Chapter 2

The 2 Affections of Sound

Descartes Descartes
4 min read
Table of Contents

Praeconsiderables

  1. Each Sense is capable of some pleasurable sensation.

  2. This pleasurable sensation requires a certain proportion of the object to the sense.

For instance:

  • the noise of Thunder and Guns are not convenient to Music because they offend the Ear
  • the sun hurts the sight
  1. The Object must be easy and not confusing for the Sense

For instance, we prefer a shapes than complex ones.

  1. The sense perceives Objects that have less differences* between their parts.

Distinction is the first Note or Term of any Consonance, or other Musical Intervall, an Union; and the other, according to its difference, in found, from the former.

Sounds can only be distinguished, or their Differences be known than by their mutual habitude.

This creates ratios as Audible Differences.

The Sounds of strings are according to their Rations, not visible Differences.

For Example, as these 3 Chords have (a :: b :: c), Union, an equality of Rations:

(for (6 :: 1 :: 2) Eighth (a, b :: b, c), for their Sounds (c :: 1 :: 1) (4 :: 2) Twelfth, (an Union, Eighth, and Fifteenth) have an equality of Differences. (For (1 + 7 = 8), and (8 + 7 = 15).) And as these (a :: b :: c), Union, three Chords have an inequality of Rations: (though an equality (1 :: 1) (3 :: 2) Fifth of Differences visible, for (d + g = e), and (e + g = f), for their Sounds (an Union, Fifth, and Eighth) have an inequality of Differences audiible.

For as the Ration of (d) to (e), is (\frac{1}{2}): (and is a Fifth, by Fig. first, p. 10.) to the difference of an Union and a Fifth is a Fifth, ((1 + 4 = 5).) and as R(e) to (f) is (\frac{1}{2}): (and is a Fourth by Fig. first, p. 10.) to the difference of a Fifth and an Eighth is a Fourth, ((5 + 3 = 8).)

Therefore, Sounds, thus numbred, are as it were imperfect (because not equally distant) audiible Indices, or Logarithms of their Chords. Here the Reader may observe that for the Difference of an Eighth, I have added only seven, of a Fifth four; and of a Fourth three: and the reason is, because the exclusive account is always one lesse than the inclusive, as is made visible Animad.

  1. The parts of an Object are more similar with each other, when they mutually hold the greater proportion* each to other.

For example, there are 2 kinds on strings:

  1. Audible

This has a Rational or Geometrical measure

  1. Visible

This has an Arithmetical measure.

  1. That proportion between the parts of an Object should be Arithmetical, not Geometrical.

This is because there are not so many things advertisable since the Differences are everywhere equal.

Therefore, it is easier for the sense to distinctly perceive all things occurring therein*.

Just like in Lines and Numbers, there are in Sounds two Proportions and Progressions:

  1. Arithmetical

Examples are Second, Third, and Fourth: for 2 - 1 = 3 - 2 = 1

  1. Geometrical

Examples are Second, Third, and Fifth: for 1, 2 :: 2, 4.

As was said before Animad, when Strings are audibly in an Arithmetical proportion, or progression, they then are visibly in a Geometrical.

This is why Chords, as a Sound, should be Geometrically divided, not Arithmetically.

This is so that the hearing has not so much to advertise since the audible Differences are always equal.

For example, the proportion of these lines below is more easily distinguished by the eyes, than the latter ones:

2 |—|—|
3 |—|—|—|
4 |—|—|—|—|

2 |—|—| [A]
√8 |—|—|—| [B @ 2.82.. So, AB is 0.8284 and BC is 1.172+]
4 |—|—|—|—| [C]

In the first batch, the eye is required only to advertise the Unity for the difference of each line.

But in the second batch, the parts AB, and BC, which have irrational ratios.

The eye:

  • cannot perfectly perceive them together and at once.
  • can only perceive their proportion Arithmetical

It sees 2 parts in AB, but 3 parts in BC.

This shows that the sense is perpetually deceived.

  1. The Mind is not pleasured by objects that are:
  • easiest to perceive
  • most difficult to perceive

Instead, the Mind is pleasured when its natural desire carries the senses towards their proper Objects which are not perceived so easily or totally, nor perceived with so much difficulty that the sense is tired by it.

  1. Variety, is most grateful in all things.

Leave a Comment