|Topic: John Keely's
Laws of Harmony
Section: Law of Transformation of Forces
Table of Contents to this Topic
| "All forces are different forms of Universal Energy unlike
in their period-frequency, merging into each other by imperceptible
increments; each form representing the compass of 21 octaves. Each form
or pitch may be transformed into an equivalent quantity of another
pitch above or below it in the scale of 105 octaves. The transformation
can occur only through its static effect, developing vibrations of
harmonic pitches above or below their fundamental vibration, or
developing with juxtaposed aggregates, resultant and difference, or
third order, as the case may be.
Scholium: A table of the intervals and harmonics of the normal harmonic scale will indicate the ratios in which the transformation of forces will occur."
Commentary February, 1987
This law tells us that the manipulation of energy and force can take place at certain numerical relations between vibrations. The numerical intervals at which this transformations may occur may be synonymous with the musical intervals. Tyndall says in his classical book "Sound": "The simpler the ratio of the two parts into which a string is divided, the more perfect is the harmony of the two sounds. Ratios with large numbers have overtones with beats. Ratios with smaller numbers are less apt to have beats or dissonance." We have assembled a list of these musical intervals in this issue as an aid in organizing this knowledge and presenting it to those who may learn to apply it. Keely's Scale of Octaves was printed in the September, 1986 issue. This scale of octaves designates the 21 octave compass of each energy type.
A point to keep in mind is the relative harmoniousness of various intervals. The lower the two numbers on each side of the colon determines the concordance of the ratio. For example a Perfect Fifth at 3 : 2 is much more coincident or harmonious than say the Greater Chromatic Semitone at 135 : 128. From the Law of Attraction & Repulsion given in issue 8, May, 1986 it follows that the lower the numbers, the greater the harmony and the greater the attractive force between vibrating aggregates. Higher numbers have greater degrees of dissonance and cause a repellant action between aggregates. This is like the old adage "birds of a feather flock together" and also may be a clue in understanding why people of "like mind" tend to join in groups of mutual activity. It may also explain why elements such as gold will aggregate about themselves forming larger quantities of itself and tends to not join together with other elements. When the elements naturally aggregate together as in an amethyst crystal with iron and silicon, the joining takes place by virtue of the relative intervals of frequencies of the atomic iron and atomic silicon. In other words, if the relative intervals of frequencies of the substances to be combined are at a low enough ratio, the substances will combine readily. If, on the other hand, they are at a greater numeric ratio, it will be more difficult to combine them into a stable form as they may be combining about the resultant or difference harmonies created. It appears from Keely's law that beat frequencies may be responsible for repellant actions.
In a more practical vein, we have seen before that a gas is composed of repellant particles. Therefore we may assume that the relative intervals between these particles is of a high numeric ratio. When the ratio has been brought into a lower numeric equation - the gas particles become less repellant and more attractive and will eventually form into a liquid state. Continue lowering the ratio or increase the number of coincident ratios and the liquid condenses into a solid
This law has tremendous implications for interpersonal relationships whether they be one-on-one, one-to-many or many-to-many as in society at large. Any leader of persons knows intuitively that when desiring action from a group the group must first be brought into some form of coherent harmony or agreement. Once this point of cooperativeness (harmony or purpose) is reached, the groups force can very easily be directed either into the same area with renewed activity or into a new direction. The same process takes place between a salesman and a new client. The first step is to bring the client into as harmonious state as is possible with the salesman before making the pitch. The salesman or speaker before a group makes light and agreeable conversation to relax the wary or dissonant attitudes before launching into his topic. This is the transformation of force in actual every day usage.
Relaxing into a lower ratio is one way of bringing the multiple aggregates into coincidence. Another way is to raise the numeric ratio of one to that of the other. This is done by adding "heat" (a vibration) or another vibrating influence such as water or other substance, to one or both elements of the mixture. If two ratios one of 3 : 2 and one of 135 : 128 are brought together, one may be either raised, the other lowered or both brought to some mutual numeric ratio relative to one another. The result would be the same excepting that if either reverts to its natural state or ratio, the mixture will breakdown or dissolve back into its individual components.
Commentary April, 1990
This law is a description of the process of transmutation of forces and hence transmutation of things.
It has been written that Keely was able to transmute elements into other elements and was thus able to create some exotic materials for some of his devices. One of these materials was his Trexnonar - a wire composed of platinum, gold and silver alloyed together in a special manner. It took Keely eight years to create this wire through which he transmitted his etheric force. In another device - his famous motor for domestic energy development and use - he "planished" the metal in such a way that the etheric force developed within it could not escape through the metal. Yet another material was used in his magnets - reported to be strong enough to hold several hundred pounds of weight and could be turned on or off at will.
