(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."

(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.

(28) So truly does advanced modern scientific thought recognize the nature of vibrations, that the axiom is announced that "The difference in things consists entirely of difference in vibrations." This axiom is akin to the ancient occult aphorism that "Things manifest differences according to their rate of vibrations." So, it is seen, all human investigation tends to prove the truth of the old occult axiom that "Everything vibrates." IV. The Principle of Rhythm The Principle of Rhythm manifests that universal regular swing or time-beat which is apparent in all the manifested world, from its highest to its lowest manifestation. The ancient occult axiom "Everything beats time" expresses this fundamental fact of the Cosmos.

(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.

(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.

(3) 3. The Principle of Vibration "Nothing rests; everything moves; everything vibrates." --The Kybalion. This Principle embodies the truth that "everything is in motion"; "everything vibrates"; "nothing is at rest"; facts which Modern Science endorses, and which each new scientific discovery tends to verify. And yet this Hermetic Principle was enunciated thousands of years ago, by the Masters of Ancient Egypt. This Principle explains that the differences between different manifestations of Matter, Energy, Mind, and even Spirit, result largely from varying rates of Vibration. From THE ALL, which is Pure Spirit, down to the grossest form of Matter, all is in vibration--the higher the vibration, the higher the position in the scale. The vibration of Spirit is at such an infinite rate of intensity and rapidity that it is practically at rest--just as a rapidly moving wheel seems to be motionless. And at the other end of the scale, there are gross forms of matter whose vibrations are so low as to seem at rest. Between these poles, there are millions upon millions of varying degrees of vibration. From corpuscle and electron, atom and molecule, to worlds and universes, everything is in vibratory motion. This is also true on the planes of energy and force (which are but varying degrees of vibration); and also on the mental planes (whose states depend upon vibrations); and even on to the spiritual planes. An understanding of this Principle, with the appropriate formulas, enables Hermetic students to control their own mental vibrations as well as those of others. The Masters also apply this Principle to the conquering of Natural phenomena, in various ways. "He who understands the Principle of Vibration, has grasped the scepter of power," says one of the old writers.

(78) Each ring includes with in its own nature all the rings within itself and is included within the natures of all the rings outside of itself. Thus, A 1--the primitive dot--controls and contains the thirty-nine rings which it encloses, all of these partaking of its nature in varying degrees according to their respective dignities. Consequently, the entire area from A 1 to D 10 inclusive is the original dot, and the rings symbolize the divisions which took place with in it and the emanations which poured out from it after its establishment in the midst of the abstract nature of AIN SOPH. The powers of the rings decrease towards the center of the diagram, for Power is measured by the number of things controlled, and each ring controls the rings within it and is controlled by the rings outside of it. Thus, while A 1 controls thirty-nine rings besides itself, B 1 controls only twenty-nine rings besides its own. Therefore, A 1 is more powerful than B 1. As the greatest spiritual solidity, or permanence, is at the circumference and the greatest material density, or impermanence, is at the center of the diagram, the rings as they decrease in Power become more material and substantial until the center sphere, D 10, symbolizes the actual chemical elements of the earth. The rates of vibration are also lower as the rings approach the center. Thus, the vibration of A 2 is lower than A 1 but higher than A 3, and so on in decreasing scale towards the center, A 1 being the highest and D 10 the lowest sphere of creation. While A 1, the ruler of creation, controls the circles marked A, B, C, and D, it is less than the three rings of AIN SOPH--X 1, X2, and X3--and therefore bows before the throne of the ineffable Creator from whose substances it was individualized.

(11) The esoteric teachings, as has been said, clearly and positively state that before there began the wonderful process of Evolution from simple to more complex forms of manifestation—from lower to higher—there must first have been an "involution" or in-folding of the World Soul into the simple, gross, elemental forms of matter. The vibrations must have been first lowered, before they can have been increased.

(22) In this chart is set forth a summary of Fludd's theory of universal music. The interval between the element of earth and the highest heaven is considered as a double octave, thus showing the two extremes of existence to be in disdiapason harmony. It is signifies that the highest heaven, the sun, and the earth have the same time, the difference being in pitch. The sun is the lower octave of the highest heaven and the earth the lower octave of the sun. The lower octave (Γ to G) comprises that part of the universe in which substance predominate over energy. Its harmonies, therefore, are more gross than those of the higher octave (G to g) wherein energy predominates over substance. "If struck in the more spiritual part," writes Fludd, "the monochord will give eternal life; if in the more material part, transitory life." It will be noted that certain elements, planets, and celestial spheres sustain a harmonic ratio to each other, Fludd advanced this as a key to the sympathies and antipathies existing between the various departments of Nature.

(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

(38) In the Pythagorean tetractys--the supreme symbol of universal forces and processes--are set forth the theories of the Greeks concerning color and music. The first three dots represent the threefold White Light, which is the Godhead containing potentially all sound and color. The remaining seven dots are the colors of the spectrum and the notes of the musical scale. The colors and tones are the active creative powers which, emanating from the First Cause, establish the universe. The seven are divided into two groups, one containing three powers and the other four a relationship also shown in the tetractys. The higher group--that of three--becomes the spiritual nature of the created universe; the lower group--that of four--manifests as the irrational sphere, or inferior world.

(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.

(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.

(54) In the Book of Coming Forth by Day, many of the Egyptian secrets have been preserved to this generation. While this ancient scroll has been well translated, only a few understand the secret: significance of its magical passages. Oriental races have a keen realization of the dynamics of sound. They know that every spoken word has tremendous power and that by certain arrangements of words they can create vortices of force in the invisible universe about them and thereby profoundly influence physical substance. The Sacred Word by which the world was established, the Lost Word which Masonry is still seeking, and the threefold Divine Name symbolized by A. U. M.--the creative tone of the Hindus--all are indicative of the veneration accorded the principle of sound.

(5) One day while meditating upon the problem of harmony, Pythagoras chanced to pass a brazier's shop where workmen were pounding out a piece of metal upon an anvil. By noting the variances in pitch between the sounds made by large hammers and those made by smaller implements, and carefully estimating the harmonies and discords resulting from combinations of these sounds, he gained his first clue to the musical intervals of the diatonic scale. He entered the shop, and after carefully examining the tools and making mental note of their weights, returned to his own house and constructed an arm of wood so that it: extended out from the wall of his room. At regular intervals along this arm he attached four cords, all of like composition, size, and weight. To the first of these he attached a twelve-pound weight, to the second a nine-pound weight, to the third an eight-pound weight, and to the fourth a six-pound weight. These different weights corresponded to the sizes of the braziers' hammers.

(26) In conclusion we would again remind you that according to the Principle of Correspondence, which embodies the truth: "As Above so Below; as Below, so Above," all of the Seven Hermetic Principles are in full operation on all of the many planes, Physical Mental and Spiritual. The Principle of Mental Substance of course applies to all the planes, for all are held in the Mind of THE ALL. The Principle of Correspondence manifests in all, for there is a correspondence, harmony and agreement between the several planes. The Principle of Vibration manifests on all planes, in fact the very differences that go to make the "planes" arise from Vibration, as we have explained. The Principle of Polarity manifests on each plane, the extremes of the Poles being apparently opposite and contradictory. The Principle of Rhythm manifests on each Plane, the movement of the phenomena having its ebb and flow, rise and flow, incoming and outgoing. The Principle of Cause and Effect manifests on each Plane, every Effect having its Cause and every Cause having its effect. The Principle of Gender manifests on each Plane, the Creative Energy being always manifest, and operating along the lines of its Masculine and Feminine Aspects.

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

(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.

(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.

(11) To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws.