Discourse.

The text begins mid-sentence, completing the definition of "Man" from the previous page. ...rational and mortal animal original: "animale rationale & mortale": which are the essential things of Man. The second type of explanation is that which, when one wishes to make another understand what a Man is—either not knowing or not wishing to express his essential qualities—we say: he is a political Animal, upright in stature, and other similar things which do not fully explain the nature of Man.

CLAV. I have understood the difference.

GIOS. It is certainly true that many times one is taken for the other; because sometimes a Definition is used in place of a Description, and at times the latter in place of the former, as far as the word is concerned. They are both called "Definition" without distinction, even though in the essence of the thing it is otherwise.

ADRIA. Which of these two is used in a Demonstration? In Renaissance logic, a "demonstration" is a formal proof that leads to certain knowledge.

GIOS. The first, as you shall see.

FRAN. Clarify a doubt for me, and then continue. If for a single thing (as I have heard many times) there is only one definition, how is it that sometimes one finds not just one, but even more?

GIOS. A truly fine doubt. However, take note that this arises because they are not properly Definitions, but Descriptions. For although a thing cannot be defined more than once, it can nonetheless be described many times, because it carries with it many accidents In philosophy, "accidents" are non-essential properties, like hair color or height, that can change without changing what the thing is.. Therefore, that proposition is not true in this case, but it is indeed true in perfect Definitions. If it were otherwise, such a proposition would be false.

CLA. From where does it come, then, that in Chapter 12 of the Second Part of the Institutes original: "Institutioni"; referring to Zarlino's famous 1558 treatise, Le Istitutioni harmoniche., you have provided two definitions of Consonance?

GIOS. It pleases me greatly that your questioning returns to the point of what I intended to say. Note, then, that a 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 thing defined. For example, if I wanted to define Man and say what he was, I would say: 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 being defined; as if I were to say: Man is a rational animal. This is because 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 In this context, "end" means the purpose or ultimate goal (the telos). of the thing; as when I would say: Man is a rational and mortal Animal, capable of Beatitude original: "Beatitudine," referring to supreme blessedness or the vision of God., in such a way that Beatitude is the end of Man.

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

GIOS. You know well that there is.

ADRI. Tell us one, and then continue with whatever you like.

GIOS. The definition that contains each of these things will be when I wish to define something like, say, Consonance; and I will put into its definition the sounds, the ratio of the Numbers, and what it is able to do. I would say: Consonance is a ratio of Numbers original: "ragione de Numeri", contained by two sounds or voices, one low and the other high, which comes sweetly to our hearing.

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

Institutes, Part 2, chapters 8 and 12.

DESI. Tell us, by your faith: does this Consonance have any other end?

GIOS. It certainly does, and you can remember it from what you have read: such as the changing of the senses, in the way that Harmony has the power to delight, and also to induce different passions in us.

DESI. That is indeed the case.

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

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

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

GIOS. For what reason would you want me not to give it? I am here to satisfy you; thus, in doing so, you will do me the greatest pleasure. Now then, so as not to waste time, I say: that since the Subject of Music is the Sonorous Number original: "Numero sonoro"; Zarlino's term for number as it relates to sound.; and since one cannot have any true knowledge of the quantity of sounds except by means of sonorous bodies (which are the strings, which are quantities that are measured); and since one cannot have any Science of the intervals except by way of the measurement of these bodies (that is, from the measurement of two sonorous bodies, or truly of at least one divided into many parts): it is necessary that between them there occurs a certain proportion of low and high sound. 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 Related Quantity original: "Quantità relata"; a mathematical category where values are defined by their relationship to each other, like 2:1.: by means of which we can, through various means, demonstrate all things that are demonstrable in Music. But to have perfect knowledge...