"All forces are different forms of Universal Energy unlike in their period-frequency, merging into each other by imperceptible increments; [these period-frequencies (if they could be seen) would look much like the light spectrum where one color imperceptibly merges with the next] each form representing the compass of 21 octaves. [See the Scale of Forces published in SVP December, 1989 where these octaves have been defined by 21 octaves, labeled and measured) Each form or pitch may be transformed into an equivalent quantity of another pitch above or below it in the scale of 105 octaves. The transformation can occur only through its static effect, [the key here is "static effect"; the cause or the force itself cannot be transformed but its static effect can be - this is like the story of Adam and Eve - mankind cannot be transformed solely through the male force but can be changed by way of the posers of the female - the progeny will be like the male and female but of a new order - fundamentally like its parents yet different - remember Fibonacci and Pythagoras with their work with numbers used as bases and generated resultants? Quantum Arithmetic is also founded on this principle. The fundamental creative forces here are 1, 2 and 3 - God, Male and Female. The static effects of a fundamental vibration can be created or brought into manifestation by evolution or progression into sub or super harmonics, modulation or demodulation of another frequency giving rise to resultant or difference tones and even tertiary harmonics. See earlier issues of SVP for discussion of these secondary and tertiary vibrations.] developing vibrations of harmonic pitches above or below their fundamental vibration, or developing with juxtaposed aggregates, resultant and difference, or third order, as the case may be.
Scholium: A table of the intervals and harmonics of the normal harmonic scale will indicate the ratios in which the transformation of forces will occur." [Some of the older music theory books have tables demonstrating this vertical (sub and super harmonics) and horizontal (secondary and tertiary harmonics) harmonic generation. Some of these older books are in the process of being re-published by Delta Spectrum Research - watch the catalogue for them.]
This law is really important because it is the key to discovering how to take a super high frequency and have its effects demonstrated within the lower frequency ranges. Likewise a lower frequency can be made to act upon the higher domains.
Many people have asked me how Keely was enabled to work in such tremendously high frequency ranges - within this law are the keys to that enigma. He used a set of vibrating plates tuned to each other such that the lower plate created vibrations of a given pitch that acted directly on the resonance of the plate above it (with a higher fundamental) causing it to vibrate. This process continued to the 40th plate in the set thus transforming a lower audible frequency into a frequency well beyond the x-ray and gamma ranges. This process no doubt worked in reverse as well.
The small disk resonators having rods of different lengths in its periphery were no doubt another set of "progressive resonators" used by Keely to attain the same end but using a different waveform (rods and plates vibrate with a different set of intervals and waveforms - any book on music synthesis plainly points this fact out - hence the manner of progressive harmonic generation will be different between rods and plate resonators - thus the need for multiple tables of these rates).
The proof for the assertions of this law can be seen in the article "Chladni Plate Modes ... An Exercise in Musical Derivation" published in SVP December, 1989 where frequencies can be very accurately predicted from a known fundamental. This method was also successfully employed several years ago to predict and verify a progressive series of vibrations emitted from a cement truck as part of an experiment performed by Shine Richards and Dale Pond. The mathematical basis for that experiment was given in SVP November, 1986 in an article titled "Calculating Harmonies of Tones".
Entire scales of musical notes are naturally derived in this same fashion. The fundamental is sounded and the full collection of notes are derived from this one tone - all remaining relative to one another. "Harmonies of Tones and Colours" and "Scientific Basis and Build of Music" both go into this process with great depth and thoroughness. It is suggested these be reviewed to better understand the process of harmonic creation. Harmonic here does not necessarily mean a doubling or halving of a frequency alone - it relates to any mathematically defined and relative pitch with the fundamental. As we have stated before - consideration solely of doubled or halved pitches is only a small part of frequency modulation and demodulation and will not yield a complete picture of the vibratory nature of anything.
Therefore when exploring mathematically the pitches from a vibration or cyclical signature one must involve these other partials as important factors to derive meaningful relationships and not just the doubled and halved harmonics. Isolating the even harmonics alone will not only be inaccurate because it leaves out the odd harmonics but will ultimately lead the investigator astray because he does not see the entire picture of what is going on. This narrow vision will result in incomplete synthesis and conclusions regarding his experiments. In fact a picture derived from such narrow consideration will only reveal 1/7th or 1/12th (depending on the degree of accuracy sought) of the entire picture. Where would music be if it only considered the doubled and halved octaves of the fundamental? A keyboard consisting of only "C" notes would be boring indeed. The other notes are ALL derived from calculations of the odd or enharmonic intervals between the "C" keys thus giving rise to the full complement of notes found on an ordinary keyboard. The very same can be said of a vibrating plate such as was analyzed in the afore mentioned article. How boring vibration analysis is without these wonderful middle notes. Enharmony or discord can be a disturbing influence and the spice of life, vibration and music.