Harmonies Of The World

By Johannes Kepler
1619

TRANSLATED BY CHARLES GLENN WALLIS
This edition translated in 1939

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TABLE OF CONTENTS
PROEM
1. CONCERNING THE FIVE REGULAR SOLID FIGURES
2. ON THE KINSHIP BETWEEN THE HARMONIC RATIOS AND THE FIVE REGULAR FIGURES
3. A SUMMARY O
F ASTRONOMICAL DOCTRINE NECESSARY FOR SPECULATION INTO THE CELESTIAL
HARMONIES
4. IN WHAT THINGS HAVING TO DO WITH THE PLANETARY MOVEMENTS HAVE THE HARMONIC
CO
NSONANCES BEEN EXPRESSED BY THE CREATOR, AND IN WHAT WAY?
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], THE MAJOR AND THE MINOR
6. IN THE EXTREME PLANETARY MOVEMENTS THE MUSICAL MODES OR TONES HAVE SOMEHOW BEEN
EXPRESSED
7. THE UNIVERSAL CONSONANCES OF ALL SIX PLANETS, LIKE COMMON FOUR
–
PART COUNTERPOINT, CAN
EXIST
8. IN THE CELESTIAL HARMONIES WHICH PLANET SINGS SOPRANO, WHICH ALTO, WHICH TENOR, AND
WHICH BASS?
9. THE GENESIS OF THE ECCENTRICITIES IN THE SINGLE PLANETS F
ROM THE PROCUREMENT OF THE
CONSONANCES BETWEEN THEIR MOVEMENTS
10. EPILOGUE CONCERNING THE SUN, BY WAY OF CONJECTURE
PROEM
THE HARMONIES OF THE WORLD
by Johannes Kepler
Concerning the very perfect harmony of the celestial movements, and the genesis of eccentricities and the semidiam eters, and the periodic times from the same.
After the model of the most correct astronomical doctrine of today, and the hypothesis not only of Copernicus but also of Tycho Brahe, whereof either hypotheses are today publicly accepted as most true, and the Ptolemaic as outmoded.
I commence a sacred discourse, a most true hymn to God the Founder, and I judge it to be piety, not to sacrifice many hecatombs of bulls to Him and to burn incense of innumerable perfumes and cassia, but first to learn myself, and af terwards to teach others too, how great He is in wisdom, how great in power, and of what sort in
goodness. For to wish to adorn in every way possible the things that should receive adornment and to envy no thing its goods