A Multiresolution Time-frequency Analysis and Interpretation of Musical Rhythm

This thesis describes an approach to representing musical rhythm in computational terms. The purpose of such an approach is to provide better models of musical time for machine accompaniment of human musicians and in that attempt, to better understand the processes behind human perception and performance. The intersections between musicology and artificial intelligence (AI) are reviewed, describing the rewards from the interdisciplinary study of music with AI techniques, and the converse benefits to AI research. The arguments for formalisation of musicological theories using AI and cognitive science concepts are presented. These bear upon the approach of research, considering ethnographic and process models of music versus traditionally descriptive methods of music study. This enquiry investigates the degree to which the human task of music can be studied and modelled computationally. It simultaneously performs the AI task of problem domain identification and constraint. The psychology behind rhythm is then surveyed. This reviews findings in the literature of the characterisation of elements of rhythm. The effect of inter-onset timing, duration, tempo, accentuation, meter, expressive timing (rubato), the interrelationship between these elements, the degree of separability between the perception of pitch and rhythm, and the construction of timing hierarchy and grouping is reported. Existing computational approaches are reviewed and their degrees of success in modelling rhythm are reported. These reviews demonstrate that the perception of rhythm exists across a wide range of timing rates, forming hierarchial levels within a wide-band spectrum of frequencies of perceptible events. Listeners assign hierarchy and structure to a rhythm by an arbitration of bottom-up phenomenal accents and top-down predictions. The predictions are constructed by an interplay between temporal levels. The construction of temporal levels by the listener arises from quasi-periodic accentuation. Computational approaches to music have considerable problems in representing