ACM - Computers in Entertainment

The geometry of musical structure

By Carol L. Krumhansl
Theoretical and Practical Computer Applications in Entertainment, [Vol. 3, No. 4]

DOI: 10.1145/1095534.1095542

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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