On the Nature of Sounds.

PROPOSITION XIII.

Sound is heard further away, that is, its sphere is larger, the stronger or larger it is: although the sphere of two, three, or more equal sounds is not double or triple, but less than double or triple.

Both parts of this proposition are established by experience, although the reason for the second part is not as clear as the first. The first part is derived from the greater movement of the air, which is struck more vehemently, or from a greater volume of air that is moved.
The second part can be understood, first, from the fact that two or more sounds do not combine simultaneously into a single sound formed from those two or three, but rather they hinder each other in the air. Second, they do not move the same part of the air in the same way, but each moves it in its own peculiar manner; this can be proven by the example of circles made in water. For different stones, even if thrown at the same time, do not concur to make the same circle, but each describes its own, and these circles taken together do not increase in proportion to the number of stones. See the second problem of section II. Third, because sounds closely follow the proportions of light; yet two equal lights do not produce double light at double the distance, nor do three or four at triple or quadruple distance. Indeed, two lights do not even produce equal light at double the distance, for the ratio of the lights must be the square of the ratio of the distances so that the light is equal at a given interval, which will be explained more clearly and extensively elsewhere. In the meantime, I deduce the following proposition from these points as a corollary.

PROPOSITION XIV.

So that a sound of the same magnitude reaches double the distance, it must be four times larger at its origin.

This is proven from Optics, in which the Opticians demonstrate that light must be fourfold to shine equally at double the distance. To shine twice as brightly at that same double distance, it must be sixteenfold, as will be established from things to be said elsewhere. By a similar reasoning, a sound must be four times larger to be heard equally from double the distance. However, so that it appears twice as large as before from the aforementioned distance, it must be sixteen times larger, which will be well understood by someone who knows the ratio of axes and bases observed in pyramids.

PROPOSITION XV.

The ratio of the high pitch and low pitch of sounds is the same as the number of movements from which they are most closely and immediately produced.

This is proven by the most certain experience: for when the number of movements is doubled, the sounds create an octave, which is situated in a double ratio, as will be said later.
From this it must be concluded that sounds are lower in pitch the smaller the number of movements of the air from which they are produced; and they are higher in pitch the greater the number of movements from which they are created, as will be demonstrated in its proper place with most excellent experiments on strings.

PROPOSITION XVI.

High and low pitch; brevity and length; strength and weakness; smoothness and roughness, are the principal differences of sounds: the rest, depending on various bodies, are infinite.

This is proven by the fact that the aforementioned differences establish the science of harmony original: "harmonicam scientiam", therefore they are the principal ones. However, roughness can be referred to a multitude of sounds, since it arises from an inequality of sounds that are nevertheless so close to one another that they seem to make a single sound, just as the protrusions and inequalities of some wooden or stone surface that is not polished seem to make a single surface, albeit a rough one.
Furthermore, it is established that other differences are infinite based on bodies of different species, whose sounds, however much they may seem to be in unison, are different, and in some way carry their own signatures or characters. This can be seen in a thousand glass cups of the same material and magnitude, which nevertheless prove their sounds to be different when struck. One can scarcely find two among many thousands of cups that produce the same sound, or that are in unison, or of the same clarity regarding their sounds. This is also observed in gold and other coins and medals.

PROPOSITION XVII.

Many properties of sounds are to be referred back to the various movements by which they are produced.

Since silence would be perpetual in the absence of movement, and sounds vary because of the diversity of movement, or indeed are nothing distinct from movement, it is certain that their effects and properties must be sought from movement, which has now been nearly original: "σχεδὸν" (schedon), a Greek term meaning "almost" or "roughly speaking" discussed; concerning these things, we shall speak specifically later. From this I conclude there is scarcely any body in the nature of things that moves the air with the exact same movement as another: otherwise its sound could in no way be distinguished from the sound of another.

Vocabulary: Sound, sphere, Optics, High pitch, low pitch, Science of harmony, movement of the air, nearly.