of Edinburgh , Session 1877 - 78 . 611 
which are one of them the same as the other taken in the reverse 
order of time. 
In every instance except the octave, the beat on the approximation 
to a binary harmony is less distinct than the beat on an approximation to 
a ternary or higher multiple harmony with only one note false. It is 
not because of the comparative slowness of the beat on the multiple 
harmony ; for by taking alternately beats with one note slightly 
false in a binary harmony, and the same note made more false in a 
ternary or multiple harmony to such a degree as to give the same 
number of beats, I have always found the beats in the latter case 
much more prominent than in the former. Thus by taking first the 
perfect harmony C E G (4, 5, 6), and the three binary harmonies 
C G (2 : 3), C E (4 : 5), E G (5 : 6), and flattening slightly any one 
of the three notes by screwing on a small mass of brass to either or 
to each prong of the tuning-fork producing it, it is easy after a little 
practice to count the beats on each of the binary harmonies. Thus, 
for example (supposing E to designate a note of a slightly lower 
pitch than E), after a little practice it is easy to count the beats on 
C E and on the E, G, and to verify that their frequencies are, the 
first of them four times, and the second of them six times the error 
of frequency of the E, , and then to verify that the much louder 
beats on the ternary harmony C E, G, are of half the frequency of the 
former, and of one-third of the frequency of the latter, and to verify 
absolutely that they are of twice the frequency of the error of E . 
If when the approximate harmony C E, is being sounded, the 
faintest sound of G is produced by a very gentle excitation of 
the fork by the bow, instantly a loud beat at half speed is heard. 
The phenomenon is rendered very striking by alternately touching 
the top of the G fork by the bow so as to stop its vibrations, 
and then drawing the bow very gently for a fraction of a second* 
along one side to re-excite them. It is marvellous how small 
an intensity of the sound G is required to give a smooth unbroken 
loud beat in the double period. I have found it difficult to excite 
* In every case, to obtain regular beats, eacb tuning-fork, after being set 
in vibration by the bow, must be left to itself. The sound is sensibly graver 
as long as the bow is applied to augment or sustain the vibration than when 
the fork is left free. Thus, if two tuning-forks nearly, but not quite, in uni- 
son, are alternately acted on by the bow and left free, the beats are less rapid 
during the time the bow is applied to the higher fork, and more rapid while to 
the lower, than when both forks are vibrating freely. 
