  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.
