Spheres.

The natural philosophers of antiquity believed that the planets are not silent in their orbits. Setting aside the question of whether they move through air or through some finer medium like ether, it seemed logical that these great bodies should make a sound, just as moving bodies do on earth; and the many theories of the Harmony of the Spheres remain as attempts to specify what that sound could be, translated into the language of music.

There are two main schools of thought as to how this translation should be made. The first one assumes that the relative distances of the planets from the earth relate harmonically, as if they were different points on a string. This theory derives from Pythagoras’s school, in which the distance of the earth from the moon’s sphere was reckoned to be 126,000 stades. Taking this distance as equivalent to a whole-tone, the distances to the other planetary spheres were proportioned like the intervals of a diatonic scale. The second school holds that it is the motions of the planets that relate harmonically, their different rates of revolution corresponding to differences of pitch. These all presume a stationary and silent earth, though it was not certain whether the revolutions should be calculated relative to the earth, in which case Saturn, having furthest to travel, would move fastest, or relative to the zodiac, in which case Saturn would be the slowest planet, taking 30 years to make one circuit, and the moon, with its cycle of 28 days, the fastest.

There are other schemes, especially those of the Arab astronomers and the various interpreters of the “scale” of Plato’s Timaeus, but they need not concern us here. What results from every scheme prior to Kepler is that the planetary tones are derived from some existing scale or interval-sequence that cannot possibly be valid in any scientific, quantitative way, because the known proportions of either distances or motions are vastly different from the proportions of the tones used to represent them. This is where Kepler’s approach differed from all his predecessors’: his work of 1619 was the first time that a theory of celestial harmony was derived directly from astronomical observation.

Hitherto, these theories had almost unanimously assigned a single, unvarying tone to each planet, as one would expect to result from a perfect circular orbit. However, with an inspired leap of the imagination Kepler saw that the planetary tones must now vary, their pitch rising and falling in proportion to their acceleration and retardation. He calculated the exact amount by comparing the daily motion of a planet at perihelion with its daily motion at aphelion, expressed as degrees of a circle. This gave a simple proportion, which like all proportions could be translated into musical intervals by regarding the two terms as different string-lengths.

CONNECT

Thank You, Jessica.