"On the one hand Keely talks about musical intervals - on the other hand he mixes in references to the orders of matter and energy, volume and divisions of chords. Which is which and when? To me, the above does NOT refer solely to musical chords. I've said this before. But instead represents a wider view of order, dynamics and structure. For instance if we view the nine strings of the CEG chord as three sets of three vibrating on 1, 2 and 3 octaves we get the possibility of the first third of the WHOLE NINE STRING CHORD being octave one, the second third being octave two and the third third as octave three of this nine string chord. The nine string chord is seen to be composed by thirds of the whole. These represent the molecular, atomic and etheric realms or levels of the matter and energy scheme being three major thirds of the whole of nature. Therefore the first third is the enharmonic (earthy earth; i.e.; terrestrial) the second represents the harmonic sixths (Russell's fulcrum?), and the third third represents the infinite ninths (celestial). Rotation is the result of a conflict between the first third (terrestrial) and the third third or ninths (celestial) as given above. I've included below quotes from Keely on his rotating sphere. If you've read Russell you will see DIRECT correlations between the two men expressing the SAME concept of rotation occurring in this manner - and ONLY in this manner. If you have not read Russell you may not see this. This being the case the CEG chord is the centralizing chord to the center while the B♭DG chord is the dispersive chord - each chord representing the in and out FLOWING STREAMS to and from the center. Keep in mind the dynasphere represents a faithful micro/macrocosm of the universal forces. The 24 resonators, tuned to musical thirds, placed in eight triplets around the Ring of Resonation are coincident to each of the three-sided corners of the cube of celestial dispersion realm while the second ring of resonation inside the sphere are tuned to B♭ keynote of the earth or spherizing element in nature." [Dale Pond See Dynasphere, clustered thirds]

"The sexless Father-Mother Creator is One. His extended sex-conditioned, male and female bodies are the completion of His Trinity.

Rest and action are three. Space and matter are three. Equilibrium and motion are three. Dimensions and pressures are three. The heartbeat of the universe, and yours, are three. Likewise, its breathings and yours, its temperatures and yours, and all things else of the universe, and you, are three." [Russell, Atomic Suicide, Chapter 5 - Prelude - The Transormation of Man]

"The swinging of the pendulum is three, as the spectrum and the fulcrum and lever, also, are three.

"The cathode is one - but its extended pairs of anodes in the electric current of man, and of space, adds up to three.

"Silence is one - but sound springs from silence when its divided moving pair collide - so sound is three, and its vibrations in sequences of rest and action, are also three.

"God is ONE in all CAUSE - but in all EFFECT He is three. And all that are three are nine - for all that are three are multiplied by three in this visible cube dominated universe of three dimensions." [Atomic Suicide, Chapter 5, Prelude, The Transformation of Man, part 1 of 2]

"The number 3 is the creative power in music, producing fifths, but it is under the control of the Octave prime - the number 2. It is the supreme octave which forms a boundary by making twelve fifths and seven octaves unite in one note. Within this horizon lies the musical system in its threefoldness - major (sharped), minor (flatted) and chromatic (accented)." [Scientific Basis and Build of Music, page 35]

dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]

The Permanence in Music of the Numbers Three and Twelve

Had D. C. Ramsay lived to weld together his findings in musical science, there would have been fewer, it any, of these desultory notes. The Editor, in endeavoring to arrange his materials so as to give sequence and fullness to them as far as possible, has thought it better to allow these fragments to appear thus as Brevia, than to intertwine them with even the kindred studies of another to any great extent, feeling assured that the light Ramsay has let in upon musical science will lead the way probably to further findings, and certainly to more perfect settings of what, being found, is here set forth in a first edition of his works. [Scientific Basis and Build of Music, page 74]

