Mr. Farey’s Letter on musical Intervals, &¢. 75 
being 358z, 3572 is the Isotonic fifth; 12of which, or 4284, 
prove to be just equal to 7 x 6123, as should be the case. 
Tf all the three columns of my notation had been here used, 
a greater degree of exactness only equal to m, or the scisth 
part of a comma, would have been gained thereby. 
Again, ifa Mean-Tone Douzeave were required to be 
calculated, where ze is the flat Temperament of the Vth; 
358—2 22, = 355! is its tempered fifth : which multiplied by 
- 11, gives 390722, and this taken from 7VIII or 4284s, 
leaves 37643, or V+ 1842, as the wolf fifth of this system 
ey GHeb) as is well Hise, although I now og 
hat I have inadvertently pala it 21z, in the Phil. Mag 
2a) 36, p. 45. 
{ can now proceed to. the main object of the present Let- 
ter, viz. to shew how the Notes of Profesor F isher’ $ 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 ; and in which state, I 
have hopes of this new Scale of Intervals, deduced with so 
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 like y to obtain, 
for reasons which have already been given her 
beginning at the bottom of the Table i in abe 194, 
aka: progressiv ely adding together the numbers therein, the 
value ie each Note of the Douzeave will ee had in 5-place 
recip, logs. ; B for instance, being -27208 ; let this be at 
tracted from the value of B in the last column of my fi 
Table, and the difference will be found =:0009212,72 ; iad 
this difference we must convert into Schismas and decimals 
by dividing by the value of Zin the Table, or by °0004901-07 ; 
and thus we get 1°87973, as the flattening or deduction to 
be made from 5555, the artificial commas of B; which 
thereby becomes 553° 1203s, as in col. 2 of the Table I. 
following. By proceeding in a similar manner, the ten other 
artificial commas and decimals in this Table may be cal- 
culated.* 
* It is a more fea. and correct mode, than by common di- 
vision, touse Logemetric Logarithms (see Edin. Ene ye. vol. XITT, 
p- *72) or the Negeri of the recip. logs. : ca oticeng that 
