| 
| 
| 
Mr, Farey’s Letter on musical Intervals, §c. 71 
neatly as follows :— H,, said he, I want to know whether, 
in Mr. Liston’s Scale, cd is a higher or a lower note than 
his BA; I find these Notes defined in his Tables, by 3'T 
+3t, and 2T+2 t+3§, respectively : but my not being 
able to carry in my head the recollection of the exact com- 
parative magnitudes of 'T, t and S (whose relations in de- 
cimals of either of them, i understand to be interminate, as 
to places of figures, such never ending, or circulating) lam 
unable to perceive which of these quantities is the largest : 
if, continued he, I suppose the first to be the largest, “and 
deduct the last from it, as eri do, I obtain T+t— 
: but here again, from not being able readily to per- 
ceve whether al —s than 3.8, I am left in doubt, 
until after. ac i ~ some- considerable. labour, for 
Ww 
tion. ¢ vos pears if want vg on whether Mr. L.’s 
Be, is higher or lower than his ¢; his expressions for them, 
respectively, are, 4 T+2 t, and 2 T+3t+2583 but such 
are not fitted for conveying at sight the information wanted : 
—if I take their difference, as before, I find it to be 2'T—t 
—2 5, which leaves me under similar difficulties, as in the 
first case. 
Long before Mr. Liston published his Essay, or I had 
heard his name mentioned by any one, I had provided a 
remedy for the inconvenience above stated, in the Notation 
to. which Professor Fisher has referred, in your 18th page: 
founded on the same principle as above, but using three 
ary small Intervals, for the terms of my Notation, derived 
from the Manuscripts of Mr. Overend, already mentioned, 
and which had been marked by him =, f and m3 but which 
{atervals, or any others, he had not adopted or used as a 
Notation ; they merely stood amongst a multitude of his 
isolated resul 
The ear: of my Terms = (or the Schisma), is the very 
same small Interval 2 T—t—2 S, which is mentioned 
above ; 3 it occurs also, between ten others of the adjacent 
notes in Mr. Liston’s Seals of 59 notes; and it is the small- 
est Interval. which can ever occur, in the calculation of even 
lar more extended Eubarmonic or untempered Scales, than 
those of Mr. Liston’s Essay, as I have since fully shewn, 
inthe Phil. Mag. vol. 39, p. 419, and vol. 49, p. 362, &c. : its 
tatio ig 2'° +38 x5; my second Term f (or the lesser 
