The Hierarchy of Rameau Groups

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.