In pattern A, the accents coincide with higher

levels in the metrical structure shown underneath the pattern, but in pattern B

they do not, nor can they be aligned with any other simple metrical structure.

Therefore, the accent pattern of pattern A readily induces a beat and an

associated metrical structure in a listener’s mind, whereas that of pattern B does

not. Pattern A is a strongly metrical (SM) rhythm, whereas pattern B is a weakly

metrical (WM) rhythm. Although musically trained listeners may be able to

impose a metrical structure such as the one shown on pattern B, this structure

does not arise spontaneously and, if imposed, results in a metrically complex

(syncopated) rhythm. More typically, the pattern is perceived merely as a set of

groups separated by longer or shorter intervals—that is, as a purely “figural”

organization (Handel, 1992, 1998).


It has been shown repeatedly that SM rhythms are easier to remember and

reproduce than WM or entirely nonmetrical rhythms, even if they are

comparable in terms of number of events and grouping structure (Essens &

Povel, 1985; Handel, 1998; Povel & Essens, 1985; Summers, Hawkins, & Mayers,

1986). This has been attributed to the fact that SM rhythms give rise to a strong

feeling of a beat, whereas WM rhythms do not. Although SM sequences may be

ambiguous with regard to the period of their main beat or tactus (Parncutt, 1994),

once perception of a tactus has been induced, this cognitive organization will

tend to be maintained unless it is strongly contradicted by subsequent events. A

tactus can also be imposed on a sequence by extrinsic markers (e.g., by an

accompanying percussion beat) or purely cognitively, for example by reading

musical notation in which the intended beat is indicated.

Before a beat has been induced, the accented events in SM and WM

patterns are equivalent. Once a beat has been established, however—and this

may take only one full presentation of a SM pattern, or less—events coinciding

with the tactus assume a special status: They are considered metrically accented

(or “strong”) relative to other (“weak”) events in the sequence. Thus, for

example, induction of an 800-ms beat by the SM pattern in Figure 1A will make

four of the five accented events metrically accented. If the same beat were

imposed on the WM sequence in Figure 1B, only one of the accented events

would be metrically accented. One way of conceptualizing metrical accents is

that they correspond to an internal representation of a repetitive action (such as

foot tapping) whose outward manifestation is inhibited. Thus, whereas

accentuation resulting from group position is purely perceptual, metrical

accentuation is perceptual-motor in nature. This added motor component results


in a differentiation of the perceived accent structure: For example, in the SM

pattern in Figure 1A the fourth accented event will seem to be relatively less

accented than the other accented events because it does not coincide with the

beat.

Metrical accents may also be regarded as resulting from periodic temporal

expectations or modulations of attention that are induced by a rhythmic pattern

(Jones & Boltz, 1989; Large & Jones, 1999; Palmer & Krumhansl, 1990). The beat

corresponds to an internal oscillatory process, and additional coupled

oscillations representing lower or higher metrical levels are likely to be active as

well (Large, 2000; Large & Jones, 1999). Metrical accentuation can be seen to arise

from coincidence of several of these internal periodicities, as illustrated

schematically in the metrical hierarchy of Figure 1A, which results in the

strongest temporal expectation and focus of attention. (The metrical hierarchy in

Figure 1B is not functional.) However, even if there were only a single internal

beat, it would be sufficient to confer metrical accentuation on the events that it is

synchronized with. By contrast, if no beat is induced by a sequence, there is no

metrical accentuation.

We are concerned here with the question of whether metrical accentuation

has obligatory behavioral consequences in rhythm production. If the internal

periodicity that represents the beat has a latent motor component, and if that

component is coupled with other motor control processes, it may involuntarily

affect ongoing motor behavior. In particular, it may cause metrically strong

actions to be produced with greater force and longer duration than metrical

weak events, and it may also affect the timing of the rhythmic action by

lengthening the IOI preceding or following an accented event.


Metrical structure often does have audible and measurable consequences

in music performance: Metrically strong events tend to be played with physical

accents (greater force, longer duration). However, it seems that these

consequences are not obligatory: A performer can play metrically strong events

without physical accents and may instead give such accents to metrically weak

events. Such off-beat accents can create tension and excitement. Nevertheless,

musicians certainly can and often intend to convey metrical structure in their

performances. To demonstrate this unambiguously, it is necessary to compare

materials that differ only in metrical structure and are equal in all other respects.

Sloboda (1983, 1985) did this by asking pianists to play two versions of the same

tune from musical notation, with the only difference between the two versions

being the placement of the bar lines. The performances were found to be

significantly different in a number of respects, and a group of listeners was able

to identify the meters of the two versions with better than chance success.

Compared to neighboring unaccented tones, metrically accented tones tended to

be played louder, sustained longer, and associated with a local slowing of tempo

(i.e., with a longer IOI to the next tone). Interestingly, Sloboda mentions that the

participating pianists did not notice that the two notated versions of the tune

contained exactly the same sequence of pitches; they seemed like two different

tunes to them.

In another study, closely relevant to the present research, Drake & Palmer

(1993) asked pianists to play rhythmic patterns and melodies from notation, first

in a musical and then in a “mechanical” fashion. By constructing their materials

so that grouping accents (cf. Fig. 1), melodic accents (pitch jumps or turns), and

metrical accents either did or did not coincide, they were able to determine the


effects of each type of accent structure on performance. Grouping was found to

have the clearest effects: Group-final tones were played louder, and the

preceding IOI was lengthened, mainly by extending its silent portion. (The tones

were unconnected.) The effects of melodic structure were less consistent and

shall not concern us here. The effects of meter were also variable: In some

materials, metrically accented events were played louder; in others, they were

preceded by a lengthened IOI. Most of these effects were reduced or absent in

intentionally mechanical performances of the rhythms, but some effects

persisted, in particular the lengthening of the IOI preceding a group-final event,

which has also been noted in more naturalistic studies of music performance

(e.g., Gabrielsson, 1974; Repp, 1999).

The physical expression and communication of metrical structure is part

of musical performance practice and is intentional in that context. Even when

musicians are asked to play like a machine, they may not be totally successful in

suppressing expressive strategies. We wanted to investigate whether metrical

structure has any unintentional, obligatory effects on the kinematics (timing,

force, velocity) of a rhythmic action. To that end, we did away with the

accoutrements of music performance, such as musical notation, melody, and use

of multiple fingers on a keyboard. Instead, like Povel and Essens (1985), we

presented simple rhythmic sequences auditorily and required participants to

reproduce the rhythms faithfully by tapping with a single finger. The tapping

task comprised two phases, synchronization and continuation (cf. Vorberg &

Hambuch, 1984; Wing & Kristofferson, 1973): First the taps accompanied the

cyclically repeated rhythm, and then the rhythm was produced by the taps

themselves. The metrical structure of the sequence either had to be inferred by


the participants (Experiment 1) or was imposed by an external beat (Experiment

2). The sounds in the sequence were physically identical, and the sounds

produced by the taps during the continuation phase likewise did not vary in

intensity or duration. Effects of metrical structure on finger kinematics under

these highly constrained conditions would suggest that meter exerts an

obligatory effect on motor behavior, and this would be of theoretical interest

because it could be interpreted as an external manifestation of the internal

oscillatory process underlying metricality. Absence of any such effects would

suggest that metrical structure represents internal processes that are autonomous

of ongoing motor behavior.

