Harmonic Demonstrations

they were to him, his compositions, and how, through him, a very great part of those things which he had already composed had come to light, which had remained almost buried. And together, having discoursed with good purpose on many things concerning Music and our friendship, there arrived by chance a worthy and honorable foreign gentleman, a friend of M. Adrian, who had likewise come to visit him. This man greatly delighted in Music, but above every other thing, he desired to hear discussion of the things of Art and Science, for he had studied Philosophy for many years before, and had read many Greek and Latin authors who treated of Music. His name was Desiderio, and he was a Lombard by nation, from Pavia. Now, after a long discussion of various things done together, he having understood from what had been said who we were, the name of each of us, the surname, the homeland, and our particular profession, and we having also fully known him and informed ourselves of his qualities and conditions, this Gentleman, turning toward us, began a new reasoning in this manner.

DESI.: Truly I believe, M. Gioseffo, regarding the desire that I hold to be able to resolve some doubts that have been in my mind for many years, after I saw and studied your Harmonic Institutions together with many other books of Music, that I could not have stumbled upon a better [opportunity] than that which I have stumbled upon today. For, remembering many things, it seems to me that everything that I read in many authors, and that I continually hear musicians recall, generates in my mind such confusion that I myself do not know how to resolve myself on many things of that which I ought to hold and believe. And to mention one that makes me doubt much: I find that Pythagoras, denying that one could pass beyond the Quadruple the ratio 4:1, as you have said in Chapter 2 of the second part of the aforementioned Institutions, did not concede that those intervals which take their form from numbers that are greater than the Quaternary the number four were consonant. This opinion was held by many, because Euclid, Prince of Mathematicians, in his Introductory of Music, clearly manifests such intervals, saying: Διάφωνα δὲ τὰ ἐλάττονα τοῦ Διατεσσάρων, Δίεσις, Ἡμιτόνιον, Τόνος, Τριημιτόνιον, Δίτονον But the dissonances are those that are smaller than the Diatessaron: the Diesis, the Semitone, the Tone, the Trihemitone, the Ditone. Having already said: Σύμφωνα μὲν οὖν ἐστὶν Διατεσσάρων, Διαπέντε, Διαπα
σw͂ν, καὶ τὰ ὅμοια Therefore the consonances are the Diatessaron, the Diapente, the Diapason, and other similar ones. And Aristoxenus, an ancient musician, in Book 2 of the Musical Elements says that we sing many intervals that are smaller than the Diatessaron, but that they are all dissonant. Ptolemy also, at the beginning of Chapter 10 of Book 1 of his Music, calls the Diatessaron by the name of ἐλαχίστης, καὶ πρώτης συμφωνίας the smallest and first Consonance. Wherefore it is clearly seen that such a thing was held as true among them. And because I see in fact, and understand from you musicians that it is the contrary, I do not know in what manner I can believe that if Pythagoras and the others who followed him denied such a thing, he denied it simply, as the words sound to us. Nor does it seem to me that this has the likeness of truth, seeing that Pythagoras and the Pythagoreans were wise men, of great judgment and elevated wit, and they have had that good sense, as one can believe, that we have, with which they could verify whether the thing was in fact as they believed and held, concerning which I am strongly amazed. Therefore, I greatly desire to understand from you whence such a thing could be born, which for me is so difficult that I cannot help, when I remember it, but call it an error.

ADRI.: I too, for a long time now, have desired to understand this thing, since I hold firmly, as Signor Desiderio was saying, that the Ancients were not deprived of the sense of hearing, nor of judgment, but that they knew the good and the bad just as well as we know them. What say you of this, M. Francesco? Do you also believe that this is true?

FRAN.: I hold it for certain, Master, that the Ancients had as much knowledge of the good and the bad as we have. And perhaps, as those who applied themselves greatly to speculations, more than we do, they had their sense more purged; but for what reason they did this, I would be very grateful to learn from M. Gioseffo.

CLAV.: Understanding this thing would be of singular favor and contentment even to me. And I praise God for having caused me to stumble today upon this place.

GIOS.: Signor Desiderio, although this thing is very difficult and a burden too heavy for my shoulders...