Extension of Neo-Riemannian PLR-group to Seventh Chords

Boris Kerkez
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 485–488

Abstract

This paper extends the concept of the PLR-group from the neo-Riemannian theory, which acts on the set of major and minor triads, to a PS-group, which acts on the set of major and minor seventh chords. Like the PLR-group, the PS-group is isomorphic to D12, the dihedral group of order 24, and only compositions of two operations are needed to generate all group elements. Unlike the actions from PLR-group, there are only two operations that both preserve the closure of the set of major and minor seventh chords, as well as map three out of four notes from a chord to a resulting image.

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