Harmonic Demonstrations

...animal, rational and mortal, which are the essential things of Man. The second is that with which, wishing to make someone understand what Man is—not knowing or not wishing to express his essential things—we say: that he is a political animal, of upright stature, and other similar things, which do not explain the nature of Man.

CLAV. I have understood the difference.

GIOS. It is very true that often one is taken for the other, because sometimes a Definition is taken in place of a Description, and at times the latter in place of the former, regarding the word; and it is called a Definition without any difference, even though as to the being of the thing, it is otherwise.

ADRI. Which of these two is posited in the Demonstration?

GIOS. The first, as you will see.

FRAN. Resolve a doubt for me, and then continue. If for one single thing (as I have often heard said) there is only one definition, how does it come to be that at times not only one is found, but also more?

GIOS. A fine doubt indeed. However, take heed that it arises from this: that they are not properly Definitions, but Descriptions. Therefore, even if a thing cannot be defined more than once, it can nevertheless be described many times, because it carries with it many accidents. Hence, such a proposal is not true in this case, but it is indeed true in perfect Definitions, because if it were otherwise, such a proposal would be false.

CLAV. From what does it come, then, that in chapter 12 of the Second part of the Institutioni, you have posited two definitions of Consonance?

GIOS. I am very pleased that your doubting returns to the purpose of what I wished to say. Therefore, note that the Definition is found to be of three sorts. The first is called Material, and it is that which contains the matter which enters into the defined thing, just as if I wished to define Man and say what he was, I would say: that he is a thing composed of flesh, bones, nerves, and other similar things that enter into his material composition. The Second is called Formal, and it is that which contains the form of the thing that is defined, just as if I were to say: Man is a rational animal, inasmuch as Rationality is the proper and true form of Man. But the third is called Final, and it is that which contains and explains the end of the thing, just as when I might say: Man is a rational and mortal animal, capable of Beatitude, in such a way that Beatitude is the end of Man.

ADRI. Is there any definition found that contains all these three things?

GIOS. You know well.

ADRI. Say one, and then continue with what you please.

GIOS. The Definition that contains each of these things will be: when I wish to define some thing, such as Consonance, and I will posit in its definition the sounds, the reason of Numbers, and what it can do; such as to say: Consonance is a ratio of Numbers, contained by two sounds or voices, one low and the other high, which comes pleasantly to our hearing.

ADRI. That stands very well, since (as you have said at other times) the Sounds or Voices are the matter; the Ratio of Numbers the form; and the pleasant coming to the hearing is the end of the Consonance.

Inst. 2. part. c. 8 & 12.

DESI. Tell us by your faith: does this Consonance have another end?

GIOS. It certainly does, and you will be able to remember it from what you have read, such as moving the senses, in the manner that Harmony has of delighting and also of inducing diverse passions in us.

DESI. That is the case.

FRAN. I believe it would be good if you now moved further ahead, because I think we understand all these things well.

CLAV. It will be good, because if anything difficult occurs, we will go on asking you about it.

DESI. Do you perhaps give us this license, M. Gioseffo?

GIOS. For what reason would you want me not to give it to you? I am here to satisfy you; hence, in doing so, you will do me the greatest pleasure. Now then, so as not to lose any time, I say that, since the Subject of Music is the sonorous Number, and one cannot have any true knowledge of the quantity of sounds except by the means of sonorous bodies—which are the strings, which are quantities that are measured—and one cannot have any Science of the intervals except by way of the measurement of those bodies (that is, from the measurement of two sonorous bodies, or truly of one at least divided into many parts), it is necessary that a certain proportion of low sound and high sound intervene between them. Hence, by the comparison of the quantity of the string that gives the low sound with that which renders the high sound, we say that Music is subject to Quantità relata related quantity, by means of which we can, with diverse methods, demonstrate all those things that are demonstrable in Music. But to have knowledge...