in their birthplace - F A C, C E G, G B D. Indeed in their birth not only is it so, but still further, the top note of the first chord is the root and generator of the third. They are linked in generative continuity.
In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common.
In the following treatise of our author Nature will be found beckoning us toward the Chromatic in an exceedingly interesting way; and the exhibition of the Chromatic as a system, and an exceedingly important system, of chords and progressions is a monument to the genius of D. C. Ramsay.
It has been found impossible in this first edition of his work to publish in extenso the musical elaboration of the Chromatic system through all its forms and progressions; this would make the volume fully twice the size it is. We must be content meanwhile to publish the musical doctrines of Ramsay, with illustrations, and leave the music for a further edition and a future time. [Scientific Basis and Build of Music, page 49]
1 See Plate XXIX., Fig. 3.
See Also
perpetual transformation processes
continuous motion
perpetual interaction
perpetual restlessness
Keely and Perpetual Motion
Law of the Perpetual Transmission and Transmutation of Energy
Perpetual Motion