Towards a Formalization of Musical Rhythm

Temporality lies at the very heart of music, and the play with rhythmic and metrical structures constitutes a major device across musical styles and genres. Rhythmic and metrical structure are closely intertwined, particularly in the tonal idiom. While there have been many approaches for modeling musical tempo, beat and meter and their inference, musical rhythm and its complexity have been comparably less explored and formally modeled. The model formulates a generative grammar of symbolic rhythmic musical structure and its internal recursive substruc-ture. The approach characterizes rhythmic groups in alignment with meter in terms of the recursive subdivision of temporal units, as well as dependencies established by recursive operations such as preparation and different kinds of shifting (such as anticipation and delay). The model is formulated in terms of an abstract context-free grammar and applies for monophonic rhythms and harmonic rhythm.