The Music of the Spheres, from Pythagoras to Kepler
The idea that planets produce an inaudible harmony spans two thousand years: from Pythagoras and Plato to Boethius and Kepler's Harmonices Mundi.
For more than two thousand years philosophers, theologians and astronomers believed that the cosmos was ordered according to the same proportions that govern music. The planets, as they turned, were thought to produce a perfect harmony which human beings cannot hear. This idea, known as the music or harmony of the spheres, was born in ancient Greece and reached the scientific revolution of the seventeenth century, where it contributed, surprisingly, to one of the fundamental discoveries of modern astronomy.
Pythagoras and Numerical Ratios
Tradition credits Pythagoras, who lived in the sixth century BC, with discovering that consonant musical intervals correspond to simple numerical ratios: the octave to two to one, the fifth to three to two, the fourth to four to three. A legend told by Nicomachus of Gerasa in the second century AD, and later taken up by Boethius, says the philosopher grasped these proportions by listening to the hammers in a blacksmith's workshop. The story is physically inaccurate, but the ratios are correct when applied to the lengths of a vibrating string.
From this discovery the Pythagoreans drew a view of the world in which number is the principle of all things. If music is number, and the cosmos is ordered, then the heavens too must be music. Aristotle, in his treatise On the Heavens, reports their answer to the most obvious objection: we do not hear the sound of the spheres because we have heard it since birth, without ever being able to compare it with silence.
Plato, Cicero and Boethius
Plato gave the idea a memorable mythical form. At the end of the Republic, in the myth of Er, he describes the spindle of Necessity around which eight concentric circles turn; on each sits a siren uttering a single note, and from them all arises a single harmony. In the Timaeus the world soul is built according to musical proportions.
Cicero took up the theme in the Dream of Scipio, where Africanus, carried up to heaven, hears the sweet sound produced by the motion of the spheres. Macrobius's commentary on this text passed the idea on to the Latin Middle Ages. At the beginning of the sixth century Boethius, in De institutione musica, distinguished three kinds of music: musica mundana, the harmony of the cosmos; musica humana, the concord between soul and body; and musica instrumentalis, the music actually heard.
Kepler and the Harmonices Mundi
The Pythagorean legacy reached its peak with Johannes Kepler. In 1619 the German astronomer published in Linz the Harmonices Mundi, the harmony of the world, in which he sought the ratios of musical intervals in the speeds of the planets. By comparing the angular velocity of each planet at its nearest and farthest points from the Sun, Kepler assigned each one a short melody.
To the Earth fell the notes mi and fa, which he read, with a bitter play on Latin words, as misery and famine. In the same book, amid these speculations, Kepler stated the third law of planetary motion, which links the period of revolution to the distance from the Sun. The search for a mystical harmony thus led him to a physical law that still holds.
After Kepler the music of the spheres gradually left science, but it remained alive in poetry, in philosophy and in music itself. Composers such as Hindemith, who in 1957 devoted his opera Die Harmonie der Welt to Kepler, have continued to reflect on that ancient dream of a sounding universe. Everyday language also keeps a trace of it, when we speak of the harmony of creation.