"Vibration is the rhythmical motion of a body within itself." [Keely See Oscillation]
"To move suddenly a square inch of air at the velocity of his vibratory circuit, on full line of graduation and at a vibration only of 2,750,000 per second, would require a force at least of twenty-five times that of gunpowder, and at 21,000 lbs. per sq. inch it would be 525,000 lbs. per square inch. The finer the substance the greater the power and velocity under such vibrations." [Snell Manuscript - The Book, page 2]
The structure of the air molecule according to Keely is as follows: Broken up, by vibratory action, he finds it to contain the "atomic triplet." This exists in a triangular position within the molecule, at its center, unless acted upon by electricity, when the molecule becomes oblate and the three atoms are ranged in a line within unless broken up by vibration. Nature never gives a vacuum, consequently the space within the molecule not occupied by the atomic triplet must be filled with something. This is where the "all-pervading ether" has made its secret abode through untold aeons. [Laurence Oliphant] [Snell Manuscript - The Book, page 3]
He has again reduced in size the instrument producing the force. From 1882 to 1884 the "Generator" was six feet long and corresponding wide and high, but failing to make the arrangement automatic upon which its mechanical usefulness depended, Keely found a new standard for research in an experiment often made by himself, but never before successful, which resulted in invention in 1885 of the "Liberator" not so large as a lady's small round worktable. He made astonishing progress with this beautiful piece of vibratory mechanism, so as to combine the production of the power, operation of the cannon, his engine and his disintegrator in a machine no larger than a dinner plate and only three or four inches in thickness. This was completed in 1886, up to which time his experiments were upon the principle of sympathetic vibration, for liberating a vapory or etheric product. His later experiments were another modification of vibratory sympathy, and the size of the instrument used now, 1888, for the same purposes is no larger than an old fashioned silver watch. A pressure of 30,000 lbs. to the square inch in raising of the lever, and all other operations, without one ounce of pressure in any part of the apparatus, are effected by the ether. The force is transmitted along a wire of platinum and silver. Keely has named this new modification "Negative Attraction." The two forms of force with which he has experimented and the attendant phenomena, are exactly antithetical. It is by changing the vibrations of the cosmic ether that Keely releases this energy. Dr. Dupuy, of New York, experimented along these lines for many years, but without success to the degree Keely had. [underline added] [Snell Manuscript - The Book, page 3]
The vibrations induced by this experiments reached over 700,000,000 per second, unshipping the apparatus, thus making it insecure for a repetition of the experiments. The decarbonized steel compressors of said apparatus moved as if composed of putty.
"The human ear cannot detect the triple chord of any vibration, or sounding note but every sound that is induced of any range, high or low, is governed by the same laws, as regards triple action of such that govern every sympathetic flow in Nature. Were it not for these triple vibratory conditions, change of polarity could never be effected, and consequently there could be no rotation. Thus the compounding of the triple triple, to produce the effect would give a vibration in multiplication reaching the ninth, in order to induce subservience, the enumeration which it would be folly to undertake, as the result would be a string of figures a mile in length to denote it. [Snell Manuscript - The Book, DISTURBANCE OF MAGNETIC NEEDLE, page 8]
"There is good reason for believing that insanity is simply a condition of differentiation in the mass-chords of the convolutions, which creates an antagonistic molecular bombardment towards the neutral or attractive centres of such convolutions. This may be compared to a knot on a violin string. As long as this knot remains, it is impossible to elicit, from its sympathetic surroundings, the condition which transfers pure concordance to its resonating body. Discordant conditions (i.e., differentiation of mass) produce negatization to coincident action. Pure sympathetic concordants are as antagonistic to negative discordants as the negative is to the positive; but the vast volume the sympathetic holds over the non-sympathetic, in ethereal space, makes it at once the ruling medium and re-adjuster of all opposing conditions, when properly brought to bear upon them. Josiah Royce is right as regards correspondent sympathetic association between two conditions. If concordance can be established, even of unlike states, no matter whether it be of the high tenuous forces of nature, gases with liquids, liquids with solids, solids with gases, the structural conditions can be perfectly adverse. Their neutral centres are the focalized seat of sympathetic concordance for controlling any differentiation that may exist outside, or in the mass that surrounds them. Certain orders of vibration can reach these centres and establish a concordant flow of sympathy, independent of any mass antagonism; in other words, certain orders of sympathetic vibratory transmission can correct and equate all differentiation that may exist between physical organisms and their cerebellic flows. Discord is disease. Harmony is health.''" - Keely." [Vibratory Physics - The Connecting Link between Mind and Matter]