In order to get at the effects of meter, we needed to distinguish them from

effects of grouping. Grouping is known to have strong and apparently

unavoidable effects on both perception and production of rhythms. Although

temporal structure (the sequence of IOIs) is only one of several factors relevant to

grouping, in our materials it was the only such factor. It is known that musicians

do not (and probably cannot) produce the temporal structure of rhythms with

mechanical exactitude (Drake & Palmer, 1993; Gabrielsson, 1974; Repp, 1999),

and conversely listeners do not perceive the IOIs of rhythmic patterns veridically

(Drake, 1993; Penel, 2000; Repp, 1998a). For example, the relative lengthening of

group-final IOIs in production corresponds to a relative shortening of these IOIs

in perception. Less is known, however, about obligatory effects of grouping on

other kinematic parameters such as movement force and velocity. Although our

study was especially concerned with effects of meter, we hoped to learn more

about effects of grouping on action as well.


In Experiment 1, we attempted to separate metrical effects from grouping

effects by means of multiple regression analysis. In Experiment 2, we took a more

direct approach by varying the two structural dimensions orthogonally.

Experiment 1 compared the production of SM and WM sequences, taken from

the classical study of Povel and Essens (1985). These sequences were comparable

in terms of their grouping structure but differed in the temporal pattern of their

elements, such that some sequences easily induced a meter while others did not

(cf. Fig. 1). By contrast, Experiment 2 compared the production of metrical

sequences that had the same temporal pattern but differed in the location of an

externally imposed beat.

Povel and Essens (1985) demonstrated that WM sequences are more

difficult to remember and reproduce than SM sequences. They used a

reproduction task similar to ours, but the continuation phase was brief (4 cycles)

and preceding synchronization was optional. Also, they reported only two crude

response measures: the number of rhythmic cycles that elapsed before

participants started to reproduce a sequence, and the average deviation of the

inter-tap intervals from the sequence IOIs during the continuation phase. Both

measures were significantly higher for WM than for SM sequences. It might also

be noted that their participants had little musical training.

We analyzed both synchronization and continuation tapping in greater

detail. Obligatory effects of either grouping or meter should be evident already

in the synchronization phase, despite the constraints that coordination with an

external signal imposes. In fact, systematic deviations from regular timing may

be enhanced in that condition because the resulting asynchronies with the

auditory events lead to automatic phase error correction (Mates, 1994; Repp,


2001; Vorberg & Wing, 1996), which increases the negative correlation between

adjacent intervals and thereby may reinforce existing biases. Continuation

tapping (reproduction) was expected to reveal influences of grouping and

metrical structure on rhythmic movement in the absence of external constraints.

Our measurement of movement kinematics were simple: Participants

tapped on a MIDI keyboard which yielded measures of inter-tap intervals (ITIs),2

dwell times (durations of key depression), and key depression and release

velocities. Nevertheless, we expected these measures to provide sufficiently rich

data for addressing the questions we were interested in.

EXPERIMENT 1

Methods

Materials. Ten rhythmic sequences were taken from the materials of

Experiment 1 in Povel and Essens (1985). These authors had used 35 cyclically

repeated sequences, each comprising 9 tones of 50 ms duration, to determine

how easily they induced a tactus (or “internal clock”). The temporal structure of

the sequences resulted from different permutations of the same 8 IOIs between

successive tones (5 of 200 ms, 2 of 400 ms, and 1 of 600 ms), and an 800-ms IOI

always separated the final tone from the first tone of the next cycle. We selected

the first 5 (SM) and the last 5 (WM) sequences. These 10 sequences are shown in

Table 1; they represent categories 1 and 7 in Table 2 of Povel and Essens (1985).

The most likely tactus (800 ms) is indicated for both SM and WM sequences,

although it was expected to be induced poorly or not at all by WM sequences.3

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Insert Table 1 here


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The sequences were instantiated as files of MIDI “note on” commands

that were played on a Roland RD-250s digital piano under the control of a MAX

patch running on a Macintosh Quadra 660AV computer.4 All sound events were

identical and represented the high-pitched tone C8 (4,176 Hz) which started

abruptly with a “knock” (key impact noise) and decayed within about 100 ms,

with some residual ringing. No “note off” commands were included in the MIDI

instructions. All tones were generated with a constant, arbitrary MIDI key

velocity of 60.

Participants. There were 10 participants, 6 women and 4 men. They

represented a wide range of age (19–55) and musical experience: one was a

professional violinist, one an advanced amateur pianist (the first author), three

were currently inactive amateur musicians with considerable training, four had

only a few years of musical training, and one had no musical training at all (the

second author). All, however, had participated in a number of previous

synchronization or other motor control experiments and had shown themselves

to have good timing control.

Procedure. Participants sat in front of the computer monitor, listened

binaurally over Sennheiser HD540 II earphones at a comfortable loudness level,

and held a Fatar Studio 37 MIDI controller (a quiet 3-octave keyboard) on their

lap. They tapped with the index finger of their preferred hand (the right hand in

all cases) on a white key of their choice. The precise manner of tapping was not

prescribed. Two participants preferred to strike the key from above because they

felt aided by the increased auditory (impact noise) and tactile feedback. The

other participants tapped in a more restrained way, by either keeping the finger


in contact with the key surface or lifting it only slightly between taps, in which

case the key generated little or no noise.

Participants were instructed to listen to each cyclically repeated rhythmic

pattern until they felt ready to tap along, and then to tap in synchrony with each

tone of the sequence for at least 10 error-free cycles. A counter on the computer

screen displayed the cycle number, and tapping always commenced with the

first tone in the pattern. At some point of their choosing, participants terminated

the synchronization phase by pressing the space bar of the computer key board

with their left hand, without interrupting their tapping. This action always

occurred during the 800-ms IOI at the end of a pattern. It terminated the

sequence playback and instead made each key depression produce a tone

identical in pitch and intensity to the previously presented sequence tones. Tone

intensity was held constant by making the MAX patch substitute a constant key

depression velocity (identical to that of the sequence tones) for the velocity

registered from the MIDI controller before sending the command to the digital

piano. Because each key depression was registered during the downward

movement of the response key, the MAX patch was programmed to delay the

onset of the feedback tone by 20 ms, so as to make it subjectively coincide with

(but actually follow) the bottom contact of the key. Participants were instructed

to continue to produce the rhythmic pattern for at least 10 error-free cycles,

without the aid of a counter. The computer registered the times of key

depressions and releases (to the nearest millisecond) as well as the associated

velocities (on an arbitrary scale ranging from 0 to 127). The ITIs (differences

between successive key depression times) and dwell times (differences between


key release and depression times) were calculated on-line before saving the data.

A schematic illustration of these dependent measures is provided in Figure 2.5

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Two practice trials were given, one using a SM and the other a WM

sequence from Povel & Essens (1985), neither of which was among the 10 test

sequences. Subsequently, the 5 SM and 5 WM test sequences were presented in

alternating fashion, in a different order for each participant. Two participants

(the authors) had gone through an earlier version of the experiment and thus

performed for the second time. In order to avoid having missing data, some of

the participants were asked to repeat problematic trials at the end of the session

or in a later session. The problem was usually an extra tap or a missing tap in

each cycle.

Analysis. The data analyses were based on the last 10 good

synchronization cycles and the first 10 good continuation cycles, respectively. If

possible, the two cycles abutting the switch between the two conditions were not

included. However, when there were fewer than 10 good cycles available in

either condition, the transitional cycle was included.6 Bad cycles were those

containing extra or missing taps or having clearly anomalous timing in

comparison to other cycles; they were omitted and replaced with earlier/later

cycles, if available. The total percentage of bad cycles, which varied widely

among participants, was 13.4 in synchronization and 4.1 in continuation. Most of

these cycles could be replaced; the percentages of missing cycles in the analysis


were 4.1 and 0.3, respectively. There were no clear differences between SM and

WM sequences in these respects.

