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The Hierarchy of Rameau Groups

  • Franck JedrzejewskiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11502)

Abstract

This paper contributes to the transformational study of progressions of seventh chords and generalizations thereof. PLR transformations are contextual transformations that originally apply only to consonant triads. These transformations were introduced by David Lewin and were inspired the works of musicologist Hugo Riemann. As an alternative to other attempts to define transformations on seventh chords, we define new groups in this article, called Rameau groups, which transform all types of seventh or ninth chords or more generally, any chords formed of stacks of major or minor thirds. These groups form a hierarchy for inclusion. We study on musical examples the ability of these operators to show symmetries in the progression of seventh chords.

Keywords

Neo-Riemannian group PLR-group Rameau-Schillinger operators Rameau groups Generalized interval systems Lewin Parsimonious voice leading 

Notes

Acknowledgements

We thank anonymous reviewers for valuable remarks and Thomas Noll for comments that greatly improved the manuscript.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Atomic Energy CommissionUniversité Paris Lumières (CEA-CIPh)ParisFrance

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