"In organ pipes, of a certain calibre, very sensitive waves occur at intervals; as according to the character of the sound evolved; but on a combination of resonators composed of brass tubes of more than nine in number, a wave of sound, induced by certain chords passing over them, produces high vortex action of the air enclosed in them. The vibration of tuning forks induces alternate condition of the air that surrounds them, if in open atmosphere; but quite a different action presents itself when the forks are exercised in resonating tubes, set to thirds of the mass chord they represent. Then high vortex action is the instant result. Vibrators cannot be set promiscuously in tubes, and get such results, any more than a musician can render a musical composition on the violin before tuning it." [Appendix I]
"I find in my researches, as to the condition of molecules under vibration, that discordance cannot exist in the molecule proper; and that it is the highest and most perfect structural condition that exists; providing that all the progressive orders are the same. Discordance in any mass is the result of differentiated groups, induced by antagonistic chords, and the flight or motions of such, when intensified by sound, are very tortuous and zigzag; but when free of this differentiation are in straight lines. Tortuous lines denote discord, or pain; straight lines denote harmony, or pleasure. Any differentiated mass can be brought to a condition of harmony, or equation, by proper media, and an equated sympathy produced." [Keely and His Discoveries, Chapter VII]
"No such thing as discord exists in the molecule. Discordance results from chords producing differentiation and may be equated by the proper chord of harmony. Every gaseous molecule is a resonator to any and all vibrations, whether concordant or discordant. That which we term discord exists in sound itself, not in matter." [Snell Manuscript - the book, DISCORD - Snell]
"The molecule itself is a world ruled by the same sympathetic forces that govern the planets of our solar system. Its three component intermolecules, each like a small sphere, oscillate within its shell-like etheric envelope with a frequency of 20,000 per second, and the molecular etheric capsule rotates about them with inconceivable velocity. Within the molecule no intermolecule ever comes in contact with even its nearest attendant. Each is held by its gravital neutral center within its proper sphere of action. Molecular dissociation by intermittent vibration does not disturb in the next higher, the atomic subdivision, the fixed neutral center of the atomic triplets. Centripetal and centrifugal forces rule the orbits and revolutions of the components of the molecule in the same manner as interplanetary forces of the same type rule the elements of the solar system. [Snell Manuscript - the book]
Every mass is an aggregation of molecules each having its "neutral center" wherein are equated its component forces consisting of the three fundamental modes of vibration. The balanced activity of these vibrations at the "neutral center" without diminution of force, makes possible the permanence of form and matter.
Since the continuity of existence of all molecules and all masses depends on the three fundamental component modes of vibration being held in balance at the "neutral center" it follows that certain orders of vibration can, by their influence on this neutral center, break the balanced equation, divide the components of the molecules, and therefore divide the components of the mass. [PERMANENCE OF FORM AND MATTER]
"Silence is one - but sound springs from silence when its divided moving pair collide - so sound is three, and its vibrations in sequences of rest and action, are also three." [Atomic Suicide, page 109]
It thus follows that all today's technical, hydraulic and chemo-dynamic machines, conveyances, agricultural implements (ploughs, harrows, disc-tillers, cultivators), dynamos, turbines, propellers, pumps, etc. are developmentally harmful, for apart from their pressure-intensifying shape, they are almost entirely constructed with materials unsuited to Nature's processes. Their use triggers off lower-grade vibrations in molecular structures. [The Energy Evolution - Harnessing Free Energy from Nature, Cadaverine Poison in Ray-Form - Ptomaine Radiation]
A Brief Description of My Discovery
Leonstein, 1945 (Schauberger Archives).