Results and discussion

Overall measures of relative difficulty. It was expected that SM sequences

would be more difficult to reproduce than WM sequences. Indeed, the average

auditory inspection time (i.e., the number of cycles before synchronization

started) was longer for WM sequences (mean = 5.5, s.d. = 3.9) than for SM

sequences (mean = 3.6, s.d. = 2.3). This difference was significant in a repeated-

measures ANOVA, F(1,9) = 7.8, p < .03. Participants also produced more

synchronization cycles for WM sequences (mean = 16.4, s.d. = 3.6) than for SM

sequences (mean = 14.0, s.d. = 2.4), F(1,9) = 10.8, p < .01, before switching to the

continuation phase. If inspection and synchronization cycles are added and the

required 10 synchronization cycles are subtracted, the results (11.9 vs. 7.6) are

quite similar to those of Povel and Essens (1985), who combined inspection and

(optional) synchronization phases in their analysis. Thus, the WM patterns (as a

group) were perceived as somewhat more challenging than the SM patterns.

As an overall measure of timing accuracy, the average absolute percentage

deviation of the ITIs from the corresponding sequence IOIs was computed.7

There are other possible ways of calculating an overall measure of timing

accuracy (Povel and Essens,1985, reported the average absolute difference

between IOIs and ITIs), but any such measure was expected to reveal smaller

deviations for SM than for WM patterns, as Povel and Essens had found. A

repeated-measures ANOVA on the obtained values, with the variables of

metricality (SM, WM) and condition (synchronization, continuation), indeed


yielded a significant main effect of metricality, F(1,9) = 6.6, p < .04, but also a

Metricality x Condition interaction, F(1,9) = 5.4, p < .05. Interestingly, it turned

out that SM patterns were produced more accurately than WM patterns during

synchronization (deviation values of 3.8% vs. 5.8%), but not during continuation

(5.0% vs. 5.1%). This result was surprising in view of the large difference in favor

of SM patterns obtained by Povel and Essens in their continuation task.

However, it seems likely that they computed their absolute difference scores on a

cycle-by-cycle basis, so that cycle-to-cycle variability in ITI durations (see below)

was included in their measure.8

The average signed percentage deviations tended to be positive during

continuation tapping, which suggested a slight slowing of tempo. However, as

Povel and Essens (1985) noted, it is not advisable to apply a “tempo correction”

to the data because selective lengthening of long ITIs may give a false impression

of general slowing. Indeed, the shortest IOIs (200 ms) tended to be reproduced

very accurately during continuation (see below).

Cycle-to-cycle variability of ITI durations. By averaging ITI durations

across cycles, the overall deviation measure discussed above excluded the cycle-

to-cycle variability of corresponding ITIs, which we shall examine now to see

whether it reveals an advantage for SM over WM patterns. Figure 3 shows the

between-cycle standard deviations (averaged across participants) of the

individual ITIs of all sequences (25 of nominally 200 ms, 10 of 400 ms, 5 each of

600 and 800 ms) as a function of ITI duration (averaged across cycles and

participants), with best-fitting quadratic regression lines (forced through zero).

Four findings are evident.

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First, ITI variability increased with ITI duration, as has been observed

consistently in isochronous sequence production (e.g., Collyer & Church, 1998;

Ivry & Hazeltine, 1995; Peters, 1989; Semjen, Schulze, & Vorberg, 2000). Figure 3

shows that the relationship also holds in rhythmic sequence production (see also

Krampe et al., 2000; Repp, 1997). Although the relationship is typically linear, in

the present data it was mildly curvilinear, mainly because the longest ITIs

(nominally 800 ms) tended to be less variable than expected. This may have been

due to their function as between-group intervals at the highest level of grouping

(cf. Fig. 1). A 2 x 2 (metricality by condition) repeated-measures ANOVA on the

quadratic coefficients of the regression lines for individual participants showed

the nonlinearity to be significant overall, F(1,9) = 7.5, p < .03, and greater in

synchronization than in continuation, F(1,9) = 7.7, p < .03. This latter difference

may reflect compensatory adjustments of timing (phase correction) at the

beginning of each pattern during synchronization.

Second, the increase in ITI variability with ITI duration was steeper in

WM than in SM sequences, and this was true in both tapping conditions. The

longer ITIs were more variable in WM than in SM sequences, but there was little

or no effect of metricality on the variability of the shortest ITIs. A 2 x 2

(metricality by condition) repeated-measures ANOVA on the linear coefficients

of the regression lines for individual participants showed a significant main

effect of metricality, F(1,9) = 10.3, p < .02; the interaction was not significant.9

Third, the variability of ITIs was smaller in the continuation condition

than in the synchronization condition. A 2 x 2 (metricality by condition)


repeated-measures ANOVA on the 500-ms “centercepts” (Wainer, 2000) of the

regression lines yielded a significant main effect of condition, F(1,9) = 32.1, p <

.001. Although this effect may include some improvement with practice, since

continuation always followed synchronization, its main source is probably the

presence of phase error correction in the synchronization condition, which

increased the negative covariance of adjacent ITIs and thus the overall variance

(see Semjen et al., 2000).

Finally, and most importantly, there was also a main effect of metricality

in the analysis of the centercepts, F(1,9) = 11.0, p < .01. The Condition x

Metricality interaction was not significant. Thus, the produced timing of SM

patterns was more stable from cycle to cycle than that of WM patterns in both

synchronization and continuation, which is consistent with the findings of Povel

and Essens (1985).

Having established that metricality did facilitate the reproduction of the

rhythmic patterns, we now proceed to an examination of how grouping and

metrical accentuation affected the timing, dwell times, and velocities of the

participants’ taps.

Systematic deviations from IOI durations. The clustering of the data

points around the vertical grid lines in Figure 3 gives a rough impression of the

average accuracy with which the sequence IOIs were reproduced. It can be seen

that 200-ms IOIs were quite accurately reproduced, whereas 400-ms IOIs clearly

tended to be lengthened, more so in WM than in SM sequences. In WM

sequences, 600-ms and 800-ms IOIs tended to be shortened, whereas they were

reproduced more accurately in SM sequences. These tendencies were quite

similar in synchronization and continuation tapping. One way of capturing this


similarity was to calculate the average percentage deviation from the IOI

duration for each individual ITI in the synchronization and continuation

conditions and to compute the correlation between these deviations across all

rhythmic patterns. This correlation was .87 for SM sequences and .83 for WM

sequences (d.f. = 43, p < .0001).

For a closer look at the timing deviations, Figure 4 shows the average

percentage deviations of the ITIs from the IOIs as a function of IOI duration.

These percentages have been averaged over all individual intervals within each

IOI duration category, and the standard errors represent the variability across

these individual intervals (after averaging across participants). It is clear from the

error bars that the tendency to lengthen 400-ms IOIs was consistent across

individual intervals, and that it was more pronounced for WM patterns than for

SM patterns. In turn, the ITIs corresponding to longer (600-ms and 800-ms) IOIs

tended to be relatively shorter in WM than in SM sequences. To determine

whether these differences were reliable across participants as well, a repeated-

measures ANOVA was conducted on the percentage deviations for individual

participants, after averaging across individual intervals in each IOI duration

category. The variables were duration category (4), metricality (2), and condition

(2). The Greenhouse-Geisser correction was applied to the p values of effects with

more than one degree of freedom, and the epsilon (e) value is reported. In this

overall analysis, the most striking effects were the main effect of duration, F(3,27)

= 12.1, p < .001, e = .69, and the Duration x Metricality interaction, F(3,27) = 11.9,

p < .002, e = .64. However, the main effects of metricality and condition and the

Duration x Condition interaction also reached significance. Therefore, separate 2-


way ANOVAs were subsequently carried out on each IOI duration category.

