Mapping Triadic Transformations: Computational Parsing and Visualization

Abstract

In this paper, a framework for the analysis of chord progressions based on the neo-Riemannian music theory is introduced, focusing on the Parallel (P), Leittonwechsel (L), and Relative (R) transformations. This paper is a continuation of the theoretical framework of music analysis, particularly the geometric and algebraic approaches of Fiore et al. A parser is introduced that can analyze raw symbolic musical data into normalized pitch class sets. These sets can then be transformed into geometric data for the analysis of the relationships of the chords. The framework is useful in analyzing conventional and non-traditional chord progressions, such as those produced by computers, which do not follow the conventional diatonic norms. The system can transform the raw symbolic data into two- and three-dimensional tonal space diagrams that can illustrate the relationships of the chords, which may not be clear in the conventional symbolic notation. The results show the potential of the use of computers in expanding the conventional models of music analysis.