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_; 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 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.
[Q] "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. Readers interested in the details of this invention are referred to the above-mentioned magazine article.