ORIGIN AND NATURE OF MINOR 211 



The diatonic sol at each N.B. in the above minor 

 melody calls for a series of observations. Through 

 sol in the above relation, original harmony in one 

 voice discloses a curious and interesting fact which 

 throws a strong and clear light upon consequent 

 complex chord-formations so numerous in modern 

 music. The above minor melody is the exact coun- 

 terpart in minor of the parallel melody in major, and 

 sol arises in the minor melody on the line of least 

 resistance. Previously we met sol as small third but 

 as a by tone to regnant /. Now we meet sol again as 

 a small third, but this time as a regnant tone and, 

 what is more, as a regnant tone in cadence. Observe 

 that the cadence-tend of sol in this relation is much 

 stronger than that of the parallel tone ti in the major 

 melody. And why ? Because of the presence of the 

 large third si in the concomitant harmony of sol. 

 That is to say, this sol a reports si 3 in its concomitant 

 harmony, it means that we feel and hear the small 

 third and the large third of the same root simulta- 

 neously. Hence the stronger cadence- tend of sol s to 

 fa 9 than that of the parallel major ti 3 to la 9. Hence 

 the important fact reported by harmony in one voice 

 that there are harmonies containing double thirds^ 

 that is, two thirds of one root. Hence the inference 

 that there may be other double harmonics as double 

 fifths and the like, an inference to be verified later. 

 From this important fact adduced from and verified 

 by harmony in one voice we naturally draw the 

 logical conclusion that chords may be compounded 

 of double harmonics, that is, of double thirds and the 

 like. Such chords may be named double chords. 



