Effects of phase perturbations
on unimanual and alternating bimanual
synchronization with auditory sequences
Bruno H. Repp
Haskins Laboratories, New Haven, CT
UNPUBLISHED MANUSCRIPT, 8/14/04
Bruno H. Repp Haskins Laboratories 270 Crown Street New Haven, CT 06511-6695 phone; (203) 865-6163, ext. 236 fax: (203) 865-8963 e-mail: [email protected]
Repp: Unimanual vs. bimanual tapping 2
Abstract
When both hands are employed to tap in alternation, is their timing governed by
a single timekeeper or oscillator, or by two slower oscillators (one for each hand) that
are coupled in anti-phase? This question was addressed in two experiments by
comparing unimanual and alternating bimanual synchronization with isochronous
auditory sequences containing local phase perturbations. The single-oscillator
hypothesis predicts no difference in phase correction between unimanual and bimanual
tapping, whereas the coupled-oscillators hypothesis predicts a smaller lag-1 (other-
hand) and a larger lag-2 (same-hand) phase correction response in the bimanual than in
the unimanual condition. The results clearly support the single-oscillator hypothesis. A
manipulation of single versus alternating pitch in the auditory sequences was likewise
ineffective, suggesting that pitch structure is irrelevant to phase correction. Surprisingly,
however, the experiments provided little evidence that the sequences were perceived as
hierarchical metrical structures, in contrast to findings in other recent studies. Two brief
follow-up experiments succeeded in eliciting effects suggestive of metrical structure but
failed to pinpoint the reason for the weakness of these effects in the first two
experiments.
Repp: Unimanual vs. bimanual tapping 3
When the two hands are employed in alternation to carry out a rhythmic task
such as isochronous finger tapping, there are in theory two possible ways in which
timing might be controlled. One possibility is that a single central timekeeper or
oscillator generates a stream of impulses that are directed alternately to the motor
control systems of one or the other hand. The other possibility is that each hand has its
own timekeeper or oscillator, and that these two mechanisms are coordinated (i.e.,
coupled) so as to maintain an alternating (i.e., anti-phase) relationship. Each of these
hand-specific mechanisms would have a period that is twice as long as that of a single
oscillator driving both limbs. It should be noted right away that this second kind of
model is difficult to apply to more complex patterns of alternation between the hands,
in which the movements of one or both hands are aperiodic (e.g., L-R-L-R-R-L-R-L-R-
R...). However, it remains a theoretical possibility for the case of simple alternation.
Wing, Church, and Gentner (1989) addressed this theoretical issue by analyzing
the covariances among inter-tap intervals (ITIs) at various lags. The well-known two-
tiered model of Wing and Kristofferson (1973), which assumes separate sources of
variance due to a central timekeeper and motor delays, respectively, predicts a negative
covariance of ITIs at lag 1 and zero covariance at longer lags. This result was obtained
by Wing et al. in both unimanual and bimanual alternating tapping, but the bimanual
lag-1 covariances were more negative than predicted, and the ITI variance was also
greater in bimanual than in unimanual tapping. To account for these findings, Wing et
al. modified the model of Wing and Kristofferson by assuming that successive motor
Repp: Unimanual vs. bimanual tapping 4
delays of the two hands are negatively correlated, without abandoning the assumption
that there is only a single timekeeper. This modified model accounted well for the
bimanual data, whereas an alternative model based on two coupled timekeepers, one
for each hand, did not predict the pattern of covariances well.
Coupled-oscillator models have been favored by investigators who examined
the coordination of bimanual periodic movements at a variety of phase relationships
(e.g., Tuller & Kelso, 1989; Yamanishi, Kawato, & Suzuki, 1980). It is commonly found in
these studies that variability is smaller for in-phase and anti-phase coordination than for
other phase relationships, and that anti-phase movement becomes unstable and
switches to in-phase movement at fast movement rates. These differences in relative
stability of different phase relationships are predicted by coupled-oscillator models (e.g.,
Haken, Kelso, & Bunz, 1985). However, the tasks usually involve continuous limb
movements that do not produce discrete contacts or sounds, and hence they do not
really involve rhythm production in a musical sense.
Semjen and Ivry (2001) conducted a bimanual finger tapping study in which they
varied the relative phase between the two hands, much as Yamanishi et al. (1980) and
others had done, and obtained a similar pattern of variability. However, they obtained
the same variability pattern when a single hand was used to tap the same rhythms, and
this was true both in synchronization with a rhythmic pacing sequence and in self-paced
continuation of the rhythm. Therefore, Semjen and Ivry attributed their findings not to
coupled oscillators, which are intrinsic to bimanual action, but to “control of specific
time intervals to form a series of well-defined motor events” (p. 251), which may
involve a hierarchy of task-specific (but not hand-specific) timekeepers (Vorberg &
Repp: Unimanual vs. bimanual tapping 5
Hambuch, 1978, 1984; Vorberg & Wing, 1996). It could be that different tasks require
different theoretical explanations, with coupled-oscillator models being more
appropriate for continuous movement tasks and interval-based models, for rhythm
production tasks.
The question of whether a single timekeeper or two hand-specific timekeepers
are involved in isochronous bimanual tapping has also been considered by Ivry and
colleagues (Helmuth & Ivry, 1996; Ivry & Richardson, 2002; Ivry, Richardson, &
Helmuth, 2002) in connection with simultaneous bimanual (in-phase) tapping. These
researchers have consistently found that simultaneous tapping with two hands yields
lower variability of the ITIs of each hand than unimanual tapping. This led them to
postulate a system of separate timers or oscillators whose output is integrated before
being routed to both hands. Drewing and colleagues (Drewing & Aschersleben, 2003;
Drewing, Hennings, & Aschersleben, 2002; Drewing, Stenneken, et al., 2004) have
suggested an alternative integration hypothesis, namely that the anticipated sensory
effects (the temporal action goals) of each hand movement are integrated in timing
control.
Wing et al. (1989) observed a reduction in within-hand ITI variability also in
alternating bimanual tapping (compared to unimanual tapping with the same period as
each hand in bimanual tapping), which they attributed to subdivision of the ITIs by the
other hand. However, this occurred only at a slow tempo (ITI = 800 ms). At faster tempi
(ITI = 400 or 200 ms), the within-hand ITI variability was actually larger in alternating
bimanual than in unimanual tapping. This is consistent with other findings suggesting a
lower limit to the benefit of subdivision (Repp, 2003; Semjen, Vorberg, & Schulze, 1992).
Repp: Unimanual vs. bimanual tapping 6
By contrast, the reduction in variability of bimanual in-phase tapping compared to
unimanual tapping (Helmuth & Ivry, 1996) seems to occur regardless of tempo. Thus,
multiple-timer models developed to account for bimanual in-phase tapping (Ivry et al.,
2002) probably do not apply to bimanual anti-phase tapping.
Although the evidence reviewed so far suggests that bimanual alternating
tapping is controlled by a single timekeeper whose output is routed alternately to the
two hands, and not by two separate but coupled oscillators, additional attempts to test
these theoretical alternatives with new methods may still have merit. The present study
took a new approach by measuring the automatic response of each hand to phase
perturbations in an isochronous pacing sequence during unimanual and bimanually
alternating synchronized tapping.
Previous experiments have shown that a local phase perturbation while taps are
synchronized with an isochronous tone sequence causes an involuntary shift of the
immediately following tap, even when that shift results in an increased asynchrony
(Repp, 2002a, 2002c). This is the case when the perturbation is an event onset shift (EOS),
that is a displacement of a single tone onset, so that the original phase of the sequence is
restored after the perturbation. The involuntary shift of the tap following the EOS,
called the phase correction response (PCR), is in the same direction as the EOS but smaller
in magnitude (typically less than 50%). The asynchrony created by the PCR is corrected
in the course of subsequent taps. This phase correction function typically follows an
exponential decay, as is illustrated schematically by the dashed line connecting triangles
in Figure 1.
