374 On Musical Temperaments. 



being nearly full, must be well corked, set in a cool place, 

 and suffered to stand undisturbed for three or four months, 

 or until all the water shall have subsided, with the mucilage 

 on the top of it, and the oil, perfectly transparent, swim- 

 ming upon the'top of the mucilage. When time has thus 

 completed the operation, the pure oil must be poured off 

 into very small phials, and kept in a cool place, well corked, 

 to preserve it from the air. 



Lynn, Nov. 13, 1810. E. WALKER. 



LXVIII. A further Set of Fifteen Corollaries, to the Musical 

 Theorems in Page 39, by means of which, the Tempera- 

 ments of any one of the Concords being given, all the other 

 Temperaments ana all the Wolves can be calculated with 

 the greatest facility . By Mr. John Farey. 



To Mr. Tilloch. 



Sir, X he six musical Theorems which you did me the 

 favour to print in your 147th Number having given much 

 satisfaction to several of my musical acquaintances, I am 

 induced to send you 15 other Corollaries in addition to the 

 12 inserted at page 44: they are naturally divisible into 

 three classes, viz. 



1st. When the temperament of the ffth is given. 



Corollary 13. The temperament of the Hid is = 1 1 2-f-m 



— 4 x temperament of the Vth. 



_, , lis— 4r u-r-4t . . 



By theorem 3, 2 + m is the tern- 



s u 



4r At 



perament of the Hid, and 2 + — m is 4 times 



the temperament of V, by theorem 1 : the sum of these 

 is 1 1 2 -f m, whence the truth of the corollary is 

 manifest : as indeed it is, by merely abbrevating and 

 ordering theorem 3. 



Corollary 14. 1 12 -f m •— 3 x temperament of V = tem- 

 perament of VI. 



lis u Zr 3t lis— 3r 

 Here 2 H m 2 m = 2 



s u s u s 



ii 3/ 



A m, as in theorem 6 : — and so of all the fol- 



u 



lowing. 



Corollary 15. 11 x temperament of V — 12 2 — m 

 = Vth wolf. 



Corollary 



t 



