# thirds

"The rhythmic relations in which force acts are everywhere, under all conditions, and at all times, the same. They are found experimentally to be universally expressible by the mathematical relations of thirds. [Keely, KEELYS PHYSICAL PHILOSOPHY - Snell]

Keely
"The aerial propeller has a sympathetic polar accumulator and disperser in one instrument, which is entirely distinct from any of the devices intended for terrestrial use; also other mechanical adjuncts not needed on land nor water.

All forms of non-sympathetic machinery have, associated with them, conditions of centrifugal force on the ratio of the velocity induced; the diverging power from the center of induction being governed specifically by its gravital weight according to the diameter it occupies in its circle of rotation.

In a sympathetic negative circuit this order of conditions is reversed; for the power of neutral attraction draws the molecules of any mass, no matter what the weight, toward the center of rotation (instead of toward its periphery) according to the intensity of the negative vibration that is induced upon that particular circle.

Our earth, in its routine of revolution, is governed by the same law in every particular; its mass tending toward its centre of neutrality with a force that is equivalent to the character and velocity of its rotation.(3) If its rotation were increased, the tendency of everything associated with it would be increased toward its centre of neutrality on the same ratio. That is, a pound in weight would, under certain conditions of increased velocity, become two pounds in weight. The laws governing the sympathetic rotation of vibratory machinery are the same laws that govern planetary suspension. To those who have not witnessed the operation of my devices, my theories must indeed seem wild; but the laws of nature are the same yesterday today and forever. They know no change; and sympathetic physics, demonstrated mechanically, must triumph over all ridicule and opposition in the end. To contradict the laws governing sympathetic rotation is to contradict the laws governing planetary suspension, as I am prepared to demonstrate.

If the earth were rotated on a shaft by mechanical force, the present condition of its rotations would be reversed; everything on its surface would fly off at a tangent, on the ratio of the velocity induced. The equilibrium of all things would also be changed.

The gyroscope reveals astounding facts in relation to this philosophy, even when operated mechanically. No other known device is so nearly associated with sympathetic vibratory physics.

The vitalization of the disks for the polar and depolar field is established on the ratio of thirds, sixths, and ninths; the ninths being the circuit occupied by the polar field, must represent, in the scale of vitalized focalized intensity, 100 in my system: sixths in the depolar field, or 66 2/3; and in the neutral field, or thirds, 33 1/3. The triplets must represent one true chord of equation. The sympathetic transmitter transfers any degree of intensity desired from zero up to disintegration; all the transfers being made above the line of the first inaudible, as associated with my resonating system of transfer. On the sixths and ninths, in the progressive triple subdivision of the elements (4) of water, the nearest sympathetic approach is made to the high luminous, which is the main sympathetic link to the earth's polar negative envelope, and the one whereby coordination is effected for commercial work. In short, this progressive condition establishes the necessary association between celestial radiation and terrestrial outreach, in regard to controlling the polar negative attractive force in mechanics; whether for aerial navigation or for terrestrial commercial work, in all its multiplied forms.

The atmospheric envelope of our earth owes its activity and its volume entirely to celestial radiating forces.(5) Reception and dispersion are kept up by atomic and interatomic conflict between the dominant and enharmonic currents of the triune polar stream. The harmonic and enharmonic current with the dominant (in the electric stream) by their sympathetic association evolve the energy of matter.

The mechanical proof of the correctness of my theories, in sympathetic or spiritual physics, is so overwhelming in its simplicity that it needs but to be witnessed to convince the most learned or the most simple mind that this system will place both science and commerce on a platform which will elevate each to a level far higher than those they now occupy." [The Operation of the Vibratory Circuit]

"All vibrations that are negative in their character as toward destroying the harmonic relations that exist between the magnetic current and its coincident polar, to carry out the simile, close up the aperture whereby illumination (or transfer) is continuously conducted.

