RHYTHM AND TONE 



87 



consonance-thread, therefore each includes the other 

 two as concomitant elementary harmonics, or briefly, 

 as concomitants. Thus the root includes third and 

 fifth as concomitants ; the third includes root and fifth 

 as concomitants; the fifth includes root and third as 

 concomitants. All three appear in the following 

 melody, in each tone of which we all hear and feel 

 the same harmonic complex or form and the same 

 harmonic relation as specified by the harmonic num- 

 bers 1, 3, 5 over the notes. 



13151351 



^ 



I 



_,fi- 



r^ 



This provisionally illustrates what I mean by origi- 

 nal harmony in one voice, which asserts and reports 

 itself without chords. The numbers 1, 3, 5 explain 

 what I mean by the common reports of common feel- 

 ing and perception, since they faithfully register the 

 inherent relations which we all hear and feel in com- 

 mon. The number 1 indicates a root. The numbers 

 3 and 5 imply a root and indicate the relation of a 

 tone to its root. I have said that an isolated tone 

 generates and opens up its thread of harmony both 

 above and below and that we follow the thread up or 

 down at will. In the above melody we move from 

 root up to third, then back to root, then down to fifth 

 and so on. That every tone arises in a thread of har- 

 mony is not the only point to be emphasized. In this 

 melody we are now on a root, now on a third, now on 

 a fifth of a thread. The word now is used with pur- 



