order, characteristic of all that has life. Nature has her wiles, and persuades man, obstinately opposed though he be to progress and change; Nature progresses continually and changes unremittingly, but with so even and unnoticeable movement that men perceive only quiescence. Only on looking backward from a distance do they note with astonishment that they have been deceived.

The Reformer of any given period excites irritation for the reason that his changes find men unprepared, and, above all, because these changes are appreciable. The Reformer, in comparison with Nature, is undiplomatic; and, as a wholly logical consequence, his changes do not win general acceptance until Time, with subtle, imperceptible advance, has bridged over the leap of the self-assured leader. Yet we find cases in which the reformer marched abreast of the times, while the rest fell behind. And then they have to be forced and lashed to take the leap across the passage they have missed. I believe that the major-and-minor key with its transpositional relations, our “twelve-semitone system,” exhibits such a case of falling behind.

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That some few have already felt how the intervals of the Series of Seven might be differently arranged (graduated) is manifested in isolated passages by Liszt, and recently by Debussy and his following, and even by Richard Strauss. Strong impulse, longing, gifted instinct, all speak from these strains. Yet it does not appear to me that a conscious and orderly conception of this intensified means of expression had been formed by these composers.

I have made an attempt to exhaust the possibilities of the arrangement of degrees within the seven-tone scale; and succeeded, by raising and lowering the intervals, in establishing one hundred and thirteen different scales. These 113 scales (within the octave C–C) comprise the greater part of our familiar twenty-four keys, and, furthermore, a series of new keys of peculiar character. But with these the mine is not exhausted, for we are at liberty to transpose each one of these 113, besides the blending of two such keys in harmony and melody.

There is a significant difference between the sound of the scale c-d♭-e♭-f♭-g♭-a♭-b♭-c when c is taken as tonic, and the scale of d♭ minor. By giving it the customary C-major triad as a fundamental harmony, a novel harmonic sensation is obtained. But now listen to this same scale supported alternately by the A-minor, E♭-major, and C-major triads, and you cannot avoid a feeling of delightful surprise at the strangely unfamiliar euphony.

But how would a lawgiver classify the tone-series c-d♭-e♭-f♭-g-a-b-c, c-d♭-e♭-f-g♭-a-b-c, c-d-e♭-f♭-g♭-a-b-c, c-d♭-e-f-g♭-a-b♭-c?—or these, forsooth: c-d-e♭-f♭-g-a♯-b-c, c-d-e♭-f♭-g♯-a-b-c, c-d♭-e♭-f♯-g♯-a-b♭-c?

One cannot estimate at a glance what wealth of melodic and harmonic expression would thus be opened up to the hearing; but a great many novel possibilities may be accepted as certain, and are perceptible at a glance.

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With this presentation, the unity of all keys may be considered as finally pronounced and justified. A kaleidoscopic blending and interchanging of twelve semitones within the three-mirror tube of Taste, Emotion, and Intention—the essential feature of the harmony of to-day.

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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.

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:

then indicating the third-tones by sharps and flats:

The question of notation seems to me subordinate. On the other hand, the question is important and imperious, how and on what these tones are to be produced. Fortunately, while busied with this essay, I received from America direct and authentic intelligence which solves the problem in a simple manner. I refer to an invention by Dr. Thaddeus Cahill.[Q] He has constructed a comprehensive apparatus which makes it possible to transform an electric current into a fixed and mathematically