Temperaments of different musical Systems. 51 



1 1 41 



be flattened -c """37° or ~""l48~ C ' whic ^ ls 



— 3-049662; or more correctly it is — 3*048112; — c 



being —3*057742 in the system of this scholium. 



Scholium 11. If a douzeave be required, wherein the 

 major third (±) and the major sixth (f) shall beat 

 equally quick, the former sharp and the latter flat ; 



115— 4r 

 we have from theorems 3 and 6, as 5 : 5 : : — : 



3r —11? 



, whence 11 5— Ar = 3r — 1 Is or 225 =7^ and 



s J 



r 22 , u — At Zt — u . 

 = — -• also, as 5 : 5 : : : , whence 



s 7 u u 



t 2 22 



u — At = 3t — u or 2u = It and — = — ; and -— -S 



2 2 



4- - -m or -- c is the temperament of the fifth. 



Which in theorem 3, gives — 2 '— — - m, or—c, 



the flat temperament of the major third; and in theo- 

 rem 6, gives —2 + ~m, or — c, the sharp tem- 

 perament of the major sixth*. 



This is the system which Dr. Smith ' barely 

 mentions at page 220 3 011 account of its dif- 

 fering so little from equal harmony, in my last 



5 35 



scholium; wherein -— - or -t^c is the tempera- 

 18 120 



2 36 



ment of the fifth, which here is — , or — — - : the dif- 



ference being only the -rr~-th part of a major comma or 

 1 20 



•0873642: also - or -^-, and —• or JL have, a 



difference of v -^-c, or '349462, but little more consi- 



1 7 1 



derable, in the major thirds ; and ~x- or , and — 



J 42 '. 7 



f\ 1 



or -— have a difference of — c, or *262092 in the 



major sixths. 



This system differs more from that of M. Henfling; 



* Mentioned by .Dr. Robison, Sup. Enc. Brit. 3d edit. ii. 662, 



D 2 (see 



