'the Temperament of Mufcal Injlrumenis . 243 
organ, guitar, or any other inftrument in which the notes are 
fixed, fo as not to be alterable by the performer’s hands, mull 
be imperfect even when tuned in the belt manner poffible ; for 
by the temperament we caii divide, but not annihilate, the 
imperfection . 
Other inftruments, in which the notes are not fixed, as the 
violin, violoncello, &c. are perfect, becaufe the performer flops 
the firings upon them in different places, even for founding 
the notes of the fame name. Thus a fkilful performer, in' 
order to found A, will flop the firing a little farther from the 
bridge when he plays in the key of C, viz. when C is conli- 
dered as the key-note, than when he plays in the key of D. 
Mofl people imagine, that the fcale of mufic is capable of 
many different temperaments ; and, agreeable to this fuppofi- 
tion, the writers on harmonics have propoled different tempe- 
raments; but it will be fhewn in the fequel, that the nature 
of the fcale admits of only one temperament capable of ren- 
dering the imperfection and the harmony equal throughout ; 
and that it is impoffible to form a different and more advan- 
tageous fcale. 
Before we begin with the invefligation of this fubjeCt, it 
will be neceflary to explain certain principles, the want of 
which may poflibly raife feme doubts in the minds of thofe 
perlons who are not much acquainted with the theory of mu- 
fical founds. In the firfl place it mufl be obferved, that the 
proportion of 2 to 3 for the fifth, the proportion of 1 to 2 
for the oClave, and in fhort the proportions of all the notes, 
are not aflumed at pleafure; but they have been determined 
from conflant experience, viz. from the agreeable or difagree- 
able effects produced when two different notes are founded at 
the fame time. 
Vol. LXXVJII. L 1 
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