First.

the diversity of the Sciences arises from the variety of things considered in many ways. These can be considered in three modes. Firstly, there are some whose being depends on matter, and without it, they cannot be defined. Secondly, there are some that cannot exist far from that matter, but in their definitions, such matter is not posited. Beyond this, there are others that do not depend on such matter, not only according to their being but also according to their reason or definition; and these are those that fall under that divine Science we call Metaphysics. This is because those things which it considers either are never found to be in matter, as is God blessed, and other separate substances, or because they are not universally in it, as are Substance, Potency, and Act, and that which philosophers call Being; wherefore in their definition, because they are not corporeal things, matter is not posited. But the first, which are natural things and are considered in the natural Science which they call Physics, have their being in sensible matter and are subject to movement; they are defined by the aforementioned matter. Hence, when we define what Man is, we say that he is a rational and mortal animal; and the Animal is without any doubt a natural thing, and has its being among the things of nature. The others, then, are all things pertaining to the mathematical sciences, such as points, lines, surfaces, bodies, and all those things together that belong to multitude and magnitude. Hence, in their definition, sensible matter is not posited, even though they cannot exist without it; for it is not said that the Triangle is a figure of wood, or of stone, or of iron, or of any other metal or material whatsoever, but it is said that it is a figure which has within itself three angles equal to two right angles, even though the Triangle has its being in matter, as you will be able to know by discoursing.

ADRI. This discourse has pleased me greatly.

DESI. And me as well; all the more so because I see almost a new thing, that in the reasonings of Music, one also speaks of things pertaining to Philosophy.

1. Part, chap. 20.

GIOS. Do you not know, Sir, that Music, being partly a mathematical science and partly natural, as you have been able to see in my Institutioni Foundations [of Music], is subject to Philosophy?

DESI. I know it for certain, but these things delight me greatly, especially when I see them drawn to some beautiful purpose.

1. Part, chap. 18 & 19.

GIOS. Know that all this discourse has been made so that, since Music is, as I already said in the Institutioni, a science of Relation and has as its subject the Numero sonoro sonorous number, it does not come to be part Mathematical and part Natural without purpose. Since, considered in the first state, because its being depends on numbers, it is enumerated among the things already mentioned and placed in the third place; but considered in the second mode, since Sounds have their being among natural things, it is placed among those things that possess the second. Therefore, I believe you remember what I call Matter and what I name Form of the consonances.

ADRI. Continue with your speech, for we possess these things excellently.

GIOS. You must therefore know that, even though we have the true knowledge of the things of Music through the means of quantities, since it is not simple mathematics, in the definition of the Consonance and of any other interval, Musicians are accustomed at times to posit the Matter, as we have been able to see in many definitions in which Sounds or Voices are posited, which are the Matter of the consonances and of every other interval. For Musicians contemplate such intervals in act, which are not without matter, which Arithmeticians do not do, nor even Geometers, because the former contemplate Number, and the latter contemplate measurable Quantities insofar as they are distant from it.

DESI. For this reason, therefore, some who have defined the Consonance have said that it is the distance between a low sound and a high one.

GIOS. It is so; but there have also been some others who have said that Consonance is formed air. However, take heed that in explaining what things are (I speak to those who do not know), we use two kinds of Declaration. The first is called Definition, and it is that which explains the thing by its essential components; and the second is called Description, and it is that which does not speak of the thing by its essentials, but by its accidents.

CLAV. Give us, if it pleases you, an example of one and the other.

GIOS. The first is when we define Man, and we say that he is a rational and mortal animal...