Tonnetz and Beyond : In Search of Functional Representations of Harmonic Structures through Algebra and Geometry
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In this paper, we wish to explore underlying mathematical structures of tonal music with the use of group theoretic and geometric models. We will begin by examining trends in the current literature on the subject in attempts to focus on tonal harmonies. We will review some neo-Riemannian theory in the form of the Tonnetz and PL-R-group before turning towards the work of Dmitri Tymoczko, specifically with regard to chord geometries. Finally we submit the skeleton of a new framework for studying two-note chords which we believe to be promising, both for its explanatory power of functional tonal harmonies and for its potential expansion to three- and four-note chords.