The Harmony of the World
The Harmony of the World: Book V – XLII. Proposition – By Joahannes Kepler [1571-1630]
Kepler’s Harmonices Mundi
The greater common proportion of Mars and the Earth, or that of their diverging motions, was necessarily made 54:125, less than the harmony 5:12 confirmed by the a priori arguments.
For Mars`s own proportion had to be a diapente, from which a diesis was removed, by the previous proposition. However, the common proportion of the converging motions of Mars and the Earth, or the lesser common proportion, had to be a diapente, 2:3, by XV. Last, the Earth’s own proportion is a doubled diesis, from which a comma has been removed, by XXVI and XXVIII. Now of these elements elements is composed the greater proportion, or that of the diverging motions, of Mars and the Earth; and it comes to two diapentes [or 4:9, that is 108:243] together with one diesis which is mutilated of a comma, that is together with 243:250. That is, it comes to 198:250, or 54:125, that is 608:1500. But that is less than 625:1500, that is, than 5:12, by the factor of 608:625, and that is nearly 36:37, less than the smallest melodic interval.