being also the center of the diatonic triplet, B, D, F, which is the diatonic germ of the chromatic system. Four minor thirds upward or downward from C# we have a second chromatic chord, its central note being G. The dual1 of C# is E?; and there is the same order of keys on the keyboard2 below C# as there is above E?. Four minor thirds from E? upward or downward forms a third chromatic chord, the central note of which is A. The dual A, the center of the third chromatic, is G, the center of the second; and these two notes, by their duality, and by the duality of the two chords throughout, balance each other exactly on the keyboard on either side of the first chromatic chord, which contains all its own duals, and by this self-duality sits in the center, like the tonic chord among the diatonic three.
The CHROMATIC SYSTEM of chords is developed from these three primitive chromatic chords, and in the course of its development one or two notes are brought in semitonic progression to the middle, one or two to the root, and one or two to the top of all major and minor tonic chords. Likewise, at one time or another in the course of the system, there is one note in common with the middle, one note in common with the root, and one note in common with the top of all the major and minor tonic chords.
The notes of each primitive chromatic chord are all different from the notes of the other two, so that there is no mistaking of the one for the other; any one note decides the chromatic chord to which it belongs.
It is the function of the chromatic chord, in the course of its systematic development, to bring two notes, the one above and the other below, in semitonic progression to each of the three notes of the tonic chord; and likewise, without interfering with the imperial character of the tonic chord, it brings two notes in semitonic progression to each note of the other two chords; so that, although at first the subdominant and dominant chords are only like satellites to the tonic chord, they, with their chromatic chords, are now raised to the dignity of planets as it were, having the chromatic chords as their satellites.
1 See the Chapter on Duality. 2 See Plate III.