De institutione musica I.3: De vocibus ac de musicae elementis.
Consonance, which rules all musical melody, cannot come about without sound, and sound is not given forth without a certain pulse and striking, and pulse and striking can in no way be unless motion has gone before. For if all things are immovable, one cannot run against another so that one is driven by the other, but if all things stand and lack motion, no sound need be made. Therefore sound is defined as a striking of the air unbroken as far as the hearing. Of motions some are swifter, others slower, and of the same motions some are rarer, others denser. For if anyone looks at a continuous motion, he must there perceive either swiftness or slowness; if someone moves his hand, he will move it either with frequent motion or rare. And if the motion is slow and rarer, grave sounds must be produced, by the very slowness and rarity of the striking. But if the motions are swift and dense, acute sounds must be rendered. For this reason the same string, if it is stretched more, sounds high, if relaxed, low. For when it is tighter, it gives a swifter pulse and returns more quickly and strikes the air more frequently and densely. But one that is looser sends forth loose and slow pulses and rare ones, by the very weakness of its striking, and does not tremble so long. For one must not think that every time a string is struck only one sound is uttered or that there is one stroke in it, but the air is struck as often as the trembling string has struck it. But since the swiftnesses of the sounds are joined, no gap is perceived by the ears and one sound strikes the sense, either grave or acute, although each consists of many, the grave of slower and rarer, the acute of swifter and denser: as if someone carefully turns on the lathe a cone, which they call a top, and draws on it one line of red or another colour, and spins it as fast as he can, then the whole cone is seen tinged with red colour, not that it is wholly so, but that the swiftness of the red line takes in the pure parts and does not let them appear. But of this later. Since, then, acute voices are stirred by denser and swifter motions, grave voices by slower and rarer, it is clear that by an addition of motions acuteness is increased from gravity, and by a subtraction of motions gravity is relaxed from acuteness. For acuteness consists of more motions than gravity. Whatever differs by plurality must consist in a certain numerosity. And all paucity is related to plurality as number compared to number. Of those things that are compared according to number, some are equal to one another, some unequal. Wherefore sounds also are partly equal, partly distant by inequality. But in those voices which are discordant by no inequality there is no consonance at all. For consonance is the concord, reduced to one, of voices unlike one another.