246 Mr. Cavallo’s Obfervations on 
mufic muft be fo ordered as that, for the fake of modulation, 
any note may be confidered as the key-note ; therefore having 
found the fifth of the whole firing by taking two-thirds of its 
length, which gives a note called G, we mull; fuppofe, that 
this G may be confidered as the key-note, confequently muft 
find its fifth, which gives D, as fhewn in the figure, and fo 
on, until we find one of thofe fucceflive fifths, which coin- 
cides with one of the fucceflive odlaves ; for after that, to find 
more fucceflive fifths would be only repeating the fame thing 
over again. 
Indeed, if we carry the fucceflion of odlaves and of fifths 
indefinitely far, we fhall find, that no one of the fifths ever 
coincides perfectly with one of the odlaves, and therefore the 
divifion would have no end. However, as the length of the 
feventh odlave comes fo very near to the twelfth fifth, we mull 
be contented with taking this feventh odlave for the fifth of 
F, the difference between this note and the perfect fifth of 
F being about the hundredth part of its length ; whereas, if 
we carry on the fucceflion of fifths and of odtaves, we fhall 
find, that amongft thirty and more fifths none comes nearer 
to one of the ottaves than the above-mentioned one, as may 
be feen in the following table, which contain s a feries of fuc- 
ceflive odlaves, and another feries of fucceflive fifths, as in fig. 
2. ; but in the table the divifions are carried farther on than in 
the figure : 
Odtaves. 
Fifths. 
13286025 
1 3286025. 
6643012,5 
885735°. 
33 2I 5 ° 6> 2 5 
5904900. 
1660753,125 
3936600. 
8 3 ° 37 6 > 5 62 5 
2624400, 
Odtavea 
