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position

Keely
"If matter without form preceded creation of energy, it was only when life was given that the atoms became grouped in individualities through their intrinsic properties. The hypothesis of Macvicar and demonstrations of Keely pivot on the law of assimilation "providing at once for the free and the forced ... for mind and matter, and placing them ... in relationship." This law is summarized as "Every individualized object ... assimilates itself to itself in successive moments of its existence and all objects tend to assimilate one another." In its own nature, matter is wholly plastic or devoid of fixed innate properties wholly assimilative - both with respect to its own portions and to surrounding objects, as well as its position in space and insofar as it is capable, to the mind of its Creator. In the ether are constructed groups of ethereal elements generating material elements." [Snell Manuscript - The Book, page 2]

The structure of the air molecule according to Keely is as follows: Broken up, by vibratory action, he finds it to contain the "atomic triplet." This exists in a triangular position within the molecule, at its center, unless acted upon by electricity, when the molecule becomes oblate and the three atoms are ranged in a line within unless broken up by vibration. Nature never gives a vacuum, consequently the space within the molecule not occupied by the atomic triplet must be filled with something. This is where the "all-pervading ether" has made its secret abode through untold aeons. [Laurence Oliphant] [Snell Manuscript - The Book, page 3]


Ramsay
"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]

Position - The relative place of chords in a key. [Scientific Basis and Build of Music, page 63]

Music, and mathematics have nothing more to do with it. Already the Law of Position has guided the genesis upward in the major; and while mathematical primes were generating the chords one after another in precisely the same way and form, like peas in a pod, the Law of Position was arranging them one over the other, and so appointing them in their relative position each its own peculiar musical effect bright and brighter. And when the major had been thus evolved and arranged by ratios and position, another law, the Law of Duality, gave the mathematical operation its downward direction in the minor; and while the primes which measured the upward fifths of the major also measure the downward fifths of the minor, the Law of Position is placing them in their relative position, and appointing each its own peculiar effect grave and graver. [Scientific Basis and Build of Music, page 68]

The varied effect of position in chords. When a chord stands as C E G C, having its root also at the top, it has its softest, dullest, most united effect; it is undramatic, with little contrast. When it stands as E G C E, having its third at the top and bottom, it has a more ticklish, interesting, far-away effect. In reveries composers often finish thus, as if it had vanished - an unsettled effect. When it stands as G C E G, with its top at top and bottom, it has its most dominant character - loud, swelling. In the position C E G C it stands mixingly with the subdominant C E f G a C, and in this its first position its unseen filling in is chiefly from the region of gravity; hence its soft, grave, dull, heavy effect; and it passes very easily to the subdominant chord. When it stands as G C E G it stands mixingly with the dominant G b C d E G, and has its third position and most brilliant effect and uprising, for its unseen filling in is then chiefly from the region of levity; and it passes easily to the dominant chord. When in its second position, its middle position E G C E, its unseen filling in is mixingly both subdominant and dominant, E f G a b C d E; it has then its most interesting and puzzling effect; on the one hand its softest, dullest, and one-est, on the other hand its most brilliant effect, as if it would at once both sink and soar. [Scientific Basis and Build of Music, page 72]

The effects of different positions of chords. The first position is clear and solid; the second is light and pretty. The notes which have the most varied effect in a stream of harmony are the upper and under notes, the edges of the stream; the two outlines determine the effect:-

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[Scientific Basis and Build of Music, page 84]

"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]

SYSTEM OF THE THREE PRIMITIVE CHROMATIC CHORDS.


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 is an illustration of the chromatic chord resolving by two semitonic progressions and one note in common into four key-notes, which are shown in different positions and inversions; for example F A C F, A C F A, C F A C. Like a universal joint, the chromatic chord turns to each in a suitable form for resolution. [Scientific Basis and Build of Music, page 116]


This plate illustrates how the chromatic chord resolves into four key-notes, in different positions, by one semitonic progression and two notes in common; for example, G B D G, B D G B, D G B D. In a pianissimo and slow passage this resolution has a subtle, soft effect; like a snake in the grass. [Scientific Basis and Build of Music, page 116]

See Also


Law of Position

Created by Dale Pond. Last Modification: Wednesday January 13, 2021 03:23:23 MST by Dale Pond.