On the Group of Transformations of Classical Types of Seventh Chords

Cannas, Sonia; Antonini, Samuele; Pernazza, Ludovico

doi:10.1007/978-3-319-71827-9_2

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2019

2022

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Cited by 6 publications

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“…They also consider triads, whereas the main focus of this work is four-tone harmonic chords or seventh chords. The work of [1] is focused on seventh chords, but again is more concerned with absolute pitches. Also, unlike in these previous interesting studies, we are more concerned with deriving the basic harmonic three-tone and four-tone chords axiomatically and with representing this relationship graphically.…”

Section: Introductionmentioning

confidence: 99%

A group-theoretical classification of three-tone and four-tone harmonic chords

Polak

2020

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We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, majorminor duality, and augmented-diminished duality. These actions correspond to elements of symmetric groups, and also correspond directly to intuitive concepts in the harmony theory of music. We produce a graph of how these actions relate different seventh chords that suggests a concept of distance in the theory of harmony.

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Section: Introductionmentioning

confidence: 99%