--------------------------
Repp: Unimanual vs. bimanual tapping 7
Insert Figure 1 here
--------------------------
It should be noted that Figure 1 does not plot asynchronies (the conventional
measure of synchronization accuracy) but relative shifts, that is deviations from
expected times defined by an isochronous temporal grid. For the tone sequence, this
grid is extrapolated from the tones preceding the EOS; for the taps, the tap coinciding
(roughly) with the EOS (Position 0 in Figure 1) serves as the reference, and the grid is
extended forward and backward in time from the reference point, using the sequence
inter-onset interval (IOI) as the interval. This is the metric used in the present study.
Relative asynchronies (with the tap in Position 0 still serving as the reference) can be
obtained by subtracting tone shifts from tap shifts. Thus, in Figure 1 the relative
asynchrony in Position 0 is –100 ms, but in subsequent positions it is equal to the
relative shift of the tap.
Results similar to the dashed function in Figure 1 have been obtained in various
unimanual tapping experiments (Repp, 2002a, 2002c). Consider now what might
happen in alternating bimanual tapping. In that case, the EOS occurs when one hand
taps, but the next tap is made by the other hand, followed by a tap by the first hand,
and so on. If there is a single timekeeper controlling both hands, the PCR and the
subsequent phase correction should be identical to what is observed in unimanual
tapping. However, if each hand is controlled by a separate oscillator and if the coupling
between them is not extremely strong, then the hand that tapped when the EOS
occurred might respond more strongly to the perturbation than the other hand, even
though its action is further removed from the EOS in time (Position 2 in Figure 1).
Repp: Unimanual vs. bimanual tapping 8
Conversely, the immediate PCR (Position 1 in Figure 1) should be reduced because it
occurs in the other hand. The shape of the phase correction function following an EOS
thus would change: Instead of a smooth decay of shifts across several taps, an initial
plateau or even an initial increase might be seen, as illustrated by the dotted function
connecting open circles in Figure 1. Later portions of the function might show step-like
changes as well, if each hand has to some extent its own phase correction function.
These predictions are not entirely implausible because the asynchrony generated by the
EOS is partially hand-specific, involving tactile and proprioceptive feedback from the
tapping finger. This hand-specific asynchrony may engage a hand-specific phase
correction mechanism if it exists.
The present study also addressed three secondary questions. One concerned
possible differences in PCR magnitude between the hands. It is known that people can
tap faster with their preferred hand (e.g., Peters, 1980; Todor & Kyprie, 1980), and at
least one study has also found lower variability of the preferred hand when tapping at a
moderate tempo (Truman & Hammond, 1990). It has not yet been investigated,
however, whether the non-preferred hand shows a smaller or larger PCR than the
preferred hand. A smaller PCR would indicate less effective phase correction, whereas a
larger PCR would indicate less effective suppression of unintended phase correction.
(Of course, these two differences might cancel each other if they should both be
present.) Any such hand asymmetries in either unimanual or bimanual tapping would
be consistent with different timing control systems for the two hands.
A second question was whether alternation of pitches in the pacing sequence
would have any effect on the PCR, analogous to the possible effect of alternating hands
Repp: Unimanual vs. bimanual tapping 9
in tapping. Although genuine auditory streaming (as described in Bregman, 1990) was
not likely to occur at the moderate tempi used here, alternating pitches nevertheless
impose a perceptual organization on a tone sequence that may affect behavior,
especially when it occurs in combination with alternating hands, so that each hand taps
to a different pitch. However, earlier studies of synchronization in which pitch was
varied have shown phase correction to be remarkably insensitive to that variation
(Repp, 2000, 2003).
A third, related question was whether the pacing sequences would be perceived
as hierarchical (two-level) metrical structures, and whether that perception would be
reflected in the PCRs. This question pertained primarily to a condition in which
participants tapped unimanually to every other tone of a fast pacing sequence (2:1
tapping). In that condition, it seems natural to think of tones coinciding with taps as
beats (i.e., metrically strong), and of the intervening tones as subdivisions (i.e.,
metrically weak). An EOS then can occur either on a beat or on a subdivision. If it occurs
on a beat, an unperturbed subdivision tone intervenes before the next tap occurs. If the
EOS occurs on a subdivision, the next tap follows immediately. If no beat were
perceived, a PCR should occur only to a subdivision EOS, not to a beat EOS. However, a
recent set of experiments (Repp, 2004) has shown that PCRs occur in both cases, which
suggests that participants perceive and monitor both levels of a two-level metrical
structure (see also Large, Fink, & Kelso, 2002). Moreover, these experiments have
shown that the beat-level PCR increases and the subdivision-level PCR decreases when
the sequence tempo is increased. It was hypothesized that alternation of pitches and/or
Repp: Unimanual vs. bimanual tapping 10
of hands in the present study would induce a (or reinforce an already existing) two-
level metrical interpretation of the sequences, consisting of beats and subdivisions.
Four experiments are reported. Surprisingly, the results of Experiment 1 did not
provide any evidence for metrical structure. This discrepancy with previous results led
to several follow-up experiments which focused on that particular issue. Experiment 2
differed from Experiment 1 mainly in that it used a faster sequence tempo. Experiments
3 and 4 attempted to bridge methodological differences between Experiments 1–2 and
earlier experiments, in order to determine the reason for the conflicting results.
EXPERIMENT 1
Experiment 1 comprised 20 conditions, which resulted from the combination of
five variables: sequence tempo (slow or fast), sequence pitch (single or alternating),
tapping tempo (slow or fast), tapping mode (unimanual or bimanual), and tapping
hand (preferred or non-preferred). The pacing sequence could be either slow or twice
as fast; if it was fast, it could be composed either of identical tones or of tones of
alternating pitch (i.e., of two interleaved slow sequences differing in pitch). With each of
these three sequence types, participants tapped either at a slow rate or at a rate twice as
fast; at the fast rate, they tapped either with a single hand or with the two hands
alternating (i.e., each hand tapping at a slow rate). This resulted in 3 x 3 = 9 experimental
conditions, to which was added an antiphase tapping condition (slow sequence, slow
tapping). Each of the resulting 10 conditions was performed either (starting) with the
preferred or (starting) with the non-preferred hand, hence 20 conditions in total.
Repp: Unimanual vs. bimanual tapping 11
The 10 conditions (ignoring the hand variable) are depicted schematically in
Figure 2. Alternating thick and thin bars represent alternating pitches in a sequence or
alternating hands in tapping. Horizontal arrows symbolize an EOS in the sequence
(open arrow heads) or a PCR in tapping (filled arrow heads). The names of the
conditions refer first to the sequence (Slow, Fast, or Alt[ernating]) and then to the
tapping (slow, fast, alt[ernating], or [slow] anti[phase]). The 10 conditions can be
arranged into four groups that yield comparisons of interest, as indicated by the
horizontal separators in the figure.
--------------------------
Insert Figure 2 here
--------------------------
Group 1 includes the Slow/slow (1:1 in-phase tapping) and Slow/anti (1:1
antiphase tapping) conditions. This comparison serves to determine whether the
temporal distance of the critical tap from the EOS affects the magnitude of the PCR. This
distance is smaller in the antiphase than in the in-phase condition. Based on earlier
results for similar conditions (Repp, 2002a, 2004), no difference in the PCR was
expected.
Group 2 includes the Slow/fast and Slow/alt conditions. In these two conditions,
the taps are twice as fast as the sequence (1:2 tapping). The sequence tones (and the taps
coinciding with them) will tend to function as beats, and the intervening taps as
subdivisions. Given that the EOS necessarily occurs on a beat, the question of interest is
whether the PCR will occur on the next tap (a subdivision tap) or on the next beat-level
tap, or on both. (Both are indicated in Figure 2.) When the hands alternate, that
Repp: Unimanual vs. bimanual tapping 12
question can be posed as follows: Will the PCR occur in the hand that tapped when the
EOS occurred, or will it occur in the other hand, or in both? This question pertains both
to the metrical structuring of the taps by the tones and to the issue of separate
timekeepers for the two hands. The expected effects are congruent: Whatever pattern
of PCRs metrical structuring produces in unimanual tapping (cf. Figure 1) should be
further enhanced by alternating the hands.
