Effects of phase perturbations on unimanual and alternating bimanual synchronization with auditory sequences

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 (otherhand) 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-RR...). 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 twotiered 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) twolevel 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.