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.
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