198 On Musical Temperament. 
TABLE XIII. 
Mean Kirn- Stan- 
Systems. Temp. Youngs’. berger’s. French. hope’s. Hawkes’. | scaie, 
Disso-( Vths | 309| 494] 681! 561| 595| 665 “810 
nance » IIIds 12184, 1541; 1397! 1346)1175| 925 | 533. 
of the 7 3ds |2740, 2448] 2019) 212111992! 1676 |1563 | 
Total 59331 4483! 4097; 4028 3762] 3266 [2703 | 
From an inspectton 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, 
ceteris paribus, to be a disadvantage. It is even somewhat 
greater than in the scheme of Mr. Hawkes, although by 0 
means in the same ratio, as the aggregate dissonance is less. 
It contains one Vth, which will be somewhat harsh, and four 
IlIds and three 3ds, which will be quite harsh. But these, a8 
will appear from an inspection of Table IX., are, of all others, 
of by far the most unfrequent occurrence ; so that the unplea- 
sant effect of a transition from a better to a much worse hat- 
mony will be very seldom felt. In the six simplest keys of 
the major, and in the three of most frequent occurrence m 
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 appeat 
from Table III., comprise more than five times as much of the 
music examined as all the rest. The same remarks might me 
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 than 
counterbalancing the objection to this system, derived from the 
greater inequality in the distribution of its temperament 
