609 
of Edinburgh, Session 1877-78. 
principles the decidedly agreeable effect produced on the ear by a 
succession of major and minor thirds of pianoforte notes. It is, no 
doubt, to the slowing of the heats by the superposition of a third 
note upon either of the binaries C (0f or (& in the ternary com- 
bination C (0? (!i>, because of its comparatively close approximation to 
C G 0 (for which the heats are only five per second), that the com- 
paratively smooth harmoniousness of the common chord in the 
tempered scale is due. 
It is not generally known how easily beats on approximations to 
other harmonies than unison are heard, even when the constituent 
notes are simple tones. Through the kindness of Professor 
M‘Kendrick I have been allowed the means of testing them in very 
varied combinations, by aid of a series of excellent tuning-forks of 
Koenig’s, each mounted on a wooden box resonator, after the 
manner of Marloye. For such experiments Koenig’s tuning-forks 
are much superior to Marloye’s, because of the greater quantity of 
metal in each fork, in virtue of which it gives a louder and more 
enduring sound. The sound proceeding from such a source is 
essentially a simple tone, or very nearly so. I have tested that in 
every case the number of beats counted is the smallest that could 
be according to the preceding theory ; for it is to be remarked that 
the theory only gives the whole period of the phenomenon, but 
does not answer the question — Does the ear perceive a gradual varia- 
tion of quality through the whole period, or does it fail to distin- 
guish the difference of quality between two halves of the period, 
or between three-thirds of it, and so on 1 My experiments demon- 
strate that in every case the ear does distinguish the two halves of 
the period of each beat. Thus, for example, in the beat on an 
approximation to the harmony (1:2) in which the variation of air- 
pressure on the ear is represented by the preceding curves for four 
instants of the period noted, I find that the ear distinguishes the 
quality of the sound represented by the sharp-topped and flat- 
hollowed curve from that represented by the flat-topped and sharp- 
hollowed curve. In the one case the pressure of air close to the ear 
rises very suddenly to, and falls very suddenly from, its maximum, 
and (as in cases of tides in which there is a long hanging on low 
water) there is a comparatively slow variation of pressure for a few 
ten- thousandths of a second on each side of the instant of minimum 
