A Coupled Oscillator Model of Interactive Tapping

Abstract

Background: Synchronization in music has been a popular experimental basis for studying social interactions, as musicians are required to synchronize to each other’s beats and integrate abstract social information in order to coordinate their actions as part of a non-verbal communication process. A finger-tapping paradigm has been used in studies of sensorimotor synchronization as well as coordination dynamics within and between people (Repp 2005). Recent models of tapping dynamics have included two error-correction mechanisms: phase and period correction (Repp & Keller). They have generally been linear models, which are oversimplifications of these dynamics. Aims: To model the dynamics capturing entrainment between pairs in a finger-tapping paradigm. Method: Pairs of subjects were asked to tap on their respective keyboards following an 8-beat auditory stimulus sent through their headphones. Subjects were instructed to keep the given beat as precisely as possible as well as synchronize with the ‘other’. They were in scenarios where they received auditory feedback of themselves tapping, the other, or the computer metronome. Results: A dynamical systems approach was taken to model the tapping dynamics, using a system of two oscillators coupled in both phase and frequency, corresponding to phase and period correction. The model demonstrated that the tapping dynamics depend on the four coupling constants (phase and frequency for each oscillator), and are highly sensitive to noise. Conclusions: Both phase and frequency coupling is required to capture the tapping dynamics of dyads. Coupling constants can be used to capture the degree of interaction.