effects of phase perturbations on unimanual and alternating … · 2006-02-06 · repp: unimanual...

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UNPUBLISHED MANUSCRIPT, 8/14/04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.


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


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 &


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).


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.

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Insert Figure 1 here

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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).


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


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


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.


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.

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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


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


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.


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


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-


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.

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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


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.

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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,


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)


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.

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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


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.

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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).


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


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.


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.


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.


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


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


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.


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


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.


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


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


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.

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


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

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


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


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


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


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


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.


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.

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


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

GENERAL DISCUSSION


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


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


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.


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.


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]).


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%.


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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).


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.

effects of phase perturbations on unimanual and alternating … · 2006-02-06 · repp: unimanual...

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