Abstract
Two experiments investigated the effects of interval duration ratio on perception of local timing perturbations, accuracy of rhythm production, and phase correction in musicians listening to or tapping in synchrony with cyclically repeated auditory two-interval rhythms. Ratios ranged from simple (1:2) to complex (7:11, 5:13), and from small (5:13 = 0.38) to large (6:7 = 0.86). Rhythm production and perception exhibited similar ratio-dependent biases: rhythms with small ratios were produced with increased ratios, and timing perturbations in these rhythms tended to be harder to detect when they locally increased the ratio than when they reduced it. The opposite held for rhythms with large ratios. This demonstrates a close relation between rhythm perception and production. Unexpectedly, however, the neutral “attractor” was not the simplest ratio (1:2 = 0.50) but a complex ratio near 4:7 (= 0.57). Phase correction in response to perturbations was generally rapid and did not show the ratio-dependent biases observed in rhythm perception and production. Thus, phase correction operates efficiently and autonomously even in synchronization with rhythms exhibiting complex interval ratios.
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Notes
Dynamic systems approaches to rhythmic bimanual coordination also employ a form of hierarchical interval ratio, namely relative phase (e.g., Haken, Kelso, & Bunz, 1985; Tuller & Kelso, 1989; Yamanishi, Kawato, & Suzuki, 1980). A 1:2 interval ratio implies a 1:3 ratio between the shorter interval and the cycle duration (a normalized relative phase of 0.33). It is well known that in-phase and anti-phase movements are easy to perform accurately, whereas other phase relationships between the hands are more difficult to produce, show greater variability, and are typically distorted in the direction of the closer of the two “attractors,” in-phase and anti-phase. These studies, however, are usually not concerned with the production of musical rhythm, and they often use visual pacing signals (but see Semjen & Ivry, 2001). In bimanual production of auditory two-interval rhythms, in-phase and anti-phase movements both imply isochrony and thus are avoided (i.e., do not function as attractors) unless the two target interval durations are difficult to discriminate.
This was really the primary purpose of this research, at least as we saw it initially. However, because we obtained rhythm production data as a byproduct of the synchronization task that we employed to measure phase correction and then realized the perception task could easily be conducted with the identical materials, we did not want to miss this opportunity to compare rhythm production and perception. Thus, we expanded the scope of the present research.
The Greenhouse–Geisser correction was applied to the p value of any effect with more than two levels.
These results would change little if the perception data were analyzed in terms of fitting psychometric functions to the response percentages and comparing their slopes and 50% thresholds. It was clear from inspection of the average response functions that, whenever a change was more difficult to detect, the function had both a shallower slope and a higher threshold, and in some cases it did not reach 50%.
Each PCR function also yielded a measure of the y-axis intercept. This intercept was different from zero in non-isochronous rhythms and corresponded closely to the difference between the mean asynchronies of taps with first and second tones (Fig. 2).
We first attempted to derive separate PCR estimates for negative and positive phase shifts by regression analysis, but the results were highly variable due to the small number of data points. Therefore, separate PCRs for negative and positive phase shifts are not shown in Fig. 5.
We note here briefly that Experiment 1 was preceded by a very similar experiment in which the timing perturbations were event onset shifts (Repp, 2002) rather than phase shifts. Event onset shifts change both IOIs in a cycle in a complementary fashion, thereby creating a larger change in interval ratio than a phase shift created in the present experiment. However, the results were almost identical and therefore are not reported here in detail. In the perception task, participants generally responded to the change in the shorter IOI, but the pattern of asymmetries was the same as in Fig. 4. The analysis of PCRs yielded only one reliable effect, a larger PCR in the 1:1 than in the 4:5 rhythm (cf. Fig. 5).
It did not seem necessary to consider the results with author BHR’s data excluded because of his small PCRs in isochronous rhythms. His mean PCR was rather small in 360/360 but comparable to that of some other participants in 840/840.
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This research was supported by National Science Foundation grant BCS-0642506.
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Repp, B.H., London, J. & Keller, P.E. Perception–production relationships and phase correction in synchronization with two-interval rhythms. Psychological Research 75, 227–242 (2011). https://doi.org/10.1007/s00426-010-0301-8
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DOI: https://doi.org/10.1007/s00426-010-0301-8