190 On Musical Temperameni. 
equally tempered, unless by rendering them unequal, theit 
medium temperament could be diminished ; but this appears, 
from the Lemma, to be impossible. By tempering them un- 
equally, the aggregate dissonance heard in a given time, by 
supposition of their equal frequency, would not be diminished, 
whilst the disadvantage of a transition from a better to a worse 
harmony would be incurred. Some advocates of irregular 
systems of temperament have, indeed, maintained this irregu- 
larity to be a positive advantage, as giving variety of character 
to the different keys. But this variety of character is obvi- 
ously neither more nor less than that of greater and less de- 
grees of dissonance. Now, what performer on a perfect in- 
strument ever struck his intervals false, for the sake of variety? 
Who was ever gratified by the variety produced in vocal mu- 
sic by a voice slightly out of tune? If this be absurd, when 
applied to instruments capable of perfect harmony, it is scarcely 
less so to urge variety of character as being of itself a sul- 
ficient ground for introducing large temperaments into the 
scale. For these large temperaments will have nearly the 
same effect, compared with the smaller ones, that small ‘tem- 
peraments would have, when compared with the perfect har- 
mony of voices and perfect instruments. Possibly a discord- 
ant interval, or a concord largely tempered, might, in a few 
instances, add to the resources of the composer. But when a 
instrument is once tuned, the situation of these intervals is fix: 
ed beyond his control, and by occurring in a passage where his 
design required the most perfect harmony, it might as often 
thwart as favour the intended effect. 
Since, then, the proposition is true in reference to the Vihs, 
Ilfds, and Sds, when separately considered, it will be equally 
true when they are considered jointly, that is, as formed into 
harmonic triads, unless, by rendering the concords of the same 
name unequal in their temperament, the mean temperament 0 
the Vths could be increased, and that of the ILIds and Sds p'™ 
portionally diminished. Could this be done, it might be * 
question whether the more equal distribution of the temper® 
ment among the concords of different names, might not j¥S y 
the introduction of some inequality among those of the oan 
