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distance

Ramsay = wave amplitude, swing of a pendulum, space.

Keely
Fichte writes: "The will is the living principle of the world of spirit as motion is of the world of sense." Newton said that this subtle ether interpenetrates all matter and is concealed in their substance, through the strength and activity of which, bodies attract each other and adhere together when brought in contact, annihilating distance, as if objects might touch each other. Through this "life spirit" light also flows, is refracted and reflected and bodies are warmed. Pythagoras viewed this as a divine luminous principle or substance which permeates all things and at the same time contains all things. They called it the astral light. The Germans call it the "Welgeist". [Snell Manuscript - The Book, page 2]


Ramsay
"In the laws of quantities and motions there are three primary ratios from which the musical system of vibrations is developed.
Pendulums, from the slowness and continuance of their motions, are well adapted to give an ocular demonstration of the relative motions of each of these three primary ratios when compared and combined with the unity and with each other. The numbers 2 and 4 express the first condition in the first ratio; as, in falling bodies, when the times are 2 the distances are 4. In the case of two pendulums, when the length of the one is one fourth part of the other the motions are 1:2; and when two is counted for the upper one, the oscillations of these two pendulums will meet at one. The numbers 3 and 9 express the first condition of the second ratio; as, in falling bodies, when the times are 3 the distances are 9. In the case of two pendulums, when the length of the one is the ninth part of the other, the motions are 1:3; and when three is counted for the upper one, the oscillations of these two pendulums will meet at one. The numbers 5 and 25 express the first condition in the third ratio; as, in falling bodies, when the times are 5 the distances are 25. In the case of two pendulums, when the length of the one is twenty-fifth part of the other, the motions are 1:5; and when five is counted for the upper one, the oscillations of these two pendulums will meet at one.
In the system of motions in pendulums, the three primary ratios indicated in the foregoing paragraph, namely, 2:4, 3:9, and 5:25, are compared and combined with three different units. In their comparison, 1 is the unit of quantities, that is lengths, and 1 is the unit of motions. The numbers 1/4, 1/9, and 1/25, when taken together with 1 as unity, express the first comparison and combination of quantities; and the numbers 2, 3, and 5, taken together with 1 as unity, express the first comparison and combination of motions." [Scientific Basis and Build of Music, page 15]

The law of gravitation is the law of Music as well as of Astronomy. The cycles of the distances, that is the intervals, in Music correspond to the cycles of the periods in Astronomy. In Astronomy the distances and quantities of matter are primary, and determine the periods; in Music the periods and quantities are primary, and determine the distances or intervals. In Astronomy the distances are commensurable; in Music the periods are commensurable. In Astronomy the periods are incommensurable; in Music the distances or intervals are incommensurable. In Astronomy, because the simplicity is not in the periods, the conjunctions are very few at one time; in Music, because the simplicity is in the periods, the conjunctions are very many at one time. And herein lies in the one case the harmony and permanence of the solar system, and in the other case the harmony and beauty of the musical system. The periods and distances in Astronomy and Music are inversely related. [Scientific Basis and Build of Music, page 30]

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]

"There are two distinct laws which rule in astronomy - viz., masses and distances; and there are two distinct laws which rule in music - affinities and proximities. The notes produced by simple ratios as 1:2, 2:3, 3:4, etc., are attracted to each other by the law of affinity; notes which are beside each other in the octave scale and have moderately complex ratios as 9:10 and 15:16, are attracted to each other by their proximities. F and C, and C and G, and G and D are related to each other by affinity. C is related to the fifth below and the fifth above; G is related to the fifth above and the fifth below. F and C, C and G, and G and D are never nearer to each other than a fifth or a fourth, and in either case they [Scientific Basis and Build of Music, page 95]

It will be observed that this plate represents intervals by its areas, that is, the distances between the notes; and the notes themselves appear as points. But it must be remembered that these distances or intervals represent the vibrations of these notes in the ratios they bear to each other. So it is the vibration-ratios which constitute the intervals here pictorially represented as areas. The area, as space, is nothing; the note itself is everything. [Scientific Basis and Build of Music, page 107]

See Also


Amplitude
Eighteen Attributes or Dimensions
first condition of the second ratio
first condition in the third ratio
Motion
Number
Period
Proximity
Ratio
Relativity
Time
wavelength

Created by Dale Pond. Last Modification: Tuesday January 12, 2021 04:36:10 MST by Dale Pond.