connection between music and astronomy stimulated the imagination of Johannes Kepler as he devoted much of his time after publishing the Mysterium Cosmographicum (Mystery of the Cosmos), looking over tables and trying to fit the data to what he believed to be the true nature of the cosmos as it relates to musical sound. In 1619, Kepler published Harmonices Mundi (literally Harmony of the Worlds), expanding on the concepts he introduced in Mysterium and positing that musical intervals and harmonies describe the motions of the six known planets of the time. He believed that this harmony — while inaudible — could be heard by the soul, and that it gave a "very agreeable feeling of bliss, afforded him by this music in the imitation of God." In Harmonices, Kepler — who took issue with Pythagorean observations — laid out an argument for a Christian-centric creator who had made an explicit connection between geometry, astronomy, and music, and that the planets were arranged intelligently. Harmonices is split into five books, or chapters. The first and second books give a brief discussion on regular polyhedron and their congruences, reiterating the idea he introduced in Mysterium that the five regular solids known about since antiquity define the orbits of the planets and their distances from the sun. Book three focuses on defining musical harmonies, including consonance and dissonance, intervals (including the problems of just tuning), their relations to string length which was a discovery made by Pythagoras, and what makes music pleasurable to listen to in his opinion. In the fourth book, Kepler presents a metaphysical basis for this system, along with arguments as to why the harmony of the worlds appeals to the intellectual soul in the same manner that the harmony of music appeals to the human soul. Here, he also uses the naturalness of this harmony as an argument for heliocentrism. In book five, Kepler describes in detail the orbital motion of the planets and how this motion nearly perfectly matches musical harmonies. Finally, after a discussion on astrology in book five, Kepler ends Harmonices by describing his third law, which states that — for any planet — the cube of the semi-major axis of its elliptical orbit is proportional to the square of its orbital period. In the final book of Harmonices, Kepler explains how the ratio of the maximum and minimum angular speeds of each planet (i.e., its