Arising from an exhaustive and in-depth observation of Nature, my discovery consists in the fact that all life and growth is shaped and fashioned through vibration and movement. This naturalesque form of motion I finally discovered after decades of research and countless series of experiments. It is the creative curving form of motion found in Nature that I have come to describe as 'cycloid-space-curve-motion', which in more common language is perhaps more easily understandable as a 'life-curve', 'curve of Nature' or even as a 'bio-curve'. [The Energy Evolution - Harnessing Free Energy from Nature, NEW FORMS OF TEMPERATURE]
When the fruit juices that have flourished in the Sun begin to ferment, it is a sign that reactive temperature differences have triggered the fermenting movement, which in the initial stages has to separate the inferior from the superior. The former will be separated and centrifugated out through cycloid-space-curve-motion. The latter interconnects with itself, as it were, and the product of this remarkable marriage process is that something, which also brings us out of the delicately balanced equilibrium that the Earth ceaselessly enjoys. Not being in a state of stable equilibrium, she has constantly to rotate about her own axis in a form of movement that declinates and oscillates in two directions. This is how she generates the inversely symmetrically- and inversely proportionally-acting force, which enables everything that crawls and flies on this dung-heap Earth to move 'originally' (autonomously) in order to seek out its food, which also contains allotropic energy-producing substances. These are then broken down through the vibration of the organs, leading to the familiar development of physical strength and mental vigour, whose ur-causes have not been perceived by physico-technical scientists, who calculate with common calories and measure them with decimal scales and rulers. Moreover, they also believe they have captured everything with their tweezers that is proper to Nature. Unfortunately, however, this cannot be accomplished with such an instrument, because the producer of 'measure' and 'weight' is an imperceptible extraordinary energy-form, which as the 'essential' is the 'reactivated' itself, which actively moves the ordinary. [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]
In order to round off this understanding, the concept of 'mass' (matter) must also be explained in greater detail. Mass is here to be understood as the product of tripolar motion. It represents the partial solidification, as it were, of a motive force that is latent in a neutral carrier-substance and which to a certain extent acts as the resistance to possible inner motion (vibration). [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]
"While vibrations are the sound-stuff, the protoplasm of notes, semitones are, as it were, the atoms of which music is composed. We may think and talk of quarter tones and commas, apotomes and skismas, and dots, but these have no place as intervals for the musical ear, nor any part in the compositions which so charm us of the great masters." [Scientific Basis and Build of Music, page 20]
Different writers have put forth different views of what constitute a musical vibration, but their various views do not make any difference in the ratios which the notes of this sound-host bear to each other. Whether the vibrations be counted as single or double vibrations, the ratios of their relative motions are the same. Nevertheless, a musical vibration is an interesting thing in itself, and ought to be correctly defined.
A string when vibrating musically is passing and re-passing the central line of its rest or equilibrium with a certain range of excursion. Some writers have defined a vibration to be the passage of the string from one extreme of its excursion to the other, while some have preferred to define it as the passage of the string from the one extreme of its excursion to the other and back again. D. C. Ramsay has been led in his researches to define a vibration as the movement of the string from its central line of rest to the extreme of its excursion on one side, and back to the central line of rest; and from the central line of rest to the extreme of its excursion on the other side, and back again to the "right line," as he calls it, as a second vibration. His reasoning on this will be seen in what follows. (See Fig. 3, Plate IV.) [Scientific Basis and Build of Music, page 21]
Musical sounds are usually caused in the ear by certain vibrations of the surrounding air, which originate from solid bodies in a state of vibration from some force exerted upon them. Vibrations of the air require to attain a certain rate of speed before they become audible to the human ear; and they require to have certain ratios of rate of rapidity in order to constitute that beautiful host of sounds which constitutes the music of mankind. These musical vibrations may arise in the air from a vibrating organ pipe, or a vibrating tuning fork, or a bell, or a sounding glass, or a strand of wire or gut-string, or other rhythmically vibrating body; but to explain and define the nature of a musical vibration from the action upon it of an elastic string is to explain and define it for all. But before defining what a vibration of a string is, let us hear what others have said about it. Charles Child Spencer, Treatise on Music, p. 6, says- "It is customary in calculating the ratios of vibration of musical strings, and which answer to the waves of the atmosphere, to reckon by double vibrations, so that instead of saying there are 32 single vibrations in the lowest sound, C, writers on this branch of music say there are 16 double vibrations in this sound. This method of calculation, therefore, gives 256 vibrations for the fourth Octave C." Playfair, in his Outlines of Natural Philosophy, p. 282, says- "It is usual to reckon the vibrations of a string different from those of a pendulum; the passage from the highest point on one side to the highest point on the other is reckoned a vibration of a pendulum; the passage from the farthest distance on one side to the farthest distance on the other and back again to its first position, is the accounted a vibration of a musical string. It is properly a double vibration." Holden, in his Rational System of Music, says- "Mr. Emerson reckons the complete vibration the time in which a sounding string moves from one side to [Scientific Basis and Build of Music, page 22]
