Ramsay
Through the whole system, in the progression of major scales with sharps and minor scales with flats, the new sharp is applied to the middle of the major dominants, and the new flat to the middle of the minor subdominants. In the progression of major scales with flats and minor scales with sharps, the new flat is applied to the root of the major subdominant, and the new sharp to the top of the minor dominant.2 [Scientific Basis and Build of Music, page 43]
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]
See Also