With a more stringent significance criterion of p < .01, only two effects reached

significance: The main effect of metricality for 400-ms IOIs, F(1,9) = 17.5, p < .003,

and for 800-ms IOIs, F(1,9) = 25.9, p < .0008.

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These results indicate that WM patterns were produced with greater

temporal distortions than were SM patterns. Thus, WM patterns offered less

resistance to the forces that produced the timing deviations. What were these

forces? Duration category is closely tied to the grouping structure: The longer the

IOI, the larger are the groups that it separates (see Fig. 1). Thus it can be

concluded that participants tended to emphasize grouping at the lowest level (by

lengthening 400-ms IOIs) and perhaps to compensate for this emphasis at the

higher grouping levels (by shortening 600-ms and 800-ms IOIs), particularly in

WM patterns.

So far, all IOIs within each duration category have been lumped together.

However, the individual IOIs, and especially the within-group (200-ms) IOIs, can

be distinguished further according to position within the group and according to

whether or not they are initiated by a metrically accented event. Therefore, the

temporal context of each IOI was coded in terms of the duration of the

immediately preceding IOI and the immediately following IOI, whereas metrical

structure was coded numerically as a three-level hierarchy, corresponding to the

three metrical levels in Figure 1 (i.e., four 800-ms beats subdivided twice). Thus,

positions 1, 5, 9, and 13 in the 16-point metrical grid were coded as “3” (strongly


accented), positions 3, 7, 11, and 15 as “2” (weakly accented), and the remaining

positions as “1” (unaccented). The same metrical hierarchy was imposed on SM

and WM patterns (cf. Fig. 1), even though it was assumed to be induced poorly

or not at all by WM patterns. Each IOI or corresponding ITI could then be

classified with regard to the metrical accent strength of the current (initiating) or

following (terminating) event.

A stepwise multiple regression analysis was conducted on the percentage

deviations of the individual ITIs from the corresponding IOI durations (averaged

across participants). The four predictor variables were: initial metrical accent

strength, terminal metrical accent strength, preceding IOI duration, and

following IOI duration. For each of three IOI duration categories (600-ms and

800-ms IOIs were combined), four regression analyses were carried out, one for

each combination of metricality and condition. It was expected that any effects of

metrical structure would be evident in SM but not in WM sequences, whereas

effects of grouping would be independent of metricality. Because of the multiple

analyses, a significance criterion of p < .01 was adopted.

For ITIs corresponding to 200-ms IOIs (n = 25), a significant positive effect

of following IOI (ITI) duration was obtained in three of four regression analyses.

(There was only a tendency in synchronization with WM sequences.)

Correlations ranged from .55, p < .01, to .77, p < .001. This effect represents the

well-documented tendency for group-final intervals to be lengthened (Drake &

Palmer, 1993; Gabrielsson, 1974). Preceding IOI (ITI) duration also made a

significant contribution in two analyses, a secondary one in continuation of SM

sequences (partial r = –.55, p < .01) but a primary one in synchronization with

WM sequences (r = .51, p < .01). Note the contrasting directions of the effect: In


the former situation, 200-ms ITIs tended to be shorter when preceded by a long

ITI (i.e., group-initial shortening), whereas in the latter situation, the opposite

was the case (i.e., group-initial lengthening). The reason for this difference is

unclear. There were no significant effects of temporal context (grouping) on

longer ITIs.

Metrical accents did not make a significant contribution in any of the

regression analyses. Thus, there was no evidence that metrically strong taps were

produced with longer ITIs, or were preceded by longer ITIs, than metrically

weak taps.

Dwell times. We now turn to an analysis of the dwell times, calculated as

the time from registered key depression to registered key release (Fig. 2). The

question of main interest was whether metrically accented taps were associated

with longer dwell times.

The average dwell times are shown in Figure 5 as a function of IOI

duration, with standard errors computed across individual IOIs within duration

categories. The individual participant data were subjected to a 4 x 2 x 2 repeated-

measures ANOVA with the variables of IOI duration, metricality, and condition.

Dwell times clearly increased with IOI duration, F(3,27) = 5.9, p < .03, e = .41.

Thus, participants held the key down longer when there was more time before

the next tap. Dwell times during 200-ms ITIs were not affected by condition, but

dwell times during longer ITIs were longer in continuation than in

synchronization, as indicated by a significant Duration x Condition interaction

F(3,27) = 5.1, p < .05, e = .36. The Duration x Metricality interaction also reached


significance, F(3,27) = 4.5, p < .05, e = .43: During long ITIs, dwell times tended to

be longer in SM than in WM sequences.

--------------------------


--------------------------

The individual ranges of variation of dwell times (after averaging across

rhythm cycles) varied dramatically, from less than 10 ms to more than 470 ms. In

other words, participants differed greatly in their kinematic strategies: Some (n =

5) basically repeated a stereotypical tapping movement, whereas others (n = 5)

adapted their movements to the rhythmic grouping structure. Naturally, the

average data in Figure 5 are more representative of the latter participants. The

individuals with short and nearly constant dwell times tended to be the ones

with greater musical training. Their average dwell times increased from 93 to 106

ms as the IOIs (ITIs) increased from 200 to 800 ms, but this increase did not reach

significance in a separate analysis, F(3,12) = 5.6, p < .07, e = .40.

To determine whether dwell times showed any effects of metrical

accentuation, stepwise multiple regression analyses analogous to those

conducted on the timing deviations were conducted on the dwell times during

individual IOIs (averaged across participants). The four predictor variables

(appropriately renamed) were: metrical accent strength, metrical accent strength

of the following tap, preceding IOI duration, and following IOI duration.

Preceding IOI duration had a positive effect on dwell time during short (200-ms)

IOIs in WM sequences, both in synchronization (r = .54, p < .01) and continuation

(r = .64, p < .001) conditions, but not in SM sequences. Thus, group-initial taps in


WM sequences made contact a little longer than group-medial or group-final

taps. Following IOI duration tended to have a negative effect on dwell time

during 400-ms IOIs, but it did not reach the p < .01 significance level. There were

no effects of metrical accent strength in these analyses, except for one effect in

long IOIs that can be explained as an artifact of sequence structure.

It may be concluded, then, that metrically strong taps did not have longer

dwell times than metrically weak taps. Grouping structure, however, had strong

effects on dwell times, at least in some participants.

Key depression velocities. Key depression (“attack”) velocities, which

were registered in terms of arbitrary units ranging from 0 to 127, basically

reflected the force of key depression. They were highly correlated with key dwell

times: The higher the velocity (the greater the force), the shorter the dwell time.

Correlations computed across the individual IOIs of all rhythm patterns, with the

data averaged across cycles and participants, ranged from –.84 to –.89 (d.f. = 43, p

< .001) in the four data sets defined by metricality and condition. In part, this

high correlation was mediated by IOI duration, which affected both dwell times

(see above) and velocities (see below). However, moderate negative correlations

were generally also present within IOI duration categories, suggesting a direct

relation between velocity and dwell time, probably due to a faster rebound when

the key is depressed with greater force.

As can be seen in Figure 6, key depression velocities decreased as IOI

duration increased, F(3,27) = 8.6, p < .01, e = .42, with the effect being mainly due

to taps initiating the shortest ITIs being executed with greater force than other

taps. Velocities tended to be higher in WM than in SM sequences and higher in

synchronization than in continuation, but neither effect reached significance.


--------------------------


--------------------------

Stepwise multiple regression analyses on the data for 200-ms IOIs showed

a positive effect of preceding IOI duration in SM sequences, in both conditions (r

> .56, p < .01). Thus, the response key tended to be depressed with greater force

when the preceding ITI was long, which amounts to group-initial accentuation.

