But these things have perhaps had more than sufficient time spent on them. This, however, is evident, that they properly attribute to this God the number of five, saying that it sometimes of itself produces itself like fire, and other whiles the number of ten, like the world. But do we think that this number is not also concerned with music, which is of all things most acceptable to this God For the chiefest operation of harmony is, as one may say, about symphonies. Now that these are five and no more, reason convinces even him who will by his senses without reasoning make trial either on strings or pipe-holes. For all these accords take their original in proportions of number; and the proportion of the symphony diatessaron is sesquitertial, of diapente sesquialter, of diapason duple, of diapason with diapente triple, and of disdiapason quadruple. But as for that which, transcending all measures, the musicians add to these, naming it diapason with diatessaron, it is not fit we should receive it, gratifying the unreasonable pleasure of the ear against proportion, which is as the law. I may therefore let pass the five positions of the tetrachords, and also the five first,—whether they are to be called tones, tropes, or harmonies,—according to the changes of which by rising or falling, either to more or less, the rest are bases or trebles. And, whereas there are many or rather infinite intervals, are not five of them only used in music, to wit, diesis, hemitonion, tons, triemitonion, and ditonon? Nor is there in the voice any other space, either greater or less, that, being distinguished by base or treble, comes into melody.