(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.

(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.

(53) And I asked the angel of peace who went with me: 'For whom are they preparing these instruments?'

(67) Now what is it that makes the Hearing, that you can hear that which stirs and makes a Noise? Wilt thou say that it is caused by the Noise of that outward Thing which gives the Sound? No! there must also be somewhat that must receive the Sound, and qualify or mix with the Sound, and distinguish the Sound of what is played or sung; the outward cannot do that alone, the inward must receive and distinguish the Noise. Behold, here you find the Beginning of the Life, and the Tincture wherein the Life consists; for the Tincture of the Crack in the Springing up of the Life, in the Breaking-open of the dark Gate, stands in the Sounding, and has its Gate open (next the Fire-flash near the Eyes) and receives the Noise of whatsoever sounds.

(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.

(27) "When the revolving object reaches a certain degree or rate of vibration, its molecules disintegrate, and resolve themselves into the original elements or atoms. Then the atoms, in turn disintegrate, and are resolved into the countless corpuscles which constitute the atom. And finally even the corpuscles disintegrate, and a condition of ethereal substance is produced. Science does not dare to follow the illustration further, but the occultists teach that if the vibrations were continuously increased the revolving object would mount up the successive states of manifestation, and would display the various higher stages of consciousness." The occultists teach that each and every mental or emotional state has its own distinctive rate of vibration, and that the secret of "emotional contagion" is due to the fact that similar vibrations are set up in the emotional nature of persons subjected to the influence of strong emotion in another person. All manifestations of thought, emotion, will, desire, or feeling, or any other mental state, are accompanied and caused by vibrations of a certain high rate, and that these vibrations tend to influence others in their field of "induction," and tend to set up in the others similar vibrations. In this fact lies the secret of Mental Influence, Personal Magnetism, etc. A knowledge and mastery of the science of mental vibrations enables the skilled Rosicrucian to change the rate of his mental vibrations at will, and to thus maintain a state of mental calm and power, unaffected by the thought vibrations of those around him.

(4) O thou who guidest the Bark of Rā, sound is thy rigging and free from disaster as thou passest on to the Tank of Flame

(4) 2. “Man was generated by far the wisest of all [terrestrial] animals. For he is able to contemplate the things which exist, and to obtain from all things science and wisdom. To which also it may be added, that divinity has engraved and exhibited in him the system of universal reason, in which all the forms of things in existence are distributed, and the significations of nouns and verbs. For a place is assigned for the sounds of the voice, viz. the pharynx, the mouth, and the nostrils. But as man was generated the instrument of the sounds, through which nouns and verbs are signified, so likewise of the conceptions which are beheld in the things that have an existence. And this appears to me to be the work of wisdom, for the accomplishment of which man was generated and constituted, and received organs and powers from divinity.

(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

(9) Tired, but not discouraged, as the result of the fruitlessness of his efforts, C.R.C. returned to Germany, where he built a house in which he could quietly carry on his study and research. He also manufactured a number of rare scientific instruments for research purposes. While he could have made himself famous had he cared to commercialize his knowledge, he preferred the companionship of God to the esteem of men.

(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."

(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.

(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.

(20) And why is there a tail at the bottom of the ג? He said: ג has a head on top, and is like a pipe. Just like a pipe, ג draws from above through its head, and disperses through its tail. This is ג.

(6) Then he touches it, saying: c Thou art the moving. Thou art the glowing. Thou art the full. Thou art the steadfast. Thou art the sole resort. Thou art the sound hin that is made. Thou art the making of the sound hin} Thou ait the Loud Chant (udglthd). Thou art the chanting. Thou art that which is proclaimed. Thou art that which is proclaimed in the antiphone. Thou art the flaming in the moist. Thou art the pervading. Thou art surpassing. Thou art food. Thou art light. Thou art destruction. Thou art the despoiler.'

(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.

(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.

(46) 3. He established twenty-two basic letters, formed by the voice and impressed upon the air by the breath. He set them to be audibly uttered in five different parts of the human mouth: namely, Gutturals, א ה ח ע; Palatals, ג י כ ק; Linguals, ד ט ל נ ת Dentals, ז ש ס ר ץ; Labials, ב ו מ ף.

(2) "How this worthy Science was first begunne, I shall tell. Before Noah's Flood, there was a man called Lameck as it is written in the 4 Chap. of Gen.: and this Lameck had two Wives. The one was called Adah, and the other Zillah; by the first wife Adah he gott two Sons, the one called Jaball, and the other Juball, and by the other wife Zillah he got a Son and Daughter, and the four children found the beginning of all Crafts in the world. This Jaball was the elder Son, and he found the Craft of Geometric, and he parted flocks, as of Sheep and Lambs in the fields, and first wrought Houses of Stone and Tree, as it is noted in the Chap, aforesaid, and his Brother Juball found the crafte of Musick, of Songs, Organs and Harp. The Third Brother [Tubal-cain] found out Smith's craft to work Iron and steel, and their sister Naamah found out the art of Weaving. These children did know thatt God would take Vengeance for Sinne, either by fire or water, wherefor they wrote these Sciences which they had found in Two Pillars of stone, thatt they might be found after the Flood. The one stone was called Marbell--cannott burn with Fire, and the other was called Laturus [brass?], thatt cannott drown in the Water." The author of this Constitution there upon declares that one of these pillars was later discovered by Hermes, who communicated to mankind the secrets thereon inscribed.

(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.