Musical combinatorics, tonnetz, and the CubeHarmonic

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.