All maximal-pairs in step-leap representation of melodic sequence

  • Authors:

  • Emilios Cambouropoulos;Maxime Crochemore;Costas S. Iliopoulos;Manal Mohamed;Marie-France Sagot

  • Affiliations:

  • Department of Music Studies, University of Thessaloniki, 540006 Thessaloniki, Greece;Institut Gaspard-Monge, University of Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2, France and Department of Computer Science, King's College London, London WC2R 2LS, England, United K ...;Department of Computer Science, King's College London, London WC2R 2LS, England, United Kingdom;Department of Computer Science, King's College London, London WC2R 2LS, England, United Kingdom;Inria Rhône-Alpes, Laboratoire de Biométrie et Biologie ívolutive, Université Claude Bernard, 69622 Villeurbanne Cedex, France

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special ''binary don't care'' symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established ''step-leap'' representation is examined. In the step-leap representation, each melodic diatonic interval is classified as a step (+/-s), a leap (+/-l) or a unison (u). Binary don't care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don't cares and z is the number of reported maximal-pairs.