232 THE NATURE OF MUSIC 



and fifth omit the harmonic root, the sixth omits 

 both the harmonic root and third. The superposed 

 harmonic numbers show that mi is the harmonic 

 root of all of the six chords. In § 39 we pointed 

 out and explained by means of the harmonic self- 

 reports of homophony the necessary distinctions be- 

 tween harmonic roots and chord-roots, between har- 

 monic intervals and chord-intervals and by the same 

 means demonstrated that chords are often incom- 

 pletely represented by one or two components, some- 

 times appearing detached from their harmonic roots, 

 sometimes from their harmonic roots and thirds, some- 

 times even from their chord-roots. These distinctions 

 and facts being exemplified in the above groups of 

 chords and having previously been explained it is 

 enough here to call attention to them. 



By comparing the above minor group of consonant 

 and dissonant chords with the corresponding major 

 group in § 39 the reader will observe that two chords 

 identical both as to form and component tones appear 

 in both groups. They are: li in major and iv in 

 minor; vii° in major and //° in minor. Despite their 

 identity in form and component tones these triads 

 make one report in major and a very different report 

 in minor, as shown below. 



5 7 9 3 5 7 



1. Major: 



2. Minor: 



IV ir 



