78 Mr. Farey’s Letter on musical Intervals, &e. 
2dly. We will suppose that I was at first at a loss to recol- 
lect, which is the note in the upper octave, that limits the 
major third above B; I have, for removing this difficulty, 
only to add 197 to 553, which gives 7502; and to observe 
that this is the nearest to eb, which 1s 763°8974= ; from this 
therefore, | must take B or 553°1203, and 210°7771 re- 
mains; which exceeds 197, by 13°77712, and shews this 
last to be the sharp Temperament of this major third wolf, 
Besides distinguishing those ‘Temperaments in col. 4, 
which differ from the title thereof, in being sharp, mstead 
of flat, I have added a w to distinguish the fifth wolf; the 
same remark applies to col. 5, as to the temperament of the 
IlId on A being fiat, and to the four major third wolves, and 
also to the three minor third wolves, in col. 6. JI have at 
the bottom of the columns, added up the sharp and flat tem- 
peraments, in order to shew that the Sum in col. 4 is 
—12°02; in col. 5, =+84-02; and in col. 6, =—96°0=; 
these Tt being general properties of all Douzeave systems : 
which, if my knowledge and memory correctly serve me, | 
was the first to publish, in the Phil. Mag. Vol. 28, plate 5, 
and to demonstrate in Vol. 36, p. 43. 
The order of the several Coukor ic. as to their degrees of 
harmoniousness, measured by ee Temperaments, to the 
nearest tenth of a Schisma, or ;}; of a comma, are as fol- 
lows : 
CH, D, Fe, G and Bb, require to be altered m, and those on Et 
and F, require correcting 2 m3; all of these, by increasing the 
Temperaments. 
One example must suffice; in the Text, the Temperament of 
the wolf Ilfd on B, has already been found 13°77712, which it now 
appears, is to be increased ‘0}57=, and made 13-7928z. This 
trouble might have been lessened, if the correction‘in Table X. had 
been calculated at first in Schismas and decimals. by applying the 
numbers in Table IX, to the numbers of an Isotonic Douzeave. 
composed of multiples “of 513. 
+ When the corrections of the Temperaments, on accont of 
the m’s, are made, the casting will stand thus, viz. —23-7527 
+11°7448, —12-00079= ; + 84:2669 —-2040, —84-06293; and 
—96-07 7083, which accord with my determinations in the Philo- 
sophical Magazine. 
