They reckoned one tone from the earth to the moon, half a tone from the moon to Mercury, another half-tone to Venus, one tone and a half from Venus to the sun, one from the sun to Mars, a semitone from Mars to Jupiter, half a tone from Jupiter to Saturn, and a tone and a half from Saturn to the fixed stars; but these distances were not, as we shall see, universally agreed upon. According to Timaeus, the sphere of the fixed stars, which contains within it no principle of contrariety, being entirely divine and pure, always moves with an equal motion in the same direction from east to west. But the stars which are within it, being animated by the mixed principle, whose composition has been just explained, and thus containing two contrary forces, yield on account of one of these forces to the motion of the sphere of fixed stars from east to west, and by the other they resist it, and move in a contrary direction, in proportion to the degree with which they are endowed with each; that is to say, that the greater the proportion of the material to the divine force that they possess, the greater is their motion from west to east, and the sooner they accomplish their periodic course. Now the amount of this force depends on the matter they contain. Thus, according to this system, the planets turn each day by the common motion with all the heavens about the earth from east to west, but they also retrograde towards the east, and accomplish their periods according to their component parts. The additions which Plato made to this theory have always been a proverb of obscurity, and none of his commentators have been able to make anything of them, and very possibly they were never intended to. So far the harmony of the heavenly bodies has been explained with reference to numbers only, and we may add to this that they reckoned 126,000 stadia, or 14,286 miles, to represent a tone, which was thus the distance of the earth to the moon, and the same measurement made it 500,000 from the earth to the sun, and the same distance from the sun to the fixed stars. But Plato teaches in his _Republic_ that there is actual musical, harmony between the planets. Each of the spheres, he said, carried with it a Siren, and each of these sounding a different note, they formed by their union a perfect concert, and being themselves delighted with their own harmony, they sang divine songs, and accompanied them by a sacred dance. The ancients said there were nine Muses, eight of whom, according to Plato, presided over celestial, and the ninth over terrestrial things, to protect them from disorder and irregularity.