No other effects reached significance. Thus there was no evidence that metrically

accented taps were executed more forcefully.

Key release velocities. Key release velocities reflect the velocity of the

upward movement of the finger, provided that the finger stays in contact with

the key. Two participants struck the key hard from above, so that it often

bounced back by itself. Their key release velocities were frequently at the

maximum of 127 and thus showed a ceiling effect; nevertheless, their data were

included in all analyses because occasional lower velocities did provide some

information.

Overall, the correlations between key release velocity and key depression

velocity were mildly negative, ranging from –.14, n.s., to –.33, p < .05, in the four

data sets defined by metricality and condition. This surprising relationship was

evidently due to divergent effects of IOI duration on the two velocities (see Figs.

6 and 7). Within IOI duration categories, the correlations tended to be positive,

especially for 200-ms IOIs (ranging from .32, p < .10, to .77, p < .001), as should be

expected if the down-up movement is a single dynamic gesture. The overall

correlations between key release velocity and dwell time were positive, ranging

from .38 to .54. Within IOI duration categories, however, these correlations were


smaller or absent, which again suggests a mediating role of IOI duration, which

affected average dwell times and key release velocities in similar ways (see Figs.

5 and 7).

Figure 7 shows that average key release velocity increased with IOI

duration, F(3,27) = 16.3, p < .001, e = .73. This consistent effect implies that the

key was released more quickly when there was a long interval before the next

tap. This seems surprising, but it may be due to a smaller upward excursion of

the finger in preparation for the following tap when the ITI was short. In other

words, during rapid movements the finger probably stayed in close contact with

the key and thereby retarded the mechanical rebound. Key release velocities

were also slightly faster in WM than in SM sequences, F(1,9) = 5.8, p < .04.

Although Figure 7 suggests some two-way interactions, they were not

significant. The triple interaction reached significance, F(3,27) = 3.5, p = .05, e =

.68, but is difficult to interpret.

--------------------------


--------------------------

Stepwise multiple regression analyses on the data for 200-ms IOIs showed

a strong positive effect of preceding IOI duration in all four data sets (r > .88, p <

.001). Thus the response key was released more quickly when the preceding ITI

was relatively long (i.e., when the tap was group-initial). The same effect was

observed for 400-ms IOIs in all four data sets and even for longer IOIs in SM

sequences, although it did not reach the strict level of significance adopted here.

In general, however, group-final taps were associated with slower key releases


than singleton taps. Thus, these effects of grouping structure were quite robust.

By contrast, effects of metrical structure were basically absent. The only effect to

reach significance occurred with WM sequences and therefore was

uninterpretable.

Summary. Metrical structure facilitated the reproduction of rhythmic

sequences: SM patterns yielded shorter auditory inspection times, fewer

synchronization cycles, smaller cycle-to-cycle variability of ITIs, and smaller

systematic deviations of the ITIs from the sequence IOI durations. However,

there was no evidence of any effects of metrical accentuation on any of the four

dependent measures in SM sequences. By contrast, there were large and

consistent effects of low-level rhythmic grouping structure on tap timing and

kinematics: Between-group ITIs were generally lengthened. Group-final taps

were preceded by lengthened ITIs and were produced with longer dwell times,

slower key depression velocities, and faster key release velocities. Group-initial

taps tended to be produced with longer dwell times, faster key depression

velocities, and faster key release velocities.


EXPERIMENT 2

In Experiment 1, effects of metricality were assessed indirectly by

inducing a metrical structure through rhythmic patterning and by contrasting

SM with WM sequences. It could be argued that the negative results were due to

this indirect approach. Experiment 2 took a more direct route by imposing a

metrical structure on identical sequences by means of extraneous signals. In that

way, metrical structure was varied independently of grouping structure.

Methods

Materials. Twelve sequences were constructed, which are shown

schematically in Table 2. Each of four 5-tone rhythmic patterns was repeated

cyclically in three different metrical frameworks, defined by an explicit beat. The

sequence events were high-pitched, freely decaying digital piano tones (4,176

Hz), as in Experiment 1. The added beats were low-pitched digital piano tones

(52 Hz) of 50 ms nominal duration (i.e., not including the damped vibrations

following the “note offset” specified in the MIDI instructions). One rhythmic

cycle lasted 2400 ms and comprised 12 metrical time points separated by 200 ms.

The beats occurred twice per rhythmic cycle (every 1200 ms). They were rather

slow to function as a tactus and therefore were really “downbeats” marking the

beginnings of “bars”, each containing three beats 400 ms apart (i.e., a triple

meter). The downbeats could coincide with either a sequence tone or with

silence. Even though they may not have played the role of a tactus, they were


undoubtedly a salient part of the metrical structure, which can be described as 2

x 3 x 2.

The sequence IOIs had three different durations (200, 400, and either 1000

or 1200 ms). Although the longest IOI always marked the end of a rhythmic

group, the event terminating it did not always constitute the beginning of the

rhythmic cycle (i.e., the first downbeat); this was the case only in the sequences

labeled “a”. The relative difficulty of the patterns was expected to depend on the

placement of the downbeats. The “a” pattern in each group was expected to be

easiest to (re)produce because the downbeats always coincided with tone onsets.

In the “b” and “c” versions, the first of the two downbeats coincided with

silence, leading to syncopation.

--------------------------

Insert Table 2 here

--------------------------

Participants. The participants were the same as in Experiment 1.

Procedure. Experiment 2 followed Experiment 1 in the same session. The

procedure was exactly the same. A single practice sequence, different from the

experimental sequences, was presented first. The order of the 12 sequences was

varied across participants and constructed so that different metrical versions of

the same sequence did not immediately follow each other. Participants were

instructed to tap with and reproduce only the high sequence tones, not the low

tones. Tapping always started on a downbeat. During the continuation phase,

the low tones were absent. It was assumed that the metrical framework

established by them would outlast their physical presence and would guide the

reproduction of the rhythmic pattern.


Results and discussion

The average percentage of cycles rejected as anomalous was 5.3 in

synchronization and 3.3 in continuation; 2.3 percent of the cycles were missing in

the analysis, mainly because two participants often produced fewer than 10

synchronization cycles.

Overall measures of relative difficulty. The average auditory inspection

time was 4.2 cycles for non-syncopated sequences (“a”) and 4.6 cycles for

syncopated (“b”, “c”) sequences, a nonsignificant difference. The average

number of synchronization cycles was 14.9 and 16.9, respectively; this difference

did reach significance, F(1,9) = 8.2, p < .02, indicating that participants found the

syncopated patterns somewhat more challenging.

Variability of ITI durations. Figure 8 shows the cycle-to-cycle standard

deviations (averaged across participants) of all individual ITIs in the 12 rhythms

as a function of average ITI duration, separately for synchronization and

continuation. The data for the continuation task suggest a linear relationship

between IOI duration and standard deviation, like the data for SM sequences in

Experiment 1 (Fig. 3b). However, the synchronization data show a strong

curvilinear trend, and the individual ITIs within duration categories (200, 400,

1000, 1200 ms) also differ more from each other. All ten participants showed this

strong nonlinearity in synchronization. Overall, short ITIs were less variable in

continuation than in synchronization, but the opposite was the case for long ITIs.

In this respect, the results differ from those of Experiment 1, where variability

was generally higher in synchronization than in continuation. Interestingly, the


long ITIs of syncopated patterns tended to be less variable than those of non-

syncopated pattern and thus contributed especially to the nonlinear trend.