Group 3 includes the Fast/slow and Alt/slow conditions, where the beats are
defined by the taps and the coinciding tones (2:1 tapping), and the intervening tones
function as subdivisions.The alternating pitches in the Alt/slow condition are expected
to enhance the distinction between beats and subdivisions. Here the EOS can occur
either on a beat, that is on a tone coinciding with a tap, or on a subdivision. The
questions are whether the presence of an intervening unperturbed sequence tone
reduces or eliminates the PCR to a beat-level EOS (compared to the Slow/slow and
Slow/anti conditions, where there is no intervening tone), and whether there is a PCR
to a subdivision-level EOS at all. These same questions were the primary concern of the
recent study by Repp (2004).
Group 4 includes the Fast/fast, Alt/fast, Fast/alt, and Alt/alt conditions. The
questions of interest here are a combination of those for Groups 2 and 3. In the
Fast/fast condition, there is minimal structural support for a two-level metrical
structure, although it may arise spontaneously because of a preference for a slower
beat (tactus) when the tempo is fast (Parncutt, 1994). When pitches and/or hands
alternate, the metrical structure becomes increasingly salient, and the PCR may shift
Repp: Unimanual vs. bimanual tapping 13
increasingly to the higher level in the hierarchy, that is to the second tap following the
EOS.
Methods
Participants. There were 9 participants (5 men, 4 women) who included 7 paid
volunteers, a research assistant, and the author. All but the research assistant were
regular participants in synchronization experiments in the author’s laboratory. Musical
training ranged from professional level to none at all. Ages ranged from 18 to 32,
except for the author who was 57 years old at the time. The handedness of all
participants was assessed by administering a version of the Edinburgh Handedness
Questionnaire (Oldfield, 1971; http://porkpie.loni.ucla.edu/LabNotes/edinburgh.html),
on which scores range from –20 to 20. Eight participants were classified as right-handed
(scores of 9 to 20) and one as left-handed (score of –11).
Materials. Pacing sequences were generated on a Roland RD250s digital piano
according to musical-instrument-digital-interface (MIDI) instructions which specified
key depression times, key release times, pitches, and key velocities. The tones had a
rapid amplitude rise and a nominal duration of 20 ms. (Some decay followed the
nominal offset.) Sequence playback and recording of finger taps was controlled by a
program written in MAX 3.0 which ran on a Macintosh Quadra 660AV computer.1
Instead of including completely isochronous sequences as a baseline, this
experiment included sequences containing a gap (i.e., a missing tone). This was thought
to reduce the likelihood that participants would mistake a delayed tone (i.e., a positive
EOS) for the end of the sequence.
Repp: Unimanual vs. bimanual tapping 14
Slow sequences contained between 7 and 11 tones, with either an EOS or a gap
occurring four positions from the end, so that three unperturbed tones followed. Fast
and alternating sequences contained between 13 and 22 tones, with the EOS or gap
occurring seven positions from the end, so that six unperturbed tones followed. The IOI
was 800 ms in slow sequences and 400 ms in fast sequences. The EOS was either +100 or
–100 ms. Slow and fast non-alternating sequences were composed of tones having the
musical pitch of C8 (4,192 Hz). Alternating sequences began with two successive tones
at that high pitch, followed by a regular alternation of low and high tones. The low
tones had a musical pitch of E7 (2,640 Hz). Thus the pitch difference was 8 semitones. An
apparent loudness difference favoring the low tones was approximately neutralized by
assigning MIDI key velocities of 60 and 50 to the high and low tones, respectively (a
difference of about 3 dB).
Four blocks of randomly ordered trials were created for each sequence category
(slow, fast, alternating). Each block of slow sequences contained 15 trials (3 kinds of
perturbation x 5 possible locations), whereas each block of fast or alternating sequences
contained 30 trials (3 kinds of perturbation x 10 possible locations). Some of the blocks
were used repeatedly, in different tapping conditions.
Procedure. Participants sat in front of the computer monitor on which the
current trial number was displayed and listened to the sequences over Sennheiser
HD540 II earphones at a comfortable intensity. They tapped on a Fatar Studio 37 MIDI
controller (a quiet three-octave piano keyboard) by depressing a white key with the
index finger. In bimanual tapping, different white keys were used which were about
two octaves apart on the keyboard. The MIDI controller was held on the lap, and
Repp: Unimanual vs. bimanual tapping 15
participants were asked to keep their finger(s) in contact with the response key(s),
which moved vertically by about 1 cm. The keys had cushioned bottom contacts and
did not produce any audible sound.
Participants were instructed to make their first tap in synchrony with the second
tone when the sequence was slow (Conditions 1–4) and with the third tone when the
sequence was fast (Conditions 5–10). In each case, tapping thus started on (what was
assumed to be) the second beat. The computer monitor displayed a red “button” which
lit up 1 s after the end of a sequence and stayed bright for 1 s. The next sequence started
3 s later. Participants were told to synchronize with the sequence tones but not to react
to any EOS or gap, and to continue tapping until the red light came on. These
instructions were intended to prevent participants from hesitating when a delayed tone
or gap occurred.
The conditions were presented in the order in which they are listed in Figure 2.
Counterbalancing was not considered necessary in view of the experience of the
participants and the automaticity of the PCR. Participants came for two sessions, with
the conditions being divided between the two sessions. (The break was usually between
Conditions 6 and 7.) The sessions were typically one week apart. In each condition,
participants first did one block of trials (starting) with the right hand and then
immediately another block (starting) with the left hand.
Analysis. PCRs and shifts of subsequent taps were computed relative to an
isochronous temporal grid with the tap in Position 0 as the reference, as described in
connection with Figure 1. The values thus obtained were averaged across the different
EOS or gap locations in the sequences. The PCR data were submitted to repeated-
Repp: Unimanual vs. bimanual tapping 16
measures ANOVAs with the variables of EOS direction (negative, positive), hand
(preferred, non-preferred), and condition (depending on the analysis). The signs of the
PCRs to negative EOSs were reversed in the ANOVAs to eliminate trivial effects of EOS
direction. The PCRs to gaps were treated separately. Only the PCRs (i.e., the shift of the
first tap, or the shifts of the first two taps, following an EOS or gap) were subjected to
statistical analysis.
Results
The results are presented in the upper panels of Figures 3–6. The lower panels
show the results of Experiment 2, which will be discussed later.
Figure 3 (A, B) plots the results for the Slow/slow and Slow/anti conditions
(Group 1). Each panel shows the average shifts of the four taps following an EOS or a
gap, with between-participant single standard error bars. The shift of the first tap is the
PCR. The dotted line, drawn by eye from the zero point to the approximate average of
the data points in the last position, indicates the results that presumably would have
been obtained with a completely isochronous sequence; it takes into account slight
phase drift across positions.
--------------------------
Insert Figure 3 here
--------------------------
As expected, the PCRs in in-phase and antiphase tapping were of the same
magnitude, even though the latter occurred closer to the EOS in the sequence, as
indicated by the shifted abscissa labels in Figure 3B. No effects involving condition were
Repp: Unimanual vs. bimanual tapping 17
significant in the ANOVA. This result implies that any differences in PCRs between
other conditions which involve different temporal distances between an EOS and the
critical tap should not be attributed to temporal distance as such.
There was a tendency for a gap in the sequence to elicit a positive PCR, but this
tendency did not reach significance due to large individual differences. Figure 3
furthermore illustrates the fact that phase correction following a perturbation in a slow
sequence took about three taps to complete.
Figure 4 (A, B) shows the results of the Slow/fast and Slow/alt conditions
(Group 2). Here the rate of the taps was twice as fast as that of the sequence (1:2
tapping); therefore, the positions along the abscissa are numbered in half steps, with
integer numbers indicating beats. There were two PCRs of interest: the one on the
subdivision (or off-beat) tap following a perturbation (Position 0.5) and the other on the
on-beat tap (Position 1); therefore, position (2 levels) was included as a variable in the
ANOVA.
--------------------------
Insert Figure 4 here
--------------------------
Even though the EOS was immediately followed by an off-beat tap, a larger PCR
was observed on the subsequent on-beat tap, F(1,8) = 41.0, p < .005. This is consistent
with the hypothesis that PCRs occur on both levels of a metrical hierarchy (cf. Figure 1).
