A Wavelet-Based Approach to Pattern Discovery in Melodies

We present a computational method for pattern discovery based on the application of the wavelet transform to symbolic representations of melodies or monophonic voices. We model the importance of a discovered pattern in terms of the compression ratio that can be achieved by using it to describe that part of the melody covered by its occurrences. The proposed method resembles that of paradigmatic analysis developed by Ruwet (1966) and Nattiez (1975). In our approach, melodies are represented either as ‘raw’ 1-dimensional pitch signals or as these signals filtered with the continuous wavelet transform (CWT) at a single scale using the Haar wavelet. These representations are segmented using various approaches and the segments are then concatenated based on their similarity. The concatenated segments are compared, clustered and ranked. The method was evaluated on two musicological tasks: discovering themes and sections in the JKU Patterns Development Database and determining the parent compositions of excerpts from J. S. Bach’s Two-Part Inventions (BWV 772–786). The results indicate that the new approach performs well at finding noticeable and/or important patterns in melodies and that filtering makes the method robust to melodic variation.