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Topic: Keely Information Section: Scale of Forces in Octaves Table of Contents to this Topic |
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SCALE OF THE FORCES IN OCTAVES John Ernst Worrell Keely, 1894 "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 approxi- imately 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." Fraunhofer Lines "The Fraunhofer lines represent the silences, or the places of invisible pitches between the luminous pitches of rad-energy. They cannot therefore be conveniently used as data from which to measure the fundamental pitches of the atoms undergoing examination. When a series of sound-pencils are projected upon a screen, they undergo a combination of overtones and under-tones at the point of contact producing tones of a pitch either too low to be recognized by the human ear or too high to be called sound. The Fraunhofer lines are not therefore simply silences, but may be the higher invisible ultra-actinic rays. The fact is that some of the Fraunhofer lines are capable of producing a variety of chemical actions, when reflected and focalized. Observation thus far shows that these lines do not bear any definite ascertainable relation to the pitches producing them, but that they do bear some uniform relation from which the fundamental pitch could be determined cannot be doubted. The relation of the Fraunhofer lines to the luminous spectra are undoubtedly such as would enable one to compute the creative pitches producing them; but as yet no such determinations have been made. The accurate method of determining them is from the mutual relation of the harmonic pitches of the luminous spectra. A table representing the harmonic overtones and undertones of simple vibrations, and the resultant harmonics of associate vibrations, will be of great convenience in making these determinations. The natural unity of sonity lies above 1 per second, and below 2 per second, and for this reason the numbering of the octaves is accomplished by calling the end of the first octave No. 1 instead of No. 2. At the end of the twenty-first octave sono-thermity commences, and the bodies oscillating at this pitch are either correspondingly smaller by 1/8 than the preceding sonitic aggregates; or larger aggregates undergo vibration in submultiple portions of themselves. In either case the originating oscillation of sono-thermic pitch is that of an isolated or localized aggregation. This first class of forces, or first double gamut, is included within the range of about forty-three octaves. The bodies of the translatory pendulous motion and produce waves of the transverse form, while the bodies of the second gamut undergo internal nodal vibration and produce waves of a longitudinal form. Beyond the upper limit of the forty-third octave we reach bodies of a size (determined by the same method as in sonity) which we know to be about the size of an atom as approximately determined by various physicists to lie between eleven and twelve micromillimeters (hydrogen molecules), which gives the highest pitch of the known atoms, and from which can be roughly estimated the pitch of the heavier atoms. Starting with the approximate pitch of hydrogen as determined from its associate spectrum with oxygen, and working back to the size of the largest atoms, we again reach a pitch corresponding to the highest sono-thermic vibrations. Starting with the known temperature and pitch of a heated body, emitting definite rays of light, and working back to absolute zero, we again reach the pitch of the sono-thermic limit." FIRST CLASS Scale of Forces in Octaves Sonity, Sound, and Sonism begins 1st Octave 2 2nd 4 3rd 8 4th 16 5th 32 6th 64 7th 128 8th 256 9th 512 Keynote Molecular Chord 620 First Octave Keynote Atomic Chord 630 Second Octave 10th 1,024 11th 2,048 12th 4,096 13th 8,192 Keynote Etheric Chord 12,000 Third Octave Heat (highest rate of) 14,000 Vibro-Atomic 14th 16,384 Lowest Molecular Vibration 20,000 Harmonic Thirds 15th 32,768 42,800 Dissociation of Water 16th 65,536 17th 131,072 Trans. of Odor in Molecules 220,000 Sympathetic Negative 18th 262,144 First Inter-Atomic Lowest 300,000 Full Harmonic Chord 19th 524,288 First Inter-Atomic Highest 780,000 Full Harmonic Chord 20th 1,048,576 1,620,000 Major 5th 21st 2,097,152 Major 5th 3,145,728 Ninths Sono-thermity, Sono-therm, Sono-thermism 22nd 4,194,304 23rd 8,388,606 24th 16,777,216 25th 33,554,432 26th 67,108,864 Highest Molecular Vibration 100,000,000 Harmonic 3rds 27th 134,217,728 28th 268,435,456 Highest Inter-Molecular 300,000,000 Enharmonic 6ths Atmospheric 519,655,633 Highest made in air 29th 536,870,912 Atomic Vibration 900,000,000 Diatonic 9ths 30th 1,073,741,824 31st 2,147,483,648 32nd 4,294,967,296 Highest Etheric 8,100,000,000 Dominant Etheric 6ths 33rd 8,589,934,592 34th 17,179,869,184 Highest Inter-Etheric 24,300,000,000 Inter-Etheric 9ths 35th 34,359,738,368 36th 68,719,476,736 37th 137,438,953,472 38th 274,877,906,944 39th 549,755,813,888 40th 1,099,511,627,776 41st 2,199,023,255,552 42nd 4,398,046,511,104 SECOND CLASS Thermism, Rad-energy, Chemism 43rd 8,796,093,022,208 Dark heat begins 44th 17,592,186,044,416 45th 35,184,372,088,832 46th 70,368,744,177,664 Chemism begins 47th 140,737,488,355,328 Infrared (Light begins) 48th 281,474,976,710,656 Major 4th (above) 49th 562,949,953,421,312 Below Major 4th 50th 1,125,899,906,842,624 (Light ends) 51st 2,251,799,813,685,248 52nd 4,503,599,627,370,496 Limit Actinic Rays 53rd 9,007,199,254,740,992 54th 10,814,398,509,481,984 55th 36,028,797,018,963,968 Chemism ends 56th 72,057,594,037,927,936 57th 144,115,188,075,855,872 Full Ninths 156,057,552,198,220,000 58th 288,230,376,151,711,744 59th 576,460,752,303,423,488 60th 1,152,921,504,606,846,976 61st 2,305,843,009,213,693,952 62nd 4,611,686,018,427,387,904 63rd 9,223,372,036,854,775,808 64th 18,446,744,073,709,551,616 Major 5th Major 5th 27,670,116,110,564,327,424 Limit of thermism Electricity, Induction, Magnetism 65th 36,893,488,147,419,103,232 66th 73,786,976,295,838,206,464 67th 147,573,952,591,676,413,928 68th 295,147,905,183,352,827,856 Copper-zinc couple 69th 590,295,810,366,705,655,712 70th 1,180,591,620,733,411,311,424 71st 2,361,183,241,466,822,622,848 50,000 volts 72nd 4,722,366,482,933,645,245,696 73rd 9,444,732,965,867,290,491,392 74th 18,889,465,931,745,580,982,784 75th 37,778,931,863,469,161,965,568 76th 75,557,863,726,938,323,931,136 77th 151,115,727,453,875,647,862,772 78th 302,231,454,907,753,295,724,544 79th 604,462,909,815,506,591,449,088 80th 1,208,925,819,631,013,182,898,176 81st 2,417,851,639,762,026,365,796,352 82nd 4,825,703,278,524,052,731,592,702 83rd 9,671,406,557,048,105,463,185,408 84th 19,342,813,114,096,210,926,370,816 85th 38,685,626,228,192,421,852,741,632 86th 77,361,252,456,384,843,705,483,204 The limit of electricity and the beginning of atomolity. |
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