Mr. Farey’s Letter on musical Intervals, &c. 67 
excited in the air, for yielding different sounds ; because it 
is the ratios, only, of these, that can be applied to the com- 
paring or calculating of musical Intervals; involving, in 
all such cases, the unnatural and laborious substitution 
of the multiplication of vulgar Fra actions, in the plate of 
simple addition, and the substitution of division o 
Fractions, in the place of simple subtraction, of the Suter 
vals under consideration : a consequence of which is, that 
the smaller the Intervals are, the larger do the numbers ex- 
pressing them become, and the more difficult of conception 
and the more laborious, does the expressing or calculating 
of them become ; and hence it can excite no wonder, that 
nearly all who may not have been induced to cultivate 
some acquaintance with aianenescn for its own sake, sar 
as Mu , been so | 
a the very outset of their attempts to understand this im- 
tand fundam 
oven up the pursuit; being content to remain ignorant of 
that which was presented to them by the professed Writers 
on the subject, in so unnatural and forbidding a form. 
It is observable, that the small Intervals above alluded to, 
as oecasioning the chief stumbling block, are not merely 
such as curiosity only, and not utility, requires to be 
brought into review, but they concern each and every one of 
the Intervals which are considered, when we attempt to 
speak of the Temperaments of the Musical Scale : and hence, 
it has been next to impossible, that the mere Arithmetician, 
who proceeded to add and subtract Intervals according to 
the unnatural plan above mentioned,* could ee the 
calculation, or understand the true nature, of any om 
various modes in which the musical Scale — sone 
ed, or even comprehend the untempered Scale itself, in so 
much of its generality as the same is now actually exhibit- 
ed, on the Euharmonic organs of Mr. Liston, and always 
has, although almost unperceived, been practiced, by the 
correct Singer, the Violinist, and a few other Practitioners 
ost indefatigable pa hte the late Mr. Marmaduke Overend, 
pienso in this way, and brought his labours to no usefnl conclusions, €x- 
en mentioned by Authors, and of some few other new Intervals, whic 
are somewhat a dee * I have fully percha in Mr. Tilloch’s Philosophical 
Magazine, in Vol. 28. p. 140. 
