Harmonice Mundi by Johannes Kepler
The three laws of motion:
- the planets move in elliptical, not circular, orbits
- their speed is greatest when nearest the sun
- the sun and planets form an integrated system
Musical harmony as we know it exists in simple integer relationships. In a system of just intonation those relationships can be seen in the movement of celestial bodies. From the viewpoint of the sun, Saturn travels 135 seconds in a single day when it is closest and 106 seconds in a day when it is farthest due to the planet’s elliptical orbit. When Kepler simplified the ratio of Saturn’s apsides, 135:106, he came up with 5:4 - a pure major third. See the second picture for an example. He found that Mars orbited as a perfect fifth, Jupiter a minor third and so on…. these are his universal harmonies - the same intervals that are common in popular music around the world today.
[Photo: NASA’s Voyager 1]
[Photo 2: Carl Sagan’s Cosmos]