"the other, like as we also reckon the vibrations of a pendulum." Holden adds that Dr. Smith, in his Harmonics, reckons the complete vibration to be double of this. Lees, in his Acoustics, says- "The travel of a vibrating elastic body from one extreme to the opposite and back again is called a vibration. Continental writers define a vibration to be the travel of a vibrating body from one extreme position to the opposite. This corresponds to our definition of the oscillation of a pendulum." [Scientific Basis and Build of Music, page 23]
It is in their inverse relations that the major and the minor are equal. Every note, chord, and progression in the one has its reciprocal or corresponding note, chord, and progression in the other. This is the Law of Duality. And this general law of Nature is so deeply rooted in music, that is the numbers which represent the vibrations in the major system be made to represent quantities of string, these quantities will produce the minor system (beginning, of course, with the proper notes and numbers); so that when the quantities are minor the tones are major, and when the quantities are major the tones are minor.1[Scientific Basis and Build of Music, page 44]
After vibrations the next thing is musical notes, the sounds produced by the vibrations falling into the ear. Sounds arise in association. There are no bare simple sounds in music; it is a thing full of the play of sympathy. Such a thing as a simple solitary sound would be felt as a strange thing in our ears, accustomed as we are to hear affiliated sounds only. These affiliated sounds, called "harmonics," or "partials" as they have also been called, because they are the parts of which the sound is made up, are like perspective in vision. In perspective the objects lying in the line of sight, seem smaller and smaller, and more dim and indefinite as they stretch away into the distance; while nearer objects and those in the foreground are apparently larger, and are more clearly seen. This is the way of a musical sound; one of its component elements, the fundamental partial, being, as it were, in the foreground to the ear, is large and pronounced; while the other elements are less distinctly heard, and are fainter and fainter as they recede into the musical distance in the perspective of the ear. Few have any idea of the number of these weaker partials of a musical sound. Tyndal's illustrations in his very instructive work on Sound show a string spontaneously divided into twenty segments, all vibrating separately, being divided by still nodes along its length; and a vibrating string will keep thus [Scientific Basis and Build of Music, page 58]
which seems to show that not only has one part of a vibrating string sympathy with another part of it so as to go into harmonic partials, as we have just seen, but as if the very air itself had sympathy with harmoniously vibrating strings; for Tartini observed that two harmonious sounds being produced and sustained as they can be, for example, by a strong bow on the violin, a third sound will be heard. Tartini's name for it was simply "a third sound." This is not an overtone, as Helmholtz has called the harmonic partials of one sounding string, but an undertone, because it is a "grave harmonic," away below the sounds of the two strings which awaken it. The subject of these undertones has been carefully studied since Tartini's day, and more insight has been obtained since we are now able to count and register the vibration of any musical sound. Helmholtz has called these third sounds of Tartini's "difference sounds," because when awakened by two strings, for example, the vibration-number of the third tone is the difference of the vibrations-numbers of the two tones which awaken it. The note C with vibration-number 512, and another C whose vibration-number is 256, the octave, awakened no third sound, because there is no difference between the two numbers - the one is just the doubled or halved; but if we take C256 and G381, its fifth, the difference number is 128; this being a low octave of C256, it has the effect of strengthening the upper one. Helmholtz found this to be the law of the third sound as to its producing, and the effect of it when produced. This third sound, mysteriously arising in the air through the sympathy it has with all concordant things, is another among many more suggestions that the whole Creation is measured and numbered to be in sympathy one part with another. The Creation is a universe. [Scientific Basis and Build of Music, page 60]
The individual character of any note, and the comparative degree of contrast between any two notes in the system, depends on at least three different causes. The first is the genetic relation of the two notes. If the one note has 2 vibrations and the other 3, or the one 4 and the other 5, or the one 5 and the other 8, because of this, and because of the excess of the vibration of the one over the other, "a third sound" or "grave harmonic" being awakened between them, the different ratios have different degrees of complexity, and, in a general way, the greater the complexity the greater the [Scientific Basis and Build of Music, page 60]
We have gone from vibrations to musical notes; from notes to chords; and now we proceed to scales - that is, groups of notes or chords in succession, which are bound and unified in some clear and definite way. [Scientific Basis and Build of Music, page 64]
If it be asked why no more primes than 2, 3, and 5 are admitted into musical ratios, one reason is that consonances whose vibrations are in ratios whose terms involve 7, 11, 13, etc., would be less simple and harmonious than those whose terms involve the lesser primes only. Another reason is this - as perfect fifths and other intervals resulting from the number 3 make the schism of a comma with perfect thirds and other intervals resulting from the number 5, so intervals resulting from the numbers 7, 11, 13, etc., would make other schisms with both those kinds of intervals. [Scientific Basis and Build of Music, page 75]