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 intervening chord between the Diatonic and Chromatic systems, B, D, F. - This chord, which has suffered expatriation from the society of perfect chords, is nevertheless as perfect in its own place and way as any. From its peculiar relation to both major and minor, and to both diatonic and chromatic things, it is a specially interesting triad. F, which is the genetic root of all, and distinctively the root of major subdominant, has here come to the top by the prime 2. D, here in the middle, is diatonically the top of the major dominant, and the root of the minor subdominant; and on account of its self-duality, the most interesting note of all; begotten in the great genesis by the prime 3. B, the last-begotten in the diatonic genesis, top of the diatonic minor, middle of the dominant major, and begotten by the prime 5, is here the quasi root of this triad, which in view of all this is a remarkable summation of things. This B, D, F is the mors janua vitae in music, for it is in a manner the death of diatonic chords, being neither a perfect major nor a perfect minor chord; yet it is the birth and life of the chromatic phase of music. In attracting and assimilating to itself the elements by which it becomes a full chromatic chord, it gives the minor dominant the G# which we so often see in use, and never see explained; and it gives the major subdominant a corresponding A♭, less frequently used. It is quite clear that this chromatic chord in either its major phase as B, D, F, A♭, or its minor phase as G#, B, D, F, is as natural and legitimate in music as anything else; and like the diatonic chords, major and minor, it is one of three, exactly like itself, into which the octave of semitones is perfectly divided. [Scientific Basis and Build of Music, page 101]

When Leonhard Euler, the distinguished mathematician of the eighteenth century, wrote his essay on a New Theory of Music, Fuss remarks - "It has no great success, as it contained too much geometry for musicians, and too much music for geometers." There was a reason which Fuss was not seemingly able to observe, namely, that while it had hold of some very precious musical truth it also put forth some error, and error is always a hindrance to true progress. Euler did good service, however. In his letters to a German Princess on his theory of music he showed the true use of the mathematical primes 2, 3, and 5, but debarred the use of 7, saying, "Were we to introduce the number 7, the tones of an octave would be increased." It was wise in the great mathematician to hold his hand from adding other notes. It is always dangerous to offer strange fire on the altar. He very clearly set forth that while 2 has an unlimited use in producing Octaves, 3 must be limited to its use 3 times in producing Fifths. This was right, for in producing a fourth Fifth it is not a Fifth for the scale. But Euler erred in attempting to generate the semitonic scale of 12 notes by the use of the power of 5 a second time on the original materials. It produces F# right enough; for D27 by 5 gives 135, which is the number for F#. D27 is the note by which F# is produced, because D is right for this process in its unaltered condition. But when Euler proceeds further to use the prime 5 on the middles, A, E, and B, and F#, in their original and unaltered state, he quite errs, and produces all the sharpened notes too low. C# for the key of D is not got by applying 5 to A40, as it is in its birthplace; A40 has already been altered for the key of G by a comma, and is A40 1/2 before it is used for producing its third; it is A40 1/2 that, multiplied by 5, gives C#202 1/2, not C200, as Euler makes C#. Things are in the same condition with E before G# is wanted for the key of A. G# is found by 5 applied to E; not E in its original and unaltered state, E30; but as already raised a comma for the key of D, E30 3/8; so G# is not 300, as Euler has it, but 303 3/4. Euler next, by the same erroneous methods, proceeds to generate D# from B45, its birthplace number; but before D# is wanted for the key of E, B has been raised a comma, and is no longer B45, but B45 9/16, and this multiplied by 5 gives D#227 13/16, not D225, as Euler gives it. The last semitone which he generates to complete his 12 semitones is B♭; that is A#, properly speaking, for this series, and he generates it from F#135; but this already altered note, before A# is wanted for the key of B, has been again raised a comma [Scientific Basis and Build of Music, page 107]

There are 42 intervals exclusive of the octave interval with ratio 1:2. There are seven seconds of three magnitudes, so determined in the genesis of notes - two in the ratio of 15:16; two, 9:10; and three, 8:9. There are seven corresponding sevenths - two in the ratio of 8:15; two, 5:9; and three. 9:16. There are seven thirds - one in the ratio of 27:32; three, 5:6; and three, 4:5; and there are seven corresponding sixths - three in the [Scientific Basis and Build of Music, page 109]

