Pythagorean tradition: planetary distances mirror musical ratios, octave, fifth, fourth, producing the harmonia ton sphairon. Plato's Timaeus builds the world-soul on these ratios; Kepler's Harmonices Mundi (1619) spent a book deriving the planets' actual 'melodies' and found the third law hiding inside the music.
The modern revival: sonified telescope data marketed as the music of the spheres, NASA's audio clips as fulfillment of the prophecy. The data-sonification is real; it is not what Pythagoras claimed, which is why the claim still stands alone.
The doctrine's subtlest feature: the music is defined as unheard, ears not attuned since birth. A harmony nobody can hear is unfalsifiable, which is either its fatal flaw or its precise point: order exists whether or not the listener does.
If the cosmos is music, is physics the score or the noise floor?