Temporal-Logic Representation of Co-ordination in Music

Alan Marsden

Temporal logic is a well proven tool for understanding temporal processes and representing computation. Musical performance requires certain kinds of co-ordination between players, with varying kinds of cues. A paradigm `triangle-player problem' is proposed and examined from the perspective of a number of different formulations of temporal logic. Two common characteristics of musical time are a regularly occurring (but not necessarily precisely even) sequence of beats, and subdivision of those beats into a small number of shorter time divisions. A novel formulation of the S (since) and U (until) operators of temporal logic is proposed on this basis, allowing a natural representation of common phenomena of musical co-ordination and the incorporation of scheme of temporal representation of music proposed in earlier work (Alan Marsden, Representing Musical Time: A Temporal-Logic Approach, Swets & Zeitlinger, 2000).