The twelve major scales
—The term key-note employed in the ordinary sense of the musician
—The twelve key-notes, with the six notes of each as they veer round in trinities, are written in musical clef, and the scales added
—The reversal of the four and three of the key-note and its trinities in the seven of its scale
—The twelve keys follow each other seven times through seven octaves linked into the lower and higher series
Keys mingled
—The modulating of scales, the eleventh notes rising to higher keys, . . . . . . 26 [Harmonies of Tones and Colours, Table of Contents2 - Harmonies]

The three lowest of the six tones are complementary pairs with the key-note and its two highest tones. Observe the curious order in which the tones sound, avoiding consecutive fifths. First, we have the key-note and its root, or fellow; next A; then D and its root; and then E, whose root, A, has already sounded between the first and the second pair. B, the fourth and central tone in depth, sounds seventh, and, finding no fellow within the compass of the harmony developing it, is isolated. Observe also how closely a key-note and its kindred tones are linked into each other. The Primaries spring from the key-notes, the Secondaries from the Primaries; the first pair comprises a key-note and a tone of the Primaries, the other two pairs have each a tone of the Primaries and a tone of the Secondaries. The key-note, after giving out its tones in trinities, or [Harmonies of Tones and Colours, Diagram II - The Twelve Keynotes1, page 23]

The twelve key-notes, with the six notes of each as they veer round in trinities, are again written in musical clef, and the scales added. The key-note leads the scale, and, after striking the two next highest notes of the seven of the harmony, goes forward, with its four lowest, an octave higher. The seven of each harmony have been traced as the three lowest, thus meeting the three highest in three pairs, the fourth note being isolated. Notwithstanding the curious reversal of the three and four of the scale, the three lowest pair with the three highest, and the fourth with its octave. The four pairs are written at the end of each line, and it will be seen how exactly they all agree in their mode of development. Keys with sharps and keys with flats are all mingled in twelve successive notes. If we strike the twelve scales ascending as they follow each other, each thirteenth note being octave of the first note of the twelve that have developed, and first of the rising series, the seventh time the scales gradually rise into the higher series of seven octaves beyond the power of the instrument. Descending is ascending reversed. After the seven and octave of a scale have been sounded ascending, the ear seems to lead to the descending; but ten notes of any scale may be struck without the necessity of modulation; at the seventh note we find that the eleventh note in the progression of harmonics rises to meet the seventh. For instance, B, the seventh note in the scale of C, must have F#. This point will be fully entered into when examining the meeting of fifths. To trace the scale of C veering round as an example for all, we may begin with C in Diagram II., and go forward with F, G, A, and B an octave higher. If the twelve scales were traced veering round, they would be found to correspond with the twelve as written in musical clef. [Harmonies of Tones and Colours, Diagram IV - The Development of the Twelve Major Scales, page 26a]

The following table shows the regularity of each seven of the twelve key-notes ascending by fifths, and the use of the two poles is again seen. The key-notes and their trinities are closely linked into each other, the three highest notes of the lower fifth key becoming the three lowest of the higher fifth key, and the four lowest becoming the four highest in an octave higher. The twelve keys, rising in each note a tone higher and descending a tone lower, cause the meetings by fifths. Having examined the table, we may strike the keys by fifths as written in the musical clef, beginning with the lowest C in [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys1, page 29]

