What's the mathematical description of harmony
Qualitatively, mathematical description of harmony allows you to predict which two (or more) tones are harmonious.
Quantitatively, knowing the frequencies of two notes, a formula would give you a yes (it's harmonious) or no (it's disharmonious) answer. You will note that orbital parameters of planets, just as vibrating strings, are frequencies. You should also note that harmony is absolute, for we are able to agree whether two tones are (sound) harmonious.
More specifically, the book Quantum Pythagoreans will treat you to a specific and objective answer.
Cheers, Mike I.