The thirds, on the subdivision of the one hundred and twenty-eight thousand four hundred vibrations, represent the negative antagonism, whereby this peculiar condition is brought about, viz., forty-two thousand eight hundred on the positive; the same on the negative and on the neutral, as associated with the sympathetic negative transmitter.

The keeper is first placed on the magnet, which has an attachment whereby a transmitter can be centrally associated with it; the other terminal having three connections that can be attached to this medium. The impulse is given simultaneously to the three leads after setting the instrument to represent forty-two thousand eight hundred vibrations on the harmonic, the same on the enharmonic and on the diatonic.

If this impulse is given properly, the neutralization will take place within fifteen seconds." [The Operation of the Vibratory Circuit]

"These (three modes of vibration), it will be noted, correspond to the three laws of being. It is not to be understood that any one of these three modes of vibration can exist independently. Each by itself is called a "current," and all three must be present in every "stream" or "flow" of force. The relations of the currents in every flow are expressible in thirds, and it is experimentally demonstrable that the relations of the three are in the order named: as 33 1/3 : 66 2/3 : 100." [Keely and His Discoveries, Conclusion, Keelys Physical Philosophy]

"Reception and dispersion are kept up on the atmospheric envelope of the earth by the atomic and interatomic conflict as "between the dominant and the enharmonic". This is brought about by the reception and dispersion of sympathetic streams, the ruling mode of whose vibration is the dominant, and the density of the coarser grades of matter, whose ruling vibratory mode is the enharmonic.

As every mass consists of vibrations in thirds, balanced in harmonic equilibrium without cancellation or diminution of energy, it stands therefore in harmonic relation to every other mass. All forms of matter and of motion are thus interrelated and interchangeable. Through resonance, increasing this sympathy, we can control the states of matter." [Mass Action, Snell Manuscript - the book]

"Electricity is the result of three differentiated sympathetic flows, combining the celestial and terrestrial flows by an order of assimilation negatively attractive in its character. It is one of Nature's efforts to restore attractive differentiation. In analyzing this triple union in its vibratory philosophy, I find the highest order of perfection in this assimilative action of Nature. The whole condition is atomic, and is the introductory one which has an affinity for terrestrial centers, uniting magnetically with the polar stream; in other words, uniting with the polar stream by neutral affinity. The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. E flat- transmissive chord or dominant; A flat- harmonic; A double flat- enharmonic. The unition of the two prime thirds is so rapid, when the negative and the positive conditions reach a certain range of vibratory motion, as to be compared to an explosion. During this action the positive electric stream is liberated and immediately seeks its neutral terrestrial center, or center of highest attraction." [Vibratory Physics - The Connecting Link between Mind and Matter]

"In analyzing this triple union in its vibratory philosophy, I find the highest order of perfection in this assimilative action of Nature. The whole condition is atomic, and is the introductory one which has an affinity for terrestrial centres, uniting magnetically with the Polar stream, in other words, uniting with the Polar stream by neutral affinity. The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. Eb, - transmissive chord or dominant; Ab - harmonic; Abb - enharmonic. The unition of the two prime thirds is so rapid, when the negative and the positive conditions reach a certain range of vibratory motion, as to be compared to an explosion. During this action the positive electric stream is liberated, and immediately seeks its neutral terrestrial centre, or centre of highest attraction." [True Science]

"In setting the conditions of molecular sympathetic transmission by wire," writes Keely, "the same law calls for the harmonious adjustment of the thirds, to produce a non-intermittent flow of sympathy. Intermission means failure here. That differential molecular volume is required of sympathetic flow, seems at first sight to controvert the very law established by the great Creator, which constitutes harmony, a paradoxical position which has heretofore misled physicists who have propounded and set forth most erroneous doctrines, because they have accepted the introductory conditions, discarding their sympathetic surroundings. The volume of the neutral center of the earth is of no more magnitude than the one of a molecule, the sympathetic condition of one can be reached in the same time as the other by its coincident chord." Keely has ... attained the transmission of the etheric current in the same manner as the electric current with this one notable difference, that, in order to show insulation to the skeptical, he passes the etheric current, through blocks of glass in running his vibratory devices. [Snell Manuscript - The Book, page 2]

