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Harmonices Mundi
''Harmonices Mundi''〔The full title is ''Ioannis Keppleri (Harmonices ) mundi libri V'' (''The Five Books of Johannes Kepler's The Harmony of the World'').〕 (Latin: ''The Harmony of the World'', 1619) is a book by Johannes Kepler. In the work Kepler discusses harmony and congruence in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called "third law of planetary motion".〔Johannes Kepler, ''Harmonices Mundi'' (Harmony of the World ) (Linz, (Austria): Johann Planck, 1619), (p. 189. ) From the bottom of p. 189: ''"Sed res est certissima extactissimaque quod ''proportio qua est inter binorum quorumcunque Planetarum tempora periodica, sit præcise sesquialtera proportionis'' mediarum distantiarum, id est ''Orbium'' ipsorum; … "'' (But it is absolutely certain and exact that the ''proportion between the periodic times of any two planets is precisely the sesquialternate proportion'' (the ratio of 3:2 ) of their mean distances, that is, of the actual ''spheres'', … "
An English translation of Kepler's ''Harmonices Mundi'' is available as: Johannes Kepler with E.J. Aiton, A.M. Duncan, and J.V. Field, trans., ''The Harmony of the World'' (Philadelphia, Pennsylvania: American Philosophical Society, 1997); see especially (p. 411 ).〕
==History==
It is estimated that Kepler had begun working on ''Harmonices Mundi'' sometime near 1599, which was the year Kepler sent a letter to Maestlin detailing the mathematical data and proofs that he intended to use for his upcoming text, which he originally planned to name ''De harmonia mundi''. Kepler was aware that the content of ''Harmonices Mundi'' closely resembled that of the subject matter for Ptolemy’s ''Harmonica'', but was not concerned because the new astronomy Kepler would use, most notably the adoption of elliptic orbits in the Copernican system, allowed him to explore new theorems. Another important development that allowed Kepler to establish his celestial-harmonic relationships, was the abandonment of the Pythagorean tuning as the basis for musical consonance and the adoption of geometrically supported musical ratios; this would eventually be what allowed Kepler to relate musical consonance and the angular velocities of the planets. Thus Kepler could reason that his relationships gave evidence for God acting as a grand geometer, rather than a Pythagorean numerologist.〔Field, J. V. (1984). A Lutheran astrologer: Johannes Kepler. Archive for History of Exact Sciences, Vol. 31, No. 3, pp. 207-219.〕
The concept of musical harmonies intrinsically existing within the spacing of the planets existed in medieval philosophy prior to Kepler. Musica Universalis was a traditional philosophical metaphor that was taught in the quadrivium, and was often referred to as the “music of the spheres.” Kepler was intrigued by this idea while he sought explanation for a rational arrangement of the heavenly bodies.〔Voelkel, J. R. (1995). The music of the heavens: Kepler's harmonic astronomy. 1994. Physics Today, 48(6), 59-60.〕 It should be noted that when Kepler uses the term “harmony” it is not strictly referring to the musical definition, but rather, a broader definition encompassing congruence in Nature and the workings of both the celestial and terrestrial bodies. He notes musical harmony as being a product of man, derived from angles, in contrast to a harmony that he refers to as being a phenomenon that interacts with the human soul. In turn, this allowed Kepler to claim the Earth has a soul because it is subjected to astrological harmony.〔Field, J. V. (1984). A Lutheran astrologer: Johannes Kepler. Archive for History of Exact Sciences, Vol. 31, No. 3, pp. 207-219.〕
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