However, there is an alternative explanation which will be presented in the Discussion
section. Only after a positive EOS in the Slow/alt condition did the off-beat and on-beat
PCRs not differ, and this was reflected in a triple interaction between position,
Repp: Unimanual vs. bimanual tapping 18
condition, and direction, F(1,8) = 11.1, p < .02. Clearly, alternating the hands did not
increase the relative magnitude of the on-beat PCR.
There was a tendency for positive PCRs to be elicited by gaps, primarily in the
off-beat position. Gap PCRs were significantly larger in Position 0.5 than in Position 1,
F(1,8) = 6.4, p < .04, and they were also larger for the non-preferred than for the
preferred hand, F(1,8) = 5.8, p < .05. Figure 4 further shows that it took about as long
for phase correction to be completed in the Slow/fast and Slow/alt conditions as it did
in the Slow/slow and Slow/anti conditions (Figure 3). In other words, the decay of the
phase correction function did not depend on the number of taps made, only on the
number of sequence tones. This is consistent with the fact that phase correction requires
sensory information (Repp, 2002b), be it from tap-tone asynchronies or from
perceptual monitoring of sequence events. Indeed, after a negative EOS the reduction in
the shift of taps tended to occur in a stepwise fashion, with phase correction occurring
only on off-beat taps, which are the taps that followed perception of an asynchrony.
After a positive EOS, this expected pattern was less evident.
A statistical comparison of the on-beat PCRs (Position 1) in the Slow/fast and
Slow/alt conditions with the PCR in the Slow/slow condition (Figure 3A) revealed no
significant differences. Thus, an intervening subdivision tap did not affect the beat-level
PCR.
Figure 5 (A–D) presents the results of the Fast/slow and Alt/slow conditions
(Group 3). Here there were two possible locations of the EOS or gap in the sequences:
either on the beat (panels A and B) or off the beat, on a subdivision (panels C and D). In
the case of an on-beat perturbation, an unperturbed subdivision tone (position 1)
Repp: Unimanual vs. bimanual tapping 19
intervened before the next tap (position 2). In the case of an off-beat perturbation, there
was no such intervening tone. The results in Figure 5 should be compared to those of
the Slow/slow and Slow/anti conditions, respectively (Figures 3A and 3B), where the
same temporal relationships hold between the perturbation and the subsequent taps,
but where there are no subdivision tones.
--------------------------
Insert Figure 5 here
--------------------------
It can be seen that very different results were obtained for on-beat and off-beat
perturbations. There was no PCR at all to on-beat perturbations (panels A and B). In
other words, the intervening unperturbed subdivision tone completely obliterated any
beat-level PCR, in stark contrast to the results of Repp (2004) who consistently obtained
beat-level PCRs in similar conditions. However, there were substantial PCRs to off-beat
perturbations, including gaps; although they seemed smaller than those in the
Slow/anti condition (Figure 3B), this difference was not significant. There were no
differences between the Fast/slow and Alt/slow conditions: Alternating the hands did
not create an on-beat PCR or reduce the off-beat PCR.
It is noteworthy that phase correction following an off-beat EOS was virtually
complete within two taps (Figures 5C and 5D), in contrast to the Slow/anti condition,
where it took three or four taps (Figure 3B). Clearly, perceptual monitoring of
subdivision tones accelerated phase correction.
Finally, the results of the Fast/fast, Alt/fast, Fast/alt, and Alt/alt conditions
(Group 4) are shown in Figure 6 (A–D). No distinction was made here between on-beat
Repp: Unimanual vs. bimanual tapping 20
and off-beat perturbations because the location of the beat (if any) is somewhat
ambiguous in all four conditions. The ANOVAs treated the condition variable as a 2 x 2
factorial combination of sequence pitch and tapping mode. There was a significant main
effect of sequence pitch, F(1,8) = 12.3, p < .009, due to larger PCRs when the sequence
contained tones of alternating pitch. Three interactions also reached significance but are
difficult to interpret and therefore are not discussed in detail.
--------------------------
Insert Figure 6 here
--------------------------
Phase correction generally took three to four taps to complete, as in the
Slow/slow tapping condition (but in only half the time). The relative shifts of the taps
decreased monotonically across positions in all conditions. The PCRs to gaps were quite
small and nonsignificant.
The PCRs in these last four conditions were clearly smaller than in most
preceding conditions. To determine the relative importance of sequence tempo and
tapping tempo while holding the temporal distance between the EOS and the critical tap
constant, a 2 x 2 ANOVA was conducted on the PCRs in the Slow/anti, Slow/fast (off-
beat tap), Fast/slow (off-beat EOS), and Fast/fast conditions. There were significant
main effects of both sequence tempo, F(1,8) = 7.2, p < .03, and tapping tempo, F(1,8) =
17.6, p < .003, with the PCRs being larger at the slow tempo in each case. This is
consistent with previous findings that phase correction is more effective at a slower
tempo (Pressing, 1998; Semjen, Schulze, & Vorberg, 2000).
Repp: Unimanual vs. bimanual tapping 21
Discussion
Alternating the hands in fast tapping produced results that were
indistinguishable from those obtained in fast unimanual tapping. This finding clearly
favors the hypothesis of a single common timekeeper for the two hands and thus is
consistent with the findings of Wing et al. (1989) and of Semjen and Ivry (2001).
Incidentally, the separate-timekeepers hypothesis also predicts that PCRs in alternating-
hands tapping should be larger than in unimanual fast tapping because each hand
moves at a slow pace, and PCRs generally are larger at a slow than at a fast tempo.
However, no such difference was observed.
There was also little evidence for differences between the preferred and non-
preferred hand in terms of phase correction. Although the hand variable was involved
in some significant interactions in some conditions, in general the PCRs were of the
same magnitude in both hands.
It is interesting that gaps elicited a positive PCR in most conditions. Although the
PCR to a positive EOS was always larger than that to a gap, it seems that there should
be some positive EOS magnitude for which the average PCR is the same as that for a
gap. That EOS magnitude may well be near the detection threshold, which is typically at
about 4% of the IOI duration (Friberg & Sundberg, 1995; Repp, 2002a). If so, this would
suggest that a gap is processed initially as a positive EOS until it becomes clear that
there is no delayed tone onset, and that this initial processing informs the phase
correction process in an irrevocable manner.
Surprisingly, in view of Repp’s (2004) findings, the Group 3 conditions
(Fast/slow and Alt/slow) did not provide any evidence of beat-level PCRs: An
Repp: Unimanual vs. bimanual tapping 22
unperturbed subdivision tone intervening between a beat EOS and the critical tap
prevented a PCR from occurring. In other words, there was complete phase resetting
following the subdivision tone. This result suggests that the sequences were not
perceived as an alternation of beats and subdivisions, merely as a sequence of beats.
Moreover, alternation of pitches did not create or enhance a two-level metrical
structure: The pitch manipulation was just as ineffective as the alternation of hands.
One other finding, however, is suggestive of metrical structure: the increase in
the PCR from the first to the second tap following an EOS in the Slow/fast and Slow/alt
conditions (Figure 4). Since the first tap following an EOS in these conditions did not
coincide with a tone and thus did not yield any sensory asynchrony information, the
second tap should have shown the same relative shift as the first tap. However, the shift
increased from the first to the second tap, which could reflect a beat-level PCR.
However, there is a possible alternative explanation for this increase: The EOS caused
an IOI in the sequence to be shorter or longer than usual, and this may have affected
the internal period as well as the phase of the motor activity, especially since the
perturbation was rather large and clearly detectable (Repp, 2001; Repp & Keller, 2004).
Such strategic period correction would lead to a positive shift of the on-beat tap
following a positive EOS and to a negative shift of the on-beat tap following a negative
EOS, as was observed. Indeed, Repp (2002c) observed a similar phenomenon, albeit
only after positive EOSs. Therefore, the increase in the PCR between the first and
second tap following an EOS does not provide clear evidence of an effect of metrical
structure.
