The music of the heavens : Kepler's harmonic astronomy

Chapters 2-4 give pre-Keplerian background. Chapter 5 presents the polyhedral theory of planetary distances of Kepler's Mysterium cosmographicum of 1596. Chapter 7 discusses Kepler's reading of Ptolemy's work on celestial harmony. Chapter 8 gives an overview of Kepler's Harmonice mundi of 1619. Finally, half the book consists of chapter 9, which is a detailed analysis of book 5 of the Harmonice mundi. Now, musical harmony consists in simple numerical relationships, namely 1:2, 3:5, 5:8, 2:3, 3:4, 4:5, 5:6. The twelve numbers given by the extreme angular velocities of the six planets as perceived from the sun exhibit many harmonic interrelations. This is the point of attack for Kepler in his attempt to unveil the divine design of the universe. His crowning achievement is the deduction of these harmonies from a set of axioms based on basic harmonic principles and the regular polyhedra. The angular velocities thus being determined, Kepler also deduces the eccentricities of the planetary orbits. Aside from this main argument the Harmonice mundi contains several interesting side topics, such as "Kepler's third law" and a classification of "universal harmonies" (i.e. possible states of the solar system where the angular velocities of the planets are all in harmony). Valued today for its development of the third law of planetary motion, Harmonice mundi (1619) was intended by Kepler to expand on ancient efforts to discern a Creator's plan for the planetary system--an arrangement thought to be based on harmonic relationships. Challenging critics who characterize Kepler's theories of harmonic astronomy as "mystical," Bruce Stephenson offers the first thorough technical analysis of the music the astronomer thought the heavens made, and the logic that led him to find musical patterns in his data. In so doing, Stephenson illuminates crucial aspects of Kepler's intellectual development, particularly his ways of classifying and drawing inferences. Beginning with a survey of similar theories associating music with the cyclic motions of planets, from Plato to Boethius, the author highlights Ptolemy's Harmonics , a source of inspiration for Kepler's later work. Turning to Kepler himself, Stephenson gives an account of his polyhedral theory, which explains the number and sizes of the planetary orbits in terms of the five regular poly-hedral. He then examines in detail an early theory that relates the planets' vel-ocities to a musical chord, and analyzes Kepler's unpublished commentary on Ptolemy's Harmonics . Devoting most of his attention to Book Five of Harmonice mundi, in which Kepler elaborated on the musical structure of the planetary system, Stephenson lays important groundwork for any further evaluation of Kepler's scientific thought. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. Valued today for its development of the third law of planetary motion, Harmonice mundi (1619) was intended by Kepler to expand on ancient efforts to discern a Creator's plan for the planetary system - an arrangement thought to be based on harmonic relationships. Challenging critics who characterize Kepler's theories of harmonic astronomy as "mystical," Bruce Stephenson offers the first thorough technical analysis of the music the astronomer thought the heavens made, and the logic that led him to find musical patterns in his data. In so doing, Stephenson illuminates crucial aspects of Kepler's intellectual development, particularly his ways of classifying and drawing inferences. . Beginning with a survey of similar theories associating music with the cyclic motions of planets, from Plato to Boethius, the author highlights Ptolemy's Harmonics, a source of inspiration for Kepler's later work. Turning to Kepler himself, Stephenson gives an account of his polyhedral theory, which explains the number and sizes of the planetary orbits in terms of the five regular polyhedral. He then examines in detail an early theory that relates the planets' velocities to a musical chord, and analyzes Kepler's unpublished commentary on Ptolemy's Harmonics. Devoting most of his attention to book five of Harmonice mundi, in which Kepler elaborated on the musical structure of the planetary system, Stephenson lays important groundwork for any further evaluation of Kepler's scientific thought. Valued today for its development of the Third Law of Planetary Motion, "Harmonice mundi" (1619) was intended by Kepler to expand on ancient efforts to discern a Creator's plan for the planetary system - an arrangement thought to be based on harmonic relationships. Challenging critics who characterize Kepler's theories of harmonic astronomy as "mystical," Bruce Stephenson offers a thorough technical analysis of the music the astronomer thought the heavens made, and the logic that led him to find musical patterns in his data. In so doing, Stephenson illuminates crucial aspects of Kepler's intellectual development, particularly his ways of classifying and drawing inferences. Beginning with a survey of similar theories associating music with the cyclic motions of planets, from Plato to Boethius, the author highlights Ptolemy's "Harmonics", a source of inspiration for Kepler's later work. Turning to Kepler himself, Stephenson gives an account of his polyhedral theory, which explains the number and sizes of the planetary orbits in terms of the five regular polyhedral. He then examines in detail an early theory that relates the planets' velocities to a musical chord, and analyzes Kepler's unpublished commentary on Ptolemy's "Harmonics"