228 THE NATURE OF MUSIC 



since the existence of such a series of undertones has 

 never been demonstrated, nor has it ever been heard 

 by the musical ear. It cannot be gainsaid that from a 

 mathematical point of view this hypothetical series of 

 undertones is both charming and fascinating, since to 

 the eye its explanation of the minor chord appears 

 both logical and satisfactory. This probably explains 

 why the theory has won so many adherents. But mu- 

 sical hearing, feeling and perception refuse thus to be 

 deceived. The common harmonic self-report of the 

 minor triad at h) is this : F is the root, Al? the third, 

 C the fifth. The triad is F-minor, not C-minor. One 

 might as well try to invert one's self and walk on the 

 ceiling as try to perceive C as the root of this triad. 

 The test of harmonic self-reports on the above hypo- 

 thetical minor series is as follows: 1; or C = 6. 2; or 

 C= 6. 3; or F= 1. 4; or C= «. 5; or A>= s. 

 6; or F= i. 8;or C= s. 



Next I present the Zarlino-Riemann minor scale, 

 the tones of which are arbitrarily conceived as the 

 components of three pendant primary minor triads 

 supposed to hang suspended from the aerial roots C, 

 F and G. Below compare this pendant minor scale 

 with the ascending major scale and observe the per- 

 fect correspondence of the whole and half steps. Just 

 as in the case of the triad so also here in the case of the 

 scales the minor is the exact inverse of the major. 



-iS^ 



Majai 

 Scale 



iE=E ^=,=^.=^ '• - ±J 



