noun: a series of events that happen again and again in the same order or at the same times
noun: a set of things that a machine does as part of a process
noun: a set of poems, songs, or pieces of music on a particular subject
noun: a single complete execution of a periodically repeated phenomenon ("A year constitutes a cycle of the seasons")
noun: a periodically repeated sequence of events ("A cycle of reprisal and retaliation")
noun: a series of poems or songs on the same theme ("Schubert's song cycles")
noun: an interval during which a recurring sequence of events occurs ("The neverending cycle of the seasons")
noun: a wheeled vehicle that has two wheels and is moved by foot pedals
noun: the unit of frequency; one Hertz has a periodic interval of one second
verb: pass through a cycle ("This machine automatically cycles")
verb: cause to go through a recurring sequence ("Cycle the laundry in this washing program")
verb: recur in repeating sequences

"If all cosmical action is cyclical, matter, when existing free in the ether, must ultimately tend to dissolve into pure ether again, for, if the law of creation is as a cycle, in which, after development and as its fruit, the last term gives the first, then has he grounds for his conjecture that complication in structure is necessary to the segregation of nervous matter, and the construction of a "myo-neuro-cerebral system" and that ether and matter, after developing a molecular economy, as the mother and nurse of a soul or monad of a higher order than the merely material element, through or by this organism, complete the cycle of the economy of material nature, and eventually touch upon the spiritual world again and contribute to it. This true protoplasm, the ether, Keely claims to ... liberate by vibratory machinery as the medium of a motive power, which he calls "sympathetic negative attraction." [Snell Manuscript - The Book, page 2]

"The economy of creation is not regarded in this philosophy as a theory of development all in one direction; but as a cycle in which, after development, and as its fruit, the last term gives again the first. Herein is found the link by which the law of continuity is maintained throughout - the link which is missing in the popular science of the day; with this very serious consequence that, to keep the break out of sight, the entire doctrine of spirit and the spiritual world is ignored or altogether denied". [True Science]

"To aid in making such new thinking clear we will endeavor to express our thoughts by using the language of diagrams and familiar examples, which we will confine within one cycle of the electric current in principle. In thus confining our description of this new thinking within the demonstrable effects within one cycle of the electric current we sincerely hope that future thinking and reasoning will have a better basis upon which to form conclusions, which are not affected by the illusions of motion, that have for so long, and so disastrously, affected human reasoning." [Atomic Suicide, page 286-287]

"The ratio of 2:3 twelve times, in Fifths, is so near the ratio of 1:2 seven times, in Octaves, as to allow this cycle of the mathematical scales to be closed without losing any of its vitality. The reason why there are thirteen instead " [Scientific Basis and Build of Music, page 29]

The mathematical scales, if followed out regardless of other laws which rule in music, would read like a chapter in Astronomy. They would lead us on like the cycles of the moon, for example. In 19 years we have 235 moons; but the moon by that time is an hour and a-half fast. In 16 such cycles, or about 300 years, the moon is about a day fast; this, of course, is speaking roughly. This is the way seemingly through all the astronomical realm of creation. And had we only the mathematical ratios used in generating the notes of the scale as the sole law of music, we should be led off in the same way. And were we to follow up into the inaudible region of vibrations, we should possibly find ourselves where light, and heat, and chemical elective motions and electric currents are playing their unheard harmonies; or into the seemingly still region of solid substances, where an almost infinite tremor of vibrations is balancing the ultimate elements of the world. Music in this case would seem like some passing meteor coming in from among the silent oscillations of the planetary bodies of the solar system, and flashing past with its charming sound effects, and leaving us again to pass into the higher silence of those subtle vibrations to which we have referred, having no infolding upon itself, no systematic limit, no horizon. But music is not such a passing thing. Between the high silence of these intense vibrations, and the low silence of oscillating pendulums and revolving planets, God has constituted an audible sphere of vibrations, in which is placed a definite limit of systematic sounds; seven octaves are carried like a measuring line round twelve fifths; and motion and rest unite in placing a horizon for the musical world, and music comes [Scientific Basis and Build of Music, page 39]

