80 Mr. Farey’s Letter on musical Intervals, &¢. 
ments are but a trifle greater than the ‘Temperaments in 
use ; and the Vth wolf falls in the same Key, and is con- 
siderably less than half of the usual quantity ; owing to two 
others of the fifths being in small degrees sharpened, which 
seems a great and important novelty. 
As to the minor Thirds, the two most important Keys, A 
and Ej, have Temperaments which but very little exceed 
those in use, and in neither of the three next most important 
Keys D, Gand B, does the Temperament one-third ex- 
ceed those of the Mean-Tone system; and lastly, the three 
3d wolves fallin the three Keys, to which the practical 
‘Tuner assigns them ; agreeably to what is stated in my Tem- 
perament Theorems, Phil. Mag. vol. 36, p. 42: the 11th 
Scholium to which defines the chief properties of the 
Equal-harmony Douzeave of Professor Fisher, in his 3d 
proposition. 
I ‘beg leave to remark, that I have long’ been impressed 
with the importance and desirableness of what Professor 
Fisher has now performed for the Musical world, as far at 
least as Organ Music is concerned, as will be seen by refer- 
ence to the work last quoted, vol. 26, p. 176; and vol. 27, 
p- 319 and 320. 
I am not aware that any one before me, had published 
the accurate and very simple mode of calculating Beats, which 
Professor Fisher has rather too briefly mentioned, at the 
bottom of page 181: many years ago, I deduced it asa 
corollary from the 202d proposition of Emerson’s Algebra, 
whose Theorem I have quoted in the Edink. Enc. Vol. (0, 
p. 369, and there first published my Theorem. 
In a future communication to you, [ wish much that Prof. 
Fisher would mention the Temperament, or else otherwise 
define the system; which he has entitled the French one, in 
page 198: and also say, whether at the top of p. 31, he 
does not mean Vth on C, and #VIth on F? 
Iregret exceedingly that the calculations for Table IV, 
in page 34, were abridged of their three last places of 
figures, particularly the two first of these, and earnestly re- 
quest, that Professor Fisher will yet supply these, through 
the medium of your pages, and he will still further oblige, 
Sir 
Your obedt. humble servt. 
JOHN FAREY Senr. 
Howland Street, London, 30. April, 1819. 
