(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.

(11) A little reflection on what we have said will show the student that the Principle of Vibration underlies the wonderful phenomena of the power manifested by the Masters and Adepts, who are able to apparently set aside the Laws of Nature, but who, in reality, are simply using one law against another; one principle against others; and who accomplish their results by changing the vibrations of material objects, or forms of energy, and thus perform what are commonly called "miracles."

(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

(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.

(1) Since, however, we are narrating the wisdom employed by Pythagoras in instructing his disciples, it will not be unappropriate to relate that which is proximate in a following order to this, viz. how he invented the harmonic science, and harmonic ratios. But for this purpose we must begin a little higher. Intently considering once, and reasoning with himself, whether it would be possible to devise a certain instrumental assistance to the hearing, which should be firm and unerring, such as the sight obtains through the compass and the rule, or, by Jupiter, through a dioptric instrument; or such as the touch obtains through the balance, or the contrivance of measures;—thus considering, as he was walking near a brazier’s shop, he heard from a certain divine casualty the hammers beating out a piece of iron on an anvil, and producing sounds that accorded with each other, one combination only excepted.

But he recognized in those sounds, the diapason, the diapente, and the diatessaron, harmony. He saw, however, that the sound which was between the diatessaron and the diapente was itself by itself dissonant, yet, nevertheless, gave completion to that which was the greater sound among them. Being delighted, therefore, to find that the thing which he was anxious to discover had succeeded to his wishes by divine assistance, he went into the brazier’s shop, and found by various experiments, that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the figure of the hammers, nor from the transposition of the iron which was beaten. When, therefore, he had accurately examined the weights and the equal counterpoise of the hammers, he returned home, and fixed one stake diagonally to the walls, lest if there were many, a certain difference should arise from this circumstance, or in short, lest the peculiar nature of each of the stakes should cause a suspicion of mutation.

Afterwards, from this stake he suspended four chords consisting of the same materials, and of the same magnitude and thickness, and likewise equally twisted. To the extremity of each chord also he tied a weight. And when he had so contrived, that the chords were perfectly equal to each other in length, he afterwards alternately struck two chords at once, and found the before-mentioned symphonies, viz. a different symphony in a different combination. For he discovered that the chord which was stretched by the greatest weight, produced, when compared with that which was stretched by the smallest, the symphony diapason. But the former of these weights was twelve pounds, and the latter six. And, therefore, being in a duple ratio, it exhibited the consonance diapason; which the weights themselves rendered apparent.

But again, he found that the chord from which the greatest weight was suspended compared with that from which the weight next to the smallest depended, and which weight was eight pounds, produced the symphony diapente. Hence he discovered that this symphony is in a sesquialter ratio, in which ratio also the weights were to each other. And he found that the chord which was stretched by the greatest weight, produced, when compared with that which was next to it in weight, and was nine pounds, the symphony diatessaron, analogously to the weights. This ratio, therefore, he discovered to be sesquitertian; but that of the chord from which a weight of nine pounds was suspended, to the chord which had the smallest weight [or six pounds,] to be sesquialter.

For 9 is to 6 in a sesquialter ratio. In like manner, the chord next to that from which the smallest weight depended, was to that which had the smallest weight, in a sesquitertian ratio, [for it was the ratio of 8 to 6,] but to the chord which had the greatest weight, in a sesquialter ratio [for such is the ratio of 12 to 8.] Hence, that which is between the diapente and the diatessaron, and by which the diapente exceeds the diatessaron, is proved to be in an epogdoan ratio, or that of 9 to 8. But either way it may be proved that the diapason is a system consisting of the diapente in conjunction with the diatessaron, just as the duple ratio consists of the sesquialter and sesquitertian, as for instance, 12, 8, and 6; or conversely, of the diatessaron and the diapente, as in the duple ratio of the sesquitertian and sesquialter ratios, as for instance 12, 9, and 6.

After this manner, therefore, and in this order, having conformed both his hand and his hearing to the suspended weights, and having established according to them the ratio of the habitudes, he transferred by an easy artifice the common suspension of the chords from the diagonal stake to the limen of the instrument, which he called chordotonon . But he produced by the aid of pegs a tension of the chords analogous to that effected by the weights.

(11) But the tone of voice riseth up in the middle centre, in the flash or lightning, where the light is generated out of the heat, where the flash or lightning of life riseth up. Observe how this is done:

(7) Scientists have offered 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 low rate of speed--we will call this revolving thing "the object" in following out the illustration. Let us suppose the object moving slowly. It may be seen readily, but no sound of its movement reaches the ear. The speed is gradually increased. In a few moments its movement becomes so rapid that a deep growl or low note may be heard. Then as the rate is increased the note rises one 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. 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 heard from the revolving object, the rate of motion being so high that the human ear cannot register the vibrations. Then comes the perception of rising degrees of Heat. Then after quite a time the eye catches a glimpse of the object becoming a dull dark reddish color. As the rate increases, the red becomes brighter. Then as the speed is increased, the red melts into an orange. Then the orange melts into a yellow. Then follow, successively, the shades of green, blue, indigo, and finally violet, as the rate of sped increases. Then the violet shades 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 manifest 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.

(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.

