Melodic pattern discovery by structural analysis via wavelets and clustering techniques

We present an automatic method to support melodic pattern discovery by structural analysis of symbolic representations by means of wavelet analysis and clustering techniques. In previous work, we used the method to recognize the parent works of melodic segments, or to classify tunes into tune families (Velarde, Weyde & Meredith, 2013), and in this study, we use it to discover melodic patterns. Wavelet analysis is a mathematical tool that compares time-series with an oscillation — the wavelet — at different positions and scales, returning similarity coefficients. We explore properties of the wavelet coefficients in relation to segmentation and similarity detection. For this purpose, we sample symbolic representations of monophonic pieces into one-dimensional (1D) pitch signals, which are contour like representations of those pieces, and apply the continuous wavelet transform (CWT) with the Haar wavelet. The returning wavelet coefficients are used to set local boundaries at different time-scales, considering the coefficients’ zero crossings, local maxima or local extrema. The wavelet coefficients are also used to represent segments in a transposition invariant manner. We use k-means to cluster melodic segments into groups of measured similarity and obtain a raking of the most prototypical melodic segments or patterns and their occurrences. We test the method on the JKU Patterns Development Database and evaluate it based on the ground truth defined by the MIREX 2013 Discovery of Repeated Themes & Sections task. We compare the results of our method to the output of geometric approaches. Finally, we discuss about the relevance of our wavelet-based analysis in relation to structure, pattern discovery, similarity and variation, and comment about the considerations of the method when used to support human or computer assisted music analysis and teaching.