104 ox THE PHYSIOLOGICAL CAUSES OF 



the five first, which form the octaves, fifths, and major 

 thirds of the fundamental tone. Hence, in the mixture 

 stops of the organ, additional pipes are used, giving the 

 series of upper partial tones corresponding to the pipe 

 producing the fundamental tone, in order to generate a 

 penetrating, powerful quality of tone to accompany con- 

 gregational singing. The important part played by the 

 upper partial tones in all artistic musical effects is here 

 also indisputable. 



We have now reached the heart of the theory of har- 

 mony. Harmony and dysharmony are distinguished by 

 the undisturbed current of the tones in the former, 

 which are as flowing as when produced separately, and 

 by the disturbances created in the latter, in which the 

 tones split up into separate beats. All that we have 

 considered, tends to this end. In the first place the 

 phenomenon of beats depends on the interference of 

 waves. Hence they could only occur, if sound were due 

 to undulations. Next, the determination of consonant 

 intervals necessitated a capability in the ear of feeling 

 the upper partial tones, and analysing the compound 

 systems of waves into simple undulations, according to 

 Fourier's theorem. It is entirely due to this theorem 

 that the pitches of the upper partial tones of all service- 

 able musical tones must stand to the pitch of their fun- 

 damental tones in the ratios of the whole numbers to 1, 

 and that consequently the ratios of the pitches of con- 

 cordant intervals must correspond with the smallest 

 possible whole numbers. How essential is the physio- 

 logical constitution of the ear which we have just 

 considered, becomes clear by comparing it with that of 

 the eye. Light is also an undulation of a peculiar 

 medium, the luminous ether, diffused through the uni- 

 verse, and light, as well as sound, exhibits phenomena of 

 interference. Light, too, has waves of various periodic 



