Rhythm as Periodic Displacement: Entrainment, the Rhythmic Ground State, and the Synchronization of Biological and Musical Oscillators

We apply the Displacement Framework to rhythm across biological and musical domains. S0_rhythmic is the resting oscillatory baseline. Entrainment is attractor-basin coupling between oscillators. HRV is formalized as a cardiac basin-depth index. The musical beat is S0_beat; syncopation is displacement from it; the backbeat is metrical displacement from classical expectation. The blues shuffle is a micro-displacement cycle.

Groove is edge-of-basin dynamics: the phenomenology of entrainment at the attractor boundary. Social synchrony increases trust and cooperation through joint S0 construction. The Kuramoto model provides the formal entrainment mechanism.