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(2015) Mathematics and computation in music, Dordrecht, Springer.
Finding optimal triadic transformational spaces with Dijkstra's shortest path algorithm
Ryan Groves
pp. 122-127
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
DOI: 10.1007/978-3-319-20603-5_12
Full citation:
Groves, R. (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, pp. 122-127.
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