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Published in:
2015 | OriginalPaper | Chapter
Finding Optimal Triadic Transformational Spaces with Dijkstra’s Shortest Path Algorithm
Author : Ryan Groves
Published in: Mathematics and Computation in Music
Publisher: Springer International Publishing
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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.