Pitch-and-rhythm interrelationships and musical patterns: Analysis and modelling by subdivision schemes

Sigalit Hed*, Robert O. Gjerdingen, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This article presents a new model for pitch-and-rhythm interrelationships and demonstrates the importance of these interrelationships as features for music analysis and classification. We show that the model is capable of identifying certain musical patterns and categorising pieces created by Mozart's dice game by identifying their quality. We discuss the cognitive foundation of this model and present future directions and applications.We employ the subdivision-based music analysis methods introduced earlier by the present authors to model certain pitch-and-rhythm interdependencies and symmetry patterns in selected pieces, shedding more light on the analogy proposed between subdivision schemes and musical structures. Our approach to pitch-and-rhythm interactions points out an interesting phenomenon, according to which the relations between neighbour pitches may be related to their timing through a relatively simple model. We propose hierarchical reductions and indicate that their levels are interrelated through simple subdivision schemes using new criteria, yielding features for classification.

Original languageEnglish
Pages (from-to)45-73
Number of pages29
JournalJournal of Mathematics and Music
Issue number1
StatePublished - 2 Jan 2015


  • Mozart's dice game
  • multiresolution analysis
  • music analysis
  • pitch-and-rhythm interrelationships
  • rhythm tree
  • rhythmic patterns
  • subdivision schemes
  • symmetry


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