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Distributional Analysis of n-Dimensional Feature Space for 7-Note Scales in 22-TET

  • Gareth M. HearneEmail author
  • Andrew J. Milne
  • Roger T. Dean
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

Many scale features have been defined in an effort to account for the ubiquity of the diatonic scale in tonal music. In 12-TET, their relative influences have been difficult to disentangle. In 22-TET however, the features are spread differently across different scales. We sought here to to establish a set of 7-note scales in 22-TET that represent the major clusters within the whole population of scales. We first calculate numerous features of every 7-note scale in 22-TET that may relate to their perception in harmonic tonality. This feature space is then reduced by the step-by-step removal of features which may be most completely expressed as linear combinations of the others. A k-medoids cluster analysis leads finally to the selection of 11 exemplar scales, including approximations of four different tunings of the diatonic scale in just intonation.

Keywords

Diatonic scale features K-medoids cluster analysis 22-TET 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Gareth M. Hearne
    • 1
    Email author
  • Andrew J. Milne
    • 1
  • Roger T. Dean
    • 1
  1. 1.The MARCS Institute for Brain, Behaviour and DevelopmentWestern Sydney UniversityPenrithAustralia

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