Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations

  • Tom Collins
  • David Meredith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7937)

Abstract

Representing musical notes as points in pitch-time space causes repeated motives and themes to appear as translationally related patterns that often correspond to maximal translatable patterns (MTPs) [1]. However, an MTP is also often the union of a salient pattern with one or two temporally isolated notes. This has been called the problem of isolated membership [2]. Examining the MTPs in musical works suggests that salient patterns may correspond more often to the intersections of MTPs than to the MTPs themselves. This paper makes a theoretical contribution, by exploring properties of patterns that are maximal with respect to their translational equivalence classes (MTEC). We prove that a pattern is MTEC if and only if it can be expressed as the intersection of MTPs. We also prove a relationship between MTECs and so-called conjugate patterns.

Keywords

Pattern Discovery Motivic Analysis Repetition in Music Point-Set Patterns Music Analysis Geometric Music Representations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tom Collins
    • 1
  • David Meredith
    • 2
  1. 1.Department of Computational PerceptionJohannes Kepler University LinzAustria
  2. 2.Department of Architecture, Design and Media TechnologyAalborg UniversityDenmark

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