Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

226944

Finding optimal triadic transformational spaces with Dijkstra's shortest path algorithm

Ryan Groves

pp. 122-127

Abstract

This paper presents a computational approach to a particular theory in the work of Julian Hook—Uniform Triadic Transformations (UTTs). A UTT defines a function for transforming one chord into another, and is useful for explaining triadic transitions that circumvent traditional harmonic theory. By combining two UTTs and extrapolating, it is possible to create a two-dimensional chord graph. Meanwhile, graph theory has long been studied in the field of Computer Science. This work describes a software tool which can compute the shortest path between two points in a two-dimensional transformational chord space. Utilizing computational techniques, it is then possible to find the optimal chord space for a given musical piece. The musical work of Michael Nyman is analyzed computationally, and the implications of a weighted chord graph are explored.

Publication details

Published in:

Collins Tom, Meredith David, Volk Anja (2015) Mathematics and computation in music: 5th international conference, MCM 2015, London, UK, June 22-25, 2015. Dordrecht, Springer.

Pages: 122-127

DOI: 10.1007/978-3-319-20603-5_12

Full citation:

Groves Ryan (2015) „Finding optimal triadic transformational spaces with Dijkstra's shortest path algorithm“, In: T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, 122–127.