On Musical Temperament. li 
although in a loose and conjectural manner, to make the pro- 
minent chords of the simplest keys the nearest to perfection, 
whilst a greater temperament is thrown upon those which oc- 
cur only in the mere complex keys. Thus Dr. Young, in the 
Philos. Trans. for 1800, recommends a scheme which increa- 
ses the temperament of the Iifds, on the key note of the 
successive keys, as we modulate by fifths from C, nearly in 
arithmetical progression. Earl Stanhope assigns as a reason 
for the small temperament which is given to several of the 
IIlds in his system, that they are on the tonic of the simpler 
keys. The irregularities in Mr. Hawkes’s scheme may be 
traced to the same cause. And, with the instrument-makers, 
it is a favourite maxim to lay the wolf, as they term it, where 
it will be most seldom heard. 
But if the above consideration desérves any weight at all, it 
deserves to be accurately investigated. Not only ought the 
relative frequency of different chords to be ascertained with 
the greatest accuracy, of which the nature of the subject is sus- 
ceptible, but the degree of weight which this consideration 
ought to have, when compared with the two others above men- 
tioned, should be determined ; fer it is plain that neither of 
them ought to be ever left out of view. 
Accordingly, the principal design of the following propositions 
will be to investigate the actual frequency of occurrence of 
different chords in practice ; and from this, and the two other 
above-mentioned considerations united, to deduce the best 
system of temperament for a scale, containing any given number 
of sounds to the octave, and particularly for the common Dou- 
zeave, or scale of twelve degrees. 
Proposition IL 
All consonances may be regarded, without any sensible error 
in practice, as equally harmonious in their kinds, when 
equally tempered; and when unequally tempered, within 
certain limits, as having their harmoniousness diminished in 
the direct ratio of their temperaments. 
As different consonances, when perfect, are not pleasing to 
the ear in an equal degree, some approaching nearer to the 
