Sympathetic Vibratory Physics

verb: bring to an end; settle conclusively
noun: firm determination to do something
(Mus.) To let the tones (as of a discord) follow their several tendencies, resulting in a concord.

Ramsay
less variety of effect than we find in the diatonic chords; for although these chords may appear with their notes diversely named, there are still only the three. On account of their cosmopolitan character they need, and they have, no compounding with anything else. They are themselves at home everywhere; like a universal joint, they can turn any way, and affiliate in all directions. Being 4-note chords, and all of minor thirds, their effect is always minor, and they fall with loving softness to the diatonic chords to which they resolve. How this chord in its germ is found in the diatonic chord-scale; how it becomes a 4-note chord of minor thirds; how it variously resolves, each one of the three, in three manners with 24 tonic chords - all this is so fully set forth in the pre-note and treatise on the chromatic chord that it need not be more discussed in this place. See also Plates XVI., XVII., XVIII., XIX., and XX. [Scientific Basis and Build of Music, page 73]

notes attracted by proximity are attracted in the direction of the center of the tonic chord, major or minor. But if D in the major is attracted by C, the root of the tonic, then it would be moving away from the center. Two notes which have the ratio of 8:9, as C and D, or two notes which are produced by the same ratio as C and D, or two notes where each of them is either a root or a top, as C and D, never resolve to each other by proximity. It is an invariable order that one of the notes should be the middle of a chord. [Scientific Basis and Build of Music, page 99]

"If it had been the case that D resolved to the root of the major tonic, the resolving notes to the tonic would then have been one upwards and three downwards, instead of two upwards and two downwards, according to the Law of Duality. [Scientific Basis and Build of Music, page 99]

"What we have thus said about the resolving notes to the major tonic has been allowed in the case of the minor. No one ever said that the second of the minor scale resolved to the root of the tonic. Notwithstanding the importance of the tonic notes, the semitonic interval above the second of the scale decided the matter for the Law of Proximity; and no one ever said that D, the root of the subdominant minor, did not resolve to C, the center of the tonic minor, on the same terms that two notes are brought to the center of the tonic major; with this difference, that the semitonic interval is above the center in the major and below it in the minor. The other two notes which resolve into the tonic minor are on the same terms as the major; with this difference, that the semitonic interval is below the root of the tonic major and above the top of the tonic minor. And the small tone ratio 9:10 is above the top of the tonic major and below the root of the tonic minor. If it has been the case that D resolved to the root of the tonic major, then, according to the Law of Duality, there would have been another place where everything would have been the same, only in the inverse order; but, fortunately for itself, the error has no other error to keep it in countenance. This error has not been fallen into by reasoning from analogy. [Scientific Basis and Build of Music, page 99]

PLATE XVI.

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]

PLATES XVII. & XVIII.

CHROMATIC RESOLUTIONS, MAJOR AND MINOR.

These two plates show the chromatic chord resolving into the twelve major and twelve minor tonic chords of the twenty-four scales. There seems to be twenty-five, but that arises from making G? and F# in the major two scales, whereas they are really only one; and the same in the minor series, E? and D# are really one scale. C in the major and A in the minor, which occur in the middle of the series, when both sharps and flats are employed in the signatures, are placed below and outside of the circular stave to give them prominence as the types of the scale; and the first chromatic chord is seen with them in its major and minor form, and its typical manner of resolving - the major form rising to the root, and falling to the top and middle; the minor form falling to the top, and rising to the root and middle. The signatures of the keys are given under the stave. [Scientific Basis and Build of Music, page 116]

PLATE XIX.

THE CHROMATIC CHORD IN TWO-SEMITONIC PROGRESSION.

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]

PLATE XX.

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]

PLATE XXVI.

VIEW OF THE CHROMATIC CHORDS RESOLVING.

In the three open columns are the three chromatic chords. In the close columns are the same chromatic chords, with the same designations, on the left. The middle row of letters are the chords of the major keys; the letter with the figure being the key note. The right hand row of letters are the chords of the minor keys marked in the same way. The artist will have no difficulty in making use of the other resolutions of this abundant store; but the young student should make similar tables of the other manners of resolution; he will find abundant help for this in other parts of this work. [Scientific Basis and Build of Music, page 119]

Fig. 4 is a setting of the minor and the major chord-scales, showing how they stand linked by notes in common in their direct sequence from dominant minor to dominant major. To each of the six chords is placed the first chromatic chord, showing how it resolves in its three-fold manner by 1, 2, and 3 semitonic progressions in each mode, and by 1 and 2 notes in common variously in each mode; and here again the law of duality is seen in its always symmetrical adjustments. Duality, when once clearly and familiarly come into possession of musicians, will be sure to become an operative rule and test-agent in composition. [Scientific Basis and Build of Music, page 121]

Sympathetic Vibratory Physics

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