#Hypercube in mathematica how to#
#Hypercube in mathematica Pc#

Zassenhaus, H.: Rubik’s cube: a toy, a galois tool, group theory for everybody. Williams, R.: The Geometric Foundation of Natural Structure. From MathWorld-A Wolfram Web Resource (2014). Undark, H.P.: A brief history of the Rubik’s cube. Tymoczko, D.: The geometry of musical chords.

#Hypercube in mathematica how to#

Staff, M.: How to play a Rubik’s cube like a piano (2015). Rotman, J.: An Introduction to the Theory of Groups. Riepel, J.: Grundregeln zur Tonordnung Insgemein. Polfreman, R., Oliver, B.: Rubik’s cube, music’s cube. World Scientific, From School to Postgraduate Levels, Singapore (2018) (eds.): Theoretical and Practical Pedagogy of Mathematical Music Theory: Music for Mathematics and Mathematics for Music.

Montiel, M., Gómez, F.: Music in the pedagogy of mathematics. Miyazaki, K., Ishii, M., Yamaguchi, S.: Science of Higher-Dimensional Shape and Symmetry. Mazzola, G., Mannone, M., Pang, Y.: Cool Math for Hot Music. Mannone, M., Kitamura, E., Huang, J., Sugawara, R., Chiu, P., Kitamura, Y.: CubeHarmonic: a new musical instrument based on Rubik’s cube with embedded motion sensor. Mannone, M., Kitamura, E., Huang, J., Sugawara, R., Kitamura, Y.: Musical combinatorics, tonnetz, and the cubeharmonic. (eds.) Mathematics and Computation in Music, MCM 2019. Mannone, M.: Have fun with math and music! In: Montiel, M., Gomez-Martin, F., Agustín-Aquino, O.A. Huang, J., Sugawara, R., Chu, K., Komura, T., Kitamura, Y.: Reconstruction of dexterous 3D motion data from a flexible magnetic sensor with deep learning and structure-aware filtering.

The Magic Cube’s cubies are twiddled by cubists and solved by cubemeisters. Hofstadter, D.: Metamagical Themas, March 1981. ĭ’amore, B.: Salvador Dalì e la geometria a quattro dimensioni (2015). (eds.) Mathematics and Computation in Music, MCM 2011. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. īaroin, G.: The planet-4D model: an original hypersymmetric music space based on graph theory. Online 21(3) (2015)Īndreotti, E., Frans, R.: The connection between physics, engineering and music as an example of STEAM education.

#Hypercube in mathematica Pc#

34(2), 107–136 (2012)Īmiot, E., Baroin, G.: Old and new isometries between pc sets in the planet-4D model. HCH, as an augmented musical instrument, opens new scenarios for STEAM teaching and performing, allowing us to hear the “sound of multiple dimensions.” KeywordsĪlegant, B., Mead, A.: Having the last word: Schoenberg and the ultimate cadenza. 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.

To gain intuition about HCH complexity, we present two practical implementations of HCH based on the three-dimensional development of the hypercube. We present the basics of the hypercube theory and of the 4-dimensional Rubik’s cube, investigating its potential for musical applications. 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). Permutations of notes can also be heard through the CubeHarmonic, a novel musical instrument. Abstract permutations can be visualized through the Rubik’s cube, born as a pedagogical device. Musical chords and chord relations can be described through mathematics.