As you specifically mention Pythagoras, I'll post a quibble with the definition
as requiring human manipulation. Pythagoras has been thought of as a mathematician, but in his life was more a musician and metaphysician and teacher of arcane wisdom, frequently using mathematics as metaphor in explanation. He said that in his meditations he began to hear the voice of the sun, and later the voices of the planets "as they make their stately march about the sun". He called this "the music of the spheres", and said that the planets sit outward from the sun in the the same mathematical ratios as the notes in the octave. These same ratios are the subject of
Da Vinci's Vitruvian man, and speak to the nature of what nature perceives
as harmony. Whether or not it is music could be said to be a statement of
whether it fits those ratios. Or not. Hotly debated for a long time now.


As always, I know little or nothing. Any accuracy is attributed to good teachers, all error is because I'm an idiot and recall incorrectly.