Twelve Books on Harmony

...while it is established by a thousand experiments that two bodies rarely produce the same sound, or two men the same voice; for although the sounds of different bodies do not differ in pitch, they differ in other qualities, such as smoothness, roughness, thickness, and so on.

PROPOSITION XVIII.

Sounds joined together, or compared, have certain properties that they lack when considered separately.

For sound viewed by itself has no ratio, as Ptolemy Claudius Ptolemy, the 2nd-century astronomer and music theorist. best teaches in Book 1, chapter 4: therefore each sound by itself is irrational, since it is indifferent to itself, but a ratio is always in relation to something: for there can be no ratio unless at least two extremes are compared with each other. He intended to signify this with the following words: in two magnitudes. From the conjunction, or union of sounds, all consonances and dissonances arise, along with their properties and effects. Thus, a sound that was pleasing when taken alone may become unpleasant when joined with another sound with which it clashes, and vice versa.

PROPOSITION XIX.

Sounds meeting one another hinder each other.

This is proven both by experience and by reason. Two men speaking different things with the same force cannot be understood. The movements of air made by different people, especially those opposite each other, hinder one another like the circles produced by stones thrown from opposite sides into a river. It is like two opposing winds: a contrary motion breaks or at least diminishes the other motion. We will also show in Book 3 that the strings of instruments change their sounds when they are struck together. A sound that resulted from purely horizontal motion when alone may, through the company of another sounding string, result from a composite or mixed motion. One string meeting another produces a vertical or perpendicular motion in the other. The same is to be said of voices, the sounds of drums, and so on.

PROPOSITION XX.

We can use sounds in geodesy and for carrying messages throughout the whole world.

This is proven because it can be established in what space of time a given sound travels through a given distance. Men placed in certain stations, separated by five hundred paces for example, could shout loudly to carry news from one kingdom to another. They could relay things that happened recently or that are usually learned through couriers. Cleomedes A Greek astronomer from the 1st or 2nd century AD. asserts in Book 2 that this was done by the King of the Persians. If someone used the massive crash of military cannons, far fewer stations would be necessary. However, as far as geodesy the science of measuring the Earth's surface and distances is concerned, it would not be as certain. Sound does not always take the same time to travel a given space. The constitution of the air is almost always different, not only in distant places but even in the same place. This does not matter for establishing the stations for the messengers mentioned above, provided they are not so far apart that a voice cannot easily reach from one to the other at any time, even against the wind. We will discuss elsewhere how much time a voice needs to pass through the entire Kingdom of France, or even around the whole world.

PROPOSITION XXI.

Someone can explain their mind to listeners and converse familiarly with them about any matter using the sounds of a lute or any other musical instrument.

Just as various combinations of letters form words, so can combinations and divisions of sounds form any utterances. Who would deny that everything can be explained by these utterances? It would certainly be most pleasing and useful to every listener if all sciences were taught by practitioners through sounds, and if the practitioners themselves conversed about the sciences. This can be done in several ways. For example, twenty sounds can be chosen to represent the twenty letters of our alphabet. The range of the lute Latin: testudo, literally "tortoise," referring to the instrument's bowl-shaped back. without using frets could define these. The remaining three letters could easily be supplied by the first three frets or any others on the neck. I omit the various systems of ciphers, as they are called, which can be sought from the treatise on the lute and other instruments, and from the books on the Voice and Songs.

PROPOSITION XXII.

There are many divisions of sound taken universally Greek: katholikōs, which is called psophos noise or sound in general by the Greeks. It is discrete or continuous; seen as standing or in motion; harmonic, which the Greeks call phthongos a musical note or tone and that which is unsuitable for music; stable and mobile; apycnos, barypycnos, mesopycnos, and so on.

There is no need for us to deal with more of these divisions here. They will be discussed extensively in the book on the Voice and Instruments. These divisions concern harmony more than the explanation of the nature and properties of sound, which we are investigating especially in this and the following book. Briefly, I say that a continuous sound is called that which is without certain pauses and tensions or relaxations...