In the development of the key-notes, the sharp or flat is written to each note, but not to the keys. The reversal of the three and four notes of each seven of the twelve key-notes and their trinities meeting by fifths having been traced, we will now examine the twelve scales meeting by fifths, and the results arising from the reversal of the three and four notes of each fifth lower scale in the fifth higher. Take as an example the scale of C: C D E F G A B, and that of G: G A B C D E F#. The four lowest notes of the seven of C are the four highest, an octave higher, in G; F, the central and isolated note of the seven of C, having risen a tone higher than the octave in the scale of G. The twelve scales thus modulate into each other by fifths, which sound the same harmonies as the key-notes and their trinities. Refer to the twelve scales written in musical clef ascending by fifths, and strike them, beginning at the lowest C in the bass clef; this scale sounds no intermediate tones, but these must be struck as required for all the scales to run on in fifths. After striking the seven notes of C, if we fall back three, and repeat them with the next four notes of the seven; or strike the seven and octave of C, and fall back four, repeating them and striking the next four, the four last notes of each scale will be found to be always in the harmony of the four first of the fifth higher scale. When the twelve scales ascending have been thus gained, as we trace them also on the table, they may be struck descending by following them as written in musical clef upwards, and [Harmonies of Tones and Colours, Diagram VII - The Modulating Gamut of the Twelve Keys2, page 30]

Let us first examine the meeting of the key-notes and their trinities in musical clef; the isolated fourths rising through the progression of the twelve now meet, seven and seven pairing. We must notice how closely they are linked into each other, the three highest notes of the lower seven being the three lowest of the higher seven an octave higher, and the four lowest becoming the four highest an octave higher; we descend by following the keys as written in musical clef upwards. [Harmonies of Tones and Colours, Diagram XIV - The Modulating Gamut of the Twelve Minor Keys by Fifths1, page 39]

