Dimostrationi Harmoniche

First.

Within the Perfect Fifthoriginal: "Diapente". An interval spanning five notes of a scale., no middle string can fall that does not, in some part, offend the sense. After this, in third place, follows the Perfect Fourthoriginal: "Diatessaron". An interval spanning four notes. between 4 and 3 in the natural order of numbers: which receives no middle note that produces a good effect. Thus, when all these consonances are placed one after the other upon an instrument in order—without placing any other string in between—they produce a most grateful sound and sweet harmony. But if, by chance, the Octaveoriginal: "Diapason". were to be divided in the low register in such a way that the Fifth was heard in the low part and the Fourth in the high part, one would immediately hear the harmony change its form, becoming something not quite so pleasing to the ear as the first arrangement.

And if, furthermore, a string were interposed within this Fifth which divided it into two parts—that is, into a Major Thirdoriginal: "Ditono". and a Minor Thirdoriginal: "Semiditono".—and the latter were placed in the high part and the former in the low part, then one would hear something that would bring great displeasure to the ear. Yet this is not the lowest degree of an unpleasing gathering of consonances, for one finds even worse. This occurs when the Minor Third comes to hold the place of the Major Third, and the Major Third the place of the Minor Third, and they were placed within the Fifth contrary to how they were before—that is, the Major Third held the high place and the Minor Third the low. For then one would hear that extreme ruin that consonances gathered together can make. I believe that all those who have judgment and practical experience with organs can know this very well. For on large organs, when they are played in full—more so than is done on other instruments—such a jarring clashing is revealed. This is manifest to our Master Claudio Claudio Merulo (1533–1604), a famous Italian composer and organist at St Mark's Basilica., who plays them every day (as he said a moment ago). So it seems to me, Lord Desiderio, that you can now understand what this consists of, and what the difference is that you previously asked of me.

DESI. In truth, I have heard something very new to me, with great benefit and delight. But tell me further, by your faith: why do these two intervals you just named cause such great ruin when placed in the low register, more than they do when situated in the high?

GIOS. For two reasons: the first, because the proper place for the Major and Minor Third is not in the low register, but rather in the high. The second, because these two intervals, when placed in the manner described, are not arranged in order according to their degrees and proper places, but rather the opposite. This is because those intervals which have a larger proportion naturally desire the lower place, and those of smaller proportion, conversely, the higher place. Nor will you ever find in the natural order of consonances that the Major Third follows immediately after the Minor Third toward the high register; rather, you will find the contrary—that is, the Major Third holding the lower place, while the Minor Third immediately follows it toward the high register. Thus, such disorder arises from these causes, even though both intervals are consonant.

DESI. Therefore, from what I see, the poor agreement that the parts of a composition sometimes make proceeds not only from the mixing in of dissonancesIntervals that sound unstable or clashing. that are occasionally placed within, but from placing the consonances themselves in a bad order.

GIOS. That is exactly the case.

ADRI. It was not, therefore, without purpose that in my compositions I have avoided, as much as I could, placing such consonances in the low register in the manner you have declared. Indeed, it seemed to me that they did not sit well, even though I did not know how to give any reason for it; I only heard that they did not fully satisfy my sense.

GIOS. There are also other observances, Sir, in our compositions which you have learned by means of the senses, and which are of no small importance. Though you may not know how to state the reason for them, there is no lack of those who can state it for you. Now, to return to our first purpose, I say: the reason that moved the Pythagoreans—and Pythagoras first—to say that all intervals smaller than a Fourth were dissonant is this, in my judgment, and as I have declared to you: because they had no knowledge of the degrees and proper places of the consonances, nor in what manner they ought to be disposed, nor in what order. Thus, having recognized that those consonances smaller than a Fourth—such as the Major and Minor Thirds, which are so pleasing to us—generate dissonance rather than consonance when placed in the low part, they did not recognize the difference: namely, that when placed in their proper and natural places, they generate a grateful sound to the ear, and conversely an ungrateful one when outside of their na—