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

  • Tom Collins
  • David Meredith
Conference paper

DOI: 10.1007/978-3-642-39357-0_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7937)
Cite this paper as:
Collins T., Meredith D. (2013) Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations. In: Yust J., Wild J., Burgoyne J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science, vol 7937. Springer, Berlin, Heidelberg

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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