3. A Summary Of Astronomical Doctrine Necessary : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 3. A SUMMARY OF ASTRONOMICAL DOCTRINE NECESSARY FOR SPECULATION INTO THE CELESTIAL HARMONIES First of all, my readers should know that the ancient astronomical hypotheses of Ptolemy, in the fashion in which they have...
8. In The Celestial Harmonies Which Planet : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], p. 1049 8. IN THE CELESTIAL HARMONIES WHICH PLANET SINGS SOPRANO, WHICH ALTO, WHICH TENOR, AND WHICH BASS? Although these words are applied to human voices, while voices or sounds do not exist in the heavens...
Title Page : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], THE HARMONIES OF THE WORLD BY JOHANNES KEPLER TRANSLATED BY CHARLES GLENN WALLIS Annapolis, The St. John's Bookstore [1939] Scanned , April 2007. Proofed and formatted by John Bruno Hare. This text is in the public...
6. In The Extreme Planetary Movements : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 6. IN THE EXTREME PLANETARY MOVEMENTS THE MUSICAL MODES OR TONES HAVE SOMEHOW BEEN EXPRESSED [294] This follows from the aforesaid and there is no need of many words; for the single planets somehow mark the pitches...
10. Epilogue Concerning The Sun : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 10. EPILOGUE CONCERNING THE SUN, BY WAY OF CONJECTURE 1 From the celestial music to the hearer, from the Muses to Apollo the leader of the Dance, from the six planets revolving and making consonances to the Sun...
7. The Universal Consonances Of All Six Planets : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 7. THE UNIVERSAL CONSONANCES OF ALL SIX PLANETS, LIKE COMMON FOUR-PART COUNTERPOINT, CAN EXIST [295] But now, Urania, there is need for louder sound while I climb along the harmonic scale of the celestial movements...
2. On The Kinship Between The Harmonic Ratios : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 2. ON THE KINSHIP BETWEEN THE HARMONIC RATIOS AND THE FIVE REGULAR FIGURES [273] This kinship ["cognatio"] is various and manifold; but there are four degrees of kinship. For either the sign of kinship is taken...
Proem : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], p. 1009 THE HARMONIES OF THE WORLD BY JOHANNES KEPLER "Concerning the very perfect harmony of the celestial movements, and the genesis of eccentricities and the semidiameters, and the periodic times from the same"...
5. In The Ratios Of The Planetary Movements : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 5. IN THE RATIOS OF THE PLANETARY MOVEMENTS WHICH ARE APPARENT AS IT WERE TO SPECTATORS AT THE SUN, HAVE BEEN EXPRESSED THE PITCHES OF THE SYSTEM, OR NOTES OF THE MUSICAL SCALE, AND THE MODES OF SONG [GENERA CANTUS]...
1. Concerning The Five Regular Solid Figures : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 1. CONCERNING THE FIVE REGULAR SOLID FIGURES [271] It has been said in the second book how the regular plane figures are fitted together to form solids; there we spoke of the five regular solids, among others...
9. The Genesis Of The Eccentricities : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 9. THE GENESIS OF THE ECCENTRICITIES IN THE SINGLE PLANETS FROM THE PROCUREMENT OF THE CONSONANCES BETWEEN THEIR MOVEMENTS Accordingly, since we see that the universal harmonies of all six planets cannot take place by...
Untitled : Nature, which is never not lavish of herself, after a lying-in of two thousand years, has finally brought you forth in these last generations, the first true images of the universe. By means of your concords of various voices, and through your ears, she has whispered to the human mind, the favorite...
4. In What Things Having To Do With The Planetary : * "Harmonies of the World", by Johannes Kepler, tr. Charles Glenn Wallis [1939], 4. IN WHAT THINGS HAVING TO DO WITH THE PLANETARY MOVEMENTS HAVE THE HARMONIC CONSONANCES BEEN EXPRESSED BY THE CREATOR, AND IN WHAT WAY? Accordingly, if the image of the retrogradation and stations is taken away...
