Mr. Cavallo’s ObfervatioriSy &c. 239 
other refpefl, excepting in their lengths, becaufe the number 
of vibrations, which they perform in a given time, is (imply 
in the proportion of their lengths, we (hall confider only thofe 
in the prefent invefligation, the number of vibrations per- 
formed by other lorts of fonorous bodies being eafily deduced 
from them. 
As the above-mentioned 13 founds are all different from 
each other, the firings which produce them differ in length, 
and of courfe in the number of the vibrations, which, when 
flruck, they perform in a certain time. Here follow the pro- 
portions which the numbers of vibrations performed in a given 
time, or the length of the firings which exprefs thofe 13 
founds, bear to the firfl, prime, or key-npte. 
Firfl 1 
Second minor 44 - 
Second 4 
Third minor 4 
Third major 4 
Fourth 2 . 
4 * 
Fourth major 44 
Fifth 4 
Sixth minor 4 
Sixth major 4 
Seventh minor JL 
Seventh major -j 8 .. 
Octave 4 
If, inftead of many firings having thofe lengths in order to 
exprefs the 13 founds, or notes of an o&ave, one firing be 
divided according to thofe proportions, and this firing be flopped 
confecutively in the different points or divisions ; on being 
flruck, it will exprefs the correfponding founds. Thus, if a firing 
flretched between two fixed points, as CZ fig. 1. Tab. III. be 
flruck, it will produce a found called the prime, firfl or key-note ; 
if it be flopped in the middle, one-half of the firing will found 
the odtave, its length, compared to that of the whole firing, 
being in the proportion of 2 to 1 ; if twm-thirds of the firing 
be caufed to vibrate, the found produced will be the fifth, its 
length. 
