Distortions in Reproduction of Two-Interval Rhythms: When the “Attractor Ratio” Is Not Exactly 1:2

when rhythms consisting of two unequal intervals are reproduced cyclically, their interval ratio tends to be distorted in the direction of 1:2 (= 0.5), which thus seems to function as an “attractor ratio” (AR). However, recent results for musicians in a synchronization task (Repp, London, & Keller, 2011) have suggested an upward-shifted AR (USAR) somewhat greater than 0.5. Three new experiments suggest that this shift is not due to synchronization versus continuation tapping, the range of interval ratios employed, unimanual versus bimanual tapping, intensity differences between taps, or mental subdivision of the long interval, although some of these factors may affect its size. The new results also show that the USAR is found more consistently in musicians than in nonmusicians and seems to arise in rhythm production, not in perception. While the exact causes of the USAR remain unclear, the results suggest that the AR is not necessarily the mathematically simplest interval ratio.

Systematic Distortions in Musicians’ Reproduction of Cyclic Three-Interval Rhythms

In a classic study, Fraisse (1956) demonstrated that sequences of four sounds defining three different interval durations exhibit characteristic distortions in reproduction: The two more similar intervals tend to be assimilated to each other, resulting in a rhythm containing just two interval durations. The present study examined whether highly trained musicians (including percussionists) are able to perform such rhythms accurately in a synchronization-continuation tapping paradigm. Eleven rhythms, a subset of those used by Fraisse, were presented cyclically at his original tempo and also at a slower tempo. The musicians produced significant rhythm distortions, though they were smaller than those observed by Fraisse and not always assimilative. They were relatively larger at the fast than at the slow tempo and occurred in both synchronization and continuation. In contrast to Fraisse’s data, the most variably reproduced target rhythm was the one in which the two longer intervals were identical. The pattern of distortions suggested attraction towards ideal rhythms in which all three interval durations are different, representing metrical categories with nominally simple interval ratios (some permutation of 1:2:3) that were probably activated by the cyclic presentation of the rhythms. However, these attractors themselves seemed to be somewhat distorted, perhaps reflecting the simultaneous presence of a nonmetrical attractor that differentiated two interval categories regardless of ratio, as observed by Fraisse.

Metrical Subdivision Results in Subjective Slowing of the Beat

FOUR EXPERIMENTS INVESTIGATED whether metrical subdivision affects perceived beat tempo. In Experiment 1, musically trained participants tapped in synchrony with the beat of an isochronous pacing sequence and continued tapping the beat after the sequence stopped. Continuation tapping was slower when the pacing beat was subdivided than when it was not. Experiment 2 found the same effect when the subdivisions during synchronization were self-generated. The effect was neutralized, however, when subdivisions were tapped during continuation. In Experiment 3, an effect of subdivision was found in a purely perceptual tempo judgment task. Experiment 4 tested musicians and nonmusicians in matched perception and reproduction tasks. Musicians showed the expected effect of subdivision in both tasks, whereas nonmusicians showed a larger effect in reproduction but a smaller effect in perception. Overall, the findings suggest that subdivided inter-beat intervals are subjectively longer than empty intervals, in agreement with the "filled duration illusion" in psychophysics.

Synchronization and Continuation Tapping to Complex Meters

The goal of this study was to assess the ability of North American adults to synchronize and continue their tapping to complex meter patterns in the presence and absence of musical cues to meter.We asked participants to tap to drum patterns structured according to two different 7/8 meters common in Balkan music. Each meter contained three nonisochronous drumbeats per measure, forming intervals in a short-short-long (SSL) or a long-short-short (LSS) pattern. In the synchronization phase of each trial, participants were asked to tap in synchrony with a drum pattern that was accompanied by either a matching or a mismatching Balkan folk melody. In the continuation phase of the trial, the drum pattern was turned off and participants continued tapping the drum pattern accompanied by the same melody or by silence. Participants produced ratios of long to short inter-tap intervals during synchronization that were between the target ratio of 3:2 and a simple-meter ratio of 2:1. During continuation, participants maintained a similar ratio as long as the melody was present but when the melody was absent the ratios were stretched even more toward 2:1. Tapping variability and tapping position relative to the target locations during synchronization and ratio production during both synchronization and continuation showed that the temporal grouping of tones in the drum pattern was more influential on tapping performance than the particular meter (i.e., SSL vs. LSS). These findings demonstrate that people raised in North America find it difficult to produce complex metrical patterns, especially in the absence of exogenous cues and even when provided with musical stimuli to aid them in tapping accurately.