NOTICE 1.

I had decided to attach everything pertaining to motion to this book. For example, I intended to include the speed at which heavy bodies travel when they descend toward the center in a straight, circular, or oblique path, and the manner in which they accelerate their motion and descent. Furthermore, I planned to discuss the proportion by which the motion of projectiles is diminished, at what point they acquire the greatest force in striking, and the nature of the motion of heavy objects on any given plane. I also considered whether it is due to motion that objects weigh more on the longer arms of levers or scales, and whether a peculiar sound can be assigned to each of these motions. However, I believed these matters should be postponed to another place, since they require a specialized treatise. Therefore, I proceed to the efficient causes of sounds, in the explanation of which many things pertaining to the aforementioned motions will be revealed.

NOTICE 2.

There will perhaps be some who say that I should have weighed the entire eighth chapter of the third book of Aristotle's On the Soul Latin: De Anima in the first book. In particular, they might point to that small section: when it is struck and prevented from dissipating, this motion is sound original Greek: ὅταν δὲ κρουσθῇ σήπηται, ὁ τοῦτο κίνησις ψόφος. That is, when air is prevented from scattering, its motion is sound, which is why it must be struck very quickly. Indeed, this speed anticipates the dissipation of the air. But since Aristotle relates many things in that chapter concerning the voice, echo, hearing, and animals, which require other locations, and because the striking of the air depends on the efficient cause of sounds (which is treated in the following book), we shall not deal with them here. We assume the mind of the reader is already imbued with Aristotelian doctrine, so there is no need to explain his text. Nonetheless, with God's help, nothing will escape us that we do not touch upon in the following books, or that cannot be deduced from them with very little effort.

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TABLE OF PROPOSITIONS

FOR THE SECOND BOOK.

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The preceding book opened up the nature of sound, but this one reveals its causes and demonstrates many things that have been unknown until now. This can be easily gathered from the list of propositions. This is especially true regarding the proportions that heavy bodies maintain in the velocities of their descent, which are discussed most extensively in propositions 24 and 27, at the conclusion of which excellent corollaries may be read.

I. The difference in magnitude and shapes seen in bodies creates differences in sounds.
II. The more humid homogeneous bodies are, the lower the sounds they produce; the drier they are, the higher the sounds.
III. Harder bodies produce higher sounds, while softer ones produce lower sounds, for the most part.
IV. Highness and lowness of sounds do not always follow the weight and lightness of bodies.
V. The density and rarity of bodies create differences in sounds, both regarding pitch and other properties of sound. However, the ratio of sounds is not the same as the ratio of density and rarity in bodies.
VI. As the length of one body relates to the length of another homogeneous body, or as space relates to space, so does sound relate to sound.
VII. When strings are equally tensioned, their thicknesses must maintain a squared ratio to the musical interval that is sought.
VIII. For a given string producing a certain sound to rise to a higher sound, it must be stretched by forces that have at least a squared ratio to the interval to be reached.
IX. If strings are unequal in length but equal in thickness, they will become unisons if the ratio of the weights or tensioning forces is the square of the ratio of the lengths.
X. If strings are equal in length but unequal in thickness, the ratio of the tensioning forces must be the same as the ratio of the thicknesses for them to become unisons.
XI. When strings are unequal in both length and thickness, the force by which they are made unisons must be composed of a simple ratio compensating for the thicknesses and a squared ratio compensating for the lengths.
XII. Given the strings, to provide the forces or weights by which they must be stretched to produce a given sound.
XIII. Given the forces or weights, to provide the strings, the sounds, and their ratios.
XIV. That a deaf person can bring a cithara, viol, lute, and other stringed instruments into tune.
XV. Equal strings under equal tension have equal motion when they are struck equally.
XVI. The motions of strings that are unequal in length, thickness, or tension are unequal.
XVII. The ratio of the slowness and velocity of motions is the same as the ratio of the length of strings that are equal in thickness and length. Mersenne likely means the ratio of vibrations here.
XVIII. Given the length, thickness, material, and tension of a string, to provide the number of its vibrations. And given the number of vibrations, to provide the length and tension of the string. The Latin 'recursus' refers to the back-and-forth movement or return of the string.
XIX. Given the sound, to provide the frequency or number of vibrations by which the string trembles. Given the number of vibrations, to provide the sound. Also, given either of these, to provide the string. Finally, given the string, to provide either or both of the others.
XX. The ratio of the thickness of strings is the square of the ratio of the number of vibrations the strings produce.
XXI. To establish a standard and stable sound by which we can define and measure other sounds and the number of vibrations.
XXII. From the preceding knowledge of vibrations, to divide the hour, minutes, and any other particles of an hour into any parts mi- The text cuts off mid-word, likely heading toward 'minimas', meaning 'smallest parts'.