Repp: Unimanual vs. bimanual tapping 23
EXPERIMENT 2
At about the same time as Experiment 1, another experiment (Repp (2004:
Experiment 1) was conducted with the same participants and yielded reliable beat-level
PCRs. Therefore, the absence of beat-level PCRs in the Group 3 conditions of the
present Experiment 1 was puzzling. There were many methodological differences
between these experiments. One was that Repp (2004) used two sequence tempi,
corresponding to inter-beat intervals (IBIs) of 720 and 540 ms, with subdivision tones
occurring in these intervals. At the slower tempo (which was slightly faster than the
tempo in the present Experiment 1), beat-level PCRs were significantly greater than
zero but much smaller than subdivision-level PCRs. At the faster tempo, however,
beat-level PCRs were much larger than at the slower tempo, whereas subdivision-level
PCRs were smaller. This indicated a relative increase in the importance of the beat level
in the metrical hierarchy, as would be expected at a faster tempo (Parncutt, 1994).
The absence of a beat-level PCR in the present Experiment 1 may have been due
to the relatively slow sequence tempo (IBI = 800 ms). Therefore, a second experiment
was conducted in which the sequences were presented at a faster tempo (IBI = 560 ms),
similar to that in the faster sequences of Repp (2004). Inclusion of all conditions of
Experiment 1 (Figure 2), although not strictly necessary to examine possible effects of
metrical structure, provided an opportunity to confirm (or disconfirm) with a mostly
new group of participants the negative results of Experiment 1 with regard to hand
alternation and hand preference.
Repp: Unimanual vs. bimanual tapping 24
Methods
Participants. Seven new paid volunteers (6 women, 1 man) and the author
participated. The male volunteer was the same age as the author; the women were all
below 30 years of age. Their tapping experience were comparable to those of the
participants in Experiment 1, but their musical experience was higher on average. (They
had at least 6 years of musical training and included two professional-level musicians.)
All participants were right-handed (Edinburgh Handedness Questionnaire scores of 12
to 20).
Materials. The materials differed from those in Experiment 1 in the following
ways: The IOI was 560 ms in slow sequences and 280 ms in fast sequences. The EOS was
either –70 or +70 ms. The pitches of the tones were lower than in Experiment 1, with the
high pitch being E7 (2,640 Hz) and the low pitch G#7 (1,660 Hz), but the pitch difference
in alternating sequences (8 semitones) remained the same. Because there was no
obvious loudness difference between these tones, they were played with the same
MIDI velocity.
Procedure and equipment. The conditions were the same as in Experiment 1 (see
Figure 2) and were presented in the same order, except that the order of the Alt/fast
and Fast/alt conditions was accidentally reversed. Trials were self-paced: Participants
pressed the space bar of the computer keyboard, and the sequence started 2 s later. The
procedure of signaling the end of a sequence with a red light was abandoned. Instead,
there was a “repeat” button on the screen which participants were asked to click if they
noticed that they had reacted to either an EOS or a gap. If a trial was repeated, only the
repeat was included in the analysis.
Repp: Unimanual vs. bimanual tapping 25
Instead of tapping on the white keys of a quiet MIDI controller, participants
tapped on the upper left and upper right pads of a Roland SPD-6 electronic percussion
unit which had two rows of three pads each. The electronic sound output of the unit
was not used, but the taps made audible thuds on the pads, in proportion to the tapping
force. Most participants rested their hands and other fingers on the pad and tapped
with the index finger only, but some tapped “from above” by moving their arm at the
elbow joint.
Results
The results are shown in the lower halves of Figures 3–6. In general, the PCRs
were smaller than in Experiment 1 (note the different y-axis scales), not only because of
the smaller absolute magnitude of the EOSs but also because phase correction tends to
be less effective at a faster tempo (Pressing, 1998; Semjen et al., 2000).
The results of the Group 1 conditions are shown in Figures 3C and 3D. In
contrast to Experiment 1 (Figures 3A and 3B), PCRs to EOSs were larger in the
Slow/anti than in the Slow/slow condition, F(1,7) = 17.1, p < .005. Moreover, there were
larger positive PCRs to gaps in anti-phase than in in-phase tapping, F(1,7) = 19.2, p <
.005. Both differences suggest that, at the tempo of the Experiment 2 sequences, anti-
phase tapping was less stable than in-phase tapping and therefore more sensitive to
perturbations. As in Experiment 1, phase correction following a perturbation took
about 3 taps to complete.
The results of the Slow/fast and Slow/alt conditions (Group 2) are shown in
Figures 4C and 4D, respectively. As in Experiment 1, the PCRs were significantly larger
Repp: Unimanual vs. bimanual tapping 26
in Position 1 than in Position 0.5, F(1,7) = 32.8, p < .001. Although this may suggest a
delayed (i.e., beat-level) PCR in Position 1, it is also consistent with the idea that
strategic period correction occurred in addition to phase correction, as was argued in
the discussion of Experiment 1. There was again a tendency for positive PCRs to be
elicited by gaps, but there were no significant effects in the ANOVA on gap PCRs.
Stepwise phase correction in the taps following the initial PCRs can be observed in
some conditions but not in others.
In Experiment 1, statistical comparisons of the on-beat PCRs (Position 1) in the
Slow/fast and Slow/alt conditions with those in the Slow/slow condition had revealed
no significant differences. Thus, an intervening subdivision tap did not affect the beat-
level PCR. In Experiment 2, however, the on-beat PCR following a positive EOS was
actually larger in the Slow/fast and Slow/alt conditions than in the Slow/slow condition,
F(1,7) = 20.7, p < .005, and 11.9, p < .02, respectively. This is an unexpected result.
Because the difference was restricted to PCRs following a positive EOS, the Condition x
Direction interaction was also significant in each of the two comparisons, F(1,7) = 47, p <
.001, and 15.6, p < .01, respectively. Furthermore, a significant Condition x Hand x
Direction interaction, F(1,7) = 21.5, p < .005, emerged in the comparison of the
Slow/slow and Slow/alt conditions, because the Condition x Direction interaction just
described was present only when the non-preferred hand tapped on the beat.
The Fast/slow and Alt/slow conditions (Group 3, Figures 5E–H) are the ones
which pertain most directly to effects of metrical structure and which are similar to
conditions included in Repp’s (2004) study. In contrast to Experiment 1, where there
was no evidence at all of beat-level PCRs in these conditions, a small PCR to on-beat
Repp: Unimanual vs. bimanual tapping 27
perturbations emerged in the Fast-slow condition of Experiment 2 (Figure 5E).
However, no such PCR was observed in the Alt/slow condition (Figure 5F), even
though the alternation of pitches was thought to enhance the distinction between beats
and subdivisions. The difference in PCRs between the two conditions was significant,
F(1,7) = 18.2, p < .005. PCRs to off-beat perturbations (Figures 5G and 5H) were
substantial and did not differ between the Fast/slow and Alt/slow conditions.
However, they were smaller than the PCRs in the Slow/anti condition (Figure 3D),
F(1,7) = 19.0, p < .005, which again suggests relative instability of anti-phase tapping.
The results of the Group 4 conditions are shown in Figures 6E-H. In contrast to
Experiment 1, pitch alternation in the sequence made no difference, but now PCRs
tended to be larger when the hands alternated in tapping than when they did not, F(1,7)
= 6.3, p < .05. No other effects reached significance. In the unimanual tapping conditions
(Figures 6E and 6F), phase correction was much slower following positive EOSs than
following negative EOSs ; the reason for this is not clear. Gaps again elicited positive
PCRs.
In agreement with Experiment 1, a 2 x 2 ANOVA comparing PCRs in the
Slow/anti, Slow/fast (off-beat tap), Fast/slow (off-beat EOS), and Fast/fast conditions
yielded significant main effects of both sequence tempo, F(1,7) = 17.2, p < .005, and
tapping tempo, F(1,7) = 23.3, p < .005, with the PCRs being larger at the slow tempo in
each case. In addition, the interaction reached significance, F(1,7) = 11.2, p < .02, because
the largest difference by far was between the Slow/anti condition and the other three
conditions, again reflecting the relative instability of anti-phase tapping in this
experiment.
Repp: Unimanual vs. bimanual tapping 28
Discussion
Experiment 2 largely replicated the negative results of Experiment 1 with regard
to hand alternation. An effect of alternating hands was found only in the Group 4
conditions, where PCRs were larger when the hands alternated. This is not consistent
with a coupled-oscillator model, in so far as it predicts a reduced PCR when the
response is in the other hand (i.e., the one that did not tap when the EOS occurred).