(67) Timaeus: and that large motion produces “loud” sound, and motion of the opposite kind “soft” sound. The subject of concords of sounds must necessarily be treated in a later part of our exposition. We have still remaining a fourth kind of sensation, which we must divide up seeing that it embraces numerous varieties, which, as a whole, we call “colors.” This consists of a flame which issues from the several bodies, and possesses particles so proportioned to the visual stream as to produce sensation; and as regards the visual stream, we have already stated merely the causes which produced it.

(10) Every thought, emotion or mental state has its corresponding rate and mode of vibration. And by an effort of the will of the person, or of other persons, these mental states may be reproduced, just as a musical tone may be reproduced by causing an instrument to vibrate at a certain rate--just as color may be reproduced in the same may. By a knowledge of the Principle of Vibration, as applied to Mental Phenomena, one may polarize his mind at any degree he wishes, thus gaining a perfect control over his mental states, moods, etc. In the same way he may affect the minds of others, producing the desired mental states in them. In short, he may be able to produce on the Mental Plane that which science produces on the Physical Plane--namely, "Vibrations at Will." This power of course may be acquired only by the proper instruction, exercises, practice, etc., the science being that of Mental Transmutation, one of the branches of the Hermetic Art.

(24) By music we harmoniously relax the excessive tension of gravity. And as those who wish to address the people, do so often by the herald, that what is said may be better heard; so also in this case. For we have the word, that was spoken to many, before the common tradition. Wherefore we must set forth the opinions and utterances which cried individually to them, by which those who hear shall more readily turn.

(5) When the Creator and the Maker saw that it was impossible for them to talk to each other, they said: "It is impossible for them to say our names, the names of us, their Creators and Makers. This is not well," said the Forefathers to each other.

(47) Timaeus: the perturbable to the imperturbable; and that, through learning and sharing in calculations which are correct by their nature, by imitation of the absolutely unvarying revolutions of the God we might stabilize the variable revolutions within ourselves. Concerning sound also and hearing, once more we make the same declaration, that they were bestowed by the Gods with the same object and for the same reasons; for it was for these same purposes that speech was ordained, and it makes the greatest contribution thereto; music too, in so far as it uses audible sound,

(12) As one of the old Hermetic writers has truly said: "He who understands the Principle of Vibration, has grasped the scepter of Power."

(2) From these things, therefore, the signs of those that are inspired are multiform. For the inspiration is indicated by the motions of the [whole] body, and of certain parts of it, by the perfect rest of the body, by harmonious orders and dances, and by elegant sounds, or the contraries of these. Either the body, likewise, is seen to be elevated, or increased in bulk, or to be borne along sublimely in the air, or the contraries of these, are seen to take place about it. An equability, also, of voice, according to magnitude, or a great variety of voice after intervals of silence, may be observed. And again, sometimes the sounds have a musical intension and remission, and sometimes they are strained and relaxed after a different manner.

(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.

(507) I do indeed wish, I replied, that I could pay, and you receive, the account of the parent, and not, as now, of the offspring only; take, however, this latter by way of interest 11 , and at the same time have a care that I do not render a false account, although I have no intention of deceiving you. Yes, we will take all the care that we can: proceed. Yes, I said, but I must first come to an understanding with you, and remind you of what I have mentioned in the course of this discussion, and at many other times. What? The old story, that there is a many beautiful and a many good, and so of other things which we describe and define; to all of them the term ‘many’ is applied. True, he said. And there is an absolute beauty and an absolute good, and of other things to which the term ‘many’ is applied there is an absolute; for they may be brought under a single idea, which is called the essence of each. Very true. The many, as we say, are seen but not known, and the ideas are known but not seen. Exactly. And what is the organ with which we see the visible things? The sight, he said. And with the hearing, I said, we hear, and with the other senses perceive the other objects of sense? True. But have you remarked that sight is by far the most costly and complex piece of workmanship which the artificer of the senses ever contrived? No, I never have, he said. Then reflect; has the ear or voice need of any third or

(3) Modern Science has proven that all that we call Matter and Energy are but "modes of vibratory motion," and some of the more advanced scientists are rapidly moving toward the positions of the occultists who hold that the phenomena of Mind are likewise modes of vibration or motion. Let us see what science has to say regarding the question of vibrations in matter and energy.

(47) And when one power toucheth or stirreth the other, and tuneth or soundeth, then the tune or sound goeth forth, and riseth up again in all the powers of the Father; and so all the powers of the Father are again affected therewith, whereby they are always impregnated with the tune, and continually generate it again in every power:

(1) What you afterwards say is as follows: “ That some of those who suffer a mental alienation, energize enthusiastically on hearing cymbals or drums, or a certain modulated sound, such as those who are Corybantically inspired, those who are possessed by Sabazius, and those who are inspired by the mother of the Gods .” It is necessary, therefore, to discuss the causes of these things, and to show how they are definitely produced. That music, therefore, is of a motive nature, and is adapted to excite the affections, and that the melody of pipes produces or heals the disordered passions of the soul, changes the temperaments or dispositions of the body, and by some melodies causes a Bacchic fury, but by others occasions this fury to cease; and, likewise, how the differences of these accord with the several dispositions of the soul, and that an unstable and variable melody is adapted to ecstasies, such as are the melodies of Olympus, and others of the like kind; all these appear to me to be adduced in a way foreign to enthusiasm. For they are physical and human, and the work of our art; but nothing whatever of a divine nature in them presents itself to the view.