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Music

Musical Combinatorics, Tonnetz, and the CubeHarmonic

Profile image of Maria MannoneMaria Mannone

2018, Journal of Collected papers of Academy of Arts

https://doi.org/10.5937/ZBAKUM1801104M
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13 pages

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Abstract

In this paper, we give an overview of some applications of combinatorics and permutations in music through the centuries. The concepts of permutation and tonnetz (spatial representation of voice leading and modulation) can be joined together in a physical device, the CubeHarmonic, a musical version of the Rubik’s cube. We finally describe a prototype of the CubeHarmonic that uses the magnetic tracking technology developed at the Tohoku University.

Figures (3)
BASS = A technical prototype has been recently developed in collaboration with the ICD team of the Tohoku University, headed by Prof. Yoshifumi Kitamura, see Figure 3. The prototype uses a novel magnetic tracking technology (Huang et al., 2015, 2016). The system generates a magnetic field to drive multiple, tiny, and wireless LC coils and detects the resonant magnetic flux to compute their 3D location and rotation. When the LC coils are attached to a Rubik’s cube, the movements of the facets can be tracked in real-time. Thus, it is possible to visualize the Rubik’s cube in a virtual environment as well as to convert the facet combination into sounds. Instead of choosing which facet or which slid e to play, it has been chosen to play all the notes at the same time. To avoid any chaotic effects, the variety of chords was limited first to two chords (a chord per each grou each grou different | p of three faces, with several doublings), and then to three chords (a chord for p of two facets). Moreover, to improve the idea of ,,motion“ and ,,twisting,“ oudness levels, accordingly to the position of the facets, were set (with the simple choice of the horizontal distance concerning the screen). The farther the notes are from t he screen, the louder they play. In this way, we can have a Doppler-like effect of ,,approaching“pieces of the cube during a 45-degree rotation forward of the right (or left) side. Even if we do not change the pitch but only the loudness of the notes The very first prototype (developed by Mannone) used a giant cube with sound modules (of greeting cards) on each facet; see Figure 2 (left: the cube with big sound modules; right: a detail of a small sound module covered with paper). This allowed the playing of each facet separately, of each slice, and the selection of random melodies selecting different paths on the cube. However, there are still open problems, such as an adequate substitution of batteries, and the reduction of the size of the cube (depending on the minimal size of the loudspeaker and electric circuit on each facet).
BASS = A technical prototype has been recently developed in collaboration with the ICD team of the Tohoku University, headed by Prof. Yoshifumi Kitamura, see Figure 3. The prototype uses a novel magnetic tracking technology (Huang et al., 2015, 2016). The system generates a magnetic field to drive multiple, tiny, and wireless LC coils and detects the resonant magnetic flux to compute their 3D location and rotation. When the LC coils are attached to a Rubik’s cube, the movements of the facets can be tracked in real-time. Thus, it is possible to visualize the Rubik’s cube in a virtual environment as well as to convert the facet combination into sounds. Instead of choosing which facet or which slid e to play, it has been chosen to play all the notes at the same time. To avoid any chaotic effects, the variety of chords was limited first to two chords (a chord per each grou each grou different | p of three faces, with several doublings), and then to three chords (a chord for p of two facets). Moreover, to improve the idea of ,,motion“ and ,,twisting,“ oudness levels, accordingly to the position of the facets, were set (with the simple choice of the horizontal distance concerning the screen). The farther the notes are from t he screen, the louder they play. In this way, we can have a Doppler-like effect of ,,approaching“pieces of the cube during a 45-degree rotation forward of the right (or left) side. Even if we do not change the pitch but only the loudness of the notes The very first prototype (developed by Mannone) used a giant cube with sound modules (of greeting cards) on each facet; see Figure 2 (left: the cube with big sound modules; right: a detail of a small sound module covered with paper). This allowed the playing of each facet separately, of each slice, and the selection of random melodies selecting different paths on the cube. However, there are still open problems, such as an adequate substitution of batteries, and the reduction of the size of the cube (depending on the minimal size of the loudspeaker and electric circuit on each facet).

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