the shortest; the next thirty days he adds a third part; to all the rest till the equinox he adds a half; and so by sextuple and triple distances he makes even the irregularity of time. Moreover, the Chaldaeans make the spring to hold the proportion of a diatessaron to autumn; of a diapente to the winter, and of a diapason to the summer. But if Euripides rightly divides the year, where he says, Four months the parching heats of summer reign, And four of hoary winter’s cold complain; Two months doth vernal pride the fields array, And two months more to autumn tribute pay, then the seasons shall be said to change in octave proportion. Others there are, who fancy the earth to be in the lowest string of the harp, called proslambanomenos; and so proceeding, they place the moon in hypate, Mercury and Venus in the diatoni and lichani; the sun they likewise place in mese, as in the midst of the diapason, a fifth above the earth and a fourth from the sphere of the fixed stars. 32. 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[197] 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.