See Thirds

"Keely has discovered and was the first to demonstrate that electricity has never been handled; that it is not merely a force or a form of energy, - that it is matter; and that what we call electricity, and have diverted for commercial use in electric lighting, is but one of the triune currents, harmonic, enharmonic, and diatonic, which are united in pure electricity; that the enharmonic current seems to be sympathetically and mysteriously associated with the dominant current; and that the dominant current can no more be brought under control than can the lightning itself. The diversion of the dominant current would mean destruction to any mechanical medium used for that purpose, and death to the operator. The intense heat evolved by the electric stream Keely attributes to the velocity of the triple subdivision at the point of dispersion, as each triple seeks its medium of affinity. Sudden unition induces the same effect; but demonstration shows that the concentration of this triple force is as free of percussion as is the breath of an infant against the atmosphere; for the three currents flow together as in one stream, in the mildest sympathetic way, while their discharge after concentration is, in comparison to their accumulation, as the tornado's force to the waft of the butterfly's wing. The enharmonic current of this triple stream, Keely thinks, carries with it the power of propulsion that induces disturbance of negative equilibrium; which disturbance is essential to the co-ordination of its flow, in completing the triune stream of electricity. When this fluid is discharged from the clouds, each triplet or third seeks its terrestrial concordant, there to remain until that supreme law which governs disturbance of equilibrium again induces sympathetic concordant concentration, continuing to pass through its evolutions, positively and negatively, until the solar forces are expended." [Keelys Contributions to Science]

Music - The interval between a fundamental tone and the third diatonic tone above.

The interval comprised by two notes written on adjacent lines or spaces. A major third has two whole tones, a minor third a tone and a semitone, and a diminished third a whole tone.

The mode of a triad is determined by its third, as is the mode of a scale, since the sixth and seventh degrees are treated as variable in the harmonic minor and melodic minor scales. The diminished third is most often used as the inversion of the AUGMENTED SIXTH, INTERVAL, IMPERFECT INTERVAL [Westrup, J.A., Harrison, F. L.; Collin's Music Encyclopedia; William Collins Sons, & Co., Ltd., London, 1959]

1) Major Third 5:4

2) Minor Third 6:5

2.1) Augmented Third 125:96

2.2) A major third consists of four semitones, a minor third of three. A major tone is the whole tone having the ratio 8:9; a minor tone, that having the ratio 9:10. Intervals have had the term major applied to them in a conflicting manner.[Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]

3) Both occur for the first time in the third octave.

4) Are probably resultant tone, summation tone or compound tone.

5) Any two thirds make a Fifth, of which there are several:

Diminished Fifth 64:45
Diminished Fifth 36:25
Perfect Fifth 3:2
Augmented Fifth 25:16

6) They play a key role in the simplest chords: Triads, of which there are three types
a) Major
b) Minor
c) Diminished
(The material of which music is made is tone, in recognizable, orderly chord groups. The simplest chord group is the Triad, or three tone chord. The Triad always consists of fundamental (root), third and fifth. A Triad may be constructed upon every degree of the scale, Major and Minor. Upon the Major Scale tones the Triads of the key, in C Major, are shown above. These seven Triads occur in exactly the same form in every Major Key. There are three different Triad groupings in the above:
Major Triad: Major 3rd and Perfect 5th on the 1st, 4th and 5th degrees.
Minor Triad: Minor 3rd and Perfect 5th on the 2nd, 3rd and 6th degrees.
Diminished Triad: Minor 3rd and Diminished 5th on the 7th degree.)

1) The interval between a fundamental tone and the third diatonic tone above.