--------------------------


--------------------------

Deviations of ITIs from IOI durations. By comparing the data points to

the grid lines, it can be seen in Figure 8 that long IOIs were less accurately

reproduced in continuation than in synchronization; usually they were

lengthened. The percentage deviations of the individual ITIs from the IOI

durations were subjected to a separate 2 x 3 x 5 repeated-measures ANOVA for

each of the four rhythmic patterns, with the variables of condition, meter (i.e.,

downbeat placement), and ordinal position of the ITI in the pattern (with the

long ITI always coming last). The effect of primary interest in all analyses was

the Meter x Position interaction, which if significant would indicate that metrical

structure affected the timing pattern. Because of the multiple analyses, a strict

significance criterion of p < .01 was adopted.

Figure 9 shows the average timing deviations. Each panel represents a

different rhythmic pattern. The data are presented in a format different from that

of Experiment 1: Note that the abscissa is categorical here and represents the

individual IOIs in the order in which they occurred in each pattern. The main

effect of position was significant in Patterns 1–3, F(4,36) > 5.6, p < .01, e = .51 to

.70, and close to significance (p < .05) in Pattern 4, which means that different ITIs

deviated in different ways from their corresponding IOIs. There was a general

tendency to undershoot 200-ms IOIs. However, the tendency for short ITIs to be

lengthened when they preceded longer ITIs, the group-final lengthening


observed in Experiment 1, was not consistently present. This refers to the second

of the two consecutive 200-ms ITIs in Patterns 1, 2, and 3, relative to the first ITI.

Only Pattern 3 showed consistent group-final lengthening, Pattern 2 in four out

of six conditions, and Pattern 1 in only two of six conditions. The effect of main

interest, the Meter x Position interaction, was significant for all four patterns,

F(8,72) > 4.5, p < .01, e = .32 to .44. Furthermore, the triple interaction was

significant for Patterns 3 and 4, F(8,72) > 4.6, p < .006, e = .45 to .48. Some other

main effects and interactions also reached significance. Because of this complex

pattern of results, and because it appeared that most effects were more

pronounced in synchronization than in continuation, separate two-way

ANOVAs were conducted on the four rhythm patterns in each of the two

tapping conditions. The Meter x Position interaction was significant in five of

eight analyses, F(4,36) > 4.8, p < .005, e = and close to significance (p < .05) in the

remaining three. Thus, metrical structure had reliable effects on timing.

--------------------------


--------------------------

To interpret these effects, it is necessary to consider where the downbeats

fell in each pattern (see Table 2). For example, in Pattern 1a downbeats coincided

with Positions 1 and 5; in Pattern 1b, one downbeat coincided with Position 4,

whereas the other one fell inside the long ITI; and in Pattern 1c, one downbeat

coincided with Position 3, whereas the other one fell inside the long ITI.

(Positions 1–5 here refer to tone onsets, corresponding to the “x” symbols in

Table 2, which initiate the ITIs shown in Figure 9.) Careful inspection of the data


in Figure 9 according to the accent positions in Table 2 does not suggest

systematic lengthening or shortening of ITIs following or preceding metrically

accented events. Where then does the Meter x Position interaction for each

pattern come from? It seems that it is due in large part to the following

systematic effect: The long ITI (Position 5) was produced with a longer duration

when the events delimiting it were unaccented (i.e, in the syncopated versions b

and c: triangles and diamonds in Figure 9) than when they were metrically

accented (version a: circles). In the synchronization task, this furthermore seems

to have caused a compensatory adjustment in the following ITI (Position 1: filled

circles vs. filled triangles and diamonds). Thus, it was not the ITI following a

metrically accented tap (as one might have expected) but the ITI containing an

“empty” downbeat in syncopated patterns that was lengthened.

Dwell times. Figure 10 presents the results for dwell times. As in

Experiment 1 there were enormous individual differences in the range of dwell

times, so that the averages are representative mainly of those participants who

let dwell time vary. Their dwell times increased strongly with IOI duration, as in

Experiment 1. Because of the individual differences, the increase did not reach

significance in the ANOVA. Moreover, there was no general tendency to hold

metrically accented taps longer than other taps. Those participants who did show

large differences in position 5 not only held the accented tap (pattern version a,

circles in Fig. 10) longer than unaccented taps, but also held the unaccented tap

in version b (triangles) longer than that in version c (diamonds), in all four

rhythm patterns. Apparently, their dwell times were curtailed by an approaching

downbeat (see Table 2), even if it was only imagined during continuation

tapping.


----------------------------


----------------------------

Key depression velocities. The results for key depression velocities are

shown in Figure 11. It is clear that taps initiating 200-ms ITIs were associated

with greater force of key depression than taps initiating longer ITIs, just as in

Experiment 1. This was reflected in significant main effects of position for

Patterns 1 and 4, F(4,36) > 8.3, p < .007, e = .39 to .48, and nearly significant effects

(p < .02) for the other two patterns. The only other effect to reach significance was

the Condition x Position interaction for Pattern 3, F(4,36) = 6.0, p < .005, e = .69,

although it seems rather small in Figure 11c. The Meter x Position interactions

were all nonsignificant. Thus there was no tendency to produce metrically

accented taps with greater force than unaccented taps.

--------------------------


--------------------------

Key release velocities. Finally, Figure 12 presents the results for key

release velocities. There were significant main effects of position for Patterns 1, 2,

and 3, F(4,36) > 8.4, p < .004, e = .49 to .79. These effects were mainly due to a

slower upward movement for the second tap in a group of three, that is the tap

initiating the second of two consecutive 200-ms ITIs. Interestingly, there seemed

to be some effects of meter here, even though metrical structure had not been

expected to affect key release velocity. The Meter x Position interaction was close

to significance (p < .03) for Patterns 2 and 4. Inspection of Figure 12 reveals that,


in each case, metrical accentuation resulted in a relatively quicker key release. In

the three versions of Pattern 2 (Fig. 12b), the downbeats fell in Positions 1 and 5

(circles), 4 (triangles), and 2 (diamonds), respectively. In Pattern 4 (Fig. 12d), they

fell in Positions 1 and 4 (circles), 3 (triangles), and 2 (diamonds), respectively. In

most of these positions, the version having the metrical accent showed higher

release velocities than the other two versions. Position 3 of Pattern 3b (Fig. 12c,

triangles) also reflects a strong effect of metrical accentuation.

--------------------------


--------------------------

Summary. Experiment 2 confirmed that metrical accentuation affects

neither the timing, nor the dwell time, nor the force of taps. Unexpectedly,

however, key release velocity tended to be increased by metrical accentuation. In

addition, metrical accents coinciding with a silence affected the relative duration

of that ITI and the dwell time of the preceding tap (in some participants). As in

Experiment 1, there were some pronounced effects of temporal grouping

structure: Taps that were quickly followed by another tap were executed with

faster key depression velocities and shorter dwell times, and with slower key

release velocities if they occurred in the middle of a group of three taps. Group-

final lengthening of ITIs was not as strong as in Experiment 1, probably because

the groups were shorter.


GENERAL DISCUSSION

Even though the present study assessed movement kinematics in a coarse

way by using MIDI technology, it yielded considerable information about the

participants’ action patterns. Previous studies of rhythm production, such as

Gabrielsson (1974) and Drake and Palmer (1993), were primarily concerned with

musical performance, although the latter study included a “mechanical”

performance condition. The present research focused especially on the

unavoidable kinematic consequences of rhythm production. To that end, the

rhythm patterns were presented as auditory models rather than in musical

notation, and the task required both synchronization and reproduction

(continuation) by means of simple finger taps. The study may be seen as an

extension of the work of Povel and Essens (1985), who did not perform a detailed

analysis of movement parameters.

