The harmony of the spheres: the silent music of the cosmos

According to a legend told by Nicomachus of Gerasa and taken up by Boethius, Pythagoras, passing a blacksmith's workshop, noticed that the hammers produced sounds that were now consonant, now dissonant. Investigating, he discovered that musical intervals depended on simple numerical ratios: the octave on the ratio of two to one, the fifth on three to two, the fourth on four to three. The story is legendary and physically inaccurate, but it expresses a discovery that would mark Western thought for two millennia: number governs harmony, and harmony governs the cosmos.

From the Pythagoreans to Plato

The Pythagoreans drew a bold conclusion from this insight. If the planets move at different speeds and at proportionate distances, their motions must produce sounds, and these sounds must form a perfect consonance. We do not hear it, they explained, because it accompanies us from birth and we have never known silence by contrast. Aristotle, in De caelo, discussed and rejected this thesis, but acknowledged that it had been elegantly formulated.

Plato, at the end of the Republic, tells the myth of Er, a Pamphylian warrior who after an apparent death visits the afterlife and sees the spindle of Necessity, around which the circles of the heavens revolve. On each of the eight circles sits a Siren who utters a single note, and from all their voices together arises a single harmony.

Cicero, Boethius and the Middle Ages

In the Somnium Scipionis, the concluding part of Cicero's De re publica, Scipio Aemilianus dreams that he is among the stars and hears a great and sweet sound produced by the motion of the spheres. The text, commented on by Macrobius, became one of the main sources of medieval cosmology. Boethius, in the sixth century, distinguished in De institutione musica three kinds of music: that of the world, that of man, which harmonises soul and body, and that of instruments.

This classification was taught throughout the Middle Ages in schools and universities, where music was part of the quadrivium alongside arithmetic, geometry and astronomy. To study music therefore meant to study the proportions of the universe and of the soul, not only the art of composing and singing, which was considered a practical application of a higher science.

Agrippa, Gaffurio and Kepler

Cornelius Agrippa devotes several pages of the second book of De occulta philosophia to the theme, associating the planets and their spheres with notes, musical modes and Muses. Earthly music, for him, is an echo of the heavenly one and can dispose the human spirit to receive the influences of the heavens. In this he follows Ficino, who sang hymns to the accompaniment of the lyre. In 1496 the frontispiece of Franchino Gaffurio's Practica musicae had already depicted Apollo, the Muses and the planets in a single scheme.

The last great attempt to give the harmony of the spheres a scientific foundation was that of Johannes Kepler. In the Harmonices mundi, published in 1619, he sought musical proportions in the angular velocities of the planets in their elliptical orbits. In the same book he stated the third law of planetary motion, which links orbital periods to distances from the Sun.

The music of the spheres disappeared from astronomy, but it left a profound legacy in literature and art. For readers of Agrippa, it is perhaps the most beautiful image of a universe ordered according to number, in which the science of the heavens and that of sounds were two ways of listening to the same harmony.