We define the notion of spherical harmonics, as a generalization from the two-sphere case. We use coset theory to define them, and then we describe examples of spherical harmonics. The KK decomposition is defined, and then the particular cases of groups spaces and spheres are considered for the spherical harmonics.

By exploring three issues which connect music with Platonic cosmology, I argue that, according to Plutarch, this connection was at the same time very important and severely limited. (1) In several passages of De animae procreatione, Plutarch compares the demiurge to a musician. These comparisons suggest a certain degree of similarity, but also a significant degree of difference between the two and, accordingly, between cosmic harmony and music. (2) Similarly, Plutarch’s reception of the notion of ‘music of the spheres’, as it emerges from a discussion in Quaestiones convivales, confirms the connection between music and the cosmos only to a limited extent. What the answers of the discussion have in common is that they all warn against excessive appreciation of music. (3) Finally, in Amatorius and De Pythiae oraculis, Plutarch distances musical experience from divine inspiration (enthousiasmos). In general, this persistent combination of importance and limitedness can be explained by Plutarch’s interpretation of Plato’s Timaeus.