or the Division of the Octave. 177 



given key. This is of importance; e. g. in the chord c-\e-g-c 

 taken with the right hand, the first finger has to reach \e between 

 the adjoining keys e\}-f, and a little under the e. All the keys are 

 cut away so as to overhang about \ an inch for this purpose ; so 

 that though the length of each key on a plan is only 3 inches, yet 

 the tangible length is 3^ inches. Notes derived from the black 

 keys of the E.T. (ordinary) key-board are black [x—\ f 3, 6, 8, 

 10). The other keys, corresponding to # = 0, 2, 4, 5, 7, 9, 11, 

 are white. 



It results from the arrangement by intervals that all combi- 

 nations, scales, or chords of any kind have the same form for the 

 finger in whatever key they are taken, a simplification which 

 gives the learner one thing to acquire where there are twelve on 

 the ordinary key-board. 



The thirds used in positive and negative systems being differ- 

 ently derived, the resulting forms of scale on the key-board are 

 different. The positive scales can be played with a little prac- 

 tice ; and all desirable chords and combinations can be grasped 

 with ease. But as far as facility of performance goes, the nega- 

 tive systems afford the principal simplification. I believe I am 

 not exaggerating in saying that it may be possible to execute 

 in this manner passages of greater complexity and difficulty than 

 can be performed on the ordinary key -board. The movements 

 of the fingers required are less in amount and simpler in cha- 

 racter. Passages of the most rapid kind are performed with 

 ease. The mean-tone stop on my small enharmonic organ has 

 given me the opportunity of realizing what I had always antici- 

 pated in this respect. 



Practical Applications. 



The first instrument constructed with generalized key-board 

 was a large harmonium. The key-board has 84 keys to each 

 octave ; it was thus arranged in order that, in the experiment 

 with the system of 53 in particular, there might be no risk of 

 failure from any deficiency in the extent of the instrument. I 

 specially wish to direct attention to the fact that both the instru- 

 ments hitherto constructed are designed for experimental pur- 

 poses — as an objection constantly made against my instruments 

 is, that if put into a practical form their bulk would be enor- 

 mous. When a practical instrument is to be constructed, the 

 question will be, what is the least extent of development that 

 will answer ? hitherto, for the experimental instruments, it has 

 been, what is the largest development that may possibly be 

 needed ? For instance, the only practical instrument I clearly 

 see my way to at present is one for some kind of negative sys- 

 tem. My mean-tone stop has 36 notes to the octave ; but as 

 Phil Mag. S. 4. Vol. 50. No. 330. Sept. 1875. N 



