Resonance constraints on rhythmic movement.

The component frequencies of rhythmic patterns forming rational ratios, either simple (e.g., 1:2, 1:3) or complex (e.g., 2:3, 2:5), are known as mode locks or resonances. A general theory of resonances is provided by the circle map, the Farey series, and continued fractions. Predictions were evaluated in which rhythms (simple and poly) were established implicitly—the subject neither intended them nor knew their ratios. In Experiment 1, a prescribed unimanual frequency was performed as the primary task while hearing another frequency irrelevant to the task. In Experiments 2 and 3, a hand-held pendulum was oscillated at its natural frequency, while the other hand performed the primary task of following a metronome. The frequency ratio at the outset of a trial often changed during the trial. Consistent with the general theory, shifts were toward unimodular ratios of the Farey tree, and Fibonacci ratios tended to shift more than non-Fibonacci ratios.