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Unpublished manuscript, February 9, 2002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.
Repp & Saltzman: Meter and grouping 3
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
Repp & Saltzman: Meter and grouping 4
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.
Repp & Saltzman: Meter and grouping 5
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).
Repp & Saltzman: Meter and grouping 6
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
Repp & Saltzman: Meter and grouping 7
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.
Repp & Saltzman: Meter and grouping 8
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
Repp & Saltzman: Meter and grouping 9
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
Repp & Saltzman: Meter and grouping 10
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.
Repp & Saltzman: Meter and grouping 11
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,
Repp & Saltzman: Meter and grouping 12
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
Repp & Saltzman: Meter and grouping 13
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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
Repp & Saltzman: Meter and grouping 14
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
Repp & Saltzman: Meter and grouping 15
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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Insert Figure 2 here
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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
Repp & Saltzman: Meter and grouping 16
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
Repp & Saltzman: Meter and grouping 17
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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Repp & Saltzman: Meter and grouping 18
Insert Figure 3 here
--------------------------
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)
Repp & Saltzman: Meter and grouping 19
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
Repp & Saltzman: Meter and grouping 20
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-
Repp & Saltzman: Meter and grouping 21
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.
--------------------------
Insert Figure 4 here
--------------------------
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
Repp & Saltzman: Meter and grouping 22
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
Repp & Saltzman: Meter and grouping 23
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
Repp & Saltzman: Meter and grouping 24
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.
--------------------------
Insert Figure 5 here
--------------------------
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
Repp & Saltzman: Meter and grouping 25
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.
Repp & Saltzman: Meter and grouping 26
--------------------------
Insert Figure 6 here
--------------------------
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
Repp & Saltzman: Meter and grouping 27
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.
--------------------------
Insert Figure 7 here
--------------------------
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
Repp & Saltzman: Meter and grouping 28
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.
Repp & Saltzman: Meter and grouping 29
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
Repp & Saltzman: Meter and grouping 30
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.
Repp & Saltzman: Meter and grouping 31
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
Repp & Saltzman: Meter and grouping 32
long ITIs of syncopated patterns tended to be less variable than those of non-
syncopated pattern and thus contributed especially to the nonlinear trend.
--------------------------
Insert Figure 8 here
--------------------------
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
Repp & Saltzman: Meter and grouping 33
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.
--------------------------
Insert Figure 9 here
--------------------------
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
Repp & Saltzman: Meter and grouping 34
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.
Repp & Saltzman: Meter and grouping 35
----------------------------
Insert Figure 10 here
----------------------------
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.
--------------------------
Insert Figure 11 here
--------------------------
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,
Repp & Saltzman: Meter and grouping 36
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.
--------------------------
Insert Figure 12 here
--------------------------
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.
Repp & Saltzman: Meter and grouping 37
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
Repp & Saltzman: Meter and grouping 38
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
Repp & Saltzman: Meter and grouping 39
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
Repp & Saltzman: Meter and grouping 40
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
Repp & Saltzman: Meter and grouping 41
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
Repp & Saltzman: Meter and grouping 42
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.
Repp & Saltzman: Meter and grouping 43
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
Repp & Saltzman: Meter and grouping 44
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
Repp & Saltzman: Meter and grouping 45
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.
Repp & Saltzman: Meter and grouping 46
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:
Repp & Saltzman: Meter and grouping 47
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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 – – ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
Repp & Saltzman: Meter and grouping 53
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 –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––—
Repp & Saltzman: Meter and grouping 54
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).
Repp & Saltzman: Meter and grouping 55
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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