However, the finding could also be considered consistent with a coupled-oscillator
model if the more important factor is the slower tempo at which each hand moves,
because PCRs tend to be larger at a slower tempo.
Except for one very specific interaction, there was again little difference between
the preferred and non-preferred hands with regard to PCR magnitude. As in
Experiment 1, gaps generally elicited a small positive PCR. Furthermore, results
suggesting a possible involvement of strategic period correction, in addition to phase
correction, were replicated.
The main question of interest was whether an effect of metrical structure would
emerge in the Group 3 conditions, given that a faster sequence tempo was used.
Indeed, a small beat-level PCR was now apparent in the Fast/slow condition, which is
consistent with expectations. However, such a beat-level PCR was completely absent in
the Alt/slow condition, where the alternating pitches should have reinforced any
existing metrical structure. In other words, the beat-level PCR was blocked by an
intervening subdivision tone of different pitch, but not by a tone of the same pitch as
the perturbed beat tone. This makes little sense, and the results must therefore be
Repp: Unimanual vs. bimanual tapping 29
considered inconclusive with regard to the existence of a two-level metrical hierarchy in
these sequences. Despite a similar sequence tempo, effects of metrical structure clearly
were not as reliable and pronounced as in the fast (IBI = 540 ms) sequences of
Experiment 1 of Repp (2004). Two small follow-up experiments were conducted in an
attempt to determine the reasons for this discrepancy.
EXPERIMENT 3
Experiment 1 of Repp (2004) used a paradigm which involved omitting the tap
that coincided with the EOS. This procedure is known to generate large PCRs (i.e.,
phase resetting) and could have been responsible for the different findings. However,
Experiment 2 in that study (which was roughly contemporaneous with the present
Experiment 2 and had mostly the same participants) obtained reliable beat-level PCRs
without an omitted tap at a sequence tempo of IBI = 540 ms. That experiment will in the
following be referred to as Experiment 2*.
Experiment 3 considered the possible role of three methodological differences
between Experiments 2* and 2. The first difference was that Experiment 2* used a
randomized design in which many different conditions (0, 1, 2, or 3 subdivisions
between beats) were intermixed, whereas Experiment 2 used a blocked design and only
simple subdivision. The variation and unpredictability of the subdivision level from trial
to trial in Experiment 2* may have enhanced the salience of the constant beat level. The
second difference was that in Experiment 2* the beat-level tones had a higher intensity
than the subdivision tones, whereas in Experiment 2 they had the same intensity.
Repp: Unimanual vs. bimanual tapping 30
Higher intensity may have increased the relative salience of the beats and thus may
have cause beat-level PCRs. The third difference was that Experiment 2* included
isochronous sequences as a baseline, whereas Experiment 2 included sequences
containing a gap instead. Although it is unclear why gaps should have inhibited the
establishment of a two-level metrical hierarchy, gap sequences were eliminated in
Experiment 3.
Experiment 3 had four conditions (trial blocks). Blocks 1 and 2 contained
sequences with simple subdivision of IBIs, extracted from Experiment 2*. To the extent
that the beat-level PCR in these sequences was induced by the context of other
sequence types in Experiment 2*, Blocks 1 and 2 should yield a reduced beat-level PCR,
compared to the original Experiment 2* results. In Block 1, beats had a higher intensity
than subdivisions, as in Experiment 2*, whereas in Block 2 the intensities were made
equal. If relative intensity of beats and subdivisions plays a role, beat-level PCRs should
be larger in Block 1 than in Block 2. Blocks 3 and 4 were, respectively, the Fast/slow and
Alt/slow conditions of the present Experiment 2. However, in each of these blocks the
sequences containing gaps were replaced with slow isochronous sequences. If anything,
these sequences should enhance the beat level and hence should help generate beat-
level PCRs.
Methods
Participants. Five of the 8 participants (5 women, 3 men, including the author)
had participated in Experiment 2. The newcomers were likewise regular participants in
Repp: Unimanual vs. bimanual tapping 31
synchronization experiments and had a high level of musical training, except for one
who had had only a few years of music instruction.
Materials. Block 1 contained sequences consisting of alternating beats and
subdivisions differing in pitch—beats were at B-flat7 (3,729 Hz), subdivision tones at A7
(3,520 Hz)—and intensity (60 vs. 50 MIDI velocity units, a difference of about 3 dB).
Each sequence contained 15 beat-level tones, with subdivisions starting after the second
beat. The IBI was 540 ms. Each sequence either contained an EOS of –60 or +60 ms,
which could occur either on the 10th beat or on the following subdivision, or no EOS at
all. There were five repetitions of each sequence type, for a total of 25 randomly
ordered trials. Block 2 contained another randomization of the same trials, but the MIDI
velocity of the subdivision tones was raised to equal that of the beat tones. Block 3
represented the Fast/slow condition of Experiment 2, in which beat tones and
subdivision tones were physically identical. However, slow beat-only sequences (IOI =
560 ms) were substituted for sequences containing gaps. Each fast sequence contained
an EOS of –70 or +70 ms in one of 10 possible positions (5 on a beat, 5 on a subdivision).
Each slow sequence contained an EOS in one of 5 possible positions. This resulted in 30
trials which were ordered randomly, with the constraint that the first two sequences
were slow, in a deliberate attempt to prime the beat level. Block 4 was the Alt/slow
condition of Experiment 2, with the gap sequences replaced with slow sequences.
Because the beats in the fast sequences were always the lower tones, the tones of the
slow sequences were set to the same low pitch.
Procedure. Participants were instructed to start tapping with the second beat and
not to react to EOSs. For Blocks 3 and 4, they were alerted to the fact that some
Repp: Unimanual vs. bimanual tapping 32
sequences contained only beats whereas others were subdivided from the beginning. A
few sample trials were presented before Blocks 1 and 3 to make the task clear. To
present Block 1 truly out of context, the order of conditions was not counterbalanced.
Results and discussion
The top panels of Figure 7 (A, B) present the conflicting data from Experiments
2* and 2 that Experiment 3 was trying to reconcile. PCRs are shown here as percentages
of EOS magnitude, averaged across the two EOS directions. Figure 7A shows the mean
PCRs for the on-beat EOS and off-beat EOS conditions of Experiment 2*. These values
are substantially different from zero and not significantly different from each other.
Figure 7B shows the results for the Fast/slow and Alt/slow conditions of Experiment 2.
(Only the data for tapping with the right hand are included.) As could be seen
previously in Figures 6E–H, the PCRs to off-beat EOSs were robust and similar in
magnitude to those in Experiment 2*, but the PCRs to on-beat EOSs were either smaller
(in the Fast-slow condition) or absent (in the Alt-slow condition). A 2 x 2 repeated-
measures ANOVA on the data in Figure 7B revealed significant effects of condition,
F(1,7) = 6.9, p < .04, and EOS location (on-beat vs. off-beat), F(1,7) = 16.7, p < .005, as well
as a significant interaction, F(1,7) = 6.9, p < .04.
----------------------------
Insert Figure 7 here
----------------------------
The results of Blocks 1 and 2 of Experiment 3 are shown in Figure 7C. They show
on-beat and off-beat PCRs of about the same magnitude, as in Experiment 2*. A 2 x 2
Repp: Unimanual vs. bimanual tapping 33
repeated-measures ANOVA did not reveal any significant effects; in particular, the
interaction was nonsignificant, F(1,7) = 3.2, p < .12. Thus, although the relative
magnitude of PCRs to on-beat and off-beat EOSs changed somewhat in the expected
direction from Block 1 to Block 2, the intensity difference between beat tones and
subdivision tones (present in Block 1, absent in Block 2) did not seem to play a crucial
role. When the results for Blocks 1 and 2 were averaged and entered into a 2 x 2 mixed-
model ANOVA with the data from Experiment 2* (Figure 7A), ignoring the fact that
some of the participants were the same, only the main effect of experiment was
significant, F(1,14) = 5.7, p < .04, because PCRs were larger in Experiment 2* than in
Experiment 3. This suggests that context may have played a role, but there is no clear
evidence that the context selectively enhanced the beat-level PCR.
The results of Blocks 3 and 4 are shown in Figure 7D. These two blocks yielded
almost identical results, as they did in Experiment 1, which makes the interaction
obtained in Experiment 2 (Figure 7B) seem even more anomalous. The results suggest
that pitch alternation had really no effect. Although significant PCRs to on-beat EOSs
were obtained in both blocks, they were only about half the size of the PCRs to off-beat
EOSs. This difference was significant, F(1,7) = 9.6, p < .02. The presence of significant
PCRs to on-beat EOSs might suggest that the inclusion of slow beat-only sequences had
some effect. However, in a combined ANOVA of these data with those of Experiment
2, the main effect of experiment (treated as a between-participants variable) and the
Experiment x EOS location interaction were not significant. Only the main effect of EOS
location was highly reliable, F(1,14) = 26.1, p < .001, and several other effects reached or
approached significance because of the interaction shown in Figure 7B. Thus, there is no
Repp: Unimanual vs. bimanual tapping 34
evidence that the slow sequences enhanced the PCRs to beat-level EOSs. The mean
PCRs to EOSs in the slow beat-only sequences are not shown in Figure 7D; they were
quite large, as expected (37% of the EOS).
The data of Blocks 1 and 2 (averaged) were entered together with those of Blocks
3 and 4 (averaged) into a 2 x 2 repeated-measures ANOVA. Although the effect of EOS
location had been significant for Blocks 3 and 4 but not for Blocks 1 and 2, the Condition
(here meaning Blocks 1 and 2 vs. 3 and 4) x EOS Location interaction fell short of
significance, F(1,7) = 4.9, p < .07. It could be argued, therefore, that Experiment 3
achieved its goal of inducing comparable PCRs in the conditions excerpted from
Experiments 2* and 2. However, not only was the interaction close to significance, but
also the patterns of results (in Figures 7C and 7D, respectively) were not significantly
different from those of the parent experiments (Figures 7A and 7B, respectively). It
seems that some relevant difference remained between the conditions.
EXPERIMENT 4
One remaining difference was that the sequences taken from Experiment 2*
started with an empty IBI, whereas the sequences taken from Experiment 2 were
subdivided from the beginning. Conceivably, the single empty IBI could have primed
the beat level. A second difference was that in Experiment 2* the beat tones were higher
in pitch than the subdivision tones, albeit by only one semitone, whereas in Experiment
2 they were either equal in pitch (Fast/slow condition), or the beats were much lower in
pitch than the subdivisions (Alt/slow condition). Although pitch seems an unlikely
Repp: Unimanual vs. bimanual tapping 35
factor, given the absence of a difference between Blocks 3 and 4 in Experiment 3 (Figure
7D), it is worth ruling out. A third difference was that the sequences in Experiment 2*
were of fixed length, whereas those in Experiment 2 were of variable length. The fixed
length could have enhanced the perceived metricality of the sequences in the course of
a block of trials. A fourth difference was that the EOS occurred at one of two constant
and hence increasingly predictable locations in the Experiment 2* sequences, whereas it
occurred at one of ten possible locations in the Experiment 2 sequences. Although this
seems like an important difference, it is not clear why the predictability of perturbations
should have affected the relative sizes of PCRs to on-beat and off-beat EOSs. A fifth
difference was that the EOSs in the Experiment 2* sequences occurred later (i.e., on or
immediately after beat 10) than those in the Experiment 2 sequences (which occurred
on or immediately after beats 4–8). It could be that the salience of the beat level
increased in the course of each sequence. Finally, only the Experiment 2* sequences
included some sequences without any EOS. Although it is unclear why that difference
should have played a role, it was removed in Experiment 4. Two remaining
differences—in IBI duration (540 vs. 560 ms) and in EOS magnitude (±60 vs. ±70 ms)—
seem too small to have played a role and therefore were not changed in Experiment 4.
Experiment 4 juxtaposed three blocks of trials derived from Experiment 2*
(Blocks 1–3) with three blocks derived from Experiment 2 (Blocks 4–6). Block 1 consisted
of the same sequences as Block 2 in Experiment 3 (i.e., with equal intensities of beat
tones and subdivision tones, and with the former one semitone higher than the latter),
but the five isochronous baseline sequences were omitted. In Block 2, the pitch of beat
and subdivision tones was made identical and equal to that in Blocks 3–6. In Block 3, in
Repp: Unimanual vs. bimanual tapping 36
addition, the initial empty IBI was subdivided. Block 4 was the Fast/slow condition of
Experiment 2, without the slow beat-only sequences that had been included in Block 3
of Experiment 3. In Block 5, the sequence length was extended by adding five initial
subdivided beats to the sequences of Block 4, so that the EOSs occurred later in the
sequences. In Block 6, the sequence length was made constant by adding tones to the
ends of the sequences in Block 4.
The results for Block 1 were expected to replicate the results for Block 2 in
Experiment 3. There was no conceivable reason why omitting the isochronous baseline
sequences should have any effect on the PCRs. If the pitch difference between beat and
subdivision tones plays a role, then PCRs to beat-level EOSs should be reduced in Block
2 compared to Block 1. If the initial undivided IBI primes the beat level, then PCRs to
beat-level EOSs should be reduced in Block 3 compared to Block 2. The results for Block
4 were expected either to replicate those for Block 3 in Experiment 3 or to show smaller
PCRs to beat-level EOSs, which would confirm that the slow beat-only sequences in
Experiment 3 had increased the salience of the beat level. If the location of the EOS in
the sequence is critical, PCRs to beat-level EOSs should be larger in Block 5 than in Block
4. If a fixed sequence length enhances metricality, PCRs to beat-level EOSs should be
larger in Block 6 than in Block 4. If there is still a difference between results for Blocks 3
and those for Blocks 5 and 6, this would point to a role of the predictability of the EOS
location, which is the only remaining substantial difference between Blocks 1–3 and 4–6.
Methods
Repp: Unimanual vs. bimanual tapping 37
Participants. Seven of the 8 participants were the same as in Experiment 3. One
was replaced by another individual who had similarly extensive musical training and
tapping experience.
Materials. Block 1 consisted of the same sequences as Block 2 of Experiment 3,
but without any isochronous baseline sequences. An EOS of ±60 ms occurred on or
immediately after the tenth beat. Thus, the block comprised 20 randomly ordered
sequences, five replications of each of the four sequence types. The beats were one
semitone higher than the subdivisions (B-flat7 vs. A7), and the first IBI was empty. The
baseline IBI was 540 ms. Block 2 was similar, but all tones were now at the same pitch
(E7). Block 3 was like Block 2, except that the initial IBI was subdivided.
Block 4 was like Block 3 of Experiment 3, but without the slow baseline
sequences. Thus, the block comprised 20 randomly ordered sequences, 10 for each EOS
magnitude of ±70 ms. The EOS occurred on or immediately after a beat in positions 4–8.
All tones were identical (with pitch E7), subdivisions were present throughout, and the
baseline IBI was 560 ms. Block 5 was similar, except five additional beats with
subdivisions were added at the beginning of each sequence. The EOS thus occurred on
or immediately after a beat in positions 9–13. Block 6 was also similar to Block 4, except
that regular beats with subdivisions were added at the ends of the sequences, so that all
sequences contained 11 beats (22 tones).
Procedure. About one month elapsed between Experiments 3 and 4. The
procedure was the same as in Experiment 3, except that the order of the blocks was
varied across participants in a quasi-random (Blocks 1–3 and 4–6 were interleaved) and
approximately counterbalanced fashion.
Repp: Unimanual vs. bimanual tapping 38
Results and discussion
The results are shown in Figure 8. It can be gauged from the double standard
error bars that there were significant PCRs to both on-beat and off-beat EOSs in all six
blocks. Although the magnitude of the mean PCRs varied somewhat between blocks, a
repeated-measures ANOVA with the variables of block and EOS location (on-beat vs.
off-beat) revealed no significant effects (all p values > .33). Thus, PCRs to on-beat and
off-beat EOSs were of about the same magnitude, and none of the manipulations in this
experiment made any significant difference. The average magnitude of the on-beat
PCRs was 16.3%, and that of the off-beat PCRs was 21.1%. These values are more
similar to the average PCRs of Blocks 1 and 2 of Experiment 3 (18.7% and 20.6%,
respectively) than to the average PCRs of Blocks 3 and 4 in that experiment (11.6% and
24.9%, respectively). Thus, even though some conditions were very similar to those of
Experiment 2, the results are actually more in line with those of Experiment 2* (Figure
7A). This supports the findings of Repp (2004) regarding effects of two-level metrical
structure but provides no answer to the question of why beat-level PCRs were entirely
absent in Experiment 1 and in the Alt/slow condition of Experiment 2.
