Harmonic Demonstrations

the Diapente fifth cannot contain any middle string that does not in some way offend the senses. After this, in the third place, follows the Diatessaron fourth between 4 & 3 in the natural order of numbers, which does not receive any mean middle interval that produces a good effect. When all these consonances are placed one after another upon an instrument in order, without placing any other string in between, they make a most grateful sound and sweet harmony. But if, by chance, in the low range the Diapason octave were to be intersected, such that in the low part the Diapente were heard, and in the high part the Diatessaron, immediately one would hear the harmony change form, and something not as pleasing as the first would be heard by the ear. And if one were to interpose a string between this Diapente so as to divide it into two parts, namely into a Ditone major third and a Semiditone minor third, and if the latter were placed in the high part and the former in the low part, then one would hear something that would cause great displeasure to the ear. This, however, is not the lowest degree of the unpleasing assembly of consonances, for there is something worse: and this happens when the Semiditone takes the place of the Ditone, and the latter takes the place of the Semiditone, and they are placed within the Diapente contrary to how they were before, namely that the Ditone takes the high place and the Semiditone the low. For then one would hear that extreme ruin which consonances gathered together can make. And I believe that all those who have judgment and have practice with organs can know this very well, because in large organs, when they are played fully, more so than in other instruments, such shaking is discovered, as is manifest to our M. Claudio, who plays them every day, as he said a little while ago. So it seems to me, Mr. Desiderio, that now you can understand wherein it consists, and what that difference you asked of me is.

DESI. In truth, with great profit and delight I have heard something that is very new to me. But tell me further, on your faith, why do these two intervals that you have lately named cause so much more ruin when placed in the low range than they do when they are situated in the high range?

GIOS. For two reasons: one, because the place of the Ditone and the Semiditone is not to be placed in the low range, but rather in the high. The other, because these two intervals, placed in the manner mentioned, are not located in order, according to their degrees and places, but rather to the contrary: since those intervals that are of greater proportion naturally want the lower place, and those of lesser proportion, conversely, the higher place. Nor will you ever find in the natural order of consonances that the Ditone follows the Semiditone toward the high range immediately; but you will find the contrary, that is, that the Ditone holds the lower place, and the Semiditone follows it immediately toward the high range. In such a way that such disorder arises from these causes, even though both of the two intervals are consonant.

DESI. Therefore, from what I see, the lack of accord that the parts of a composition sometimes make proceeds not only from the mixing of dissonances, which is sometimes done inside them, but from placing the consonances in them with bad order.

GIOS. It is so in fact.

ADRI. It has not, therefore, been beside the point that in my compositions I have avoided, as much as I could, placing such consonances in the low part, in the manner you have declared. And indeed, it seemed to me that they did not sound well, even though I did not know how to give any reason for it; but I heard that they did not fully satisfy my sense.

GIOS. There are also other observances, Master, in your compositions, which you have learned through the means of the sense, which are not of little importance; and even if you do not know how to state the reason for them, there are those who can state it for you. Now, to return to our first purpose, I say that the reason that moved the Pythagoreans, and Pythagoras before them, to say that all the intervals that were smaller than the Diatessaron were dissonant is this, in my judgment, and as I have declared to you: because they did not have knowledge of the degrees and proper places of the consonances, and in what manner they were to be disposed, and in what order. Wherefore, having known that those consonances that are smaller than the Diatessaron, such as the Ditone and the Semiditone, so grateful to us, generate dissonance rather than consonance when placed in the low part, because such a difference had not been recognized by them—that is, that when placed in their proper and natural places, they generate a grateful sound to the ear, and on the contrary an ungrateful one when outside of their natural places—they judged that they were dissonant in every way.