Boethius, transmitting Greek harmonics to the Latin West around 500, fixed the doctrine in a curriculum. His De institutione musica ranks three musics: mundana, the harmony of the cosmos, its spheres, elements and seasons; humana, the harmony joining soul to body and part to part in a person; instrumentalis, the audible craft of voices and strings, lowest of the three.
For a thousand years every educated European learned music inside this frame, as a mathematical science of proportion neighboring arithmetic, geometry and astronomy in the quadrivium, so that the music of the spheres was not a poetic flourish laid over learning but its organizing chart: the same ratios sounding in a plucked string, tempering a healthy soul and spacing the heavens. The doctrine's strangest triumph came at its scientific funeral.
Kepler, convinced that God had built the world on harmonic archetypes, spent years in the Harmonice Mundi of 1619 hunting the heavenly consonances in real astronomical data, assigning each planet a melodic range from its varying orbital speed, Mercury a treble arpeggio, Earth the doleful semitone mi-fa, which he glossed as misery and famine. Buried in book five, produced by exactly this search for harmony, is the relation now called Kepler's third law, binding the cube of a planet's distance to the square of its period, one of the load-bearing results of modern astronomy. The spheres made no sound, it turned out, but the conviction that they must be in tune had led a man to measure until the mathematics sang, and the harmony of the world passed, intact, from theology into physics.