THEORY AND FORMULA OF AQUEOUS DISINTEGRATION

The peculiar conditions as associated with the gaseous elements of which water is composed, as regards the differential volume and gravity of its gases, make it a ready and fit subject of vibratory research. In submitting water to the influence of vibratory transmission, even on simple thirds, the high action induced on the hydrogen as contrasted with the one on the oxygen (under the same vibratory stream) causes the antagonism between these elements that induces dissociation. The differential antagonistic range of motion, so favoring the antagonistic thirds as to become thoroughly repellant. The gaseous element thus induced and registered, shows thousands of times much greater force as regards tenuity and volume than that induced by the chemical disintegration of heat, on the same medium. [Hydrogen, page 4] [Snell Manuscript - The Book, page 4]

In all molecular dissociation or disintegration of both simple and compound elements, whether gaseous or solid, a stream of vibratory antagonistic thirds, sixths, or ninths, on their chord mass will compel progressive subdivisions. In the disintegration of water the instrument is set on thirds, sixths, and ninths, to get the best effects. These triple conditions are focalized on the neutral center of said instrument so as to induce perfect harmony or concordance to the chord note of the mass chord of the instruments full combination, after which the diatonic and the enharmonic scale located at the top of the instrument, or ring, is thoroughly harmonized with the scale of ninths which is placed at the base of the vibratory transmitter with the telephone head. The next step is to disturb the harmony on the concentrative thirds, between the transmitter and the disintegrator. This is done by rotating the siren so as to induce a sympathetic communication along the nodal transmitter, or wire, that associates the two instruments. When the note of the siren becomes concordant to the neutral center of the disintegrator, the highest order of sympathetic communication is established. It is now necessary to operate the transferable vibratory negatizer or negative accelerator, which is seated in the center of the diatonic and enharmonic ring, at the top of the disintegrator, and complete disintegration will follow (from the antagonisms induced on the concordants by said adjunct) in triple progression, thus: First thirds: Molecular dissociation resolving the water into a gaseous compound of hydrogen and oxygen. Second: sixths, resolving the hydrogen and oxygen into a new element by second order of dissociation, producing what I call low atomic ether. Third: ninths, the low atomic ether resolved into a new element, which I denominate high or second atomic harmonic. All these transmissions being simultaneous on the disturbance of sympathetic equilibrium by said negative accelerator. [Snell Manuscript - The Book, page 4]

"A whole is considered as being composed of three parts. Each third part is a third. These three parts have a dynamic relationship." [See Law of Assimilation, Keelys Laws of Being, Laws of Being]

"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]

Professor Daniel Brinton
"The rhythmic relations in which force acts are everywhere, under all conditions, and at all times, the same. They are found experimentally to be universally expressible by the mathematical relations of thirds.

"These threefold relations may be expressed with regard to their results as,

"From these three actions are derived the three fundamental LAWS OF BEING:

I. Law of Assimilation: every individualized object assimilates itself to all other objects.

II. Law of Individualization: every such object tends to assimilate all other objects to itself.

III. Law of the Dominant: every such object is such by virtue of the higher or dominant force which controls these (above) two tendencies. [14.09 - Brintons Laws of Being]

Figure 11.01 - Octave composed of Equal Thirds and Triads

Musical Third
There are diverse musical thirds; Minor Third, Major Third and Augmented Third. [See Interval]

Ramsay
Euler, while treating of music, shows that there are just three mathematical primes, namely 2, 3, and 5, employed in the production of the musical notes - the first, in ratio of 2 to 1, producing Octaves; the second, in the ratio of 3 to 1, producing Fifths; and the third, in the ratio of 5 to 1, producing Thirds. [Scientific Basis and Build of Music, page 8]

