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The Music of the Spheres: From Pythagoras to Kepler

For more than two thousand years, some of the greatest minds of the West held that the cosmos is a kind of music. The planets, they believed, move in proportions like those of musical harmony. The idea began with Pythagoras, passed through Plato and the medieval schools, and reached its most surprising result in the work of Johannes Kepler, where a search for heavenly music produced one of the founding laws of modern astronomy.

Pythagoras and the numbers of music

Pythagoras of Samos lived from about 570 to 495 BCE. He left no writings of his own, and what we know of his teaching comes through his followers and later authors.

The Pythagoreans are credited with a discovery that seemed to unlock the structure of the world: the most pleasing musical intervals correspond to simple ratios of whole numbers. Halve the length of a vibrating string and its note rises by an octave, a ratio of 2:1. A ratio of 3:2 gives a fifth, and 4:3 a fourth.

If harmony in sound rests on number, the Pythagoreans reasoned, perhaps the whole cosmos is ordered by number too. They proposed that the sun, the moon and the planets each give out their own tone as they move, and that together these tones form a harmony. This is the idea known as the harmony of the spheres, or musica universalis.

Plato and the singing heavens

The first written account of this harmony appears in Plato's Republic. In the closing myth of the book, the myth of Er, Plato describes the heavens as a great system of turning circles. On each circle stands a siren singing a single note, and the notes together make one harmony. Plato took up the theme of cosmic proportion again in his Timaeus.

Music as a science of the cosmos

In the ancient and medieval world, music was not only an art. It was a branch of mathematics, one of the four great disciplines of the quadrivium, alongside arithmetic, geometry and astronomy. To study music was to study proportion, and proportion was the language of the heavens.

The Roman philosopher Boethius described three kinds of music. The first, musica instrumentalis, is the music of voices and instruments. The second, musica humana, is the harmony between the human body and soul. The third, musica mundana, is the harmony that reigns throughout the whole created world. The music we hear, in this view, is only the outermost layer of a harmony that runs through the body, the soul and the cosmos.

Kepler's search

Johannes Kepler (1571 to 1630) was the imperial mathematician of his day and a working astrologer as well as an astronomer. In 1609, in his Astronomia Nova, he had already shown that the planets move in ellipses rather than perfect circles. But he was driven by a larger question: what harmony governs the system as a whole?

In 1619 he published his answer in Harmonices Mundi, "The Harmony of the World", a work in five books. He described himself as warmed by a generous draught "from the cup of Pythagoras".

Kepler looked for musical ratios in the speeds of the planets. He compared each planet's fastest and slowest motion, as seen from the sun, and found ratios that matched musical intervals. For Saturn the ratio was close to 5:4, a major third. For Jupiter it was 6:5, a minor third. For the Earth it was about 16:15, a semitone.

These were silent harmonies. No ear could hear them; they existed in the proportions of the heavens. Not all of Kepler's ideas worked out. But his search for harmony led him, in the final book of the Harmonices Mundi, to state what we now call his third law of planetary motion: the square of a planet's orbital period is proportional to the cube of its average distance from the sun.

Kepler himself called it the harmonic law. It is still taught in every course in astronomy.

After Kepler

Kepler's laws were based on observation. Some seventy years later, Isaac Newton gave them their physical explanation in his law of universal gravitation. Newton himself believed that the ancient teaching of the harmony of the spheres had been a veiled description of the very law he had found.

The idea continued to inspire artists. In 1952 the composer Paul Hindemith wrote a symphony titled Die Harmonie der Welt, after Kepler's book, with movements named after Boethius's three kinds of music. In our own time, astronomers have found planetary systems whose orbits fall into such precise whole-number resonances that they have been translated into music.

What the harmony of the spheres teaches

The music of the spheres is not proof of any particular astrological claim. But it tells an important story about the history of science. The belief that the heavens are ordered by harmony, and that this order is reflected in human life, was not an obstacle to science. For Kepler, it was the very question that led to discovery.

It also echoes a theme at the heart of every great tradition of astrology: that the cosmos is not random, that its rhythms can be known, and that human beings are part of its music.

Related reading: Osho on Astrology, Part 1: The Oldest and Most Rejected Science.

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