Comment on "The Geometry of Musical Chords"

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Comment on "The geometry of musical chords".

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 progressions. When prototypical three-voice cadential progressions by Bach converge on the tonic, the chords migrate from the center to the edge of the orbifold.

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The geometry of musical chords.

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 sy...

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Geometry of Chords

This article provides an introduction to basic geometric investigations of the 12-tone sytem and its subsets, the chords. The various definitions and results are intended to lay a theoretical basis for 12-tone-based explorative and empirical research on occidental harmony. The entire approach is motivated by the assumption that the 12 tones do not constitute an arbitrary 12-element set with arb...

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Musical imagery: generation of tones and chords.

Four experiments are reported that examine subjects' ability to form and use images of tones and chords. In Experiments 1 and 3, subjects heard a cue tone or chord and formed an image of a tone or chord one whole step in pitch above the cue. This image was then compared to a probe tone or chord that was either the same as the image in pitch, different from the image in pitch and harmonically cl...

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ژورنال

عنوان ژورنال: Science

سال: 2007

ISSN: 0036-8075,1095-9203

DOI: 10.1126/science.1134013