The fundamental theory of algebra was developed by Gauss as higher arithmetic. Its cyclical form is synchronous with harmonic functions. The conjecture of Riemannn of the periodicity of the primes continues Gauss’ agenda, as Riemann himself insisted.
Harmonics though is much broader in its scope across all types of human endeavors. At the scale of quantum mechanics, the entanglement between photons is such a harmonic function yet to be fully comprehended. At the astronomical level gravitational waves traverse the universe. Everything physical in between exhibits action along a spectrum of long lived harmonic coherence. Least action, force free configurations of spacetime being exemplars of highly harmonic systems.
Song is embedded in the living world. Humans have been engaged in it from time immemorial. Harmonic resolution of song is the creation of music. This represents an expression of free energy available to humanity and many other species. Indeed the arts in general have this attribute in common.
Leibniz speculated that higher monads that are united via pursuit of useful knowledge or reason will always prevail in human society.