190 On Musical Temperament. 



equally tempered, unless by rendering them unequal, their 

 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 

 instrument ever struck his intervals false, for the sake of 

 variety ? Who was ever gratified by the variety produced in 

 vocal music 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 sufficient 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 

 an instrument is once tuned, the situation of these intervals is 

 tixed 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 Vths, 

 Illds, and 3ds, when separately considered, it will be equally 

 true when they are considered jointly, that is, as formed int* 

 harmonic triads, unless, by rendering the concords of the same 

 name unequal in their temperament, the mean temperament of 

 the Vths could be increased, and that of the Illds and 3ds pro- 

 portionally diminished. Could this be done, it might be a 

 question whether the more equal distribution of the tempera- 

 ment among the concords of different names, might not justify 

 the introduction of some inequality among those of the same 



