the 'Temperament of "Mufical Injlruments . 24 r 
from Z to thedivifions to which they {land near. The letters 
juft over the lines are the names of the notes or founds ex- 
prefled by the correfponding lengths of the firing. The frac- 
tional numbers exprefs the proportion which each particular 
divifion bears to the whole firing ; and the Roman numbers 
denote the numerical names of each note with refpedl to its 
diflance from the firfl, which is always included. For example, 
luppofe the whole firing to be called C, and to be 360 
inches long: then, if this firing be flopped in G, the part GZ 
will be 240 inches, viz. two-thirds of the whole firing CZ ; 
the found exprefled by it when flruck is called G, and it is 
the fifth note from C, which is the fir ft or kev-note. Again, 
if this firing be flopped in A, the part AZ will be equal to 
216 inches, viz. three-fifths of the whole; the lound pro- 
duced by it is called A, and is a fixrh to the key-note C, &c. 
It is evident, that if any of thofe di-vifions be confidered as 
the firfl or key-note, then the other notes, though they retain 
their alphabetical names* mufl have their numerical names 
altered accordingly : for example, if we take D for the key- 
note, then A will be the fifth of it, whereas A was the fixth 
when C was confidered as. the key-note; thus alfo B is the 
third of G, and the feventh of C, and fo on. 
Thus much having been premifed, we may proceed to fhew 
the meaning of what is called the temperament in a fyflem of 
mufical founds, and likewife the neceffity of it. For this pur- 
pofe it is neceffary to recollebf, firfl, that the firing, divided in 
the above-mentioned manner, exhibits the various notes or 
founds of the keys of an harpfichord, the pipes of an organ, 
&c. Secondly, that thofe divifions remain unalterable, fo that 
the harpfichord, when tuned, cannot be altered in the courfe 
of performing on it; and, thirdly, that when any one of 
c thofe 
