114 



Another complexity resulting from modulation is the 

 introduction of new tones. Modulating iuto the key of 

 G, the diatonic scale in that key is 



GAbCDef=fG 



3 27159 9 5 45 6 



1 f I I f t ¥- 2 

 Here fir is a tone new to the diatonic scale in C. By 

 successive modulations of fifths upward a key-note Ft^ 

 may be obtained, a comma greater than f#. Every suc- 

 cessive modulation, then, necessitates an addition to the 

 scale. 



Another new series of tones is demanded by the nature 

 of the relation between the three allied fundamental tones 

 in any key. The dominant is so called because whenever 

 chords are sounded based upon it, the ear demands a 

 return to the tonic harmony ; its sounding, as it were, 

 commands the tonic to be sounded. Hence those tones 

 in the dominant chord which most distinctly convey this 

 impression of return to the tonic are most important, 

 being most characteristic of the dominant harmony. It 

 w^as long ago asserted theoretically and has since been 

 confirmed by experiment that a tone whose vibration num- 

 ber bears a ratio of l to that of the dominant is a most 

 important element of the dominant harmony. For in- 

 stance, a tone so related to G, the dominant of C, when 

 broug^ht within the octave, would have a vibration number 

 H of the tonic, which does not correspond with any tone 

 of the diatonic scale. Prof. Poole has suggested that 

 tones in this series should be designated by Gothic capi- 

 tals. The interval is called the prime seventh, or domi- 

 nant seventh, and the prime seventh of G would be F. 



So far only the major mode of the diatonic scale has 

 been referred to. There is another mode of using the 

 tones of a scale to make harmonies, called the minor 



