18 On Musical Temperament. 
multiply each of these values by 100,000, which will give @ 
set of integral values having the same ratio. The octave will 
now become 301083, thé comma 540, &c.; and, in general, when 
temperaments are hereafter expressed by numbers, they are 
to be considered as so many 540ths of a comma. Had more 
logarithmic places been taken, the intervals would have been 
expressed with greater accuracy ; but it was supposed that the 
additional accuracy would not compensate for the increased la- 
bour of computation which it would occasion. This notation 
has been adopted by Dr. Robinson, in the article Temperament, 
(Encyc. Brit. Supplement 5) and for every practical purpose, 
is as much superior to that proposed by Mr. Farey, in parts — 
of the Schisma, lesser fraction and minute,* as all decimal 
measures necessarily are, to those which consist of different 
denominations. 
Proposrrion II. 
In adjusting the imperfections of the scale, so as to render — 
all the consonances as equally harmonious as possible, only the — 
simple consonances, such as the Vth, I[Id, and 3d, with their — 
complements to and compounds with the octave, can be re- — 
gard ed. 
It has been generally assigned as the reason for neglecting : 
the consonances, usually termed discords, in ascertaining the 
best scheme of temperament, that they are ef less frequent oc- 
currence than the concords. This, however, if it were the only © 
reason, would lead us, not to neglect them entirely, but merely 
to give them a less degree of influence than the concords, in 
proportion as they are less used. 
A consideration which seems not to have been often noticed, — 
renders it impossible to pay them any regard in harmonical — 
computations. All such computations must proceed on the : 
supposition that within the limits to which the temperaments | 
of the different consonances extend, they become harsher 44 : 
their temperaments are increased. It is evident that any col” 
* Tilloch’s Phil. Mag. Vol, XXVIII. p. 140. 
oy 
Ba 
, 
