EAR AS AN ORGAN FOR SOUND SENSATIONS. 



365 



composition determines the quality of the tone heard. As 

 many as ten or sixteen of these overtones may be detected from the 

 vibrating strings of a violin or guitar. When the period of vibra- 

 tion of these overtones bears a simple ratio to that of the funda- 

 mental, a ratio that can be expressed by the simple numbers, 1, 2, 

 3, 4, 5, they harmonize with it and form the harmonic overtones. 

 It should be borne in mind that, so far as the tympanic membrane 

 is concerned, it does not respond separately to the single tones 

 which constitute the compound wave, but swings in unison with 

 the movement of the compound wave. Nevertheless the internal 



a- 



Fig. 165. To illustrate the mechanism of the formation of overtones. (Helmholtz.) 

 In a the string vibrates as a whole, giving its fundamental tone; in 6, c, and d, its halves, 

 thirds, and fourths are vibrating independently. When a string is struck, plucked, or bowed 

 these movements may happen simultaneously and the fundamental note due to the vibra- 

 tions of the whole string is combined with the notes due to the vibrations of aliquot parts, 

 the overtones. The combination gives a compound wave whose form and musical quality 

 vary with the number and relative strength of the overtones. 



ear, according to the law of Ohm, is capable of analyzing the com- 

 pound wave form into the series of simple or pendular wave forms 

 of which it is composed and of distinguishing the series of corre- 

 sponding tones. While this analysis cannot be made consciously 

 except by the trained musician, it is made unconsciously, as it 

 were, by every normal ear, and in consequence of this analysis we 

 recognize the variations in quality of different compound tones. 

 The principle upon which the cochlea acts in thus separating the 

 compound tones into their elements is not explained with entire 

 satisfaction. According to the view so admirably presented by 