"The system of musical sounds is derived from the laws of motion and a particular election of numbers which give the greatest variety of simple ratios.
There are three primary and pregnant ratios which produce the chords and scales. The first is the ratio of 1:2, producing Octaves, and nothing else; the second is the ratio of 2:3, producing Fifths; the third is the ratio of 4:5, producing Thirds." [Scientific Basis and Build of Music, page 26]

In order to find the notes for the next major key above C, we have to multiply the vibration-number of D, which is the top of the dominant C, by 3 and 5. It is out of the key of C at this point that the new key sprouts and grows, and by the primes and method which produce the key of C itself. So if we would find the relative minor of C, let us take the note which is a minor third below D - that is, B - to produce the minor. The minor sprouts and grows from this point of the key of C; for the relative minor grows out of the major, as out of the man at first the woman is taken. Moreover, B is the last-born of the notes for the major scale; for the middles, that is, the thirds of chords, are always produced by the prime 5; and the tops, that is, the fifths of chords, are produced by the prime 3, and are born before the thirds, though placed after them in the chords. Well, because B is the last-born note of the major, as well as a minor third below the top of the highest chord of the major, it seems that the minor should have this for its point of departure. Again, we have seen that the major and the minor are found in their strings and their vibrations by an inverse process, that one going back upon the other; and, there taking Nature's clue, let us proceed by an inverse process of generating the minor. Making B45 our unit, as F1 was our unit for the major, let us divide by 3 and 5 for a root and middle to B, as we multiplied by 3 and 5 for a top and middle to F. B45 divided by 3 is 15; here then is our E, the root of the chord, just where we had found it coming upward; for, remember, we found E15 by multiplying C3 by 5. This E, then, is the same in major and minor. Now B45 divided by 5 is 9; [Scientific Basis and Build of Music, page 31]

The major scale is composed of three fifths with their middle notes, that is to say, their thirds. And as three such fifths are two octaves, less the small minor third D to F, taking the scale of C for example, so these three fifths are not joined in a circle, but the top of the dominant and the root of the subdominant are standing apart this much, that is, this minor third, D, e, F. Had they been joined, the key would have been a motionless system, with no compound chords, and no opening for modulation into other keys. [Scientific Basis and Build of Music, page 38]

common, to mingle with more chord-society. So those added thirds which constitute compound chords are like accomplishments acquired for this end, and they make such chords exceedingly interesting. The dominant assumes the root of the subdominant, and so becomes the dominant seventh that it may be affiliated with the subdominant chords. Inversely, the subdominant assumes the top of the dominant chord that it may be affiliated with the dominant. The major tonic may exceptionally be compounded with the top of the minor subdominant when it comes between that chord and its own dominant; and the minor tonic may in the same way assume the root of the major dominant when it comes between that chord and its subdominant. The minor subdominant D F A, and the major dominant G B D, are too great strangers to affiliate without some chord to introduce them; they seem to have one note in common, indeed, but we know that even these two D's are a comma apart, although one piano-key plays them both, and the F G and the A B are as foreign to each other as two seconds can be, each pair being 9 commas apart, and G A are 8 commas apart. In this case, as a matter of musical courtesy, the tonic chord comes in between; and when it is the minor subdominant that is to be introduced, the major tonic assumes the top of that chord, and then turns to its own major dominant and suavely gives the two to enter into fellowship; for the tonic received the minor subdominant through its semitonic E F, and carries it to the major dominant through its semitonic B C, along with C in common on the one side and G in common on the other. When it is the major dominant that is to be introduced to the minor subdominant the minor tonic fulfills the function, only the details are all reversed; it assumes the root of dominant, and by this note in common, and its A in common with its own subdominant, along with the semitonic second B C on the one hand and the semitonic E F on the other, all is made smooth and continuous. The whole of this mediatorial intervention on the part of the tonic is under the wondrous law of assimilation, which is the law of laws all through creation; but when the tonic chord has fulfilled this graceful action, it immediately drops the assumed note, and closes the cadence in its own simple form.1 [Scientific Basis and Build of Music, page 71]

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]

Six Octaves required for the Birth of the Scale

EXPLANATION OF PLATES.
[BY THE EDITOR.]