In getting the length of a string, in inches or otherwise, to produce the scale of music, any number may be fixed on for the unit; or for the vibrations of the root note any number may be fixed on for the unit; but in the fractions which show the proportions of the notes of the scale, there is no coming and going here; this belongs to the invariables; there is just one way of it. Whatever is not sense here is nonsense. It is here we are to look for the truth. The numbers which express the quantities and the numbers which express the motions are always related as being of the same kind. The fractions bring their characters with them, and we know by this where they come from. 1/4 of a string gives a note 2 octaves above the whole string, no matter what may be its length; 2 has exactly the same character as 1; 2/4 gives the note which is 1 octave above the whole string; but in the case of 3/4 here is a new ingredient, 3; 3/4 of a string gives a note which is a fifth below the [Scientific Basis and Build of Music, page 75]
There is nothing extraordinary in this. It is another fact which gives this one its importance, and that is that the musical system is composed of three fifths rising one out of another; so this note by 3/4 becomes the root not only of a chord, but the root of all the three chords, of which the middle one is the tonic; the chord of the balance of the system, the chord of the key; the one out of which it grows, and the one which grows out of it, being like the scales which sway on this central balance-beam. Thus F takes its place, C in the center, and G above. These are the 3 fifths of the system on its masculine or major side. The fractions for A, E, and B, the middle notes of the three chords, are 4/5, 3/5, and 8/15; this too tells a tale; 5 is a new ingredient; and as 3 gives fifths, 5 gives thirds. From these two primes, 3 and 5, along with the integer or unit, all the notes of the system are evolved, the octaves of all being always found by 2. When the whole system has been evolved, the numbers which are the lengths of the strings in the masculine or major mode are the numbers of the vibrations of the notes of the feminine or minor mode; and the string-length-numbers of the minor or feminine are the vibration-numbers of the notes of the major or masculine mode. These two numbers, the one for lengths and one for vibrations, when multiplied into each other, make in every case 720; the octave of 360, the number of the degrees of the circle. [Scientific Basis and Build of Music, page 76]
the excess of the vibrations of the one note over the other makes one or more sounds which are called "grave harmonics;" e.g., in the interval of the fifth, in the ratio of 2:3, the excess of 3 over 2 is 1, so the grave harmonic is an octave below the lowest of the two notes, that is, the ratio of 1:2. This reinforces the lowest note, 2, and gives it a solid effect. In this way the octave is incorporated into the fifth, and unity with variety is combined with the law of continuity at the very threshold of harmony. In 32 of the 42 intervals the grave harmonics are notes which belong to the natural scale. In the 10 remaining intervals which have not the exact number of vibrations found anywhere in the natural scale, 6 of them are from the number 7, thus - 7, 7, 7, 21, 21, 35; the remaining 4 are from 11, 13, 13, and 19. [Scientific Basis and Build of Music, page 77]
pendulum where fourth the length is double the oscillations. A third condition in this order is in springs or reeds where half the length is four times the vibrations. If we take a piece of straight wire and make it oscillate as a pendulum, one-fourth will give double the oscillations; if we fix it at one end, and make it vibrate as a spring, half the length will give four times the vibrations; if we fix it at both ends, and make it vibrate as a musical string, half the length will produce double the number of vibrations per second. [Scientific Basis and Build of Music, page 80]
2 - In the second sphere the tension of strings and other elastic bodies imbues them with forces operating upon the elastic air, producing vibrations quick enough to awaken sounds for the human ear. Here Nature plays on her tuneful harp the same grand fugue; from which everything in music is derived. [Scientific Basis and Build of Music, page 86]
The sympathy of one thing with another, and of one part of a thing with another part of it, arises from the principle of unity. For example, a string requires to be uniform and homogenous to have harmonics producing a fine quality of tone by the sweet blendings of sympathy; if it be not so, the tone may be miserable ... You say you wish I were in touch with Mr. Keely; so do I myself ... I look upon numbers very much as being the language which tells out the doings of Nature. Mr. Keely begins with sounds, whose vibrations can be known and registered. I presume that the laws of ratio, position, duality, and continuity, all the laws which go to mould the plastic air by elastic bodies into the sweetness of music, as we find them operative in the low silence of oscillating pendulums, will also be found ruling and determining all in the high silence of interior vibrations which hold together or shake asunder the combinations which we call atoms and ultimate elements, but which may really be buildings of wondrous complexity occupying different ranges of place and purpose between the visible cosmos and Him who built and evermore buildeth all things. The same laws, though operating in different spheres, make the likenesses of things in motion greater than the differences. [Scientific Basis and Build of Music, page 87]
It is a remarkable fact that the numbers for the lengths of strings producing the major scale are the number of the vibration of the notes of the minor scale; for example, string-length as 26 2/3 will give the vibrations for [Scientific Basis and Build of Music, page 87]
Whatever interval is sharpened above the tone of the open string, divide the string into the number of parts expressed by the larger number of the ratio of the interval, and operate in that part of the string expressed by the smaller number of it. For example, if we want to get the major third, which is in the ratio of 4:5, divide the string into five parts and operate on four. The lengths are inversely proportional to the vibrations. [Scientific Basis and Build of Music, page 100]
