492 



HEARING, VOICE AND SPEECH 



in the accompanying overtones as very probably the cause of difference in 

 timbre. 



There remains for us yet to consider how it is possible for the ear to 

 perceive the differences in the form of vibration caused by the overtones. 



The effect of overtones in altering the form of vibration may be repre- 

 sented diagrammatically as in Fig. 194. a' a' is the base line of reference, the 

 dotted lines a, b, and c represent the vibrations of a fundamental tone (a) 

 and its first two overtones ; the solid line d is the resulting vibration produced 

 by interference of the three. It is evident that notwithstanding the change 

 in form of the vibration the period of the fundamental tone remains 

 unchanged. 



But if these partial tones are not to be regarded as mere mathematical 

 fictions, if they have a real existence, they should produce some mechanical 

 effect which is recognizable. Such an effect we find in the phenomenon of 

 sympathetic vibration (resonance), occurring in all bodies which, once they 

 are given the impetus, run through a series of different vibrations* before they 

 come to rest. The simplest example of this is witnessed when a certain note 

 is sung into a piano. The same note is given back by the piano, its intensity 

 bearing a direct relation to the exactness with which the note of a particular 

 string is struck by the voice. Sympathetic vibrations between bodies pro- 

 ducing compound tones can be aroused even in case the vibration frequency 

 is not exactly reproduced, and this takes place more readily the smaller the 

 mass of the sympathetic body (e. g., a catgut string responds more readily 



FIG. 194. Schema illustrating the relation of overtones to their fundamental tone, after Hensen. 



than a wire string of the same diameter). But it is much more difficult to 

 induce sympathetic vibrations from a body which gives no overtones e. g., 

 from a tuning-fork because it will respond only to its own particular form 

 of vibration. 



It has been shown that a membrane adapted to a certain tone also exhibits 

 the phenomenon of sympathetic vibrations, if a lower tone, which contains 

 the tone of the membrane among its overtones, is sounded. The tympanic 

 membrane of the ear is not adapted to any one tone i. e., has no fundamental 

 tone hence does not select any single tone by resonance. 



