ir. Farey’s Letter on musical Intervals, &. ra} 
nearly as follows :— If, said he, 1 want to know whether, 
in Mr. Liston’s Seale, cb is a higher or a lower note than 
his Btt; I find these Notes defined in his Tables, by 3'T 
+3t, and 2T+2 t+3 5, 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) I am 
unable to perceive which of these quantities is the largest : 
if, continued he, | suppose the first to be the largest, and 
deduct the last from it, as algebraists do, 1 obtam T+t— 
39: but here again, from not being able readily to per- 
ceve whether T+ is larger than 3.5, I am left in doubt, 
until after a calculation of some considerable labour, for 
deciding whether | have made a wrong or a right supposi- 
tion. Again, said he, if 1 want to know whether Mr. L.’s 
B’G, is higher or lower than his ¢; his exoressions for them, 
respectively, are, 4’T'+2 t, and 2 T+3t+2S3 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 8, 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 
very 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 m; but which 
Intervals, or any others, he had not adopted or used as a 
Notation ; they merely stood amongst a multitude of his 
isolated results. 
The largest of my Terms = (or the Schzsma), is the very 
same small Interval 2 T—t—2 5, which is mentioned 
above ; 3 it occurs also, between ten fofers of the adjacent 
notes in Mr. Liston’s Scale of 59 notes; and it is the small- 
est Interval which can ever occur, in the calculation of even 
far more extended Kuharmonic or untempered Scales, than 
those of Mr. Liston’s Essay, as I have since fully shewn, 
in the Phil. Mag. vol. 39, p. 419, and vol. i p- 362, Xe. : its 
ratio Is 275 — 38x 5s my second Term f (or the lesser 
