Rhythmic Regularity Beyond Meter and Isochrony

Classical meter theory, derived from European, notation-based musical practice, requires notionally absolute isochrony. This article proposes a more flexible concept of rhythmic frequencies (or periodicities) represented by continuous functions over time, and develops rhythmic theory from it that is more global in scope. A rhythm is a good fit to a given frequency if its onsets are close to peaks of one of these functions, without having to precisely coincide. This provides some useful tools for understanding properties of rhythms and how different rhythms interact, including the rhythmic spectrum which shows all the frequencies present in a rhythm. Maximally even rhythms like the African standard pattern and tamborim rhythm of samba, are those which maximize a given frequency for a given grid, and often function as basic rhythms (e.g. “timelines” or claves) in many musical traditions, as do other rhythms, like the “Bo Diddley” rhythm and Clave Son, with strong representation of a single frequency. When rhythms expressing nearby frequencies are combined, they interact to produce slow phase shifts over longer cycles, a feature of timeline rhythms, and also more complex isorhythmic designs in, for example, the late music of György Ligeti, and recent jazz compositions by Dave King and Miles Okazaki.