KD, and their sounds, there will be a sesquioctave ratio. The sound of the chord LD is now called _mi_; but the interval which remains between the chord LD and the chord HD has not a sesquioctave ratio, but less than it almost by half, and therefore an interval of this kind was called a semitone, and also diesis or a division. But that interval which remains between the points F and E they divided after the same manner, as the space between C and H was divided, and they again found the same sounds. Let those divisions be marked by the points M and N; and here, also, between N and E, or between _mi_ and _fa_, there is in like manner another semitone. These eight sounds, therefore, are _ut_, _re_, _mi_, _fa_, _sol_, _re_, _mi_, _fa_, which compose the whole diapason. For as we have before observed, between _ut_ and the last _fa_ is the consonance diapason, or between the chord CD or AB, and the chord ED. But from the intervals which are between the sounds there are two semitones, viz. one between _mi_ and _fa_, denoted by the letters L, N, and the other between the last _mi_ and _fa_, denoted by the letters N, E. The remaining five intervals are entire tones. It must, also, be observed, that from _ut_ to the first _sol_ is the consonance diapente, which contains three tonic intervals, and one semitone; nevertheless in all there are five sounds, _ut_, _re_, _mi_, _fa_, _sol_. “Again, from _sol_ to the last _fa_ there are four sounds, _sol_, _re_, _mi_, _fa_, which are perfectly similar to the first four, _ut_, _re_, _mi_, _fa_. Nevertheless these are more grave, but those are more acute. And as from _ut_ to the first _fa_ is the diatessaron, so likewise from _sol_ to the last _fa_ is another diatessaron, from which, in the last place, it must be observed, it follows that the two consonances diatessaron and diapente constitute the whole diapason; or that the diapason is divided into one diatessaron, and one diapente. For from _ut_ to _sol_ is the diapente, but from _sol_ to the last _fa_ is the diatessaron. This will also be the case if we should say that from _ut_ to the first _fa_ is the diatessaron, as is evident from the division of the chord; but from the first _fa_ to the last _fa_ is the diapente, as is evident from the four intervals of the chord, three of which are tones, and the remaining interval is a semitone, which also in the other diapente were contained between _ut_ and _sol_.