(5) But some doubt arises when we consider the phenomena of hearing.

Perhaps we are to understand the process thus: the air is modified by the first movement; layer by layer it is successively acted upon by the object causing the sound: it finally impinges in that modified form upon the sense, the entire progression being governed by the fact that all the air from starting point to hearing point is similarly affected.

Perhaps, on the other hand, the intervenient is modified only by the accident of its midway position, so that, failing any intervenient, whatsoever sound two bodies in clash might make would impinge without medium upon our sense?

Still air is necessary; there could be no sound in the absence of the air set vibrating in the first movement, however different be the case with the intervenient from that onwards to the perception point.

The air would thus appear to be the dominant in the production of sound: two bodies would clash without even an incipient sound, but that the air, struck in their rapid meeting and hurled outward, passes on the movement successively till it reaches the ears and the sense of hearing.

But if the determinant is the air, and the impression is simply of air-movements, what accounts for the differences among voices and other sounds? The sound of bronze against bronze is different from that of bronze against some other substance: and so on; the air and its vibration remain the one thing, yet the difference in sounds is much more than a matter of greater or less intensity.

If we decide that sound is caused by a percussion upon the air, then obviously nothing turning upon the distinctive nature of air is in question: it sounds at a moment in which it is simply a solid body, until it is sent pulsing outwards: thus air in itself is not essential to the production of sound; all is done by clashing solids as they meet and that percussion, reaching the sense, is the sound. This is shown also by the sounds formed within living beings not in air but by the friction of parts; for example, the grinding of teeth and the crunching of bones against each other in the bending of the body, cases in which the air does not intervene.

But all this may now be left over; we are brought to the same conclusion as in the case of sight; the phenomena of hearing arise similarly in a certain co-sensitiveness inherent in a living whole.

(530) them are obvious enough even to wits no better than ours; and there are others, as I imagine, which may be left to wiser persons. But where are the two? There is a second, I said, which is the counterpart of the one already named. And what may that be? The second, I said, would seem relatively to the ears to be what the first is to the eyes; for I conceive that as the eyes are designed to look up at the stars, so are the ears to hear harmonious motions; and these are sister sciences—as the Pythagoreans say, and we, Glaucon, agree with them? Yes, he replied. But this, I said, is a laborious study, and therefore we had better go and learn of them; and they will tell us whether there are any other applications of these sciences. At the same time, we must not lose sight of our own higher object. What is that? There is a perfection which all knowledge ought to reach, and which our pupils ought also to attain, and not to fall short of, as I was saying that they did in astronomy. For in the science of harmony, as you probably know, the same thing happens. The teachers of harmony compare the sounds and consonances which are heard only, and their labour, like that of the astronomers, is in vain. Yes, by heaven! he said; and ’tis as good as a play to hear them talking about their condensed notes, as they call them; they put their ears close alongside of the strings like persons catching a sound from their neighbour’s wall 5 —one set of them declaring that they distinguish an intermediate note and have found the least interval which should be the unit of measurement; the others insisting that the two sounds have passed into the same—either party setting

(37) In Meno, Plato, speaking through Socrates, describes color as "an effluence of form, commensurate with sight, and sensible." In Theætetus he discourses more at length on the subject thus: "Let us carry out the principle which has just been affirmed, that nothing is self-existent, and then we shall see that every color, white, black, and every other color, arises out of the eye meeting the appropriate motion, and that what we term the substance of each color is neither the active nor the passive element, but something which passes between them, and is peculiar to each percipient; are you certain that the several colors appear to every animal--say a dog--as they appear to you?"

(30) Then the tone riseth up; and the hard spirit beateth, striketh or thumpeth; but the sweet makes that beating or striking mild; and the bitter divideth it according to the condition or kind of every quality; the fourth causes the ringing; the fifth causes joyfulness; and the compacted incorporated sounding is the tone or tune, or the sixth spirit.

