Abstract
Musical chords and chord relations can be described through mathematics. Abstract permutations can be visualized through the Rubik’s cube, born as a pedagogical device [7, 21]. Permutations of notes can also be heard through the CubeHarmonic, a novel musical instrument. Here, we summarize the basic ideas and the state of the art of the physical implementation of CubeHarmonic, discussing its conceptual lifting up to the fourth dimension, with the HyperCubeHarmonic (HCH). We present the basics of the hypercube theory and of the 4-dimensional Rubik’s cube, investigating its potential for musical applications. To gain intuition about HCH complexity, we present two practical implementations of HCH based on the three-dimensional development of the hypercube. The first requires a laptop and no other devices; the second involves a physical Rubik’s cube enhanced through augmented and virtual reality and a specifically-designed mobile app. HCH, as an augmented musical instrument, opens new scenarios for STEAM teaching and performing, allowing us to hear the “sound of multiple dimensions.”
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Notes
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In music theory, slot-machine transformations are permutations. If we have three discs with three notes in each of them, they give a sequence of 3-note chords. Rotating the discs, the chord changes. For example, the vertical sequence \(0 - 1 - 2\) becomes \(1 - 2 - 0\) after a rotation of one of the discs [1].
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Video: https://tinyurl.com/3j5csh36.
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It had been called ars magna by Ramon Llull [4].
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Night Forest: https://www.youtube.com/watch?v=1OClm1pn7-g&t=1s, Blues and Grays: https://www.youtube.com/watch?v=oMldYLbfIRE, Female Laptop Orchestra (FLO).
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Mannone, M., Yoshino, T., Chiu, P., Kitamura, Y. (2022). Hypercube + Rubik’s Cube + Music = HyperCubeHarmonic. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_20
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