Results were generally similar for synchronization and continuation

tapping. When there were differences in timing, they could be attributed to the

additional requirement of error correction in synchronization (see Semjen et al.,

2000). Continuation tapping is free of the additional adjustments in ITI duration

that error correction causes and therefore gives a clearer picture of the obligatory

consequences of rhythm production. However, the presence of all the major

effects during synchronization confirms their obligatory nature.

The results revealed effects of grouping structure and of metrical structure

on rhythm production. Effects of metrical structure were of primary interest. Our

hypothesis was that they would be of two kinds. First, as has been observed in

many earlier studies, metricality was expected to improve the accuracy of


rhythm production. This issue was addressed primarily in Experiment 1 by

contrasting strongly and weakly metrical sequences, and to some extent in

Experiment 2 by comparing non-syncopated and syncopated sequences, which

had comparable (imposed) metrical frameworks and thus differed in metrical

complexity rather than metricality as such. Second, we hypothesized that

metrically accented taps would be produced more forcefully, with longer dwell

times, and with longer ITIs than metrically unaccented taps. This hypothesis was

based on the assumption that temporal regularities of a rhythm entrain internal

periodicities that partially involve the motor control system and therefore may

involuntarily influence the ongoing motor behavior.

Experiment 1 revealed beneficial effects of metricality which confirm those

found in earlier studies, such as Povel and Essens (1985): SM patterns were

produced more accurately, with lower ITI variability, and with greater

confidence (shorter auditory inspection times and fewer extra synchronization

cycles) than WM patterns. In Experiment 2, non-syncopated patterns elicited

fewer extra synchronization cycles than syncopated patterns, but they were not

produced more accurately, and their ITI variability actually tended to be higher

than that of syncopated patterns. Thus, weak metricality was an impediment,

whereas syncopation within a strong metrical framework was not. The effects of

metricality were relatively small: The WM sequences were not particularly

difficult to reproduce.

Effects of metrical accentuation were totally absent in Experiment 1.

However, the materials and analyses in that experiment were perhaps not

optimal for assessing such effects. Also, the alternation of SM and WM sequences

may have attenuated effects of metricality. Experiment 2 provided a stronger test


by manipulating accent placement independently of grouping structure. Again,

however, metrical accentuation was found to have no effect on ITIs, dwell times,

and key depression velocities. These results disconfirm our hypothesis of an

obligatory connection between metrical structure and rhythmic action. If

induction of a beat engages the motor system, then this covert activation seems

to be uncoupled from the ongoing motor behavior, at least as long as there is no

intention to convey the beat in the rhythmic action. Alternatively, metrical

structure may be purely cognitive and for that reason has no obligatory link with

action.

Metrical structure had three unexpected effects in Experiment 2. One was

that key release velocities tended to be faster for accented than for unaccented

taps. This result is puzzling because it is not clear what key release has to do with

metrical accentuation. The other two findings were that downbeats coinciding

with silence in a syncopated rhythmic pattern caused a relative lengthening of

the ITI containing the downbeat, and also a shortening of the dwell time of the

preceding tap. These effects are not so much due to metrical accentuation as to

accent placement. The lengthening of the ITI suggests that the processing of an

actual or imagined downbeat took time or caused an underestimation of the

interval. The shortening of the dwell time can be understood as a lifting of the

finger in anticipation of the downbeat (even though, or perhaps because, the

downbeat did not require a key depression). These effects require further

investigation, perhaps using continuous recording of finger movement.

In contrast to the limited effects of metrical structure, temporal grouping

structure had pervasive effects, involving all four measured parameters of finger

movement. No participant was able to reproduce the rhythm patterns with


mechanical exactness (i.e., as presented), even when the patterns were strongly

metrical and the participant had extensive musical training. One consistent effect

in Experiment 1 was the relative lengthening of the final ITI in a group, which

has been previously documented in rhythm and music performance (Drake and

Palmer, 1983; Gabrielsson, 1974; Repp, 1999). The present study shows that the

lengthening tendency persists even in synchronization with a mechanically exact

rhythmic template. Group-final lengthening seems to be the unavoidable

consequence of instantiating rhythmic groups in action, and this may hold for

other systematic deviations from regularity as well. Drake (1993; Penel & Drake,

1998) has proposed that such timing deviations from nominal simple-ratio

intervals are caused by performers’ compensation for auditory distortions in

temporal interval perception. The present findings, however, seem more in line

with Repp’s (1998a) suggestion that the deviations originate in action, which in

turn affects perception, or that action and perception are affected in parallel but

complementary ways by rhythmic grouping.

The effects of rhythmic grouping also extended to dwell times and

velocities. The effects on dwell times must be qualified, however, by the

startlingly large individual differences in the range of dwell times. Although

even those participants whose dwell times were nearly constant showed

increases in dwell time with IOI duration, these effects were too small to be of

any significance. Thus it is possible to carry out nearly invariant tapping

movements within different rhythmic grouping structures, but presumably at the

cost of continuity of movement. Those participants who spontaneously

prolonged their dwell times when the ITI was long thereby achieved a more

continuous, more connected sequence of movements. This difference in


movement strategies may be related to the difference between “intermittent” and

“elastic” tapping discussed by Vaughan et al. (1998). Here, the intermittent

strategy, which emphasizes the temporal structure of the rhythm, was adopted

by the participants with the most extensive musical training. However, large

individual differences in dwell times as a function of interval duration have also

been observed among skilled pianists in a study of staccato articulation in

isochronous sequences played at different tempi (Repp, 1998b).

Grouping structure also affected key depression and release velocities.

Key depression velocities were faster when the ITI initiated by the tap was short,

and especially when it was preceded by a longer ITI, which implies group-initial

accentuation. Key release velocities were slower when the ITI initiated by the tap

was short, and especially when the preceding ITI was short as well, which

suggests smaller upward excursions of the finger when taps occurred in close

succession. Dwell times and key depression velocities were negatively

correlated: Longer dwell times were preceded by slower key depressions.

However, this correlation derived from those participants who allowed their

dwell times to vary widely. Inspection of the individual data of four participants

with nearly invariant dwell times suggested that their key depression velocities

did not vary systematically with ITI duration. Nevertheless, their key release

velocities increased with ITI duration, as they did in the other participants. These

different kinematic strategies deserve further study by means of continuous

movement recordings.

Analysis of timing variability revealed that standard deviations increased

with ITI duration in both synchronization and continuation tapping. This is a

standard finding with simple isochronous rhythms (e.g., Semjen et al., 2000) and


has also been observed when IOIs of different durations occur within a sequence

(Krampe et al., 2000; Repp, 1997; Vorberg & Wing, 1996). A strictly linear

relationship would suggest nonhierarchical concatenation of independently

timed intervals, and the data for continuation of strongly metrical patterns are

consistent with this interpretation (see Vorberg & Hambuch, 1984; Vorberg &

Wing, 1996). Even though cognitive metrical structure is hierarchical, rhythm

production seems to be timed serially. Deviations from linearity were observed

in the synchronization task and were probably caused by phase error correction,

which led to compensatory adjustments in ITI duration (Semjen et al., 2000;

Vorberg & Schulze, in press). A more detailed investigation of these issues

would require an analysis of the covariance structure of the ITIs (see Vorberg &

Wing, 1996), for which a large number of repetitions of each pattern would be

needed.

In closing, we should acknowledge that our task situation was somewhat

unnatural, due to the absence of any auditory feedback about dwell time and

force of key depression. Also, some of the grouping effects obtained may be

specific to tapping with a single finger on a piano key. However, the task

constraints were intentional; they were meant to test whether metrical

accentuation has consequences for action in the absence of rich auditory feedback

and of any close resemblance to music performance. Only if such consequences

emerged under these constraints could they be called obligatory. Our results

suggest, however, that metrical accentuation has few obligatory consequences in

action, despite the strong motoric quality that is associated with the feeling of a

beat.