THIS plate is a Pendulum illustration of the System of musical vibrations. The circular lines represent Octaves in music. The thick are the octave lines of the fundamental note; and the thin lines between them are lines of the other six notes of the octave. The notes are all on lines only, not lines and spaces. The black dots arranged in these lines are not notes, but pendulum oscillations, which have the same ratios in their slow way as the vibrations of sounding instruments in the much quicker region where they exist. The center circle is the Root of the System; it represents F1, the root of the subdominant chord; the second thick line is F2, its octave; and all the thick lines are the rising octaves of F, namely 4, 8, 16, 32, and 64. In the second octave on the fifth line are dots for the three oscillations which represent the note C3, the Fifth to F2, standing in the ratio of 3 to 2; and the corresponding lines in the four succeeding Octaves are the Octaves of C3, namely 6, 12, 24, and 48. On the third line in the third Octave are 5 dots, which are the 5 oscillations of a pendulum tuned to swing 5 to 4 of the F close below; and it represents A5, which is the Third of F4 among musical vibrations. On the first line in the fourth Octave are 9 dots. These again represent G9, which stands related to C3 as C3 stands to F1. On the seventh line of the same octave are 15 dots; these represent the vibrations of E15, which stands related to C3 as A5 stands to F1. On the sixth line of the fifth Octave are 27 dots, representing D27, which stands related to G9 as G9 stands to C3, and C3 also to F1; it is the Fifth to G. And last of all, on the fourth line of the sixth Octave are 45 dots, representing B45, which, lastly, stands related to G9 as E15 stands to C3, and A5 to F1; it is the Third to this third chord - G, B, D. The notes which arise in each octave coming outward from the center are repeated in a double number of dots in the following Octaves; A5 appears as 10, 20, and 40; G9 appears as 18 and 36; E15 appears as 30 and 60; D27 appears as 54; and last of all B45 only appears this once. This we have represented by pendulum oscillations, which we can follow with the eye, the three chords of the musical system, F, A, C; C, E, G; and G, B, D. C3 is from F1 multiplied by 3; G9 is from C3 multiplied by 3; these are the three Roots of the three Chords. Their Middles, that is their Thirds, are similarly developed; A is from F1 multiplied by 5; E15 is from C3 multiplied by 5; B45 is from G9 multiplied by 5. The primes 3 and 5 beget all the new notes, the Fifths and the Thirds; and the prime 2 repeats them all in Octaves to any extent. [Scientific Basis and Build of Music, page 102]
Fig. 1 - The pendulums in this illustration are suspended from points determined by the division of the Octave into Commas; the comma-measured chords of the Major key being S, 9, 8, 9, 5; T, 9, 8, 5, 9; D, 8, 9, 5, 9. The pendulums suspended from these points are tuned, as to length, to swing the mathematical ratios of the Diatonic scale. The longest pendulum is F, the chords being properly arranged with the subdominant, tonic, and dominant, the lowest, center, and upper chords respectively. Although in "Nature's Grand Fugue" there are 25 pendulums engaged, as will be seen by reference to it, yet for the area of a single key 13 pendulums, as here set forth, are all that are required. It will not fail to be observed that thus arranged, according to the law of the genesis of the scale, they form a beautiful curve, probably the curve of a falling projectile. It is an exceedingly interesting sight to watch the unfailing coincidences of the pendulums perfectly tuned, when started in pairs such as F4, A5, and C6; or started all together and seen in their manifold manner of working. The eye is then treated to a sight, in this solemn silent harp, of the order in which the vibration|vibrations of sounding instruments play their sweet coincidences on the drum of the delighted ear; and these two "art senses," the eye and the ear, keep good company. Fig. 2 is an illustration of the correct definition of a Pendulum Oscillation, as defined in this work. In watching the swinging pendulums, it will be observed that the coincidences [Scientific Basis and Build of Music, page 104]
are always when they have returned to the side from which they were started. The Pendulographer, also, when writing the beautiful pictures which the musical ratios make when a pen is placed under the control of the pendulums, always finds his figure to begin again when the pendulums have finished their period, and have come for a fresh start to the side from which the period began. This confirms our author's definition of an oscillation of a pendulum. Fig. 3 is an illustration of the correct definition of a Musical Vibration, as also given in this work. Although the definition of an oscillation is not identical with that of a vibration, yet on account of their movement in the same ratios the one can be employed in illustration of the other as we have here done. Fig. 4 is a uniform rod suspended from the end as a pendulum; it will oscillate, of course, at a certain speed according to its length. In such a pendulum there are three centers related in an interesting way to the subject of Music in its three chords - subdominant, tonic, and dominant, which roots are F, C, and G. The center of gravity in the middle of the rod at 2, suspended at which the rod has no motion, corresponds to F, the root of the subdominant, in which there is the maximum of musical gravity. The center of oscillation at 3, which is one-third of the length of the rod from the end, is like the root of the tonic whose number is 3 in the genesis of the scale from F1. In this point of suspension the oscillations are the same as when suspended from the end at 1. The point at 9 is at a ninth from the center of oscillation. Our author discovered that, if suspended at this point, the pendulum had its highest rate of speed. Approaching the end, or approaching the center of oscillation from this point, the rate of speed decreases. Exactly at one-ninth from the center of oscillation, or two-ninths from the end, is this center of velocity, as Ramsay designated it; and it corresponds in some sort also to the root of the dominant G, which is 9 in the genesis of the scale from F1; its rate of vibration is nine times that of F1. The dominant chord is the one in which is the maximum of levity and motion in music. [Scientific Basis and Build of Music, page 105]
