Sympathetic Vibratory Physics

Three single-frequency tones or sounds sounded sequentially.
A chord composed of a fundamental tone and a third and fifth above.
(1) A chord of three notes.
(2) A common chord. Triads are said to be major, minor, augmented, and diminished. [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]

Triad Types
[Major/Major Triads] - C E G# - D F# B? — E G# C - G# C E (Augmented triads)
[Major/Minor Triads] C E G - F A C - G B D - D F# A (Major triads)
[Minor/Major Triads] C E? G - D F A - C# E G# - A C E (Minor triads)
[MajorMinor/MinorMajor Triads]
[Major/Minor Triads] C E G as above
[Minor/Major Triads] as above
[Minor/Minor Triads] - B D F - C E? F#- F# A C - E? G? A (Diminished triads)

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. (Also called Fifth, where two thirds makes a Fifth). 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 Third and Perfect Fifth on the 1st, 4th and 5th degrees.
Minor Triad: Minor Third and Perfect Fifth on the 2nd, 3rd and 6th degrees.
Diminished Triad: Minor Third and Diminished Fifth on the 7th degree.

Triad, Dynamics
Passage from Coleridge, The Friend: "EVERY POWER IN NATURE AND IN SPIRIT must evolve an opposite, as the sole means and condition of its manifestation: AND ALL OPPOSITION IS A TENDENCY TO RE-UNION. This is the universal Law of Polarity or essential Dualism... The Principle may be thus expressed. The Identity of Thesis and Antithesis is the substance of all Being; their Opposition the condition of all Existence, or Being manifested; and every Thing or Phenomenon is the Exponent of a Synthesis as long as the opposite energies are retained in that Synthesis."

Hamilton notes on the above passage: "So far as I understand this principle, I would perhaps express it thus:- Power can be manifested only by its effects, that is, by overcoming Resistance, which is Contrary Power. Existence is manifested by the struggle between two opposite tendencies ... Each particular phenomenon, or individual Manifestation of Existence, is determined to be such as it is, and no other, by the kind and degree of its producing Power, that is, by its own particular combination or synthesis of two opposite tendencies. The thought of Being or Existence general (a new name, the property of which may demand a special inquiry), as distinguished from phenomena, that is, from individual manifestations of existence, arises in us along with, and as a realization or externalization of, our belief in a common ground, a hidden principle of unity, belonging to the two opposite tendencies." [Hankins, Thomas L.; Sir William Rowan Hamilton; The John Hopkins University Press]

Ramsay
The triplet B, D, F, has been called the imperfect triad, because in it the two diatonic semitones, B-C and E-F, and the two minor thirds which they constitute, come together in this so-called imperfect fifth. But instead of deserving any name indicating imperfection, this most interesting triad is the Diatonic germ of the chromatic chord, and of the chromatic system of chords. Place this triad to precede the tonic chord of the key of C major, and there are two semitonic progressions. Place it to precede the tonic chord of the key of F# major, and there are three semitonic progressions. Again, if we place it to precede the tonic chord of the key of A minor, there are two semitonic progressions; but make it precede the tonic chord of E? minor, and there are three semitonic progressions. This shows that the chromatic chord has its germ in, and its outgrowth from the so-called "natural notes," that is notes without flats or sharps, notes with white keys; and that these natural notes furnish, with only the addition of either A? from the major scale or G# from the minor, a full chromatic chord for one major and one minor chord, and a secondary chromatic chord for one more in each mode. [Scientific Basis and Build of Music, page 52]

But, as the subdominant sixth and dominant seventh suggest that the chromatic chord should be a 4-note chord, we must find out how Nature completes this diatonic chromatic triad and makes it a 4-note chord, and that according to its own intrinsic character as of minor thirds. Nature has always a rationale in her operations which it is ever delightful to discover. Wedged in between the minor dominant and the major subdominant, this triad, B D F, has already B, the top of the dominant minor, for its root; and F, the root of the subdominant major, for its top; and its middle is the mysterious D which, in its two positions as root of the minor subdominant and top of the major dominant, stands at the two extremes of the whole twofold diatonic key, bounding and embracing all; and which in its two degrees as D26 2/3 and D27 claims kindred with both minor and major modes of the twofold key system. Surely this Janus-faced D, looking this way toward the minor and that way to the major, seems to say, "the complement of this chord, of which I am the heart, is not far to seek nor hard to find on either side." It has already B in common with the minor dominant; the very next step is to the middle of this chord, G. Roots and tops of chords may not be altered, but middles may with impunity be flattened or sharpened as occasion may require. No two of them in succession in the chord-scale have the same structure; the chromatic triad, in claiming this middle, claims it sharpened, for it must have [Scientific Basis and Build of Music, page 54]

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]

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]

I. P. Cory
"All things are governed in the bosoms of this triad.
Lyd. de Men. 20.—Tay.
All things are governed and subsist in these three.
T. Proc. in I. Alcib.
For you may conceive that all things serve these three principles.
T. Dam. de Prin.
From these flows the body of the Triad, being pre-existent,
Not the first, but that by which things are measured.
Z. or T. Anon.
And there appeared in it virtue, and wisdom,
And multiscient truth.
Z. or T. Anon.
For in the whole world shineth a Triad, over which a Monad rules.
T. Dam. in Parm."
— The Chaldæan Oracles
[Ancient Fragments c. 1832 by I. P. Cory]

Sympathetic Vibratory Physics

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