Hypercube + Rubik’s Cube + Music = HyperCubeHarmonic

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 instru- ment. Here, we summarize the basic ideas and the state of the art of the physical implementation of CubeHarmonic, discussing its conceptual lift- ing 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 implementa- tions of HCH based on the three-dimensional development of the hyper- cube. 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.”