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Topic: John Keely's
Laws of Harmony
Section: Law of Harmonic Vibrations
Table of Contents to this Topic
"All coherent aggregates are perpetually vibrating at a period-frequency corresponding to some harmonic ratio of the fundamental pitch of the vibrating body; this pitch is a multiple of the pitch of the atomole."
Commentary February, 1986
This law (Keely's 4th Law of Harmony) states that everything (any body of whatever composition or size) vibrates at a frequency relative to that of its innermost constituent part, the atomole. The frequency of the atomole representing the fundamental or keynote of the chord (the eigenfrequency of the aggregate). The chord's aggregated rate of vibration is in direct proportion to that of this same atomole. In other words, if the atomole resonates at C12, then the outer body or "coherent aggregate" will vibrate to a note somewhat lower in frequency, say C2, or any other note forming harmonic relations to that fundamental frequency (see any good book on music theory). Usually referred to as summation or difference tones (beat frequencies), these derived frequencies form the "chord of mass" of any aggregated mass or object.
A prime example is a piano wire which sounds a primary note, the one usually associated with it, yet at the same time, it resonates many partials above and below its fundamental tone (see James Jeans' Science & Music). These partials are related to the fundamental or keynote by definite mathematical ratios, the same ratios that are evident throughout music theory.
As further analogy, a football team, representing a coherent aggregate, resonates to the overall fundamental idea of winning. The team's ideal, then, is the fundamental or keynote. The individual players' ideal is also to win, but must remain subservient to that of the team. In other words, he must follow through with the motions of a given play holding in abeyance his own personal determinations. Whatever he does on the field, must reflect actions harmonious to that of the team as it goes through its coordinated moves. Dis-coordination means failure here.
As no thing can exist of and by itself (it has to come from somewhere), its mere fact of existence tells us it is composed of or derived from something else. Something else being either more or less than whatever it is. Or simply, an object is composed of two or more "substances" or it is derived from something "larger" than itself. Since we all know by now that everything is vibratory in its inner nature, then these sources from which a substance comes is also vibratory. Hence, combining or merging vibrations will create summation or difference tones, therefore, we can safely say, that all aggregated bodies are "chords of vibrations" derived from other "chords of vibrations!" And the rules that define these modes of combination are the same as those found in music theory! (Oh! do I hear pencil sharpeners cranking or rocks beating against the windows?)
Commentary April, 1989
Fundamentally this law shows how the neutral center frequencies resonate throughout an aggregate. Whatever the fundamental pitch of the neutral center or what makes it up constitutes the frequency that permeates from the core outward and it is the pitch upon which the entire existence of the aggregate and its components are based. This may be likened to the manner in which Quantum Arithmetic uses a basic fundamental number from which all the others of a given set are derived.
It must be remembered that a pitch is a relative frequency and not just any number of vibrations or oscillations. It is a frequency that is derived much the same way that musical notes in a scale are derived from the fundamental upon which the scale is based. The progression of arithmetical intervals follows natural law and is not deviated from. Since the law of correspondence holds true throughout nature we might assume that the fundamental (when considered as a frequency) is the same thing as the neutral center (if considered as a thing).
Herein lies the key to all molecular substance and may point to the ancient secret of transmutation of elements. If the outer is a reflection of the inner then to change the outer one must change the inner.(Sounds a lot like personal development techniques apply to molecules just as they do to people.)
The next step would be to calculate these frequencies (beginning with a fundamental) retaining the natural relationships between them. This was done several years ago and the formula was published in SVP, Volume II, Issue 2; Calculating Harmonies of Tones. The process will not be reviewed here as it is a lengthy one and the first article gave sufficient detail.
Suffice it to say that the process follows the naturally occurring evolution of whole numbers.
Another problem yet to be solved is how to calculate the lower frequencies from a high fundamental in a descending manner. (How high does one start?) It was at first thought to reverse the above mentioned sequence but some unusual and unexplainable gliches appeared. No solution to them has yet surfaced.
The computer is a marvelous invention and without it we would be groping in the dark with all these numbers. One can easily build a spreadsheet using any set of mathematical parameters, terms and functions to create instantaneous computations. How it was that Keely could do all this math without benefit from silicon chips can only be accredited to his apparent genius of mind and thought. Another factor maybe his unspoiled mind uncluttered with nonsensical theories and dogmatic "truths" thus he was enabled to think the unthinkable and eventual do the un-doable.
We could take a fundamental number (frequency) and compute the higher tones it naturally generates using basic music theory. Once the set of numeric progression has been firmly established it is a simple matter to enter any number as the fundamental and derive the harmonics and partials. These computations are then as natural laws of progressive evolution of musical (sound or vibration) tones.
Keely's ideas concerning the molecule and the structure of its components rests on mathematical clarity. Fundamental to all orbiting bodies are three forces. An outward seeking force, an inner seeking force and a force bridging the two we call a neutral force. These forces act in straight, zig-zag and curved paths. Thus when constructing the model we naturally begin with a dot then use a straight lines to define and then connect the outer limits of activity encompassed within a circle or sphere of activity.
The outer seeking and inner seeking forces are kept in balance by the neutral force. Yet these two forces manifest as straight lines going to and fro thus forming a perfect triangle. It is from this triangle that Quantum Arithmetic takes off and even the construction of musical progressions. The attractive force of th neutral center must balance the centripetal force of inertia. "When predominance be given to the celestial forces over the terrestrial disruption occurs." (Keely) The celestial force is the outward seeking force. The terrestrial is the force that attracts towards the center of the mass - we sometimes call it gravity.
The Music of the Spheres can be discerned from the set intervals to which the molecular vibrations are naturally tuned. The various frequencies contained in a molecular structure must obey these intervals and to them they remain forever subservient. As Keely pointed out - any deviance from these intervals constitutes discord and molecular integrity is threatened. Which by the same token indicates to us how and why a molecule can be disrupted or caused to release energy. It is this introduced discordance that is the cause of energy development. And on the other hand this concept of equated forces indicates to us how nature is forever seeking and maintaining balance or harmony within itself. And yet again we can discern that it is number that rules and not matter or force or anything else.
If we can see among God's attributes one similar to harmony - pure harmony or forces - we can picture Keely's idea of the molecule as symbolizing the phrase "Where three are gathered in my name there I be also." The three individuals representing the three fundamental polarities of the same force balance each other out perfectly and perfect harmony is the result.
Harmony in a structure is perfect equation of forces (number or frequency).