Twelve Books on Harmony

The movement of the voice proceeds by rising and falling from the beginning to the end, such as in human speech. For although we lower and raise the voice while speaking, that progress and movement of the voice does not happen through the canonical intervals observed by discrete sound. Discrete sound is found in Church chants and other melodies, in which the voice is immediately stretched to a higher interval and remains there unmoved for a certain time, then is lowered, and so on. Aristoxenus Aristoxenus was a Greek philosopher and a student of Aristotle who wrote extensively on music theory. teaches this at length in Book 1, as does Euclid after him. They call one type of voice continuous original Greek: synechēs and the other intervallic original Greek: diastēmatikē. A standing sound is said to be one that remains in the same place in the musical system. A sound in motion is one that stays in no single place, such as the sound made by a comb or a plectrum when strings are touched continuously while the finger pressing the strings descends from the top of the neck to the bottom. A harmonic sound, which can also be called melodic original Greek: emmelēs, is properly a musical tone original Greek: phthongos, which is a tuneful sound placed in a specific location or degree of the system. An unharmonious sound is called discordant original Greek: ekmelēs, such as a sound that cannot enter into music. Other divisions are taken from the different steps of the musical scale, that is, of the monochord or the system. Some of these are stable and others are mobile; these will be discussed elsewhere.

We must not omit the division of sounds provided by a manuscript of an anonymous philosopher original Greek: anōnymos in a treatise on the Philosopher’s Stone. The title is On the Divine and Sacred Art of the Philosopher. In this work, after teaching that there are four most general sounds which are the foundations of music: these four are the sounds, they are the foundations, even the foundations of music, namely 1, 2, 3, and 4, from which 24 other tones distinct in kind are generated, he adds: these equals are called authentic, and plagal, and middle, and unequal, and equal. In another place, he lists the following sounds: pure, plagal, equal, authentic, unequal, and high-pitched sound; and further down he adds equal-sounding and middle-sounding.

PROPOSITION XXIII.

To explain what Aristotle taught about sounds, and to reveal the points in which he erred.

Aristotle makes sound twofold in Book 2 of On the Soul, chapter 8: Since sound is twofold, one is a certain actuality, and the other a potentiality. One is actual, the other potential. However, this is said improperly of sound, since the potential sounds are rather the sounding bodies themselves, such as solid and smooth objects. He establishes three things necessary for sound, namely which things, in what way, and in what: something that strikes, something struck, and a medium. But two seem to be sufficient, for air striking water, or water striking air, makes a sound. Even wool striking itself produces a sound, although it is very small and weak. He correctly teaches that concave bodies and smooth ones are more suited for sound than others, and that motion must precede the dissipation of the air. Yet the air rings even if the bodies striking each other are not smooth. Regarding the Echo and the innate air of the ear Aristotle believed the ear contained a pocket of "innate air" that resonated with external sounds., these must be treated in a specific book, just as we will treat the Voice and related matters.

Furthermore, it is not true that a needle struck by another needle produces no sound. Nor must a body be level original Greek: homalon, for even if it is rough, it sounds. Finally, he says that low and high pitch are manifested by sound just as colors are by light. He says high pitch is so named through briefness original Greek: di' oligotētos by those who experience it through touch. For as a sharp object moves the sense in a short time, it does so greatly original Greek: epi poly. A low sound moves the sense for a long time but only a little. Thus, the high pitch as it were punctures, a scratching of the sense, while the low pitch as it were pushes and blunts it. It is as if one supposed a high sound enters the ear at a smaller angle, and a low sound at a larger angle. Other things he has here regarding the voice, and in the book On Things Heard, and in the second section of the Problems, and in Book 5 of On the Generation of Animals, chapter 7, we will discuss in the book On the Voice.

PROPOSITION XXIV.

To explain what Ptolemy taught in Book 1 regarding sounds, and to show his errors, if there be any.

Ptolemy in Book 1, chapter 3, treats sound specifically, setting its differences according to quantity and quality. To define whether low and high pitch belong to quantity or quality, he states: The differences of sounds, he says, arise from the strength of the striker; second, from the physical constitution of the thing being struck; third, from the medium through which the strike occurs; fourth, because of the distance of the struck object from the beginning of the motion. Having stated these, he says that hardly any difference in sound arises from the object being struck. I understand this to mean as long as it is always held in the same way, otherwise a string more tightly stretched varies the sound. Next, he says the force of the stroke original Greek: bia plēxeōs makes sounds louder, but not higher in pitch. He gives two examples of this: the first is a person speaking softly or more excitedly; the second is from those blowing more slowly into, say, pipes, flutes, or similar instruments, and those striking more firmly, such as a kithara or lute. From these he says the sound becomes only louder or softer, but not lower or higher in pitch. However, one must be careful here, lest anyone think that from a greater or more vehement blowing of a flute or another tube, such as a trumpet, only a louder sound is produced, not a higher one. For daily experience proves that a trumpet or pipe blown more vehemently produces higher sounds. We will declare their leaps and the sounding sphere elsewhere.

Furthermore, he teaches that the diversity of sounds arises from the porosity and density, thinness and thickness, roughness and smoothness of a body, as well as its shape. Because of these shapes they become oblique and straight, or wandering, or broken, and a thousand such things. This is evident from human voices, which imitate all sounds, since man has a governing part of himself that is rational and imitative. There are also other sounds which are called smooth or rough because of the smoothness or roughness of the bodies from which they are made. Others, because of porosity and density, thickness and thinness, are called dense, or porous, or thick, or thin, although equivocally; these we will discuss in the book On the Voice.

To show how low and high pitch proceed from what has been said, he adds that it is a quality original Greek: poiotēta, which in an equal volume original Greek: en isō onkō has more substance or matter. That which is thicker original Greek: pachyteron de has more matter in an equal length. He says high pitch is made from the denser and thinner, and low pitch from the looser and thicker. Hence, that which is thinner is called sharper, just as that which is thicker is called duller. Certainly, I would greatly desire that some people defend what Ptolemy brings forward here when he affirms universally original Greek: kath' holou that denser things sound higher. For it is established that lead is denser than iron or brass from the very definition of Ptolemy and Aristotle, and yet brass of the same size sounds far higher, as is clear from its bells.