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Modulation Theory and Lie Brackets of Vector Fields

  • Guerino Mazzola
  • René Guitart
  • Jocelyn Ho
  • Alex Lubet
  • Maria Mannone
  • Matt Rahaim
  • Florian Thalmann
Chapter
Part of the Computational Music Science book series (CMS)

Summary

In a recent book [16], we have opened the discussion of a hypergestural restatement of mathematical counterpoint theory. The present chapter aims at a discussion in the same vein of the classical mathematical modulation theory [682, 670]. The present approach to modulation theory is based on the idea that degrees in the start tonality are interpreted as gestures that move to degrees (qua gestures) of the target tonality by means of hypergestures. This means that the symmetries relating tonalities in the classical setup are replaced by hypergestures that connect gesturally interpreted degrees. The present hypergestural model solves the problem, but it opens more questions than it answers in the sense that the construction of hypergestures that replace the classical inversion symmetries is by no means unique.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Guerino Mazzola
    • 1
  • René Guitart
    • 2
  • Jocelyn Ho
    • 3
  • Alex Lubet
    • 1
  • Maria Mannone
    • 1
  • Matt Rahaim
    • 1
  • Florian Thalmann
    • 4
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA
  2. 2.Institut de Mathématiques de JussieuUniversité Diderot Paris 7ParisFrance
  3. 3.Department of MusicUCLA Herb Alpert School of MusicLos AngelesUSA
  4. 4.School of Electronic Engineering and Computer ScienceQueen Mary University of LondonLondonUK

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