T BEA TS OF IMPERFECT HARMONIES. 397 



. ___ 



an elastic solid moving to and fro in a very 

 narrow aperture. (In the case of a slapping 

 rccd, 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 l 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 

 respectively 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 



1 Compare Trans. A.S.E., April 3Oth, 1860; re-published in 

 Vol. III. of my Mathematical and Physical Papers, " Reduction of 

 Observations of Underground Temperature," where a short descrip- 

 tion of Fourier's analysis is to be found. 



