WAVE ANALYSIS IN REFERENCE TO ACflON IN THE EAR. 



129 



leaving after a vibration or two only the element with the period of the 

 fiber. This is the case contemplated in discussing resonance theories of the 

 ear. For spoken sounds the case is different. The sound changes from 

 vibration to vibration, never remaining constant. A fiber in the ear 

 must, therefore, perform a movement representing the sum of two elements, 

 one with the period of the speech wave and the other with the period of 

 the fiber itself. This is probably one of the sources of the peculiar mental 

 impression of speech by which it is distinguished from all other sounds. 

 The question of what method of analysis is to be applied to a sound 

 curve in order to represent the action of the ear is not an easy one. For 

 a curve known to be composed of harmonic elements — as the curves of 



some musical instruments — the simple 

 harmonic analysis is evidently to be 

 used. When the nature of the curve 

 is unknown, but its form is maintained 

 unchanged from wave to wave, an in- 

 harmonic analysis is in place. For 

 the sounds of speech we can not use 

 the inharmonic analj'sis because each 

 wave is different from the next (p. 100), 

 and we know that the harmonic analy- 

 sis wdthout further treatment gives 

 absolutely false results because it 

 does not provide for the inharmonics. 

 The best we can do is to apply the 

 frictional harmonic analysis and pick 

 out the elements on the centroid prin- 

 ciple (p. 80). To be sure even this 

 does not provide for the double nature 

 of the vibratory movement of each 

 fiber, as just considered. It is self- 

 evident that the analysis must be a 

 frictional one (Chapter VIII), but we 

 have no means of obtaining the coef- 

 ficients of friction in the ear. The diffi- 

 culties are not insurmountable, but more of the action of the ear must 

 be learned before we can adopt a method of analysis to represent it. 



The negative conclusion just reached has a definite bearing. Of all 

 the methods yet proposed for the curves of speech, the simple harmonic 

 analysis is certainly the least applicable. It was originally introduced 

 into the study of vowel curves because it was supposed to represent the 



LLUj 



.illi 



111],,,.. 



Fig. 115— Relative stimulation of acoustic 

 fibers by tones of dilTerent pitch, separately 

 and simultaneously. 



