On Pitches and the Basic Principles of Music

Sound, Motion, and Percussion

Consonance, which governs all musical setting-out of pitches, cannot come about without sound; sound, for its part, cannot be produced without some pulsation and percussion; and pulsation and percussion can in no way exist unless motion has preceded them. For if all things were immobile, one thing could not run into another so that one might be impelled by another; but with all things standing still and motion absent, it follows of necessity that no sound is produced. For this reason, sound is defined as a percussion of air that remains undissolved all the way to the hearing.

Fast and Slow Motions: High and Low Pitch

Now some motions are faster, others slower; and of the same motions some are less frequent, others more frequent. For if anyone attends to a continuous motion, he must necessarily observe in it either speed or slowness; and if anyone moves his hand, he will move it either frequently or rarely. And if the motion is slow and rare, low sounds must be produced by the very slowness and rarity of the striking. But if the motions are fast and frequent, high sounds must necessarily be produced.

For this reason, if the same string is tightened further it sounds high; if it is loosened, it sounds low. For when it is tighter it produces faster pulsations, returns more quickly, and strikes the air more frequently and densely. The one that is looser produces lax and slow pulsations, and on account of that very weakness of striking, being less frequent, does not vibrate for long.

One Sound Consists of Many Strikes

Nor, when a string is struck, should one think that only one sound is produced, or that there is only one percussion among these many sounds; rather, as many times as the air is struck, the trembling string will have struck it. But since the velocities of sounds are joined together, no interval is perceived by the ears, and a single sound — whether low or high — strikes the sense, though each sound consists of many, the low of slower and rarer ones, the high of faster and more frequent ones.

It is as if someone were carefully to fashion a cone of the kind people call a top, and draw upon it one stripe of red or some other colour, then spin it with as much speed as possible: the whole cone then appears to be dyed with that red colour — not because the whole thing is in fact so, but because the speed of the red stripe overwhelms the clear parts and does not allow them to appear. But of these things more will be said later.

Pitch, Number, and Consonance

Since, therefore, high pitches are aroused by more frequent and faster motions, while low ones are aroused by slower and rarer motions, it is evident that from low pitch, high pitch is heightened by a certain addition of motions, while from high pitch, low pitch is relaxed by a lessening of motions. For high pitch consists of more motions than low. And in those matters where plurality makes the difference, that plurality must necessarily consist in a certain numerical quantity. Every smaller quantity stands in relation to a larger quantity as number to number. Of those things which are compared according to number, some are equal to one another, and others are unequal.

Accordingly sounds too are partly equal to one another, and partly stand apart from one another at a distance of inequality. But in those pitches which are discordant through no inequality, there is no consonance at all. For consonance is the concord of mutually dissimilar pitches brought together into one.