24 On Musical Temperamént. 
Scholium. 
Although the/foregoing would be the best division of the 
musical scale, if our sole object were to render the harmony 
of its concords as nearly equal as possible, yet the two other 
considerations, stated at the beginning of the essay, must by 
no means be neglected, as has been been done by Dr. Smith. It 
seems to be universally admitted, that the sum of the tempera- 
ments may be increased to a certain extent, in order to equalize 
- the harmony of the concords; otherwise the natural scale of 
major and minor tones, which makes the sum of the tempera- 
ments of the Vths, I1Ids, and 3ds but 2 commas, ought to be 
left unaltered. Yet how far this principle ought to be carried, 
may be a matter of doubt. If we make the IlIds perfect, and 
flatten the Vths and 3ds each 7 ¢, according to the old system 
of mean tones, we shall have the smallest aggregate of tempe- 
raments which admits of the different concords of the same 
name being rendered equally imperfect; but this amounts te 
23 commas. Thus far, however, it seems evidently proper to 
proceed. If we go still father, and endeavour to equalize 
the harmony of the concords of different names, it may be ques- 
tioned whether nearly as much is not lost as gained ; for the 
aggregate temperaments are increased, in Dr. Smith’s scale, 
to 22 c, and in that of the above proposition to 25 c. T 
system of mean tones, although more unequal in its harmony 
when but two notes are struck at once, yet when the chords 
are played full, as they generally are on the organ, never 
offends the ear by a transition from a better to a worse har- 
mony. For every triad is equally harmonious; being com- 
posed of a perfect IlId, and a Vth and 3d, tempered each } ¢, 
or of their complements to, or compounds with octaves, which, 
in their kinds, are equally harmonious. 
Again, if different chords, in practice, vary in the frequency 
of their occurrence, this will be a sufficient reason for deviating 
from the system of equal temperament. Suppose, for exam- 
ple, that a given sum of temperament is to be divided between 
two Vths, one of which occurs in playing ten times as often a* 
