204 H, W. Poole on Perfect Musical Intonation. 
other temperament. With these advantages, however, it is justly 
censured for its discordant fifths, and its “ wolfishness” when the 
modulation is carried into keys, where it is not prepared to play. 
. The equal TempeRAMeNT preserves the fifths nearer to 
perfection than the mean-tone system, and consequently throws 
the discord, or ‘‘ wolf,” (as it is termed by tuners, ) into the thirds. 
The fifths, however, although they are favored, are yet not given 
in perfect tune. It is found in perfect tuning, that a series of 
twelve fifths will end a comma* higher than the note commence 
with. In equal temperament, it is designed to make the series 
meet, and consequently this comma is equally divided among the 
twelve fifths, leaving each a twelfth of a comma flat. If this be 
accurately done, the octave will be divided into twelve equal 
rts, and one fifth will be equally as good (or bad) as‘another. 
To set this temperament, it is only necessary to temper the fifths 
carefully, as has been stated, without regarding the thirds at 
all. ‘The major thirds will be found sharp, by an interval eight 
times as large as the error in the fifths, that is, two thirds of a 
comma. The minor thirds will be flat three fourths of a comma, 
or the sum of the temperament of the fifth and the major third. 
As it is designed, in the equal temperament, to have every chord 
of the same name, equally tempered, the necessity of leaving the 
thirds in this condition will be further made obvious. The third 
part of the octave must be used asa major third, and as three 
perfect major thirds do not equal the octave by the diésis, each 
third must be sharped, by one third of the diésis, or two thirds of 
acomma. Again, the minor thirds must be each, one fourth of 
three commas ; this excess therefore is equally divided among 
the four minor thirds, and each is left flat, by three fourths of a 
comma. 
35. The Equal Temperament has this great advantage over 
from a better to a worse chord. It can also be demonstrated that 
in equal temperament, the swum of the temperament of all the 
chords—if the instrument be used in the twelve keys—will be 
less than in any other. Any other than the equal system, is sim- 
ply an attempt to improve part of the thirds, by sacrificing, not 
only the fifths, but the remaining thirds, 
