In the above line it will be readily observed that these three chromatic chords, having each of their intervals a minor third, involve, as necessary elements of their build, every one of the twelve semitones at one point or another of the line. This is a second witness to the legitimacy of the chromatic scale of twelve semitones. We have our first witness to the same in the evolution of the semitones progressively in the course of the modulations by which, in growth-like continuity, Nature links the successive keys; whether developed upward, as is the natural way of the majors; or downward, as in the natural way of the minors; or half upward and half downward, which is an expedient in order to simplify the signatures. In whichever direction the modulation is effected, one note is always divided, and must, true to Nature, be signified by placing a sharp or a ♭, as the case may be, to the 4-comma altered interval, and this always leaves a 5-comma interval to occupy the place to which Nature has assigned such interval in the original scale. When this operation has been twelve times performed, we have the chromatic scale of twelve semitones. Thus by two witnesses the thing is established. By further examination of these chromatic chords we find other interesting features beside their witness to the twelve semitones of the octave.
By taking four minor thirds upward from G# or downward from A♭, we have the first chromatic chord in its twofold form. Its central note is D, the top of the dominant major, and the root of the subdominant minor, being its own dual, that is to say, its minor birth being dual to its major birth.1 On the keyboard it has the same order of keys above it and below it; this dual D [Scientific Basis and Build of Music, page 56]
1 See Plate II. - The Genesis.