Though the music produced by an ensemble is influenced by multiple factors, including musical genre, musician skill, and individual interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction between two humans synchronizing rhythms. We find that the interbeat intervals 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 person's interbeat intervals on timescales up to several minutes. To understand this finding, we propose a general stochastic model for mutually interacting complex systems, which suggests a physiologically motivated explanation for the occurrence of scale-free cross-correlations. We show that the observed long-term memory phenomenon in rhythmic synchronization can be imitated by fractal coupling of separately recorded or synthesized audio tracks and thus applied in electronic music. Though this study provides an understanding of fundamental characteristics of timing and synchronization at the interbrain level, the mutually interacting complex systems model may also be applied to study the dynamics of other complex systems where scale-free crosscorrelations have been observed, including econophysics, physiological time series, and collective behavior of animal flocks.time series analysis | long-range cross-correlations | anticorrelations | musical coupling | interbrain synchronization I n his book Musicophilia, neurologist Oliver Sacks writes: "In all societies, a primary function of music is collective and communal, to bring and bind people together. People sing together and dance together in every culture, and one can imagine them having done so around the first fires, a hundred thousand years ago" (1). Sacks adds, "In such a situation, there seems to be an actual binding of nervous systems accomplished by rhythm" (2). These thoughts lead to the question: Is there any underlying and quantifiable structure to the subjective experience of "musical binding"? Here, we examine the statistical nature of musical binding (also referred to as musical coupling) when two humans play rhythms in synchrony.Every beat a single (noninteracting) layperson or musician plays is accompanied by small temporal deviations from the exact beat pattern, i.e., even a trained musician will hit a drum beat slightly ahead or behind the metronome (with a SD of typically 5-15 ms). Interestingly, these deviations are statistically dependent and exhibit long-range correlations (LRC) (3, 4). Listeners significantly prefer music mirroring long-range correlated temporal deviations over uncorrelated (white noise) fluctuations (5, 6). LRC are also inherent in the reproduction of both spatial and temporal intervals of single subjects (4, 7-9) and in musical compositions, such as pitch fluctuations (a simple example of pitch fluctuations is a melody) (10, 11) and note lengths (12). The observation of ...