68 On the Variety of Voices. 
A good approximation towards perfection being 
shewn sufficient in the present, as well as in all other 
cases of a similar kind, to satisfy our limited powers 
of perception, it will not be difficult to prove the 
small intervals of natural tones to be fit for all the 
purposes of music, being calculated to afford the most 
correct ideas of which the sense of hearing is suscepti- 
ble. For the mperfect unisons, that unite to produce 
the human voice or the sound of a musical instru- 
ment, preserve the same ratio among the times of 
their respective vibrations, in various degrees of 
acuteness, ‘This is manifest, because the identity 
of a given voice or instrument is discoverable by 
the sameness of its tone at any point of the scale to 
which it can arrive with ease, consequently the con- 
sonances that enter into the composition of such 
sounds are similar at all degrees of acuteness; or, 
in other words, the ratios of the imperfect unisons 
composing a tone, which is capable of being raised 
or depressed, are consonant among themselves un- 
der every possible variation.* The last considera- 
tion makes it clear, that what has been inferred from 
a ring of bells (namely, that their notes, though ma- 
nifestly compounded, serve all the purposes of mu- 
sic) applies with equal, if not greater, force and cer- 
tainty to those minute intervals, the cycles of which 
are not so easily perceived. 
* Smith’s Harmonics, sec, 111, art. 3. 
