Harmonice Mundi (Latin: Harmony of the Worlds, 1619) is a book by Johannes Kepler. It attempts to explain proportions and geometry in planetary motions by relating them to musical scales and intervals.

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 many infer even from the syllables that in this our home misery and famine obtain.

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 Harmonies of the World. Tr. Dr Juliet Field. pub., by American Philosophical Society. 1997 ISBN 0871692090
• Johannes Kepler, The Harmonies 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 1561591742

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