* Note: Harmonic Limit <32/19 & Errors <4.9¢

Excerpt from: Busoni, Ferruccio, "Sketch of a New Esthetic of Music," G. Schirmer, Inc., ca. 1911, reprinted in Three Classics in The Aesthetic of Music, Dover Publications, Inc., New York, 1962, pp93- 95]

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 Db; the first semitone (small) c, and its following thirds c# and db; . . . .

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. ["New Music for an Old World," Dr. Thaddeus Cahill's Dynamophone, an extraordinary electrical invention for producing scientifically perfect music. Article in McClure's Magazine for July, 1906, by Ray Stannard Baker. . . .] He has constructed a comprehensive apparatus which makes it possible to transform an electric current into a fixed and mathematically exact number of vibrations. As pitch depends on the number of vibrations, and the apparatus may be "set" on any number desired, the infinite gradation of the octave may be accomplished by merely moving a lever corresponding to the pointer of a quadrant.

Only a long and careful series of experiments, and a continued training of the ear, can render this unfamiliar material approachable and plastic for the coming generation, and for Art.

And what a vista of fair hopes and dreamlike fancies is thus opened for them both! Who has not dreamt that he could float on air? and firmly believed his dream to be reality?--Let us take thought, how music may be restored to its primitive, natural essence; let us free it from architectonic, acoustic and esthetic dogmas; let it be pure invention and sentiment, in harmonies, in forms, in tone-colors (for invention and sentiment are not the perogative of melody alone); let it follow the line of the rainbow and vie with the clouds in breaking sunbeams; let Music be naught else than Nature mirrored by and reflected from the human breast; for it is sounding air and floats above and beyond the air; within Man himself as universally and absolutely as in Creation entire; for it can gather together and disperse without losing in intensity.

12 TONE EQUAL TEMPERAMENT

24 TONE EQUAL TEMPERAMENT (QUARTER-TONES)

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December 4, 2003