68.1 Keplers Harmony of the Spheres

"Keplers De Harmonice Mundi is Keplers explanation of the Music of the Spheres. The whole basis of the treatise is Keplers conviction that the various parts of the Universe are arranged in accordance with abstract notions of the beautiful and harmonious; yet it is in this treatise he will set forth his third law of planetary motion.

The law is the result of Keplers long attempt to relate musical harmony to planetary motion and, more specifically, to find a 'musically harmonious' relation between the distances of the planets from the sun. The distances vary as the planets revolve around the sun, and so Keplers first calculations were based on the greatest and least distances. When calculations in distances failed to produce a concord, Kepler turned his attention to the angular velocities of the planets. (Velocities and distances are related, since the closer a planet approaches the sun, the greater its angular velocity with respect to the sun).

Kepler associated the varying angular velocity of each planet with a musical interval, letting the two outer notes of the interval represent the greatest and least velocities. Then he put each planets interval into a different pitch register, which was determined by the planets average distance from the sun. Next he tried to relate the average angular velocities to the average distances from the sun. When this approach did not disclose Gods harmony, Kepler substituted period of revolution for the average angular velocity.

Here he found the relation he had been seeking. Keplers third law is usually stated as a mathematical formula: T^2 / D^3 = K where T is the planets period of revolution, D is the average distance from the sun and K is a constant. The values of T and D are known for the earth. T is one year and D is 93 million miles. Therefore K can be compute, so that one can compute any other planets average distance from the sun if the period of revolution is known or the period of revolution if the average distance is known. The formula looks antiseptic but like so much of mathematics it springs from the aesthetic power of the natural order. Essentially it is this same aesthetic power that lies at the root of musics relation to number".

68.2.1

Scientific American
Unknown Source.

(Note: Another method was found to calculate planet position by use of harmonic numbers found and derived from Mayan astronomical calculations).

See David Wilcox, Part 11 and

Maurice Chatelain's discovery of The Nineveh Constant (David Wilcock)

68.3 Kepler, Johannes, Planet Aphelion / Perihelion

"The seventeenth-century astronomer, Johannes Kepler, continued and expanded upon earlier demonstrations of actual musical relationships among the spheres. By computing the theoretical musical intervals according to the angular velocities of the planets from the sun, he proposed the following proportions as demonstrations of world harmony of which the musical harmony is the expression:

1. Saturn
at aphelion 1' 46'' a.
at perihelion 2' 15'' b.

2. Jupiter
at aphelion 4' 30'' c.
at perihelion 5' 30'' d.

3. Mars
at aphelion 26' 14'' e.
at perihelion 38' 1'' f.

4. Earth
at aphelion 57' 3'' g.
at perihelion 61' 18'' h.

5. Venus
at aphelion 94' 50'' i.
at perihelion 97' 37'' k.

6. Mercury
at aphelion 164' 0'' l.
at perihelion 384' 0'' m.

68.4.1
68.5.1 - Number 384

Employing these diurnal movements of the planets in their orbits, which, Kepler points out, are apparent from the viewpoint at the sun, we then arrive at the harmonies between two planets:

Diverging- a/d = 1/3
Converging- b/c = 1/2 Saturn-Jupiter;

Diverging- c/f = 1/8
Converging- d/e = 5/24 Jupiter-Mars;

Diverging- e/h = 5/12
Converging- f/g = 2/3 Mars-Earth;

Diverging- g/k = 3/5
Converging- h/i = 5/8 Earth-Venus;

Diverging- i/m = 1/4
Converging- k/l = 3/5 Venus-Mercury.

Kepler noted, moreover, that because of the eccentricities of the orbits, there were variations in the derived orbits, and, consequently, he presumed from the ratios given in the first section of this chart (which has been separated into three parts for clarity of presentation, the note being held until the last part), that certain concordances were present between the extremes of the apparent movements of the single planets. By this means he arrived at the third section of his calculations, the harmonies between the movements of each planet itself- that is, the harmony within the movement of each planet between its aphelion and perihelion extremes of distance from the sun":

Saturn 1' 48'' : 2' 15'' = 4 : 5, a major-third;
Jupiter 4' 35'' : 5' 30'' = 5 : 6, a minor-third;
Mars 25' 21'' : 38' 1'' = 2 : 3, a fifth;
Earth 57' 28'' : 61' 18'' = 15 : 16, a semi-tone;
Venus 94' 50'' : 98' 47'' = 24 : 25, a diesis;
Mercury 164' 0'' : 394'' 0'' = 5 : 12, an octave and minor-third.

(Note: Typo, 394 possibly should be 384 in above table).

Since, in the course of a revolution, a planets' velocity would change, this theoretical tone would run through the entire range of the interval between the extremes already shown. Venus' almost circular orbit Kepler showed as possessing a single note, whereas the much more elliptical course of Mercury produces a much wider progression. These theoretical harmonies are given in modern musical notation by Mr. Elliott Carter, Jr., as shown below:

68.6 Diagram. Planets and their Theoretical Musical Notes

It goes beyond our needs in this study to attempt to delve into the complicated astronomical and mathematical calculations by which Kepler arrived at the basis for his theories. These are to be found in most of his works passim, and they are particularly developed in the Epitome of Copernican Astronomy and in The Harmonies of the World".

The Celestial Journey and the Harmony of the Spheres.
409.H37 H35

Impossible Correspondence Index