of Edinburgh , Session 1877-78. 
603 
air is forced to rush with great velocity, or when, as in the case of 
free-reed organ pipes or the reeds of a harmonium, the vibrator is 
an elastic solid moving to and fro in a very narrow aperture. (In 
the case of a slapping reed, as of trumpet stops in an organ, the 
motion of the vibrator itself is not simple harmonic, and the sound 
is excessively rich in overtones, giving it its peculiarly rich or harsh 
character.) 
A harmony is any sound of which the excitant change of air- 
pressure is strictly periodic, and is not a simple tone. According 
to Fourier’s beautiful analysis* of periodic variations, to which the 
name of the harmonic analysis has been given, any periodically 
varying quantity may be regarded as the sum of quantities varying 
separately according to the simple harmonic law, in periods respect- 
ively equal to the main period, half the main period, a third of the 
main period, and so on. According to this analysis we see that 
the variation of air-pressure constituting a harmony may be regarded 
as the sum of variations constituting simple tones, one having its 
period equal to the period of the harmony; a second, half that of the 
harmony; a third, one-third that of the harmony, and so on ; in other 
words, we may regard the harmony as compounded of these simple 
tones. 
Practically, in musical language the term harmony is not applied 
when the tone of the main period predominates in the sensory im- 
pression, and in this case the sound is simply called a note ; its 
pitch is reckoned according to the main period ; and the effect of 
the other tones, now called overtones, which enter into its composi- 
tion, are merely felt as giving it its character or quality of sound. 
Thus the name harmony is in musical practice restricted to cases in 
which there is either no tone of the main or fundamental period, or 
not enough to produce a predominating impression, and a sound 
compounded of two, three, four, or more simple tones, having com- 
mensurable periods, is heard. In ordinary musical language a 
harmony is not regarded as having any one pitch, but is thought 
of as compounded of its known constituents. The true period of 
* Compare “Trans. R.S.E.” April 30th, 1860, “Reduction of Observations 
of Underground Temperature,” where a short description of Fourier’s analysis 
is to be found. 
