Kepler's Singular Harmony

In George Gibson and Ian Johnston's article on the physics of music ( Physics Today, January 2002, page 42), box 2 on Johannes Kepler's "The Harmonies of the World" contains two interesting errors. Because a final s on a Latin word normally designates a plural, at first glance the title of Kepler's Harmonices mundi libri V suggests the translation "harmonies." However, Kepler was being erudite, taking harmonice as a Greek word and giving it the Greek genitive singular ending. Because he passionately believed in the unity of the cosmos, he used the singular form; for him the title was Five Books on the Harmony of the World.

In book 5, chapter 3, Kepler stated his newly discovered harmonic law as the constant proportion between the cube of the planet's mean distance from the Sun and the square of its period. Concerning his "wonderful speculations," he wrote in his preface to book 5,

I yield freely to the sacred frenzy; I dare frankly to confess that I have stolen the golden vessels of the Egyptians to build a temple for my God far from the bounds of Egypt. If you pardon me, I shall rejoice; if you reproach me, I shall endure. The die is cast, and I am writing the book--to be read either now or by posterity, it matters not. It can wait a century for a reader, as God himself has waited six thousand years for a witness.

Incidentally, Kepler did not call that harmonic relationship a "law" or single out three particular relationships. The idea of a "law of nature" was introduced into English when Robert Boyle used the expression decades later. "Kepler's laws" were apparently first selected and numbered by the French astronomer Joseph-Jérôme de Lalande in his Abrégé d'astronomie of 1774.