FOOTNOTES

1 These accents may differ in relative salience, but for the sake of simplicity

they will be assumed here to be roughly equal.

2 Throughout this paper, there is a terminological quandary regarding the

distinction between IOIs and ITIs because IOIs refer both to the intervals in the

computer-generated sequences and to the expected durations of participants’

ITIs. Thus, sometimes ITIs are described in terms of IOI durations (e.g., a 200-ms

ITI is an ITI with an expected duration of 200 ms).

3 A 400-ms tactus is also conceivable for SM sequences (Parncutt, 1994; Todd,

O’Boyle, & Lee, 1999). In that case, a superordinate 800-ms level is likely to exist

in the metrical structure as well, so that the metrical accents would be similar

(though perhaps less distinct).

4 A MAX patch is a program written in the graphical programming language

MAX. Due to a peculiarity of this software, the tempo of the output was about

2.4% faster than specified in the MIDI instructions, and the participants’ taps

were recorded at a correspondingly slower rate. Thus, the actual IOIs and ITIs

were somewhat shorter than reported here. Apart from this scaling factor, MAX

was believed to be accurate within ±1 ms.

5 Because the electronic registration of key actions occurred about halfway

during the key trajectories, the dwell times were somewhat longer than the

actual key bottom contact times, equivalent to contacts with a raised key bed.

The absolute difference is immaterial here. However, it may also be surmised


that the dwell times were affected by variation in key depression and release

velocities, and that ITIs were affected by variation in key depression velocities.

There are two answers to this concern: First, such effects amounted to only a few

milliseconds and thus were negligible compared to the large differences reported

below. (Average key depression velocities are typically between 0.5 and 2 m/s;

see, e.g., Conklin, 1996. This translates to about 2.5–10 ms for the 5-mm

movement path from the upper or lower key position to the registration point.

The range of variation in average key depression velocity, however, was only

about 1/5 of the possible range; see Figs. 6, 7, 11, 12 below. Therefore, the

average effects on dwell times and ITIs were probably no larger than 2 ms.

Similar arguments apply to key release velocity.) Second, this concern vanishes if

a tap is considered as a continuous down-up movement that is intercepted by the

key registrations at some arbitrary point during the trajectory (see Vaughan,

Mattson, & Rosenbaum, 1998). Viewed in this way, there is a necessary

dependence between movement velocity and dwell time, as well as ITI,

regardless of where the movement is intercepted.

6 The left-hand key press which occurred during the long interval terminating

the last synchronization cycle did not have any obvious effect on timing,

probably because it occurred near the middle of the interval and thus was

integrated into the rhythmic structure.

7 First, the durations of corresponding ITIs were averaged across cycles; then

the signed deviations of these average ITI durations from the corresponding IOIs

of each rhythm pattern were calculated and expressed as a percentage of IOI

duration; then these percentages were averaged within the same IOI duration


category (200, 400, 600, 800 ms) across all rhythm patterns; and, finally, the

absolute values of these average percentage deviations were averaged across the

four IOI duration categories.

8 Dirk-Jan Povel (personal communication, June 14, 2001) agrees but is not

certain.

9 There was also a strong main effect of condition, F(1,9) = 71.5, p < .0001, with

the linear coefficients being larger in synchronization than in continuation, but

this may in part be a consequence of the larger (negative) quadratic coefficients

in synchronization.


ACKNOWLEDGMENTS

This research was supported by NIH grants MH-51230 and DC-03663. We

are grateful to Mari Riess Jones and Amandine Penel for helpful comments on

the manuscript. Address correspondence to Bruno H. Repp, Haskins

Laboratories, 270 Crown Street, New Haven, CT 06511-6695 (e-mail:

[email protected]).


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Table 1. Sequences used in Experiment 1. Each “x” represents a tone onset

and each dash the absence of a tone onset, with 200 ms between successive

time points. Vertical bars indicate the most likely tactus (period of 800

ms), which is of questionable reality in WM sequences..

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––

Strongly metrical (SM):

| | | |1. x x x x x – – x x – x – x – – –2. x x x – x – x x x – – x x – – –3. x – x x x – x x x – – x x – – –4. x – x – x x x x x – – x x – – –5. x – – x x – x – x x x x x – – –

Weakly metrical (WM):

| | | | (?)6. x x x x – x x x – – x – x – – –7. x x x x – – x x – x x – x – – –8. x x – x x x x – – x x – x – – –9. x x – x – – x x x x x – x – – –10. x – x – – x x x – x x x x – – ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––


Table 2. Rhythmic patterns used in Experiment 2. Each “x” represents a tone onset

and each dash the absence of a tone onset, with 200 ms between successive time

points. Vertical bars indicate the externally imposed “downbeats” (period of 1200

ms).

–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––—

| |1a. x x x – x – x – – – – –1b. – – x x x – x – x – – –1c. – – – – x x x – x – x – | |2a. x – x x x – x – – – – –2b. – – x – x x x – x – – –2c. – – – – x – x x x – x – | |3a. x – x – x x x – – – – –3b. – – x – x – x x x – – –3c. – – – – x – x – x x x – | |4a. x – x – x – x x – – – –4b. – – x – x – x – x x – –4c. – – – – x – x – x – x x –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––—


FIGURE CAPTIONS

Fig. 1. Examples of a strongly metrical and a weakly metrical rhythm.

Each “x” represents a tone onset, each dash the absence of a tone onset.

Horizontal lines indicate three levels of grouping. Vertical lines indicate three

levels of metrical structure. Wedges reflect perceived accents due to low-level

grouping.

Fig. 2. Schematic illustration of two tones in a sequence and two

corresponding taps. The four dependent variables are indicated.

Fig. 3. Average standard deviations of individual ITIs as a function of

average ITI duration for strongly metrical (SM) and weakly metrical (WM)

sequences in synchronization and continuation, with best-fitting quadratic

regression lines (Exp. 1).

Fig. 4. Average deviations of ITI durations from IOI durations as a

function of IOI duration, metricality, and tapping condition, with standard error

bars calculated across individual ITIs within IOI duration categories (Exp. 1).

Fig. 5. Average dwell time as a function of IOI duration, metricality, and

tapping condition, with standard error bars calculated across individual ITIs

within IOI duration categories (Exp. 1).

Fig. 6. Average key depression velocity as a function of IOI duration,

metricality, and tapping condition, with standard error bars calculated across

individual ITIs within IOI duration categories (Exp. 1).

Fig. 7. Average key release velocity as a function of IOI duration,

metricality, and tapping condition, with standard error bars calculated across

individual ITIs within IOI duration categories (Exp. 1).


Fig. 8. Average ITI standard deviation as a function of ITI duration for

synchronization and continuation, with best-fitting quadratic regression lines

(Exp. 2).

Fig. 9. Average deviation from IOI duration for individual ITIs in four

rhythmic patterns (panels a–d), for three metrical versions (a–c in legends) in two

tapping conditions (Exp. 2).

Fig. 10. Average dwell time for individual taps in four rhythmic patterns

(panels a–d), for three metrical versions (a–c in legends) in two tapping

conditions (Exp. 2).

Fig. 11. Average key depression velocity for individual taps in four

rhythmic patterns (panels a–d), for three metrical versions (a–c in legends) in two

tapping conditions (Exp. 2).

Fig. 12. Average key release velocity for individual taps in four rhythmic

patterns (panels a–d), for three metrical versions (a–c in legends) in two tapping

conditions (Exp. 2).

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