Clapping to Auditory Salience Traces
The continuous wavelet transform (CWT) of Morlet and Grossman can also be applied to decompose a rhythm represented by a continuous trace of event "salience" derived directly from the audio signal. We use a measure of event salience developed by our EmCAP partners Prof. Sue Denham and Dr. Martin Coath at the University of Plymouth. The CWT decomposes the event salience trace into a hierarchy of periodicities (a multi-resolution representation). These periodicities have a limited duration in time (hence the term "wavelets"). Where those periodicities continue to be reinforced by the occurrence of each onset of the performed rhythm, a limited number of periodicities are continued over time, forming "ridges". The ridges can then be used to identify periods in the rhythm which match listeners sense of beat. These ridges can then be recomposed using the inverse wavelet transform to produce moments in time that match the taps of the beat.
An audio example below demonstrates beat induction of singing. The first MP3 file is the original sung fragment (Thanks are due to the Meertens Institute for supplying the Dutch folk songs from the "Onder de groene linde" collection). The second MP3 file is the same song with the beat induced by the multiresolution representation process mixed in as a hi-hat sound.