A Continuous Time-Frequency Approach To Representing Rhythmic Strata
Existing theories of musical rhythm have argued for a conceptualization of a temporal hierarchy of rhythmic strata. This paper describes a computational approach to representing the formation of rhythmic strata. The use of Gabor transform wavelets (as described by Morlet and co-workers) is demonstrated as an analysis technique capable of explicating elements of rhythm cognition. Transforms over a continuous time-frequency plane (the scalogram) spanning rhythmic frequencies (0.1 to 100Hz) capture the multiple periodicities implied by beats at different temporal relationships. Gabor wavelets have the property of preserving the phase of the frequency components of the analyzed signal. The use of phase information provides a new approach to the analysis of rhythm. Measures of phase congruence over a range of frequencies are shown to be useful to highlight transient rhythms and temporal accents. The performance of the wavelet transform is demonstrated on an example of generated rhythms.
Leigh M. Smith and Peter Kovesi
Proceedings of the Fourth International Conference on Music Perception and Cognition, Montreal 1996, pages 197-202