There are very few things in music which have not change written upon them. TWELVE and THREE, however, are stable. There is nothing that will disturb the propriety of the circle of twelve fifths, as in the tempered system of music; for, although the mathematical-intonation indulges in thirteen keys, the thirteenth is simply the first of a new cycle of twelve.
The working model of three fifths is that which possesses musical life-powers; and these life-powers go with it wherever it goes, and they go with nothing else. [Scientific Basis and Build of Music, page 74]


The middle portion with the zigzag and perpendicular lines are the chromatic chords, as it were arpeggio'd. They are shown 5-fold, and have their major form from the right side, and their minor form from the left. In the column on the right they are seen in resolution, in their primary and fullest manner, with the 12 minors. The reason why there are 13 scales, though called the 12, is that F# is one scale and G♭ another on the major side; and D# and E♭ separated the same way on the minor side. Twelve, however, is the natural number for the mathematical scales as well as the tempered ones. But as the mathematical scales roll on in cycles, F# is mathematically the first of a new cycle, and all the notes of the scale of F# are a comma and the apotome minor higher than G♭. And so also it is on the minor side, D# is a comma and the apotome higher than E♭. These two thirteenth keys are therefore simply a repetition of the two first; a fourteenth would be a repetition of the second; and so on all through till a second cycle of twelve would be completed; and the thirteenth to it would be just the first of a third cycle a comma and the apotome minor higher than the second, and so on ad infinitum. In the tempered scales F# and G♭ on the major side are made one; and D# and E♭ on the minor side the same; and the circle of the twelve is closed. This is the explanation of the thirteen in any of the plates being called twelve. The perpendicular lines join identical notes with diverse names. The zigzag lines thread the rising Fifths which constitute the chromatic chords under diverse names, and these chords are then seen in stave-notation, or the major and minor sides opposites. The system of the Secondary and Tertiary manner of resolution might be shown in the same way, thus exhibiting 72 resolutions into Tonic chords. But the Chromatic chord can also be used to resolve to the Subdominant and Dominant chords of each of these 24 keys, which will exhibit 48 more chromatic resolutions; and resolving into the 48 chords in the primary, secondary, and tertiary manners, will make 144 resolutions, which with 72 above make 216 resolutions. These have been worked out by our author in the Common Notation, in a variety of positions and inversions, and may be published, perhaps, in a second edition of this work, or in a practical work by themselves. [Scientific Basis and Build of Music, page 115]

This diagram shows pictorially the open in the spiral of the mathematical scales, in which, if written in sharps only, B# is seen a little, that is, a comma and the apotome minor, in advance of C, and as the first scale of the new cycle; for it is a violation of Nature's beautiful steps to call it a thirteenth scale of this order, since every scale in the order is 31 commas in advance of the preceding, whereas B# is only one comma and a small fraction in advance of C. If the scales be written in ♭s and #s for convenience of signature, then G# is seen a comma and apotome in advance of A♭; while the whole circle of keys advancing by fifths are each 31 commas in advance of the preceding. We may therefore cast utterly from us the idea of there being more than twelve mathematical scales, and view the so-called thirteenth as simply the first of a new round of the endless spiral of scales. There is, however, in this note a banner with the strange device, "Excelsior," for it leads us onward into ever-advancing regions of vibrations, and would at last bring us to the ultimate and invisible dynamic structure of the visible world. The tempered system of 12 keys, as in Fig. 1, is by causing the G# and A♭ to coalesce and be one, as the two D's are already literally one by Nature's own doing. [Scientific Basis and Build of Music, page 118]

See Also

13.24 - Law of Cycles
5.8.5 - The complete Contraction Expansion Cycle is as follows
8.23 - Law of Cycles
Birth Cycle
Carnot Cycle
cycle of appearance and disappearance of mass
cycle of motion
Cycle of Temperature
cycle of twelve
cycles of the distances
cycles of the periods
cycles per second
Day Cycle
Electric Current Cycle
first cycle of keys
Harvey Spencer Lewis
Heat pump and refrigeration cycle
Law of Cycles
life-death cycle
Motion Cycle
one cycle for each action
Part 27 - The Cycles of Life
Ray Tomes
Rhythmic Balanced Interchange
second cycle of keys
seven churches
seven Spirits
Ten Octave Cycle of the Elements of Matter
third cycle of keys
wave cycle
Ray Tomes, all about cycles

Created by Dale Pond. Last Modification: Monday January 11, 2021 02:33:20 MST by Dale Pond.