Cross-frequency coupling explains the preference for simple ratios in rhythmic behaviour and the relative stability across non-synchronous patterns

Rhythms are important for understanding coordinated behaviours in ecological systems. The repetitive nature of rhythms affords prediction, planning of movements, and coordination of processes within and between individuals. A major challenge is to understand complex forms of coordination when they differ from complete synchronization. By expressing phase as ratio of a cycle, we adapted levels of the Farey tree as a metric of complexity mapped to the range between in-phase and anti-phase synchronization. In a bimanual tapping task, this revealed an increase of variability with ratio complexity, a range of hidden and unstable yet measurable modes, and a rank-frequency scaling law across these modes. We use the phase-attractive circle map to propose an interpretation of these findings in terms of hierarchical cross-frequency coupling (CFC). We also consider the tendency for small-integer attractors in the single-hand repeated tapping of 3-interval rhythms reported in the literature. The phase-attractive circle map has wider basins of attractions for such ratios. This work motivates the question of whether CFC intrinsic to neural dynamics implements low-level priors for timing and coordination and thus becomes involved in phenomena as diverse as attractor states in bimanual coordination and the cross-cultural tendency for musical rhythms to have simple interval ratios.

Keywords: coordination, cross-frequency coupling, Farey tree, intrinsic dynamics, rhythm, scaling law

Supplementary material from "Cross-frequency coupling explains the preference for simple ratios in rhythmic behaviour and the relative stability across non-synchronous patterns". The Royal Society. Collection. 

https://doi.org/10.1098/rstb.2020.0333

https://doi.org/10.6084/m9.figshare.c.5501579.v1