But neither doth this pleasant conceit of the latter come near the truth, neither do the former attain perfect accuracy. However, they who will not allow the latter to depend upon Plato’s sentiments will yet grant the former to partake of musical proportions; so that, there being five tetrachords, called ὑπάτων, μέσων, συνημμένων, διεζευγμένων, and ὑπερβολαίων, in these five distances they place all the planets; making the first tetrachord from the Moon to the Sun and the planets which move with the Sun, that is, Mercury and Venus; the next from the Sun to the fiery planet of Mars; the third between this and Jupiter; the fourth from thence to Saturn; and the fifth from Saturn to the sphere of the fixed stars. So that the sounds and notes which bound the five tetrachords bear the same proportion with the intervals of the planets. Still further, we know that the ancient musicians had two notes called hypate, three called nete, one mese, and one paramese, thus confining their scale to seven standing notes, equal in number to the number of the planets. But the moderns, adding the proslambanomenos, which is a full tone in descent from hypate, have multiplied the scheme into the double diapason, and thereby confounded the natural order of the concords; for the diapente happens to be before the diatessaron, with the addition of the whole tone in the bass. Whereas Plato makes his addition in the upper part; for in his Republic he says, that every one of the eight spheres rolls about a Siren which is fixed upon each of the tuneful globes, and that they all sing one counterpoint without diversity of modulation, taking every one their peculiar concords, which together complete a melodious consort. These Sirens sing for their pleasure divine and heavenly tunes, and accompany their sacred circuit and dance with an harmonious song of eight notes. Nor was there necessity of a fuller chorus, in regard that within the confines of eight notes lay the first bounds and limits of all duple and triple proportions; the unit being added to both the even and odd numbers. And certainly from hence it was that the ancients raised their invention of nine Muses; of which eight were employed in celestial affairs, as Plato said; the ninth was to take care of things terrestrial, and to reduce and reform the inequality and confusion of error and jarring variance.