66 On the Variety of Voices. 
may be given. The ear, though it judges with 
wonderful exactness, falls short of mathematical ac- 
curacy in its discriminations: a defect to which it is 
liable in common with the other senses. The truth 
of this proposition may be exemplified by an in- 
stance familiar to every scientific musician.* 
The smoothness or agreeableness of a musical 
consonance depends on its simplicity, those conso- 
nances being called the simplest in which the sum 
of the lowest terms expressing the ratio of the single 
vibrations of the terminating sounds, is least; or, 
in case several such sums are the same, that conso- 
nance is said to be simpler than the rest, in which 
* The proof here exhibited of the ear’s inability to dis- 
tinguish sounds, that are nearly the same or equal among 
themselves, is the best I am able to advance, after consult- 
ing various authors, 
The accounts given by experimental philosophers rela- 
tive to the least sensible interval are very discordant: Dr. 
Keill observes in his Anatomy (edition gd, page 167) thata 
good ear can perceive the disagreement of two strings, 
differing only by the ;+, part of a note. M., Muschen- 
broek says, that a good ear can distinguish no more than 
forty-three tones in an octave. Mr. Atwood has recorded 
an experiment (at page 99 of his Treatise on Rectilinear 
Motion) wherein two strings appeared to be in unison 
with a fixed sound; the tones of which I have found, bya 
calculation drawn from his data, to disagree by seven 
tenths of acomma. Suchcontradictory statements proves 
indeed, the existence of the interval in question ; but 
shew, at the same time, its magnitude to be undetermined, 