(2) Employing this method, therefore, as a basis, and as it were an infallible rule, he afterwards extended the experiment to various instruments; viz. to the pulsation of patellæ or pans, to pipes and reeds, to monochords, triangles, and the like. And in all these he found an immutable concord with the ratio of numbers. But he denominated the sound which participates of the number 6 hypate : that which participates of the number 8 and is sesquitertian, mese ; that which participates of the number 9, but is more acute by a tone than mese, he called paramese , and epogdous ; but that which participates of the dodecad, nete . Having also filled up the middle spaces with analogous sounds according to the diatonic genus, he formed an octochord from symphonious numbers, viz. from the double, the sesquialter, the sesquitertian, and from the difference of these, the epogdous.

And thus he discovered the [harmonic] progression, which tends by a certain physical necessity from the most grave [i. e. flat] to the most acute sound, according to this diatonic genus. For from the diatonic, he rendered the chromatic and enharmonic genus perspicuous, as we shall some time or other show when we treat of music. This diatonic genus, however, appears to have such physical gradations and progressions as the following; viz. a semitone, a tone, and then a tone; and this is the diatessaron, being a system consisting of two tones, and of what is called a semitone. Afterwards, another tone being assumed, viz. the one which is intermediate, the diapente is produced, which is a system consisting of three tones and a semitone.

In the next place to this is the system of a semitone, a tone, and a tone, forming another diatessaron, i. e. another sesquitertian ratio. So that in the more ancient heptachord indeed, all the sounds, from the most grave, which are with respect to each other fourths, produce every where with each other the symphony diatessaron; the semitone receiving by transition, the first, middle, and third place, according to the tetrachord. In the Pythagoric octachord, however, which by conjunction is a system of the tetrachord and pentachord, but if disjoined is a system of two tetrachords separated from each other, the progression is from the most grave sound. Hence all the sounds that are by their distance from each other fifths, produce with each other the symphony diapente; the semitone successively proceeding into four places, viz. the first, second, third, and fourth. After this manner, therefore, it is said that music was discovered by Pythagoras. And having reduced it to a system, he delivered it to his disciples as subservient to every thing that is most beautiful.

(26) Finally, when the motions have reached a certain rate, the final note perceptible to human ears is reached, and the shrill, piercing shriek dies away, and silence follows. No sound is then heard from the revolving object, for its rate of motion is so high that the human ear cannot register the vibrations. Then comes the perception of rising degrees of Heat. After quite a time in which degrees of heat are being manifested without any sign of distinguishable color (though certain colors are there, but imperceptible to human vision) there gradually is manifested a dull dark reddish color in the revolving object. As the rate of speed increases, the red becomes brighter. Then, as the speed is still further increased, the red changes into an orange color. Then follow, successively, the shades of green, blue, indigo, and finally violet, as the rate of vibrations increase. Then the violet fades away, and all color disappears, the human eye not being able to register them. But there are invisible rays emanating from the revolving object, the rays that are used in photographing, and other subtle rays of light. Then begin to be manifested the peculiar rays known as the 'X Rays,' etc., as the constitution of the object changes. Electricity and Magnetism are emitted when the appropriate rate of vibration is attained.

(41) In The Principles of Light and Color, Edwin D. Babbitt confirms the correspondence of the color and musical scales: "As C is at the bottom of the musical scale and made with the coarsest waves of air, so is red at the bottom of the chromatic scale and made with the coarsest waves of luminous ether. As the musical note B [the seventh note of the scale] requires 45 vibrations of air every time the note C at the lower end of the scale requires 24, or but little over half as many, so does extreme violet require about 300 trillions of vibrations of ether in a second, while extreme red requires only about 450 trillions, which also are but little more than half as many. When one musical octave is finished another one commences and progresses with just twice as many vibrations as were used in the first octave, and so the same notes are repeated on a finer scale. In the same way when the scale of colors visible to the ordinary eye is completed in the violet, another octave of finer invisible colors, with just twice as many vibrations, will commence and progress on precisely the same law."

(23) And this stirring in the hardness is the tone, so that [there is a] sound; and the light or flash makes the ringing, and the sweet water makes the ringing soft: so that a man can use the sound to the distinction of speech, or articulation of syllables. Here observe yet more plainly the Nativity or Birth of the bitter Quality.