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the differences between the major and minor modes. It 

 will be seen at a glance that in the major mode the tonic, 

 second, fourth, and fifth are key-notes, the third, sixth, 

 and seventh thirds. In the minor mode of the same scale 

 the tonic, second, fourth, and fifth are thirds, the third, 

 sixth, and seventh key-notes. Moreover, in the major 

 mode, the tonic, dominant and subdominant are all key- 

 notes ; in the minor mode they are all thirds. 



To return to the related harmonies of the minor mode, 

 there is this peculiarity in the dominant harmony, that 

 the third is not the minor, but the major, third. To play 

 an instrument correctly in the minor mode, then, there 

 must be a series of major thirds to thirds, which does not 

 belong in the simple diatonic scale of harmony. For in- 

 stance, in the scale of which a is the tonic, there must be 

 a tone g^ which is the major third of e, the dominant of 

 a, and has the ratio V" to a, with a vibration number 75 

 when that of a is 40. This g^ might be regarded as the 

 major seventh employed in the ordinary minor scale. 

 Since every tone of the diatonic major scale deduced from 

 thirds is in turn the dominant minor, there must be an 

 additional tone for every tone of the diatonic scale de- 

 duced from thirds. This series Prof. Poole proposes to 

 designate by an Italic lower case letter. 



Digitals representing these four series of tones are 

 essential to a complete key-board justly intoned. The 

 word "digital" is used instead of the common word 

 "key," as less liable to confusion with other terms. To 

 be sure, the possible refinements of harmony do not stop 

 here. In the dominant minor harmony, for instance, the 

 prime seventh with the ratio J might be used instead of 

 the minor seventh with the ratio | ; or it might be conve- 

 nient to have a series of minor thirds from key-notes, 

 for use in sudden changes from major to minor chords ; 



