In 1618 Johannes Kepler completed his book Harmonics Mundi
(Harmony of the Worlds). In Libri V (Chapter Five) of this book
(published in 1619) he proposed an idea about the motion on the
planets which was to lead eventually to his famous Third Law.
Kepler had found what he believed to be a real harmonic
relationship between the maximum and minimum velocities of
planets about the Sun which went much further than the medieval
philosophers vague ideas about the ‘music of the spheres’.
He found that the ratio of the maximum to minimum
velocity of a planet about the Sun was a harmonic
proportion. In other words they were in the same ratios as
well known intervals in music. For example that for the
Earth is 16:15 (a semitone) for Jupiter 6:5 (almost a
tone), for Saturn 5:4 (a third) and for Venus a mere 25:24
(called a diesis in music).
Kepler called these ‘silent harmonies’ and Giorgio Abetti
in his book ‘History of Astronomy’ writes that ‘only the
Sun could hear this celestial music’.
Jupiter - a tone Saturn - a third Earth - a semitone
Unfortunately, or perhaps not, these ideas did not work for all the planets but the result of the
‘failure’ of this idea was to be Kepler’s Third Law of planetary motion.