242 Mr. Cavallo’s Obfervations on 
thofe notes or divifions is confidered as the key-note, its fecond, 
third, fourth, fifth, &c. muft bear their refpedive proportions, 
according to what has been faid in the preceding pages. 
Now, if amongft the divifions of the firing CZ, fig. i . we 
take D for the fir ft or key-note, its length being 320 inches, 
the length of its fifth muft be 213I inches, viz. two thirds 
of 330, that being the proportion which the fifth muft bear 
to the key-note ; but amongft the divifions of the firing, there 
is none equal to 213^ inches; therefore, there is not a note 
among them which may ferve for a fifth to D : however, as 
the length of AZ, viz. 216, is the neareft to 213!, this A 
muft be taken tor the fifth of D. It is evident, that this is 
an im per fed fifth of D ; but if, in order to render it perfed, 
we make AZ equal to 213} inches inftead of 216, then it will 
be a redundant fixth to C, when C is confidered as the key- 
note ; the beft expedient, therefore, is to divide the imper- 
fedion between the two lengths, viz. to make AZ neither fo 
long as 216, nor fo fhort as 213}, which will render the dif- 
agreeable fenfation, anting from the improper length, the leaft 
poflible. This alteration of the juft lengths of firings, ne- 
ceflary for adapting them to feveral key-notes, is called the 
temperament : and the beft temperament in a fet of mufical 
founds is evidently fuch a partition of the natural imperfec- 
tions, as will render all the chords equally and the leaft dif- 
agreeable poffible. 
What has been exemplified in D and A may be faid of all 
the other notes ; fo that if any one of them be a perfed third, 
fifth, &c. with refped to one key-note, it will be found to be 
impeded with refped to others. Hence it is manifeft, firft, 
that in a fet of mufical keys, pipes, or frets, a temperament is 
abfolutely necefi'ary ; and, lecondly, that the harpfichord, 
organ. 