----------------------------
Insert Figure 8 here
----------------------------
GENERAL DISCUSSION
Repp: Unimanual vs. bimanual tapping 39
The present study addressed two major questions: (1) Whether there are any
differences between the automatic responses to phase perturbations (the PCRs) in
unimanual versus bimanual alternating synchronization with an auditory sequence, and
(2) under what circumstances hierarchical metrical structure is reflected in the PCRs.
These two questions are related at an abstract level because they both concern the
potential consequences of switching from a single level of motor control or perception
to a two-level control structure: Timing of unimanual versus bimanual action, and
perception of a single-level versus a two-level metrical sequence structure, respectively.
Moreover, each of these theoretical switches was predicted to yield the same pattern of
empirical results: an enhanced PCR to a same-level perturbation (i.e., to an EOS
occurring two sequence positions back) and a reduced PCR to a different-level
perturbation (i.e., an EOS in the immediately preceding sequence position). If both
effects were present, they would mutually reinforce each other.
However, neither effect materialized reliably in Experiments 1 and 2. The general
absence of differences between unimanual and bimanual tapping implies that the two
alternating hands functioned like a single hand and were controlled by a single central
timekeeper. The present results, which were obtained in a phase perturbation
paradigm, thus support earlier conclusions reached on the basis of covariance analysis
(Wing et al., 1989) and of variability patterns in rhythm production (Semjen & Ivry,
2001). Additional consistent results were obtained in Experiment 6 of Repp (2004),
which was conducted after the present experiments had been completed.
Of course, that does not mean that the two hands always function like a single
hand. For example, Keller and Repp (2004) showed that alternating bimanual tapping in
Repp: Unimanual vs. bimanual tapping 40
anti-phase with a metronome was considerably more variable and error-prone than
unimanual anti-phase tapping, whereas there was little difference between alternating
bimanual and unimanual in-phase tapping. Also, as reviewed in the Introduction,
simultanous tapping with both hands reduces the variability of each individual hand
(Helmuth & Ivry, 1996). The latter finding has been interpreted as evidence for
integration of hand-specific timekeepers (Ivry et al., 2002) or temporal action goals
(Drewing et al., 2004). It seems that whether or not the two hands function as a single
unit depends on the task requirements.
The present findings with regard to effects of metrical sequence structure were
initially (i.e., in Experiment 1) just as negative as those concerning the use of one versus
two hands. The principal indicator of a two-level metrical structure was taken to be the
occurrence of a PCR to an EOS two tones back in a 2:1 tapping task (Repp, 2004). In
Experiment 1, the intervening subdivision tone completely blocked such a beat-level
PCR, which suggests that the sequence was perceived as a simple sequence of beats
without subdivisions. Neither alternation between the two hands nor alternation of
pitches in the sequence induced a beat-level PCR, even though both manipulations had
been expected to induce or reinforce perception of a two-level metrical structure.
Experiment 2 used a faster sequence tempo, in order to increase the relative salience of
beats and decreased that of subdivisions (Parncutt, 1994; Repp, 2004). Although a small
beat-level PCR emerged, it was present paradoxically only in uniform sequences, but
not in sequences whose pitch alternated. This finding, although statistically reliable, may
have been a fluke because Experiment 3 yielded equally small beat-level PCRs in the
same two conditions. If the average magnitude of the PCRs in the two conditions is
Repp: Unimanual vs. bimanual tapping 41
considered, it does seem that the faster tempo induced a beat-level PCR, albeit a much
smaller one than in similar conditions of Repp (2004).
It was the purpose of Experiments 3 and 4 to explore possible causes for this
difference in PCR magnitude, but the results were inconclusive. This could be attributed
to large between-participant variability, small number of trials, and effects of general
experimental context. A thorough exploration of the various methodological variables
would require a series of experiments, but may not be worth the effort. After all, all
conditions in Experiments 3 and 4 yielded significant beat-level PCRs, as did six
experiments in Repp (2004) and Experiment 2 of Large et al. (2002). Therefore, the
absence of metrical structure effects in Experiment 1 must be considered anomalous
and specific to the circumstances of that experiment.
The effect of metrical structure explored here and in Repp (2004) is akin to, but
more general than, second-order (lag-2) phase correction, an option included in some
mathematical models of synchronization (Pressing, 1998; Pressing & Jolley-Rogers,
1997; Semjen et al., 2000; Vorberg & Schulze, 2002). Second-order phase correction
increases as the sequence tempo increases (in 1:1 tapping) and also seems to be stronger
in experts than in novices (Pressing, 1998). Both these trends are consistent with an
effect of emergent binary metrical structure, and second-order phase correction can be
understood from that perspective. However, Repp (2004) has shown that the number
of subdivision tones intervening between beats (1, 2, or 3) does not affect the beat-level
PCR, as long as the IBI is constant. This finding identifies the phenomenon as being
grounded in hierarchical metrical perception and not in a simple lag-2 operation.
Repp: Unimanual vs. bimanual tapping 42
In summary, the present study provided evidence for the functional unity of the
two hands in alternating bimanual in-phase synchronization, as well as initially negative
but ultimately reassuring evidence for perception of binary metrical structure in
isochronous auditory sequences.
Repp: Unimanual vs. bimanual tapping 43
ACKNOWLEDGMENTS
This research was supported by NIH grant MH-51230. Thanks are due to Yoko
Hoshi, Helen Sayward, and Susan Holleran who helped with data analysis, and to
Amandine Penel, Susan Holleran, and Peter Keller 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]).
Repp: Unimanual vs. bimanual tapping 44
FOOTNOTES
1 All intervals are reported here as specified or recorded by the MAX software. It
is known from acoustic measurements that the real-time temporal intervals generated
or recorded by MAX in this configuration were shorter by about 2.4%.
Repp: Unimanual vs. bimanual tapping 45
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Repp: Unimanual vs. bimanual tapping 50
FIGURE CAPTIONS
Fig. 1. Schematic illustration of an event onset shift (EOS, assumed to be +100 ms
here), the subsequent phase correction response (PCR, assumed to be 50%), and the
gradual return to baseline during subsequent taps typically observed in unimanual
tapping. Hypothetical results for alternating bimanual tapping are also shown. The
metric employed here is the deviation (“shift”) from an expected time of occurrence
defined by an isochronous temporal grid whose time points are separated by the
sequence inter-onset interval. For taps, this grid is defined to start (shift = 0) with the
tap in position 0, which serves as the reference for calculating the PCR and subsequent
shifts.
Fig. 2. Schematic illustration of the different conditions in Experiments 1 and 2.
Thick and thin bars represent “beats” and “subdivisions”, respectively (either sequence
tones or taps). Open-head arrows symbolize an (on-beat) event onset shift (EOS) in the
sequence. Filled-head arrows symbolize a phase correction response (PCR). Horizontal
lines separate groups of conditions for analysis purposes. In Group 3 (but not in Group
4), two possible EOS locations are shown, as indicated by “or”.
Fig. 3. Results of the Slow/slow and Slow/anti conditions in Experiments 1 (A, B)
and 2 (C, D).
Fig. 4. Results of the Slow/fast and Slow/alt conditions in Experiments 1 (A, B)
and 2 (C, D).
Fig. 5. Results (relative shifts of taps ±s.e.) of the Fast/slow and Alt/slow
conditions in Experiments 1 (A–D) and 2 (E–H).
Repp: Unimanual vs. bimanual tapping 51
Fig. 6. Results (relative shifts of taps ±s.e.) of the Fast/fast, Alt/fast, Fast/alt, and
Alt/alt conditions in Experiments 1 (A–D) and 2 (E–H).
Fig. 7. Results of relevant conditions from Experiment 2 of Repp (2004) (A) and
from the present Experiment 2 (B), and results of Experiment 3 (C, D).
Fig. 8. Results of Experiment 4.
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