Subdivision schemes and multi-resolution modelling for automated music synthesis and analysis

• Published in: Journal of mathematics and music (Society for Mathematics and Computation in Music) Vol. 6; no. 1; pp. 17 - 47
• Main Authors: Hed, Sigalit, Gjerdingen, Robert O., Levin, David
• Format: Journal Article
• Language: English
• Published: Baton Rouge Taylor & Francis 01.03.2012; Taylor & Francis Ltd
• Subjects: algorithmic composition; Automation; computer-aided geometric design; counterpoint; monophony; multi-resolution analysis and synthesis; Music; music synthesis and analysis; pitch-and-rhythm interrelationships; polyphony; rhythmic patterns; Studies; subdivision schemes
• ISSN: 1745-9737; 1745-9745
• DOI: 10.1080/17459737.2012.680313

Subdivision schemes are special multi-resolution analysis (MRA) methods that have become prevalent in computer-aided geometric design. This paper draws useful analogies between the mathematics of subdivision schemes and the hierarchical structures of music compositions. Based on these analogies, we propose new methods for music synthesis and analysis through MRA, which provide a different perspective on music composition, representation and analysis. We demonstrate that the structure and recursive nature of the recently proposed subdivision models [S. Hed and D. Levin, Subdivision models for varying-resolution and generalized perturbations, Int. J. Comput. Math. 88(17) (2011), pp. 3709-3749; S. Hed and D. Levin, A 'subdivision regression' model for data analysis, 2012, in preparation] are well suited to the synthesis and analysis of monophonic and polyphonic musical patterns, doubtless due in large part to the strongly hierarchical nature of traditional musical structures. The analysis methods demonstrated enable the compression and decompression (reconstruction) of selected musical pieces and derive useful features of the pieces, laying groundwork for music classification.