INFINITE HARMONY
The harmony of to-day, and not for long; for all signs presage a revolution, and a next step toward that “eternal harmony.” Let us once again call to mind, that in this latter the gradation of the octave is infinite, and let us strive to draw a little nearer to infinitude. The tripartite tone (third of a tone) has for some time been demanding admittance, and we have left the call unheeded. Whoever has experimented, like myself (in a modest way), with this interval, and introduced (either with voice or with violin) two equidistant intermediate tones between the extremes of a whole tone, schooling his ear and his precision of attack, will not have failed to discern that tripartite tones are wholly independent intervals with a pronounced character, and not to be confounded with ill-tuned semitones. They form a refinement in chromatics based, as at present appears, on the whole-tone scale. Were we to adopt them without further preparation, we should have to give up the semitones and lose our “minor third” and “perfect fifth;” and this loss would be felt more keenly than the relative gain of a system of eighteen one-third tones.
But there is no apparent reason for giving up the semitones for the sake of this new system. By retaining, for each whole tone, a semitone, we obtain a second series of whole tones lying a semitone higher than the original series. Then, by dividing this second series of whole tones into third-tones, each third-tone in the lower series will be matched by a semitone in the higher series.
THE TRIPARTITE TONE
Thus we have really arrived at a system of whole tones divided into sixths of a tone; and we may be sure that even sixth-tones will sometime be adopted into musical speech. But the tonal system above sketched must first of all train the hearing to thirds of a tone, without giving up the semitones.
To summarize: We may set up either two series of third-tones, with an interval of a semitone between the series; or, the usual semitonic series thrice repeated at the interval of one-third of a tone.
Merely for the sake of distinction, let us call the first tone C, and the next third-tones C♯, and D♭; the first semitone (small) c, and its following thirds c♯ and d♭; the result is fully explained by the table below:
A preliminary expedient for notation might be, to draw six lines for the staff, using the lines for the whole tones and the spaces for the semitones:
