verb: cause to change places
noun: Change that is equivalent in degree but opposite in effect to a previous change.
noun: Patterning in which a dark motif on a light ground alternates with the same motif light on a dark ground.
1872.—"It gives me great pleasure to write to you on this subject. Music deals more with the imaginative faculty than any other art or science, and possessing, as it does, the power of affecting life, and making great multitudes feel as one, may have more than ordinary sympathy with the laws you work upon. You say 'from E, root of B, the fountain key-note F, root of C, rises.' There is a singular analogy here in the relativities of sounds, as traced by comparing the numbers made together by vibrations of strings with the length of strings themselves, the one is the inverse or the counterchange of the other. The length of B and E are the counterchange of F and C, hence they are twin sounds in harmony." [Harmonies of Tones and Colours, Extracts from Dr. Gauntlett's Letters1, page 48]
of action is the great law, and the same force that excites sensation with the auditory nerve lies at the bottom of sensation with organs of vision. When I say my plan, I talk in the old groove, and there are difficulties to be smoothed, but in a way that might be much grumbled over. One very curious thing is plain: your system meets many of the cases on which our present theorists stumble so awfully. I saw this from the first time I had the pleasure of considering it with you, and on this account never relished the idea of giving it up; and the more thought bestowed on it led to its applicability to the more ancient forms of melody—the little tunes of the old world in the East. These are said to be independent of harmony, but your system is perfect harmony. The latest theorists in Paris are all at war with the old theory, and there is now a petition lying before the governing powers of the Paris Academy of Music, praying for a total change in the teaching of harmony in that metropolis; and this memorial has been signed by all the rising celebrities in the musical world there. I really believe the best mode, after all, is the series of six tones—the two trinities; and the law of 'to and fro' is impregnable. That is all right. I should like that term to get into vogue, for it is much more plain and clear than what we call the inverse and reverse, or counterchange." "The grave, or rather extraordinary result of your system is, that so much, very much of it tallies with what may be termed the commonly unknown relatives of the tones. You offer affinities which are termed abstruse, and, although admitted, are accepted without demonstration. Why you should be able to explain the much-quarrelled-over connections is beyond my comprehension, and if I could discover the key, the result would be most important for the well-being of music. With this view your system always interests me. I suspect it lies in that wonderful adaptability of the order of numbers. With the artificial system, music is confined to a few single harmonical tones—none of which can ever be used without alteration—which we gently coax the ear into receiving." "Your system runs up the shortest way, and I find it of advantage in composing." [Harmonies of Tones and Colours, Extracts from Dr. Gauntlett's Letters2, page 49]