THE HEXATONIC SYSTEMS UNDER NEO-RIEMANNIAN THEORY: AN EXPLORATION OF THE MATHEMATICAL ANALYSIS OF MUSIC

Abstract. Neo-Riemannian theory developed as the mathematical analysis of musical trends dating as far back as the late 19th century. Specifically, the musical trends at hand involved the use of unorthodox sets of pitches. These sets had the characteristic of retaining their triadic harmonies, but of sounding atonal. Neo-Riemannian theory not only allowed for the mathematical construction and description of these sets, some of which later were called the Hexatonic Systems, but also a means to explain how these systems were used. Involving the application of the P LR Operations, the analysis of the Hexatonic Systems is a primary component of neo-Riemannian theory. In this paper, I give a self-contained description of Rick Cohn’s Hexatonic Systems, as well a