# The Geometry of Musical Chords

@article{Tymoczko2006TheGO, title={The Geometry of Musical Chords}, author={Dmitri Tymoczko}, journal={Science}, year={2006}, volume={313}, pages={72 - 74} }

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant…

## 237 Citations

Generalized Voice-Leading Spaces

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This model reveals connections between music-theoretical concepts, yields new analytical tools, unifies existing geometrical representations, and suggests a way to understand similarity between chord types.

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EIGHT SHORT MATHEMATICAL COMPOSITIONS CONSTRUCTED BY SIMILARITY

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This article offers a direct comparison of several mathematical approaches to the study of musical structure that have come to prominence in recent years. The methods include chord-based and…

Comment on "The Geometry of Musical Chords"

- GeologyScience
- 2007

Tymoczko (Reports, 7 July 2006, p. 72) proposed that the familiar sonorities of Western tonal music cluster around the center of a multidimensional orbifold. However, this is not true for all tonal…

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A generative grammar for classical Western chord progressions using ideas from Schenkerian analysis is described, which gives the general structure of a chord progression over time, but is still an abstract representation that requires additional information to become a complete score.

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- ArtArXiv
- 2013

Several kinds of metrics on musical data are described, and the implications of these metrics in two ways are explored: via techniques of classical topology where the metric space of all-possible musical data can be described explicitly, and via modern data-driven ideas of persistent homology which calculates the Betti-number barcodes of individual musical works.

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This paper considers three conceptions of musical distance (or inverse “similarity”) that produce three different musico-geometrical spaces: the first, based on voice leading, yields a collection of…

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AbstractThe aim of this paper is twofold: on one side we review the classical concept of musical modefrom the viewpoint of modern music, reading it as a superimposition of a base-chord (seventhchord)…

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