On the Roles of Complexity and Symmetry in Cued Tapping of Well-formed Complex Rhythms: Descriptive Statistics and Time Series Analysis

Production of relatively few rhythms with non-isochronous beats has been studied. So we assess reproduction of most well-formed looped rhythms comprising K=2-11 cues (a uniform piano tone, indicating where participants should tap) and N=3-13 isochronous pulses (a uniform cymbal). Each rhythm had two different cue interonset intervals. We expected that many of the rhythms would be difficult to tap, because of ambiguous non-isochronous beats and syncopations, and that complexity and asymmetry would predict performance. 111 participants tapped 91 rhythms each heard over 129 pulses, starting as soon as they could. Whereas tap-cue concordance in prior studies was generally >> 90%, here only 52.2% of cues received a temporally congruent tap, and only 63% of taps coincided with a cue. Only −2 ms mean tap asynchrony was observed (whereas for non-musicians this value is usually c. −50 ms). Performances improved as rhythms progressed and were repeated, but precision varied substantially between participants and rhythms. Performances were autoregressive and mixed effects cross-sectional time series analyses retaining the integrity of all the individual time series revealed that performance worsened as complexity features K, N, and cue inter-onset interval entropy increased. Performance worsened with increasing R, the Long: short (L: s) cue interval ratio of each rhythm (indexing both complexity and asymmetry). Rhythm evenness and balance, and whether N was divisible by 2 or 3, were not useful predictors. Tap velocities positively predicted cue fulfilment. Our data indicate that study of a greater diversity of rhythms can broaden our impression of rhythm cognition.