Mathematical Aspects of a new Spherical Musical Instrument: the SphereHarmonics

Temari balls are traditional Japanese toys and artworks. The variety of their geometries and tessellations can be investigated formally and computationally with the means of combinatorics. As a further step, we also propose a musical application of the core idea of Temari balls. In fact, inspired by the classical idea of music of spheres and by the CubeHarmonic, a musical application of the Rubik’s cube, we present the concept of a new musical instrument, the SphereHarmonic. The mathematical (and musical) description of Temari balls lies in the wide background of interactions between art and combinatorics. Concerning the methods, we present the tools of permutations and tessellations we adopted here, and the core idea for the SphereHarmonic. As the results, we first describe a classification of structures according to the theory of groups. Then, we summarize the main passages implemented in our code, to make the SphereHarmonic play on a laptop. Our study explores an aspect of the deep connections between the mutually inspiring scientific and artistic thinking.