See Also

1.11 - Ultimate Constituents of Matter
12.03 - Russell scale divisions correspond to Keelys three-way division of currents
12.05 - Three Main Parts of a Wave
12.07 - Keelys Thirds Sixths and Ninths
13.06 - Triple Currents of Electricity
13.11 - Triple Currents and Streams
13.38 - Theory of the Induction of Sympathetic Chords to Excite Rotation by Vibraphonic Trajection to and from Centers of Neutrality on Revolving Globe
14.02 - Three Six and Nine - The Principles of Creation
14.13 - Full Harmonic Chord
14.35 - Teslas 3 6 and 9
14.35.1 - Keely 3 6 and 9
14.36 - Triple Equations
15.18 - Keelys Process for Liberating Ether from Water multiple mentions in this article
16.28 - Keelys Free Electrical Energy Machine
16.29 - Triple Currents of Electricity
19.02 - Theory of the Induction of Sympathetic Chords to Excite Rotation
4.1 - Triple Vectors
4.2 - Triple Vectors and Rotation
4.3 - Three Planes and Six Directions
4.5 - Triple Rotary or Vortex Motions
4.9 - Triple Contractive Motions
6.10 - Nineness of Cubes
7B.02 - Three Forces in Harmony
7B.04 - Triplets Form Larger Units of Unity
7B.05 - Rotating Triplets
9.25 - Keplers Three Laws
atomic triplet
atomic triplets
Clustered Thirds
common chord
common root of three chords
Diatonic Scale Ring
Divine Trinity
Dynaspheric Force
Figure 10.05 - Three Orthogonal Planes where Six Gyroscopic Vortices Converge
Figure 13.08 - Triple Streams of Electricity
Figure 13.23 - Three Actuators on Shaft and Black and White Coatings
Figure 14.03 - A section from one of Keelys charts showing his generous use of Triplets
Figure 14.12 - Triple Equations to Represent a Single Sympathetic Event
Figure 16.09 - Triple Streams of Electricity
Figure 19.16 - Keelys Levitation Experiment Showing Three Glass Jars with Weights
Figure 2.1.5 - Russells Rings forming Spheres from Three Pairs of Reflecting Mirrors
Figure 2.10 - Triple Dual Vectors - In Rotary Motion
Figure 3.7 - Accumulating to Center on Three Planes
Figure 4.1 - Triple Cardinal Directions Vectors or Dimensions
Figure 4.11 - Six Planes and Three Shafts Coincide to Produce Spheres
Figure 4.13 - Triplet Originations and Centralizations of Matter
Figure 4.14 - Feynmans Triplet Structures of the Proton and Neutron
Figure 4.3 - Single Mode Electric Vector Generating Circular Motion also Shown within Triple Vectors
Figure 4.4 - Triple Vectors in Orthogonal Motions
Figure 4.6 - Triple Vectors in Motion on Triple Planes
Figure 4.7 - Triple Planes and Polar Vectors of Motion
Figure 4.8 - Triple Polar Rotations In and Out
Figure 5.4 - Vortex and Gyroscopic Motion on One Plane then on three forming Sphere
Figure 5.7 - Vortices on Three Planes 90 Degrees to Each Other
Figure 6.14 - Triple Three Cubes
Figure 6.4 - Triple Interior Planes
Figure 6.5 - Triple Planes - May Underlay some Sacred Geometry or Religious Concepts
Figure 6.6 - Russells Multiple Views of Tripleness
Figure 7.11 - Russells Vacuum becoming Matter on Three Vectors
Figure 7.13 - Keelys Chart showing how Molecules are made of three Atoms
Figure 7.3 - Step 3 - Sphere Forms Orthogonally Triple Compressing Shell Layers
Figure 7.6 - Keelys Triune Morphology
Figure 7B.05 - Triplet Forming a Unity
Figure 7B.06 - Rotating Triplets Animation
Figure 7B.09 - Feynmans Triplet Structure of Photon
Figure 7B.15 - Triple Planes relative to Center
Figure 9.8 - Triple Centers
first combination of the three primary ratios
Focalizing Neutral Concentrator
Keelys Mechanical Inventions and Instruments
Keelys Three Systems
Law of Continuity
Musical Triplet
nine magnetic mirrors
nine octave harp
nine octaves of tones
nine string chord
nine zeros
ninety degrees
one sound contains three different sounds
order of threes
Part 04 - Rotation on Three Planes
Part 05 - Three Rotating Planes Become Spheres
power of three
Power of Three
Ramsay - Music's Seal - The Number Three
Ramsay - PLATE XVI - System of the Three Primitive Chromatic Chords
Ramsay - The Chromatic System, like the Diatonic, Threefold
Ramsay - The Great Chord of Chords, the Three-in-One17
Ramsay - The Great Chord of Chords, the Three-in-One18
Ramsay - Three Chromatic Chords
resonating sphere
Rhythmic Balanced Interchange
second combination of the three primary ratios
second comparison and combination of the three primary ratios
series of twelve
sympathetic triple stream
Table 12.01 - The Divine Trinity
Table 13.02 - Vibratory and Oscillatory Triple Force Functions
Table 14.01 - All phrases in HyperVibes containing the term thirds
third combination of the three primary ratios
third comparison and combination of the three primary ratios
This Three Dimensional Cube Universe of Nine
three chords of the Diatonic Scale
three chords of the musical system major
three chords of the musical system minor
three chords of three notes
three chords
three combinations of the three primary ratios
three currents
three different causes
three differentiated sympathetic flows
three fifths
Three in One
Three Laws of Being
Three Main Parts of a Wave
three mathematical primes
three mirror planes of zero curvature
three notes
three octaves
three phases of action
three poles
three primary centers
three primary ratios
three reflecting planes of still magnetic Light
three series
three sympathetic streams
three times three chord
three-dimensional dual action universe
three-halves power law
Three-node transmitter
Three-phase electric power
triple circuit ring
Triple Concentration
triple currents
triple impulses
triple inertia planes
triple nodal transmitter
Triple Planes
Triple Point
Triple Triplet
triple union
Triple-triple Charts
Triplet Attraction
Triplet Rotation
Wave Field
We Now Build the Nine Equators of Cube-Sphere Wave-Fields

Created by Dale Pond. Last Modification: Wednesday May 12, 2021 13:11:23 MDT by Dale Pond.