Tapping in Synchrony With a Perturbed Metronome: The Phase Correction Response to Small and Large Phase Shifts as a Function of Tempo

ABSTRACT

When tapping is paced by an auditory sequence containing small phase shift (PS) perturbations, the phase correction response (PCR) of the tap following a PS increases with the baseline interonset interval (IOI), leading eventually to overcorrection (B. H. Repp, 2008). Experiment 1 shows that this holds even for fixed-size PSs that become imperceptible as the IOI increases (here, from 400 to 1200 ms). Earlier research has also shown (but only for IOI = 500 ms) that the PCR is proportionally smaller for large than for small PSs (B. H. Repp, 2002a, 2002b). Experiment 2 introduced large PSs and found smaller PCRs than in Experiment 1, at all of the same IOIs. In Experiments 3A and 3B, the author investigated whether the change in slope of the sigmoid function relating PCR and PS magnitudes occurs at a fixed absolute or relative PS magnitude across different IOIs (600, 1000, 1400 ms). The results suggest no clear answer; the exact shape of the function may depend on the range of PSs used in an experiment. Experiment 4 examined the PCR in the IOI range from 1000 to 2000 ms and found overcorrection throughout, but with the PCR increasing much more gradually than in Experiment 1. These results provide important new information about the phase correction process and pose challenges for models of sensorimotor synchronization, which presently cannot explain nonlinear PCR functions and overcorrection.

Keywords:

• perturbations
• phase correction
• sensorimotor synchronization
• tapping
• tempo

ACKNOWLEDGMENTS

This research was supported by National Science Foundation grant BCS-0924206 to BHR.

Notes

1. This is equivalent to subtracting the baseline IOI from the interval between these two taps. In the absence of a PCR, the expected intertap interval would be equal to the baseline IOI.

2. This conclusion is supported by comparison with another, as yet unpublished data set (Repp & Keller, 2010) obtained from the same participants as in Experiment 1 (except for one who differed). PSs ranged from –10 to 10% of IOIs, as in Repp (2008), and IOIs ranged from 400 to 1300 ms. The mean PCR increased from 0.83 to 1.26, and the mean slope of the increase was 0.00047. These PCRs are larger than those in Repp (2008) and more similar to those in the present experiment (a statistical comparison is problematic because the IOI values do not match precisely). The slope matches that of Repp (2008), but again the statistical difference from the present, larger slope is not significant, due to large individual differences. Thus it cannot be concluded that fixed-size and proportionally increasing small PSs yield different results.

3. A total of 20 (out of 400) trials were lost to analysis due to an unpredictable program malfunction that sometimes made sequences stop after the first two tones.

4. In Experiment 1, PCR = a ₂ − a ₁ = a ₂ − (a ₁* – PS), where a stands for asynchrony, the index refers to tap number (as in Figure 2), and a ₁* denotes the asynchrony that the first tap would have had with its corresponding tone in the absence of a PS. Therefore, in Experiment 2, PCR = a ₂−(a ₀−PS), to make the PCRs comparable to those in Experiment 1. Substituting a ₀ for a ₁ should make no difference as long as these asynchronies have the same expected value (i.e., the mean asynchrony). See also Experiment 3.

5. They were also smaller than those in Repp and Keller (2010), which—as noted in Note 2—resembled those of Experiment 1 and stemmed from nearly the same participant group. No statistical comparison was conducted in this case because the IOIs did not match exactly.

6. Some trials were lost due to the same program malfunction as in Experiment 2, which made some trials stop unpredictably after the second tone. The ninth block was included to fill in some of the resulting gaps in the data, and some participants did additional make-up blocks. Still, 15 trials out of 216 were lost in Experiment 3A, and 13 in Experiment 3B.

7. The statistical software (SPSS) used did not show the interactions of the polynomial contrasts of PS with IOI, only their interactions with the linear and quadratic components of IOI. These were not significant for the cubic contrast.

8. The fifth-order contrast was also significant, F(1, 8) = 20.55, p = .002, but does not have any clear interpretation.