226 THE NATURE OF MUSIC 



of V in minor, then as i of IV and 1 of IV in minor. 

 This pedigree is 5, ?, i, 1. 



5. La began as 3 of IV in major, next appeared as 

 9 of V in major, then as i of /, 5 of iv and 5 oi IV in 

 minor. This pedigree is 3, 9, 1, s, 5. 



6. Fa began as 7 of V in major, next appeared as 

 1 of IV in major, then as 3 of iv and © of F in minor. 

 This harmonic pedigree is 7, 1, a, 9. 



7. Ti began as 3 of V in major, next appeared as 5 

 of V and 5 of v in minor. This pedigree is 3, 5, s. 



In these pedigrees we observe that of the nine per- 

 cepts thus far accounted for do has reported three and 

 has still to appear as 1, 3, 6, 7, 9, 9; sol has reported 

 three and has still to appear as 1, 3, s, 7, 9, 9; mi has 

 reported four and has still to appear as s, 5, 7, 9, 9; 

 re has reported four and has still to appear as 3, 3, s, 

 9, 9; la has reported five and still has to appear as 1, 

 8, 7, 9; fa has reported four and has still to appear as 

 1, 3, 5, 6, 9; ti has reported three and has still to 

 appear as 1, 1, 3, 7, 9, 9. Of all these relations still 

 remaining to be reported by diatonics both the rela- 

 tions and the harmonies are either chromatic or 

 enharmonic. The above pedigrees of seven tones 

 present an aggregate of twenty-six harmonic relations 

 each of which is distinct and individual. Thus we 

 observe that the multiplication of harmonic relations 

 is very rapid while that of harmonic percepts is very 

 slow. This is true not only of homophony, but of 

 multi-voice music as well. Further back the Zarlino- 

 Riemann theory of pendant minor was alluded to as 

 an example of irreconcilable conflict between music- 

 thinking and music-feeling. This conflict becomes 



