of Edinburgh, Session 1873 - 74 . 345 
was deaf to very highly-pitched sounds which other people said 
they heard. 
These results indicate that, so far as the structure of the ear is 
concerned, those individuals who are said not to know one note 
from another, are equally capable, by the use of resonators, of ana- 
lysing a compound musical note — that is, of hearing the various 
tones of which it is- composed — with those who have a good ear. 
Physiologically, they seem to be capable of splitting up, uncon- 
sciously, the compound vibration into the simple vibrations, the 
rates of which are once, twice, or thrice that of the fundamental 
note. 
The next point which I examined was regarding the percep- 
tion by persons having no musical ear of difference and summation 
tones, which, as is well known, play an important part in the theory 
of concord and discord. 
If, on the overtone apparatus, two tones of different pitch are 
sounded, a third and deeper tone may be frequently observed. 
These tones were first discovered by a German organist, Andreas 
Sorge, in 1740. For example, if 2 : 3, or 3 : 4, or 6 : 7, or 7 : 8, &c., 
are sounded, a third and deeper tone may be perceived by the use 
of a proper resonator, which will be always found to beC 2 =l; 
that is, this combination tone is produced by 32 vibrations per 
second, the difference between the respective vibration numbers of 
the tones 2 : 3, or 3 : 4, or 6 : 7, &c. I have found that the differ- 
ence tone heard with greatest distinctness corresponds to one pro- 
duced by 128 vibrations per second. For example, on sounding 
16 : 20, or 24 or 28, or 32 and 36, with resonator No. 4, I can dis- 
tinctly hear the tone corresponding to No. 4 = 128 vibrations per 
second in each case. I have found no marked difference between 
non-musical and musical individuals in the perception of difference 
tones, except as regards intensity. I had the opportunity of ex- 
amining two persons of marked musical ability, who could distin- 
guish, by great attention, without the aid of resonators, difference 
tones to the 6th of the series, and who could observe difference 
tones, 2, 3, and 4, with comparative ease. Non-musical persons did 
not observe these difference tones without the use of resonators to 
add to their intensity ; and, in one case, the person could not hear 
them at all. In addition to these primary difference tones, I have 
