When the beat goes off: Mutually interacting complex systems

Abstract

While musical performances are determined by many factors such as the musical genre and interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction of two humans when playing rhythms. We find that the interbeat intervals (IBIs) of both laypeople and professional musicians exhibit scale-free (power law) cross-correlations. Surprisingly, the next beat to be played by one person is dependent on the entire history of the other persons IBIs on time scales up to several minutes. A general stochastic model for Mutually Interacting Complex Systems (MICS) is introduced which suggests a physiologically motivated explanation for the occurrence of scale-free cross-correlations. In addition, The MICS model may be applicable to study the dynamics of other complex systems where scale-free cross-correlations have been observed, including econophysics, physiological time series and collective behavior of animal flocks. The interdisciplinary study provides an understanding of fundamental characteristics of timing and synchronization at the inter-brain level and leads directly to applications in audio engineering.