Mi 384 + 1/8 = 432 Re 432 + 1/8 = 486 Ut 486 : 512 : : 243 : 256 Si 512 + 1/8 = 576 La 576 + 1/8 = 648 Sol 648 + 1/8 = 729 Fa 729 : 768 : : 243 : 256 Mi 768 + 1/8 = 864 Re 864 + 1/8 = 972 Ut 972 : 1024 : : 243 : 256 Si 1024 + 1/8 = 1152 La 1152 + 1/8 = 1296 Sol 1296 + 1/8 = 1458 Fa 1458 : 1536 : : 243 : 256 Mi 1536 + 1/8 = 1728 Re 1728 + 1/8 = 1944 Ut 1944 : 2048 : 243 : 256 Si 2048 + 139 = 2187 Si 2 2187 : 2304 : : 243 : 256 La 2304 + 1/8 = 2592 Sol 2592 + 1/8 = 2916 Fa 2916 : 3072 : : 243 : 256 Mi 3072 + 1/8 = 3456 Re 3457 + 1/8 = 3888 Ut 3888 + 1/8 = 4374 Si 4374 : 4608 : : 243 : 256 La 4608 + 1/8 = 5184 Sol 5184 + 1/8 = 5832 Fa 5832 : 6144 : : 243 : 256 Mi 6144 + 417 = 6561 Mi 2 6561 : 6912 : : 243 : 256 Re 6912 + 1/8 = 7776 Ut 7776 + 1/8 = 8748 Si 8748 : 9216 : : 243 : 256 La 9216 + 1/8 = 10368 Sol 10368 = 384 + 27 The empyreal heaven. Sum of all the terms, 114,695. This series they considered a complete one, because by taking the terms in their proper intervals, the last becomes 27 times the original number, and in the school of Pythagoras this 27 had a mystic signification, and was considered as the perfect number. The reason for considering 27 a perfect number was curious. It is the sum of the first linear, square, and cubic numbers added to unity. First there is 1, which represents the point, then 2 and 3, the first linear numbers, even and uneven, then 4 and 9, the first square or surface numbers, even and uneven, and the last 8 and 27, the first solid or cubic numbers, even and uneven, and 27 is the sum of all the former. Whence, taking the number 27 as the symbol of the universe, and the numbers which compose it as the elements, it appeared right that the soul of the universe should be composed of the same elements. On this scale of distances, with corresponding velocities, they arranged the various planets, and the universe comprehended all these spheres, from that of the fixed stars (which was excluded) to the centre of the earth. The sphere of the fixed stars was the common envelope, or circumference of the universe, and Saturn, immediately below it, corresponded to the thirty-sixth tone, and the earth to the first, and the other planets with the sun and moon at the various harmonic distances.