120 



is represented by horizontal hatching, orange by a dotted 

 surface, black and white by their own colors. 



The symmetrical arrangement of this key-board is per- 

 ceptible at a glance. Among the most important charac- 

 teristics of its arrangement are the following : 



All the digitals in any key in either the major or minor 

 mode are to be found hi the same horizontal line, drawn 

 through the second quarter, downward, of the key-note, 

 except the fourth of the minor mode, which is only one 

 space below such a line. 



The digitals in any key are arranged precisely the same 

 as in every other key, so that the fingering is the same 

 for all keys. 



In modulation in the regular progression by fifths, the 

 horizontal line of the new key is always only one space 

 up or down. 



All four of the notes of the different series represented 

 by different forms of the same letter, as e, e, E, and E, 

 are in the same vertical line. 



In this key-board, there need be no temperament or 

 approximation, but provision is made for just intonation 

 in every key used. If, however, it should be thought 

 desirable, for the sake of economizing space or expense, 

 to reduce the number of strings or resonators, a consid- 

 erable saving may be made by an almost inappreciable 

 temperament, which the construction of the key-board 

 renders very easy. 



Suppose that C makes 256 vibrations in a second ; a 

 number not exactly corresponding with the normal pitch, 

 but convenient because a better multiple. Then tuning 

 downward by fifths seven times, 



C b = 479tfif. 



Tuning upward, G == 384 and b = 480. 



Cj, is therefore less than b by jf f of a vibration in 



