LETTER XX. 
HAVING, in my laft letter, accounted 
for the production and propagation 
of mufical founds, the next natural queftion 
isWhat is the caufe of high and low or, 
to fpeak more mufically, of grave and acute 
founds or tones ? Thefe depend on the 
quick or flow vibrations of the founding 
body; that is, on the greater or lefs number 
of vibrations, in a given time. Large in- 
flruments and long firings, produce grave 
or deep tones; fmall inflruments and (hort 
firings, on the contrary, produce acute or 
high tones; in organ-pipes, for example, in 
proportion to their length and dimenfions: 
this is alfo true of mufical firings. If I take 
a mufical firing of any length, and divide it 
into two equal parts by a bridge in the 
middle, each half founds an o6lave, (that is, 
eight notes) higher than the tone of the 
whole firing. Their vibrations, relative to 
the whole firing, are as 2 to i: therefore, 
they perform the fame number of vibrations 
in half the time; and confequently the oc- 
tave 
