[107] [cap.37] But this number is not only a perfecter of things, but it is also, so to say, the most harmonious of numbers; and in a manner the source of that most beautiful diagram which describes all the harmonies, that of fourths, and that of fifths, and the diapason. It also comprises all the proportions, the arithmetical, the geometrical, and moreover the harmonic proportion. And the square consists of these numbers, six, eight, nine, and twelve; and eight bears to six the ratio of being one third greater, which is the diatessaron of harmony. And nine bears to six the ratio of being half as great again, which is the ratio of fifths. And twelve is to six, in a twofold proportion; and this is the same as the diapason.