2) The interval comprised by two notes written on adjacent lines or spaces. A major third has two whole tones, a minor third a tone and a semitone, and a diminished third a whole tone. The mode of a triad is determined by its third, as is the mode of a scale, since the sixth and seventh degrees are treated as variable in the harmonic minor and melodic minor scales. The diminished third is most often used as the inversion of the AUGMENTED SIXTH, INTERVAL, IMPERFECT INTERVAL. Collin's Music Encyclopedia, 1959

3) Progressive Thirds: The ultimate test of a good temperament on any piano is a smooth change of the beat rates as progressive thirds are played - both in the bearings octave, and outside it. (no reference)

4) Diatonic Thirds: "The sympathetic acoustic impulses are: the DOMINANT - a diatonic third - the HARMONIC - the connective "sixth" - and the ENHARMONIC - or diminished seventh - which Keely calls a ninth - inducing "infinite trajective velocity" or "neutral radiation" from neutral centers." The Snell Manuscript

Third, Neutral
neutral 3rd, neutral third, n3

An interval intermediate in size between the Major Third and the Minor Third.

Neutral Thirds measure about 350 cents (¢) and typical examples are 11/9 (347¢), 27/22 (355¢) and 16/13 (359¢). (from John Chalmers, Divisions of the Tetrachord)

Thirds, Sixths and Ninths
Fri, 15 Dec 2000
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 third 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 (fig. 1) while the BfDG chord is the dispersive chord (fig. 2) - each chord representing the in and out FLOWING STREAMS (fig. 5) to and from the center. Keep in mind the dynasphere represents a faithful micro/macrocosm of the universal forces as depicted on the "Universal Cosmology - Genesis" page I recently put together. 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 (fig. 17) of the cube of celestial dispersion realm (fig. 2) while the second ring of resonation inside the sphere are tuned to Bf keynote of the earth or spherizing element in nature. So much more needs to be done yet with all this but we are hot on the trail. [Dale.]

Thirds, Controlling
"The first third is controlled by the molecular, the next progressive third by the atomic and the highest third by the etheric." [Keely and His Discoveries]

Thirds and Triads
A TRIAD is composed of two thirds. There are two kinds of thirds: a Minor (mn) and a Major (mj). These may be combined in two ways to create a Triad: (mn+mj) and (mj+mn). The former creates a Minor Triad (5mn) while the second creates a Major Triad (5mj). There are several issues being sorted out here. One is how to count steps and/or intervals. This is a real problem as far as I can see especially when trying to computerize all these factors. The first column under "THIRDS" is read thusly: "A♭C" reads "A♭ to C", etc. The accented notes are not differentiated between A# and B♭ for instance; being the same note.


Interval Step Mode
A♭ to C 2 Major Third
A to C 1.5 Minor Third
A to C# 1.5 Minor Third
A# to D♭ 1.5 Minor Third
B♭ to D 2 Major Third
B to D 1.5 Minor Third
B to D# 2 Major Third
C to B♭ 2 Major Third
C to E 2 Major Third
C to D# 1.5 Minor Third
C# to E 1.5 Minor Third
D♭ to F 2 Major Third
D to F 1.5 Minor Third
D to F# 2 Major Third
D# to F# 1.5 Minor Third
D# to G 2 Major Third
E to G 1.5 Minor Third
E to G# 2 Major Third
F to A 2 Major Third
F to A♭ 1.5 Minor Third
F# to A 1.5 Minor Third
F# to A# 2 Major Third
F# to B♭ 2 Major Third
G to B 2 Major Third
B to B♭ 1.5 Minor Third
G# to B 1.5 Minor Third


C E G = 5mj = 3mj+3mn = CE+EG
C E♭ G = 5mn = 3mn+3mj = CD#+D#G
D F A = 5mn = 3mn+3mj
D F# A = 5mj = 3mj+3mn
E G B = 5mn = 3mn+3mj
E G# B = 5mj = 3mj+3mn
F A C = 5mj = 3mj+3mn
F A♭ C = 5mn = 3mn+3mj
G B D = 5mj = 3mj+3mn
G B♭ D = 5mn = 3mn+3mj
A C E = 5mn = 3mn+3mj
A C# E = 5mj = 3mn+3mn

The last triad is a Diminished triad and before the third is raised it is important to raise the fifth:

B D F = dim = 3mn+3mn
B D F# = min = 3mn+3mj
B D# F# = maj = 3mj+3mn

in their birthplace - F A C, C E G, G B D. Indeed in their birth not only is it so, but still further, the top note of the first chord is the root and generator of the third. They are linked in generative continuity. [Scientific Basis and Build of Music, page 49]

a minor third. So by adding the middle of the minor dominant, G, but made G#, that the third so produced may be a minor third, according to the nature of the chromatic chords, we have on this minor side of the chord G#, B, D, F, which we may call its minor form, inasmuch as the semitone of its second minor third is the one, B-C, which genetically arises in the minor genesis; and inasmuch as it has also received its supplemental G# from the minor dominant. How shall we find its complement on the other side? We have seen that D, the Janus-faced center of this triad, B, D, F, looks, as D27, toward the major also; it has already F in common with the major subdominant. The very next step is to the middle of this chord, A. Middles, we have just seen, are ever ready to accommodate themselves; and this minor third triad claims that A be flattened, for on this side also, though its major side, it must have a minor third; so by adding the middle of the major subdominant, A, but made A♭, according to the nature of chromatic intervals, that this F-A♭ also may be a minor third; and now we have it as B, D, F, A♭, which we may call its major form, inasmuch as the semitone of its minor third, E-F, is the one which genetically arises in the major genesis, and inasmuch as it has now received its supplemental A♭ from the major subdominant. This, then, is the chromatic chord in its native place, and in its native constitution; a 4-note chord, wholly of the minor thirds. It will be observed that it has now, in its two forms, divided the octave into minor thirds - 4 minor thirds, so it is very much at home anywhere in the octave; indeed it is at home everywhere - G#, B, D, F, A♭. And as every diatonic common chord in music is constituted of materials found in the octave of notes, it cannot be far from a chromatic chord in some one of its forms. [Scientific Basis and Build of Music, page 55]

This great genetic scale, the all-producer, the all-container, extends over six octaves on each side; for it is not till high in the sixth octave we get B in the major, and it is not till low in the sixth octave that we get F in the minor. It is in the fifth octave, however, that the note which is the distinctive mark of the masculine and feminine modes is generated. D27 in the major, and D26 2/3 in the minor, distinguishes the sex of the modes, and shows which is the head and which the helpmeet in this happy family.2 On the major side F, the root of the subdominant chord, that is the chord which is a fifth below the key-note C, is the root of all. This is the beginning of this creation. If we call the vibration-number of F one, for simplicity's sake, then F1 is multiplied by 3 and by 5, which natural process begets its fifth, C, and its third, A; this is the root, top, and middle of the first chord. From this top, C3, grows the next chord by the same natural process, multiplying by 3 and by 5; thus are produced the fifth and third of the second chord, G and E. From the top of this second chord grows the third and last chord, by the repetition of the same natural process; multiplying G9 by 3 and by 5 we [Scientific Basis and Build of Music, page 66]

The peculiar effects are exhibited when the chord-scale is next set forth. We have seen that there are six chords evolved in the genesis upward and downward, 3 in the major form and 3 in the minor. In the fifths of the minor the semitone is always in the lower third, occurring between the second and third in the subdominant and tonic, and between the first and second in the dominant chord; whereas in the major it is always in the upper third, between the fourth and fifth in the subdominant, and between the third and fourth in the tonic and dominant chords. While the thirds which the fifths contain are thus so varied, the fifths themselves have always one magnitude, whether major or minor. [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]

See Also

Figure 11.01 - Octave composed of Equal Thirds and Triads
Part 14 - Keelys Mysterious Thirds Sixths and Ninths
Table 1 - Relations of Thirds
Table 14.01 - All phrases in HyperVibes containing the term thirds
Table 14.02 - Neutral Thirds - Energy Radiates from Center - Force Contracts to Center
7.12 - Third
12.07 - Keelys Thirds Sixths and Ninths
14.04 - Thirds as Currents
14.05 - Thirds as Differentiations
14.07 - Thirds in Magnetic Action
14.08 - Thirds as Assimilatives
14.10 - Thirds as Ratios within a Whole
14.28 - Thirds as Polar and Depolar Parameters
16.08 - Polar Link in Thirds

Created by Dale Pond. Last Modification: Monday November 16, 2020 03:41:22 MST by Dale Pond.