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the width determined upon for an octave, about six and 

 one-half inches, and at the same time making them suffi- 

 ciently large for practical use, is by extending the key- 

 board in two directions. The method by which Prof. 

 Poole has done this is as follows : 



All modulations of key are made by progressing from 

 front to back of the key-board as the modulations are 

 upward, and from back to front for the reverse. All 

 scales in the same key progress from left to right upward, 

 as in the ordinary pianoforte. 



The accompanying diagram (No. 1), giving the method 

 of placing the digitals for the scale in the key of C, will 

 explain the matter. 



Dotted lines represent the horizontal lines of scales in 

 the keys of Ej,, B b , F, C, G, D, and A. 



There are in each octave of the diatonic major scale in 

 any key : 



(1.) Four key-notes, each related to four keys, in- 

 cluding its own. Thus C is the second of Bj,, the fifth 

 of F, the fourth of G, and the first or tonic of its own 

 scale. It should therefore be found in the lines of those 

 four keys. Similarly D is related to C, G, D, and A ; F 

 to E|,, BJ,, F, and C ; G to F, C, G, and D. These four 

 key-notes, then, take the positions given them on the 

 diagram. 



(2.) Three major thirds from key-notes, each related 

 to three keys. Thus b is the third of G, the sixth of D, 

 and the seventh of C. Similarly, e is related to C, G, 

 and F ; a to B[,, F, and C. These three thirds, therefore, 

 take the positions given them on the diagram. 



(3.) One prime seventh related to one key-note and 

 to be found only in the line of that key-note. 



(4.) Three tones of series 4, each bearing the ratio 

 to a tone of series 2. Since for every tone of series 2 



