Listening to musical rhythms with progressive wavelets

Analysing and modelling the human perception of musical rhythm provides insights into non-verbal knowledge representation, quantification of musicological theories, and intelligent tools for music performance and composition. Linear phase Gabor transform wavelets are an analysis technique capable of making explicit many elements of musical rhythm theory. Transforms over a continuous time-scale plane (the scalogram) spanning rhythmic frequencies (0.1 to 100 Hz) decompose the multiple temporal relationships between beats into hierarchies of periodicities. Wavelets represent well the transient nature of these rhythmic frequencies in performed music, in particular those from expressive deviations from written notation during performance. Using measures of phase congruence over a range of dilation scales are shown to be useful in highlighting structurally important beats. The performance of the wavelet transform is demonstrated on examples of performed monophonic percussive rhythms possessing intensity accents, changing meters and rubato. The transform results indicate the location of such accents and from these, the inducement of phrase structures.