Harmonices Mundi
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Harmonices Mundi (Latin: The Harmony of the Worlds, 1619) is a book by Johannes Kepler. It attempts to explain proportions and geometry in the planetary motions and the astrological aspects by relating them to harmonics (musical scales and intervals) [1] (also see Musica universalis). Kepler's The Harmony of the World is divided into five long chapters: the first is on regular polygons; the second is on the congruence of figures; the third is on the origin of harmonic proportions; the fourth on harmonic configurations in astrology; and the fifth on the harmony of the motions of the heavens.
According to Kepler, each planet produces musical tones during its revolution about the Sun, and the pitch of the tones varies with the angular velocities of those planets as measured from the Sun. Some planets "sing" relatively constant tones: for example, the Earth only varies a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion, and Venus only varies by a tiny 25:24 interval. Kepler explains the reason for the Earth's small harmonic range:
- The Earth sings Mi, Fa, Mi: you may infer even from the syllables that in this our home misery and famine hold sway.
At very rare intervals all of the planets would sing together in 'perfect concord': Kepler proposed that this may have happened only once in history, perhaps at the time of creation.
In his previous book Astronomia nova, Kepler had put forward the first two laws of planetary motion. The third law, namely the proportionality of the cube of the average distance of a planet from the Sun and the square of the length of its year, was set out in Chapter 5 of this book, immediately after a long digression on astrology.
References
- Johannes Kepler, The Harmony of the World. Tr.: Dr Juliet Field. Pub. by The American Philosophical Society, 1997. ISBN 0-87169-209-0
- Johannes Kepler, The Harmony of the World. Tr. Charles Glenn Wallis. Chicago: Great Books of the Western World. Pub. by Encyclopedia Britannica, Inc., 1952.
- "Johannes Kepler," in The New Grove Dictionary of Music and Musicians, Ed. Stanley Sadie. 20 vol. London, Macmillan Publishers Ltd., 1980. ISBN 1-56159-174-2
External links
- Kepler's Harmonices Mundi, part of a site on Kepler's process of discovery