176. 4n Musical Temperameni. 
FINE ARTS. 
oe BBA 
Aart. XXL. Essay on Musical Temperament. By Professor 
Fisuenr, of Yale College. 
[Concluded from page 35.] 
Proposition V. 
To determine that position of any degree in the scale, which 
will vender all the concords terminated by.it, at a medium 
the most harmonious, supposing their relative frequency 
given, and all the other degrees fixed. 
r 
Tt HE best scheme of temperament for the changeable scale, 
on supposition that all the concords were of equally frequent 
occurrence, is investigated in Prop. III. But it is shown, It 
the last proposition, that some chords occur in practice, fat 
more frequently than others. Hence it becomes necessary {0 
ascertain what changes in the scale above referred to, this dif- 
ferent frequency requires. Any given degree, as C, term 
nates six different concords; a Vth, I1Id, and 3d above, and 
fhe same intervals below it. Let the numbers denoting the 
frequency of these chords below C be denoted by 4 b, and & 
and their temperaments, before the position of C is cha 
by m, n,and p: and let the frequency of the chords above 0 
be denoted by a’, 6’, and c’, and their temperaments by m', 24 
and p’, respectively. If, now, we regard any two of these s 
chords, whose temperaments would be diminished by movil 
C opposite ways, and of which the sum of the temperaments 
consequently fixed, it is manifest that the more frequent ™ 
occurrence the less ought to be the temperament. Were e' 
guided only by the consideration of making the aggregate 
dissonance heard in them in a given time, the least possible 
we should make the one of most frequent occurrence pe 
and throw the whole of the temperament upon the other 
