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centrifugal force

Russell
"Observe carefully what now happens, centripetal force reaches its maximum and begins to die, and centrifugal force takes over." [Atomic Suicide, page 164]

Ramsay
"While the ratio of 1:2 corresponds to rest, and to the force of gravity, the ratio of 2:3 corresponds to motion, and to the centrifugal force. The prime 2, by any of its powers, never produces a new note. The prime 3 always produces a new note, and on this account its powers are limited to the first power, the square, and the cube, and each of these powers of 3 produces one new note." [Scientific Basis and Build of Music, page 27]

"The prime 5, like the prime 3, produces new notes. One of these, namely A5, is derived from unity, i.e., the note produced by the ratio of 1:2; the second note is produced from the note derived from the first power of 3, namely E15; and the third is produced from the note derived from the second power of 3, namely B45. The notes thus produced by the prime 5 are the middles, that is, the thirds of the chords. As it is the second and third powers of 3 which possess great centrifugal force, and not the first power of that number; and as it is only the first power of the number 5 which Nature employs in this business, so this makes the character of the notes produced by the prime 5 to depend on the character of the notes from which they are derived. One of the 3 notes produced by the prime 5 is derived from unity, that is the note produced by the ratio of 1:2, and like that note it is strongly acted on by the force of gravity.1 A second note produced by the prime 5 is derived from the note produced by the second power of 3, and like that note it possesses increased" [Scientific Basis and Build of Music, page 27]

"centrifugal force. A third note produced by the prime 5 is derived from the note produced by the first power of 3, and this note by the first power of 5 having being slightly acted on by the force of gravity, and the first power of 5 having only a little centrifugal force, the result is that this note E in the scale of C, derived from the first power of 3 by the prime 5, is balanced between the two forces. It is the only note in the system which in the octave scale has not a large interval on the one side of it nor on the other, and consequently it is the only note which attracts and is attracted by two notes from proximity. Thus it is that the musical system is composed of three notes having specific gravity and three having specific levity or bouyancy, and one note, E, the center of the tonic chord, balanced between these two forces. As the attractions of notes from proximity take place when the notes with downward tendency meet the note with upward tendency, had the notes been animated by only one of these forces there could have been no system of resolutions of the notes either in melody or harmony; they would all have been by gravity weighing it downwards, or by levity soaring upwards." [Scientific Basis and Build of Music, page 28]

"lower effect than the fifth; the seventh, B, has a higher effect than the sixth; but the eighth, C, has a lower effect than the seventh. If the effects of notes or chords depended wholly on the mathematical primes by which they are measured and located, or the ratios inherent in them, then the effects of the tonic, subdominant, and dominant chords would have been alike, for these chords are measured by exactly the same primes, and have exactly the same ratios. It is the position of the tonic chord which gives it its importance and not any special primes by which it is produced, nor any special ratios inherent in it. Notes by the power of 2 have a pure unmixed and invariable character. Notes by the first, second, and third powers of 3 have different degrees of centrifugal force; and the character of the notes produced by the first power of 5 depends on the character of the notes from which they are derived. The final character of notes and chords is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system. And no matter where these notes may be afterwards placed, like chemical elements, they never lose their original forces and tendencies. What Tyndal says of the inorganic chemical elements of the brain is true of the inorganic notes of music, "They are all dead as grains of shot." It is the organic state which gives the notes and chords their gravities and (levity|levities, and these two tendencies, the one upward and the other downward, constitute the vital principle of music. It is true that the mathematical operation is required to give birth and life to music, and that the mathematical system gives the knowledge of causes down to the law of gravitation, yet the artistic effects are fully realised from the tempered system deriving its organic harmony from this vital principle of music. The centrifugal tendencies of the notes of the subdominant, are too strong to be at all disturbed by the system being tempered. The enormous power of these chords corrects the effect which might otherwise arise from tempering, as the enormous power of the sun corrects the perturbations of the planets." [Scientific Basis and Build of Music, page 29]

If the effects of notes and chords had depended entirely on their mathematical ratios, then the effect of the subdominant, tonic, and dominant would have been alike; for these three chords have exactly the same ratios. It is the law of position which gives the tonic chord its importance, and not any special ratios embodied in its structure. The ratio of 2 to 1 has a pure, unmixed, invariable character, always realized in the interval of the octave. The notes produced from 1 by the first, second, and third powers of 3 have different degrees of centrifugal force. The character of the notes produced by the first power of 5 depends on the character of the notes from which they are derived, namely, 1, 3, and 9. The final character of the notes and chords derived by the same ratios is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system; and no matter where these notes may afterwards be [Scientific Basis and Build of Music, page 37]

A third cause of difference of contrast in notes is the individual character which belongs to them according to their place in the genetic scale - that is, their birthplace character - the amount, namely, of centrifugal force which they have inherited. [Scientific Basis and Build of Music, page 61]

"The organic structure of music is formed by the three ratios of 1:2, 1:3, and 1:5, from the laws of quantities and motions; but as it is only the ratio of 1:2 that has a pure, unmixed, invariable character, and as the notes produced by the first, second, and third powers of THREE have different degrees of centrifugal force, and the character of the notes produced by the first power of FIVE depends on the character of the notes from which they are derived, so the final character of the notes and chords is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system; and no matter how these notes may be afterwards placed, like chemical elements, they never lose their original force. [Scientific Basis and Build of Music, page 95]

Subdominant - F, A, C E G, B, D - dominant


- and it is balanced between the two forces. If the effects of notes or chords depended solely on their ratios, then the effect of the subdominant, tonic, and dominant would have been alike, for these chords have exactly the same ratios. The centrifugal force of the notes of the dominant chord would take if away from the tonic chord; but Nature, in her skill to build and mix, has in the octave scale placed the middle of the dominant B under the root of the tonic C, and the top of the dominant D under the middle of the tonic E; so that these two rising notes are inevitably resolved into the tonic chord. The gravitating tendencies of the notes of the subdominant would take it also away from the tonic; but in the octave scale Nature has placed the middle of the subdominant A above the top of the tonic G, and the root of the subdominant F above the middle of the tonic E; so that these two falling notes also are inevitably resolved into the tonic chord. In this way two notes resolve to the center of the tonic, D upwards and F downwards; one to the top, A to G, and one to the root, B to C. Nature has thus placed the notes which have upward tendencies under the notes having downward tendencies; she has also related them by proximity, the distance from the one to the other being always either a semitone or the small tone of the ratio 9:10. [Scientific Basis and Build of Music, page 95]
See Also


4plusplus
Antagonism
centrifugal
Collision
Death
Entropy
Female Force
Figure 14.08 - Force Contracts to Center - Energy Radiates from Center
Figure 14.09 - Force Contracts to Center - Energy Radiates from Center
Figure 17.00 - Opposing Forces of Gravitation and Radiation
Figure 3.8 - Force is stored in the North - Energy Disperses to the South
Figure 3.9 - Cardinal Directions of Force and Energy Flows
Radiation
Table 14.02 - Neutral Thirds - Energy Radiates from Center - Force Contracts to Center
two opposed electric forces

Created by Dale Pond. Last Modification: Friday December 11, 2020 03:54:50 MST by Dale Pond.