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

Sigalit Hed*, Robert O. Gjerdingen, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)17-47
Number of pages31
JournalJournal of Mathematics and Music
Volume6
Issue number1
DOIs
StatePublished - Mar 1 2012

Keywords

  • algorithmic composition
  • computer-aided geometric design
  • counterpoint
  • monophony
  • multi-resolution analysis and synthesis
  • music synthesis and analysis
  • pitch-and-rhythm interrelationships
  • polyphony
  • rhythmic patterns
  • subdivision schemes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Music
  • Computational Mathematics
  • Applied Mathematics

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