Mr. Farey’s Letter on musical Intervals, &c. 15 
being 3585, 3572 is the Isotonic fifth; 120f which, or 4284=, 
prove to be just equal to 7x 6122, as should be the case. 
Vf all the three columns of my notation had been here used, 
a greater degree of exactness only equal to m, or the ;,4,th 
part of a comma, would have been gained thereby. 
Again, ifa JMean-Tone Douzeave were required to be 
calculated, where ic is the flat Temperament of the Vth; 
358 — 23,3554 is its tempered fifth : which multiplied by 
11, gives 390722, and this taken from 7VIII or 4284, 
leaves 37645, or V+ 1812, as the wolf fifth of this system 
(usually Geb) as is well known, although I now perceive 
that I have inadvertently called it 215, in the Phil. Mag. 
vol. 36, p. 45. 
I can now proceed to the main object of the present Let- 
ter, viz. to shew how the Notes of eee Fisher’s pro- 
portionally-tempered Douzeave, in your 195th page, may 
be expressed in these artificial commas (and decimals of 
them) with greater accuracy, than in the 5~place recip. logs. 
in which they are now expressed 3 and in which state, 1 
have hopes of this new Scale of Intervals, deduced with sce 
much ingenuity and labour by Professor F’. attracting, in 
this country at least, a somewhat greater share of attention 
from the practical Musicians and Tuners, than, in its present 
logarithmic denomination, it seems to me likely to i 
for reasons which have already been given herein. 
By beginning at the bottom of the Table in page 194, 
and progressively adding together the numbers therein, the 
value of each Note of the Douzeave will be had in 5—place 
recip. logs. ; B for instance, being -27208 ; let this be sub- 
tracted from the value of B in the last column of my first 
Table, and the difference will be found =:0009212,72 ; and 
this difference we must convert into Schismas and decimals 
by dividing by the value of in the Table, or by 0004901-07; 
and thus we get 1°87975, as the flattening or deduction to 
be made from 555s, the artificial commas of B; which 
thereby becomes 553°12032, as in col. 2 of the Table HU. 
following. By proceeding in a similar manner, the ten other 
artificial commas and decimals in this Table may be cal- 
culated.* 
* Tt is a more ready and correct mode, than by common di- 
vision, to use Logometric Logarithms, (see Edin. Encyc. vol. XII, 
p. *72) or the logarithms of the recip. logs.: recollecting that 
