An approach to melodic segmentation and classification based on filtering with the Haar-wavelet

Abstract

We present a novel method of classification and segmentation of melodies in symbolic representation. The method is based on filtering pitch as a signal over time with the Haar wavelet, and we evaluate it on two tasks. The filtered signal corresponds to a single-scale signal w_s from the continuous Haar wavelet transform. The melodies are first segmented using local maxima or zero-crossings of w_s. The segments of w_s are then classified using the k nearest neighbour algorithm with Euclidian and city-block distances. This method proves more effective than using unfiltered pitch signals and Gestalt-based segmentation when used to recognize the parent works of segments from Bach’s Two-Part Inventions (BWV 772–786). When used to classify 360 Dutch folk tunes into 26 tune families, the performance of the method is comparable to the use of pitch signals, but not as good as that of string-matching methods based on multiple features.

Keywords:

• music analysis
• wavelet analysis
• classification
• symbolic music
• melodic analysis
• information retrieval
• folk song analysis
• melodic segmentation

Acknowledgements

We thank Peter van Kranenburg (Meertens Institute, Amsterdam) for sharing the Dutch Tune Families data set. Gissel Velarde is supported by the Department of Architecture, Design and Media Technology at Aalborg University.

Notes

¹We used the Musedata encodings of Bach’s Two-Part Inventions, available at http://www.musedata.org.

²We follow the presentation by Antoine (1999). Signals processed by digital computers have to be discretized. The term ‘continuous’ refers to the fact that all sample positions are used as shift values, as opposed to the discrete wavelet transform where shift values are much sparser.

³The Haar function was introduced by Haar in 1910 (Haar, 1910). Equation 4 uses Mallat’s (2009) notation.

⁴The algorithms are implemented in MATLAB (R2012b, The Mathworks, Inc) using the Wavelet Toolbox and the MIDI Toolbox (Eerola & Toiviainen, 2004). We use the LBDM implementation of the MIDI Toolbox, and an update of Christine Smit’s read_midi function (http://www.ee.columbia.edu/~csmit/matlab_midi.html, accessed 4 October 2012).

⁵We also tested the way that rests are represented in normalized pitch signals by assigning the value zero to rests, subtracting the average pitch (excluding rests) and assigning the value zero to rests again after normalization. This practice produced worse results than the way that rests are represented in the normalized pitch signal representation described in Section 3.1.

⁶We ran some tests with segmentation points at local extrema (i.e. local minima and maxima), but, in general, results with local maxima were better.