

PROFESSOR AT BONN 153 



Starting with the assumption made by Ohm in 1843, that 

 in auditory sensation the ear analyses the motions of the air 

 into simple vibrations, in the same way that Fourier's series 

 for each periodic function is composed of the sum of periodic 

 sine-functions, or that any wave-form may be composed of 

 a number of simple waves of different length, of which the 

 longest has the same length as the given wave-form, while 

 the others are a half, a third, or a fourth, &c. of this length, 

 Helmholtz gives the name of compound tone (Klang) to the 

 composite tone of a musical instrument, while he confines 

 the term tone to simple tones. A compound tone is really 

 a chord with a predominating prime tone ; its strength will be 

 the sum of the strengths of the individual tones which it con- 

 tains, its pitch the pitch of its prime tone. The ear analyses 

 all sound-waves according to Fourier's theorem, by resolving 

 the wave-form into a sum of simple waves. It perceives the 

 proper tone of each simple wave, whether the waves in the 

 first instance issued as such from the source of tone, or have 

 united together on the way, and by listening attentively it is 

 possible to detect the over-tones corresponding to the separate 

 simple waves. 



These considerations reinforced the views which Helmholtz 

 deduced from optics in regard to our sensations. A certain 

 compound tone is the adequate sensuous token of the presence 

 of a certain resonating body. In analysing this sound, we 

 must give the same artificial support to our attention before 

 we can perceive the over-tones, as is required in the case of 

 double images and the blind spot, just as we do not normally 

 realize that the sensuous apperception of an object corporeally 

 extended in space is built up from the two distinct retinal 

 images of our two eyes. Helmholtz further determined that 

 combination tones appear only with strong generating tones, 

 that their intensity grows much faster than that of the prime 

 tones, and that the latter may almost entirely disappear when 

 the intensity is very great. 



He now proceeded to attack the problem as a whole from 

 its mathematical aspects. He found the generally accepted 

 view of the simple superposition without mutual disturbance 

 of a system of tone-waves excited simultaneously in the air, 

 to be contrary to the laws of mechanics, and proved by strict 



