198 



On Musical Temperament. 



TABLE XIII. 



From an inspection of the sums at the foot of the table, it 

 will be seen that the amount of dissonance heard in a given 

 time is decidedly less in the new scale than in either of the 

 others ; and that it is scarcely more than half as great as in the 

 scale of equal semitones. On the other hand, the tempera- 

 ment is very unequally distributed, which must be admitted, 

 caeteris paribus, to be a disadvantage. It is even somewhat 

 greater than in the scheme of Mr. Hawkes, although by no 

 means in the same ratio, as the aggregate dissonance is less. 

 It contains one Vth, which will be somewhat harsh, and four 

 Illds and three 3ds, which will be quite harsh. But these, a* 

 will appear from an inspection of Table IX., are, of all others, 

 ©f by far the most unfrequent occurrence ; so that the unplea- 

 sant effect of a transition from a better to a much worse har- 

 mony will be very seldom felt. In the six simplest keys of 

 the major, and in the three of most frequent occurrence in 

 the minor mode, they are never heard, except in occasional 

 modulations ; and even then, generally no one, and rarely 

 more than one is heard. Now these nine keys, as will appear 

 from Table III., comprise more than five times as much of the 

 music examined as all the rest. The same remarks might bfe 

 extended to three other minor keys, were it not that the sharp 

 seventh is so generally used, that it deserves to be considered 

 as an essential note of the key. 



But there are two important considerations, more thati 

 counterbalancing the objection to this system, derived from the 

 greater inequality in the distribution of its ten)perament«4 



