"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." Keely [see Law of Cycles, 12.06 - Mid-Tones and Neutral Centers]
cps range (gamut)
? - ?
4,398,046,511,104 / 1.8014398509482E+19
2,097,152 / 4,294,967,296,000
 see Subdivision
[NOTE: 06/29/13; CPS needs to be recalculated]
Commentary July, 2017
In reading of Keely’s work with frequencies one is amazed by his masterly ability to create ultra-high vibrations and oscillations that could effect atomic and subatomic entities and their phenomena. How did he do it in the 1880s? This law is obviously part of an answer. He understood and is telling us here how one pitch may be transformed into another higher or lower pitch. Taken together with the below Scale of Forces one can get a glimmer of his consciousness working with these numbers and their possibilities.
A partial development of the "intervals and harmonics" was rendered into this chart. NOTE: This chart is not complete but does convey the idea of the table Keely mentions. The table being a plot of the keynotes and their harmonics (overtones) as they add and subtract from each other, once, twice or third removed. There can be a lot of numbers very quickly.
More detail on harmonics and overtones: Overtone series, Vibrating Rod Harmonics, harmonics, 04 - On the Pitch of Musical Sounds, Power of Beat Harmonics, 9.8 - Spontaneous Creation of Harmonic Series
Scale of Forces
"First octave (unity of sound) is approximately the lowest frequency capable of producing waves of rarefaction and condensation in the air. The atomic aggregate oscillating at this pitch can be experimentally determined, and the aggregate vibrating at a pitch one octave higher will have a mass lying between 1/8 and the cube root of the mass of the first mentioned aggregate; the exact relation under varying conditions of gravity, magnetic saturation, and pressure, can be determined only by accurate measurements. But assuming a body of a size represented by x, with a pitch represented by 1024 per second, then a pitch of 2048 per second will be produced by a body having a volume of some mean between 1/8 of x and the cube root of x. By accurately determining the pitch of a volume of any metallic sphere capable of oscillating at the pitch of, e.g., the eleventh octave of sonity (1024 per second), under normal conditions of gravity, pressure, magnetism, and then successively diminishing its size by 1/8 of itself, we get the successive octaves of pitches higher and higher in period-frequency until we pass the domain of sonity and enter the domain of sono-thermity. The point where the one form of energy merges into the other lies approximately at the twenty-first octave, and this pitch also marks the point where the air is no longer capable of vibrating at that pitch in waves of transverse form. The first gamut of 21 1/2 octaves consists of three forms; viz. sonity, sound, and sonism. The following is a tabulation of the pitches of sonity in octaves from one vibration per second to where the next form of energy commences." [Keely, from Dashed Against the Rock]
"Everything constructed by nature "grows." Growth is an accumulation and assimilation of electric potential caused by endothermic, inhalative genera-activity, followed by eliminative redistribution as the result of exhalative radioactivity. [See Law of Assimilation, Life, Death]
"Nothing in nature evades the law of growth nor knows another process.
"Nature assembles all her forms, and transforms her assembled forms, by raising their opposing pressures to high potentials from low potentials.
"Nature heats everything which she wishes to transform through growth in high pressure crucibles, and moulds them by high pressure into the desired forms.
"Nature then subjects them to sudden or gradual cooling by sudden or gradual release of pressure exactly as man cools his heated metals after moulding them into the forms desired by him." [Russell, The Universal One, page 133] [See Law of Transformation of Forces, Law of Cycles]
E equals mc2
Etheric Vibratory Scale
Figure 14.01 - Overtones Developed Musically Showing Up as Isotopes along the Vertical Axis of this Chart
Law of Cycles
Law of Harmonic Pitch
Law of Harmonic Vibrations
Part 14 - Keelys Mysterious Thirds Sixths and Ninths
Principle of Regeneration
Scale of Locked Potentials
Scale of the Forces in Octaves
Table 14.03 - Ranges of Forces Vibration Forms Types and Governing Laws
9.9 - Sympathy or Harmony Between Harmonics or Overtones
12.07 - Keelys Thirds Sixths and Ninths
15.13 - Dissociating Water Acoustically - Liberation of Quantum Constituents
15.14 - Dissociation Liberates Spontaneous Energy