In the 5th century BC, Pythagoreas said, There is geometry in the humming of strings. There is music in the spacing of the spheres"
What he was talking about was, of course, the notion that simple mathematics underlies everything, even the makeup of the heavens. Even then it was believed that the solar system consisted of nested 'celestial spheres' and the periods of their orbits around the earth, he thought, followed some simple arithmetic law.
Johannes Kepler, though he was the first to codify the 'Three Laws' of planetary motion through painstaking study of Tycho Brahe's planetary data, was also an inveterate mystic. At the beginning of his work, he attempted to find a geometric reason behind the orbits of the planets involving nested regular solids within invisible celestial spheres. He announced this in his book Mysterium Cosmographicum in 1596, however he eventually abandoned this idea of 'celestial harmony' once he began in ernest to uncover the Three Laws. His final book Harmonices Mundi announcing the Third Law, is translated as Harmonies of the World and is sometimes mis-translated as the "Music of the Spheres" following Pythagoras's quote.
At some point, and I don't recall if this is someone's idea since Kepler or before, there was the belief that the planets actually emitted some form of celestial music, each a pure tone, and that when they all sounded in perfect chordance, the end of the world would be near. Pythagoras certainly came close to this view and may even have been the official author of it.
Some years back, in the 1970's, using an electronic synthesizer, I recall an artist who constructed a simple musical scale based on the velocities of the planets in their orbits. He used astronomical tables to make certain that the motions were consistent with our calendar system, and then he let the whole thing go. Mercury was a fast-period, high pitched tone that varied as the speed of the planet around the sun changed from fast at perihelion to slow at aphelion. In the background, Pluto was a sluggish, low-pitched tone, and in between you would hear the other planets. It sounded rather peculiar as I recall upon listening to the tape, but over the thousands of years that the simulation of 'celestial music' extended, I never heard anything approaching a pure chord in harmony, it was always a cacaphony of 'noises'.