(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.

(2) The syllable Û is the sun, the syllable E is the Nihava or invocation, the syllable Auhoi is the Visve Devas, the syllable Hiṅ is Pragâpati, Svara (tone) is breath (prâna), the syllable Yâ is food, the syllable Vâg is Virâg.

(3) Twenty-two letters are formed by the voice, impressed on the air, and audibly uttered in five situations, in the throat, guttural sounds; in the palate, palatals; by the tongue, linguals; through the teeth, dentals; and by the lips, labial sounds.

(36) By that sound all powers are moved in heaven, so that all things grow joyfully, and generate very beautifully: And as the divine power is manifold and various, so also the sound or Mercurius is manifold and various.

(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.

(18) Some are strongest in the quality of the tone or sound, and those are light or bright also; and when the light shineth on them, they look like the rising of the flash of lightning, as if something would lift itself aloft there.

(1) The udgîtha, of which a poet said, I choose the deep sounding note of the Sâman as good for cattle, belongs to Agni; the indefinite note belongs to Pragâpati, the definite note to Soma, the soft and smooth note to Vâyu, the smooth and strong note to Indra, the heron-like note to Brihaspati, the dull note to Varuna. Let a man cultivate all of these, avoiding, however, that of Varuna.

(5) The Rik indeed is speech, Sâman is breath, the udgîtha is the syllable Om. Now speech and breath, or Rik and Sâman, form one couple.

(10) Hardness is the fountain or wellspring of the tone, but it alone cannot generate the same, yet it is the father thereof, and the whole Salitter is the mother; otherwise, if the hardness were both father and mother of the tone, then a hard stone also must have a ringing sound. But a hard stone does make only a noise, like a knocking, as a seed or beginning of a tone, and that it is, certainly.

(31) Every element in Nature has its individual keynote. If these elements are combined in a composite structure the result is a chord that, if sounded, will disintegrate the compound into its integral parts. Likewise each individual has a keynote that, if sounded, will destroy him. The allegory of the walls of Jericho falling when the trumpets of Israel were sounded is undoubtedly intended to set forth the arcane significance of individual keynote or vibration.

(17) The sound and the object and the thought called up by a word are confounded because they are all blurred together in the mind. By perfectly concentrated Meditation on the distinction between them, there comes an understanding of the sounds uttered by all beings.

(30) In constructing their temples of initiation, the early priests frequently demonstrated their superior knowledge of the principles underlying the phenomena known as vibration. A considerable part of the Mystery rituals consisted of invocations and intonements, for which purpose special sound chambers were constructed. A word whispered in one of these apartments was so intensified that the reverberations made the entire building sway and be filled with a deafening roar. The very wood and stone used in the erection of these sacred buildings eventually became so thoroughly permeated with the sound vibrations of the religious ceremonies that when struck they would reproduce the same tones thus repeatedly impressed into their substances by the rituals.

(3) All vowels (svara) belong to Indra, all sibilants (ûshman) to Pragâpati, all consonants (sparsa) to Mrityu (death). If somebody should reprove him for his vowels, let him say, 'I went to Indra as my refuge (when pronouncing my vowels): he will answer thee.'

(25) A writer has said: "Science offers the illustration of a rapidly moving wheel, top, or cylinder, to show the effects of increasing rates of vibration. The illustration supposes a wheel, top, or revolving cylinder, running at a high rate of speed—we will call this revolving thing 'the object' in following out the illustration. Let us suppose the object to be moving slowly. It may be seen readily, but no sound of its movement reaches the ear. Then the speed is gradually increased. In a few moments the movement becomes so rapid that a deep growl or low note may be heard. Then as the rate of motion is increased the note rises higher in the musical scale. Then, the motion being still further increased, the next highest note is distinguished. Then, one after another, all the notes of the musical scale appear, rising higher and higher as the motion is increased.

(4) Speech is Rik, and therefore when a man utters a Rik verse he neither breathes up nor down. Rik is Sâman, and therefore when a man utters a Sâman verse he neither breathes up nor down. Sâman is udgîtha, and therefore when a man sings (the udgîtha, Om) he neither breathes up nor down.

(2) O Rā, in that thy name of Rā, since thou passest through an Eye of seven cubits, whose pupil is of three: do thou then make me sound, I am a powerful Chu, let thy soundness be my soundness

(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.