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]

mathematical genesis, as seen in its D being a comma higher than that of the minor. This gravity and buoyancy of the modes is a striking feature of them. In the Thirds it is different from the Fifths; the larger hemisphere of each third seems gravitating toward the center of the tonic chord. The area of the scale has then the aspect of a planet with its north and south poles, and pervaded by a tendency towards the center; the center itself being neutral as to motion. [Scientific Basis and Build of Music, page 107]

The Octave being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the radius by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the thirds are shown by the hemispheres of the seconds which compose them facing each other in pairs. The comma-measures of the various thirds thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The attitude of the six thirds, on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their attitude gives them the appearance of being attracted towards the center of the tonic; while the attitude of the three fifths is all upward in the major, and all downward in the minor; their attraction being towards the common center of the twelve scales which Nature has placed between the second of the major and the fourth of the minor, as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]

Hughes
Helmholtz's experiments on developing colours shown to agree with the scheme
—The sounds of the Falls of Niagara are in triplets or trinities
—The Arabian system divides tones into thirds
—Two trinities springing from unity apparently the germ of never-ending developments in tones and colours
—Inequality of the equinoctial points; is the want of equilibrium the motive power of the entire universe?
—The double tones of keyed instruments, the meetings by fifths, the major and minor keys, so agree with the development of colours, that a correct eye would detect errors in a piece of coloured music
Numbers not entered upon, but develope by the same laws
Bass notes omitted in order to simplify the scheme, 18 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

"Music, pure, natural, and harmonical, in the true and evident sense of the term, is the division of any keynote, or starting-point, into it's integral and ultimate parts, and the descending divisions will always answer to the ascending, having reference to the general whole. The essence and mystery in the development of harmonies consists in the fact that every keynote, or unit, is a nucleus including the past, the present, and the future, having in itself an inherent power, with a tendency to expand and contract. In the natural system, as each series rises, its contents expand and fall back to the original limit from any point ascending or descending; we cannot perceive finality in any ultimate; every tone is related to higher and lower tones; and must be part of an organized whole." - [F. J. Hughes, Harmonies of Tones and Colours - Developed by Evolution, page 16. See Overtone Series]

The development into triplets or trinities has been especially remarked in the harmony caused by the falls of Niagara.* "A remarkable peculiarity in the Arabian system of music is the division of tones into thirds. I have heard Egyptian musicians urge against the European systems of music that they are deficient in the number of sounds. These small and delicate gradations of sound give a peculiar softness to the performances of the Arab musicians." [Harmonies of Tones and Colours, The Arabian System of Music, page 21]

thirds mentioned in the Keely Literature

antagonistic thirds
chord of its thirds
chords in intervals of thirds
chords of E flat with thirds
chords of the thirds
clustered thirds
compound vibration of their mass thirds
concentrative thirds
confliction by thirds
diatonic thirds
differential diameters of thirds
discordant thirds
dominant thirds
enharmonic thirds
expressible in thirds
harmonic attractive chord, thirds
harmonic thirds
harmonic undulatory by thirds
harmony of thirds
inversions of thirds
major thirds
mass thirds
mathematical relations of thirds
consonant thirds
minor thirds
molecular concordant thirds
movement in thirds
musical thirds
negative thirds
negative transmissive chords of the thirds
negatizing the thirds
neutral thirds
neutralized thirds
phased in thirds
progression of thirds
progressive thirds
proportions of thirds
relations of thirds
reverse thirds
simple thirds
subdivision of thirds
succession of thirds
summations of thirds
tempered thirds
thirds of the mass chord
thirds of the thirds
thirds of the whole
thirds untempered
thirds: molecular dissociation
triple thirds
varying thirds
vibrations in thirds

vibratory antagonistic thirds
Table 14.01 - All phrases in HyperVibes containing "thirds" found in the digitized Keely literature. (All of the Keely literature has yet to be digitized).