[48] Moreover the number four also comprehends the principles of the harmonious concords in music, that in fours, and in fifths,and the diapason, and besides this the double diapason from which sounds the most perfect system of harmony is produced. For the ratio of the sounds in fourths is as four to three; and in fifths as three to two; and in the diapason that ratio is doubled: and in the double diapason it is increased fourfold, all which ratios the number four comprehends. At all events the first, or the epistritus, is the ratio of four to three; the second, or the hemiolius, is that of three to two: the twofold ratio is that of two to one, or four to two: and the fourfold ratio is that of four to one.