Author: Doni, Giovanni Battista - manuscripts of italian music theory ...

On the specific differences of these three genera chapter
From the division of each genus which we have seen made in the tetrachords one can
say very probably that the difference and hallmarks of these three sorts of melody
consists in this: in the Diatonic, the fact that there are two adjacent tones; in the
chromatic, that there are two semitones, and in the Enharmonic, that there are two
Diesis. I mean that this happens in that type of Harmony which uses equal intervals,
as it is the case in the lute and in the viol, [--] and in which the ancients give
their examples, albeit in practice then, as we will see, the perfect harmony was used,
namely the one which distinguishes between larger and smaller tones and semitones.
In this Harmony the larger Semitone indicates the Diatonic, because it is its smallest
interval, and for the same reason the smallest Semitone is indicative of the Chromatic,
and the Diesis of the Enharmonic. In fact, the Chromatic does not accept the diesis
(which we always understand as enharmonic) nor the Diatonic does accept it, nor the
minor semitone. However, if we consider the third interval, which is the largest and
highest, equally we can say that the tone belongs specifically to the Diatonic, the
Semiditono to the Chromatic and the Ditone to the Enharmonic. We can also say that
the Diatessaron denotes the Diatonic in particular, not so much because one finds in it
those three intervals which derive from the first division of the last consonance of the
Ditone and Semiditone, namely, by dividing the Ditone firstly into larger and smaller
Tone and the Semiditione into major Tone and major Semitone, I say, not so much for
this reason, as Salinas maintains, but because the diatessaron was the smallest
consonance at the time when the Diatonic was the only known genus. I really hold for
certain that the fact that Chromatic and the Enarmonic began to be used generated the
opportunity to use the Ditone and Semiditone as consonances (albeit perhaps they did
not call them as such) [--] and to know them as such with the aid of the ear. I am
drawn to believe, because it is very plausible, that the larger Semitone was introduced
in singing when these two genera were first used, and it was introduced undivided in
the Chromatic and divided in the Enharmonic. From this it follows, consequently, that
the remaining part of the tetrachord is a ditone, that is really a consonance and is
composed by adding the smaller semitone to the larger, and the result is the
semiditone which is also consonant, while, as I said above, the two genera, which one
maintains that were sung in those most ancient times, were not suited to it very well.
Now, since the chromatic is based on the larger Tone and the Enharmonic on the
smaller Semitone, I do not know how to square this with what concerns the chromatic,
since, if we divide the larger tone into two semitones, what is left over is a minor third
shortened by a comma, and therefore dissonant. I believe that that division does not
suit the Chromatic, otherwise a consonance, which is its own, would be taken away.
Since the larger semitone and the smaller one, as Zarlino demonstrates very well
make up the smaller Tone and not the larger, why should one base the chromatic
genus more in this one than in that one? Now, as to the observation made by Salinas
that the 9, 16 and 25, which are the numbers of the notes [-70-] of these three genera
according to the modern division the numbers 3, 4 and 5 as their roots, of which the
third is equivalent to the other two because of that famous proposition by Euclid
which is the forty-seventh of the book, and that the nine Diatonic sounds compared to
the eight give the proportion of the larger tone 9/8 and the 16 of the chromatic
compared to the 15 give the proportion of the larger Semitone 16/15 and, finally, that
the 25 of the Enharmonic compared to the 24 create the proportion 25/24 of the
smaller Semitone, they are speculations which are more beautiful than useful, and
therefore they have been mentioned by me only in passing.