It will be observed that this plate represents intervals by its areas, that is, the distances between the notes; and the notes themselves appear as points. But it must be remembered that these distances or intervals represent the vibrations of these notes in the ratios they bear to each other. So it is the vibration-ratios which constitute the intervals here pictorially represented as areas. The area, as space, is nothing; the note itself is everything. [Scientific Basis and Build of Music, page 107]
This diagram shows pictorially the open in the spiral of the mathematical scales, in which, if written in sharps only, B# is seen a little, that is, a comma and the apotome minor, in advance of C, and as the first scale of the new cycle; for it is a violation of Nature's beautiful steps to call it a thirteenth scale of this order, since every scale in the order is 31 commas in advance of the preceding, whereas B# is only one comma and a small fraction in advance of C. If the scales be written in ♭s and #s for convenience of signature, then G# is seen a comma and apotome in advance of A♭; while the whole circle of keys advancing by fifths are each 31 commas in advance of the preceding. We may therefore cast utterly from us the idea of there being more than twelve mathematical scales, and view the so-called thirteenth as simply the first of a new round of the endless spiral of scales. There is, however, in this note a banner with the strange device, "Excelsior," for it leads us onward into ever-advancing regions of vibrations, and would at last bring us to the ultimate and invisible dynamic structure of the visible world. The tempered system of 12 keys, as in Fig. 1, is by causing the G# and A♭ to coalesce and be one, as the two D's are already literally one by Nature's own doing. [Scientific Basis and Build of Music, page 118]
This plate sets forth the essential duality of the musical system of vibrations. It is a remarkable fact that the numbers of the vibrations of the major mode are the numbers for the string proportions of the minor mode; and vice versa, the string proportions in the major are the numbers of the vibrations in the minor. We have, however, to see that we use the proper notes and numbers; we must know the secret of Nature. This secret rests in the duality of the notes, and begins from the two D's. The center of gravity of the musical system of vibrations is found in the comma space between the |two D's as they are found in the genesis of the two modes. In these |two D's the vibration number and string proportions are nearly identical. Starting from this point as the center of gravity in the [Scientific Basis and Build of Music, page 118]
dual system, as the strings are shortened the vibrations of course are more, and as the strings are lengthened the vibrations are fewer. This is household lore now; but the new insight and the deeply interesting order of Nature is that the major and the minor contain each other and respond to each other in this striking way; and while manifesting such diversity of character are so essentially one. [Scientific Basis and Build of Music,page 119]
The curved lines enclose the three chords of the major mode of the scale, with the ratio-numbers for the vibration in their simplest expression, counted, in the usual way in this work, from F1, the root of the major subdominant. The chords stand in their genetic position of F F C A, that is F1 by 2, 3, and 5; and so with the other two. The proportions for a set of ten pendulums are then placed in file with the ten notes from 1 to 1/2025 part of 1. Of course the one may be any length to begin with, but the proportions rule the scale after that. [Scientific Basis and Build of Music, page 121]
"Now comes the important question—Are the intermediate colours of the spectrum produced by vibrations that bear a definite ratio to the vibrations giving rise to the intermediate notes of the scale? According to our knowledge up to this time, apparently not." [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]
This quotation on vibrations will be seen to agree with the laws which I have gained. The fact that six of the notes of keyed instruments are obliged to act two parts, must prevent the intermediate notes bearing a definite ratio of vibrations with the intermediate colours of the spectrum. I name the note A as violet, and B ultra-violet, as it seemed to me clearer not to mention the seventh as a colour. [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]
1872.—"It gives me great pleasure to write to you on this subject. Music deals more with the imaginative faculty than any other art or science, and possessing, as it does, the power of affecting life, and making great multitudes feel as one, may have more than ordinary sympathy with the laws you work upon. You say 'from E, root of B, the fountain key-note F, root of C, rises.' There is a singular analogy here in the relativities of sounds, as traced by comparing the numbers made together by vibrations of strings with the length of strings themselves, the one is the inverse or the counterchange of the other. The length of B and E are the counterchange of F and C, hence they are twin sounds in harmony." [Harmonies of Tones and Colours, Extracts from Dr. Gauntlett's Letters1, page 48]
"Life in its manifestation is vibration. Electricity is vibration. But vibration that is creative is one thing. Vibration that is destructive is another. Yet they are from the same source." [Cayce 1861-16]
"All comes from one central vibration - taking different form." [Cayce (900-422)]
"Everything is vibratory." [Cayce (195-54)]
"As we see manifest in the electrical forces as used by man. This becoming only an atom in motion, and as the atomic force gathers this, producing such vibration as to create heat, light, and of the various natures, by the kind, class or nature of resistance met in its passage in the cycle given, reducing or raising the velocity, or better by the class of atomic force it vibrates, either with or against. These are examples of portions of universal forces." [Cayce (900-17)]
"Life in its manifestations is vibration. Electricity is vibration. But vibration that is creative is one thing. Vibration that is destructive is another. Yet they may be from the same source. As in the electrical forces in the form or nature prepared even for use in the body." [Cayce]
"Q - What is my ray?
