Hybrid dynamics in a paired rhythmic synchronization–continuation task

Synchronization is a fundamental component of a musical ensemble. Recent advancements in behavioral time series analyses have produced increasing evidence of global coordination, matching in statistical structures of fluctuation in long timescales, separate from synchronization as local coordination. Previous studies have demonstrated that strong interactions in local timescales and interactions in multiple scales with weak local interactions can be sources of global coordination. However, knowledge of global coordination in human rhythmic movement is still limited. The present study investigated fluctuation and coordination dynamics for inter-tap intervals (ITI) in a paired rhythmic tapping task, imitating duo performances, from local to global timescales. In addition, we examined parameter dynamics for a coupled oscillator model to test whether the model could replicate the task dynamics and integrate sources of global coordination. Measured ITI series demonstrated globally coordinated hybrid dynamics: persistent fluctuation and positively correlated coordination in global scales and anti-persistent fluctuation and negatively correlated coordination in local scales. Positive lag ±1 and negative lag 0 local cross-correlation suggested that the global coordination was emerged from local mutual timing adjustment processes. The coupled oscillator model for the task replicated these dynamics. Moreover, the model could generate both types of global coordination, which emerged from strong and weak local interactions. These findings can help to improve knowledge of interpersonal coordination in musical ensembles, allowing a better understanding, for example, of the basis of temporal harmony and individual differences in the coordination of each pair and their source.