112 



the key-note or tonic. Octaves of these tones are re- 

 garded m harmony as identical. 



Every tone of the diatonic scale is related very simply 

 to one of the three fundamental tones of its key, and is 

 commonly sounded together with that fundamental tone. 

 Remembering that the dominant is represented by f or its 

 octave, and the subdominant by J or its octave, the scale 

 may be thus analyzed : 



1 = tonic. 



f r= I dominant. 



^ = ^ tonic. 



I = subdominant. 



§ ^ dominant. 



1 = 1 subdominant. 

 \^- = ^ dominant. 



2 = tonic. 



The interval indicated by the ratio | is called a third, 

 and it appears that the diatonic major scale is wholly 

 made up of thirds and fifths. Prof. Poole has suggested 

 that those tones of the scale deduced from fifths be indi- 

 cated by Roman capital letters, and those deduced from 

 thirds by Roman lower case letters. That is, the diato- 

 nic major scale may be written, in the key of C, for 

 instance : 



CDeFGabC 



1 f f I f f ¥- 2 



Without carrying the development of the scale farther 

 at this point, it is time to answ^er the question. What is 

 the difficulty in constructing a key-board by w^hich the 

 simple diatonic scale may be justly intoned ? Briefly put, 

 the difficulty is this. 



From the principle of related fundamental tones already 

 referred to springs that of modulation, or the change 



