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The geometry of musical structure: a brief introduction and history

Published: 01 October 2005 Publication History

Abstract

The purpose of this article is to provide a general introduction to the idea that musical structure can be represented geometrically. It begins by defining those elements that appear in the models in the three papers that follow. A brief review is given of psychological results demonstrating that these music-theoretic definitions describe implicit knowledge that listeners have of tonal-harmonic music. This is followed by a brief historical summary of maps that were proposed previously of keys, tones, and chords, and a hybrid tone-chord map. The article then summarizes a number of issues that arise in connection with geometric representations. Finally, the innovations in the three proposed models are highlighted, particularly their contributions to visualizing the dynamics and temporal relationships that exist in extended musical pieces.

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cover image Computers in Entertainment
Computers in Entertainment   Volume 3, Issue 4
Theoretical and Practical Computer Applications in Entertainment
October 2005
116 pages
EISSN:1544-3574
DOI:10.1145/1095534
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 2005
Published in CIE Volume 3, Issue 4

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Author Tags

  1. computational music cognition
  2. geometry
  3. harmonic analysis
  4. music theory
  5. music visualization
  6. tonal analysis
  7. tonality models

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