or the Division of the Octave. 



175 



Negative Systems. 



The scales of negative systems form themselves very simply 

 according to the notation of ordinary music. It will be suffi- 

 cient to say here that, except in case of the employment of the 

 approximate harmonic seventh, the distinction between flats and 

 sharps is sufficient to indicate the proper treatment of these 

 systems. 



Concords of Regular and Regular Cyclical Systems. 



Name or n. 



Order. 



Depar- 

 ture of 

 fifth. 



Depar- 

 ture of 

 third. 



Depar- 

 ture of H. 

 seventh. 



29 



1 



1 

 29 



8 

 ~ 29 



14 



~ 29" 



41 



1 



1 

 41 



8 

 41 



14 

 - 41 



Perfect fifths. 





1 



8 

 ""51-151 



14 

 "51151 



51151 



53 



1 



1 

 53 



8 

 53 



14 



~ 53 



Positive perfect thirds. 





1 

 58-454 



8 



14 

 58-454 



58-454 



118 



2 



1 

 59 



59 



14 



59 



65 



1 



1 

 65 



8 

 65 



14 



~~ 65 



43 



-1 



1 

 43 



4 

 43 



10 

 ~ 43 



31 



-1 



I 

 ~ 31 



4 



31 



10 



" 31 



Mean tone. Negative"! 

 perfect thirds. J 





~ 29^227 



4 



10 

 "29-227 



29-227 



50 



-2 



1 

 25 



4 

 ~ 25 



10 

 25 



19 



-1 



~ f9 



4 



~ 19 



10 

 ~ 19 



Departure of perfect fifth = 0195£ 



1 





51-15 





c 

 Departure of perfect third- - -13686- ~~ 



5b , 454 



The above Table exhibits the mode of derivation of the 

 departures of the approximate fifths, thirds, and harmonic 



