Brain processes underlying the production and perception of rhythm indicate considerable flexibility in how physical signals are interpreted. This paper explores how that flexibility might play out in rhythmicity in speech and music. There is much in common across the two domains, but there are also significant differences. Interpretations are explored that reconcile some of the differences, particularly with respect to how functional properties modify the rhythmicity of speech, within limits imposed by its structural constraints. Functional and structural differences mean that music is typically more rhythmic than speech, and that speech will be more rhythmic when the emotions are more strongly engaged, or intended to be engaged. The influence of rhythmicity on attention is acknowledged, and it is suggested that local increases in rhythmicity occur at times when attention is required to coordinate joint action, whether in talking or music-making. Evidence is presented which suggests that while these short phases of heightened rhythmical behaviour are crucial to the success of transitions in communicative interaction, their modality is immaterial: they all function to enhance precise temporal prediction and hence tightly coordinated joint action.