A - "Depends on what you are thinking. Remember life is vibration. So is mind. So is matter. As to the ray, this changes. Don't think you sit on a ray and it carries you along. You make the ray." [Cayce (1861-16)]
A vibration is a rhythmic (periodic expansion (entropy) and contraction (syntropy) change of state; i.e., a periodic interexchange of seemingly opposite polar states. In each wave or vibration there are two distinct yet related unseen sets of dynamic aliquot parts or constructive currents (when considering a wave train or continuous vibration as a stream). This set of attributes is called the vibration's wavefunction. One set of attributes or parameters brings about the periodic concentration or aggregation of the vibrating media while the other set of attributes or parameters causes periodic expansion or dispersion of the media. If these unseen influences (scalar components) were not there and a dynamical constituent of each wave or vibration there could be no change of state as both states or phases would be identical and unchanging. The perceived wave or vibration is then the effect of these unseen causative (scalar) influences, attributes, parameters or currents. The details of these unseen causative (scalar) influences, attributes, parameters or currents are presented in Laws of Being, Laws of Being - Annotated, Wavefunction, Part 12 - Russells Locked Potentials and The Nature and Dynamics of Vibration and Toroids.
Vibration v Oscillation
These two rhythmic motions are not the same. Without vibration and oscillation made distinct seeming unfathomable paradoxes arise. For these paradoxes to be understood the difference between vibration and oscillation has to be clarified and acknowledged. In the ground state, at the moment of inflow of the sympathetic celestial streams or Divine Permeation (spark of Life), vibration is one cps and oscillation is one cps. From that moment on in the process of progressive rhythmic devolution, due to the Law of Harmonic Pitch, Law of Harmonic Vibrations, Law of Transformation of Forces and Law of Cycles, the One is refracted or differentiated into the multiplicity of materiality (the One becomes the Many). Demonstrating everything that is has a common origin or One Source and state of Being (sympathy; i.e., Love) regardless of outer appearance (opinion) of separateness and individuality.
What a Vibration is NOT
A vibration is not a sine wave. Sine wave patterns are developed from measuring a wave front passing by a measuring device such as a microphone or accelerometer. As the amplitude changes a sine wave is traced. I spoke about this in my 1994 SVP presentation on the video on this page Basic Principles. The typical sine wave pattern merely measures amplitude and Time. Such says nothing about the internal construct of the unseen (scalar) forces involved. [Dale Pond]
A vibration is distinctly different from an oscillation.
Christ Returns - Speaks His Truth
"Your entire universe manifests the differing frequencies of vibrations of consciousness energy particles.
As these frequencies move up or down from one level to another, so do the visible and physical structures manifest differing levels of energy and there is a change of mental patterns and emotions and appearance." [Christ Returns - Speaks His Truth, Letter 3, page 12]
"Visible things are but a manifestation of specific frequencies of vibration in consciousness which produces a 'SHIMMER OF MOTES OR PARTICLES' giving an appearance of solid 'matter'.
Each visible substance possesses its own unique vibrational frequency. A change in the rate of vibration produces a change in the appearance of 'matter'. As consciousness energies change so do the appearances of 'matter' change." [Christ Returns - Speaks His Truth, Letter 3, page 19]
Masaru Emoto “Existence is vibration. When we separate something into its smallest parts, we always enter a strange world where all that exists is particles and waves. The fact that everything is in a state of vibration also means that everything is creating sound. And as sound is created, there is a master listener to receive the sound: WATER.” [Masaru Emoto]
Laws of Vibration
Part 08 - What Vibration Is. - Part 1
Part 09 - What Vibration Is. - Part 2
Principles of Acoustics
Ramsay - The New Way of Reckoning a Vibration
Ramsay - The New Way of Reckoning a Pendulum Oscillation
Rhythmic Balanced Interchange
Table 14.03 - Ranges of Forces Vibration Forms Types and Governing Laws
What Vibration Is
7.2 - Rhythmic Balanced Interchange
8.2 - Oscillation versus Vibration