172 BELL SYSTEM TECHNICAL JOURNAL 



is then directly related to the total number of nerve fibres giving off 

 impulses. It seems to me that the spacial and intensity configura- 

 tions which are possible, according to this theory, are sufficient for 

 an educated brain to interpret all the complex sounds which are 

 common to our experience. 



In conclusion then, it is seen that the pitch of pure tones is de- 

 termined by the position of maximum response of the basilar mem- 

 brane, the high tones stimulating regions near the base and the low 

 tones regions near the apex of the cochlea. 



A person can sense two mixed tones as being distinctly two tones 

 while he cannot sense two mixed colors, since in the ear mechanism 

 there is a spacial frequency selectivity while in the eye mechanism 

 there is no such selectivity. 



The limiting frequencies which can be perceived are due entirely 

 to the dynamical constants of the inner ear as is also the dependence 

 of minimum audible intensity on frequency. 



The so-called subjective harmonics, summation and difference 

 tones are probably due to the non-linear transmission characteristics 

 of the middle and inner ear. 



These subjective harmonics account for the greater masking effect 

 of low tones on high tones than high tones on low tones. Due to 

 this non-linear characteristic, the quality as well as the intensity of 

 the sensation produced, especially by complex tones, change as the 

 intensity of the stimulus increases. 



The facts obtained from audiograms of abnormal hearing are 

 consistent with the theory of hearing which has been outlined. 



Although this theory of hearing involves the principle of reso- 

 nance, it is very different from the Helmholtz theory as usually under- 

 stood. In the latter it as assumed that there are four or five thousand 

 small resonators in the ear, each responding only to a single tone; 

 while in the former it is assumed that a single vibrating membrane 

 which vibrates for every impressed sound is sufficient to differentiate 

 the various recognizable sounds by its various configurations of 

 vibration form. 



A loudness scale has been chosen such that the loudness change 

 is equal to ten times the common logarithm of the intensity ratio. 

 A pitch scale has been chosen such that the pitch change is equal 

 to 100 times the logarithm to the base two of the frequency ratio. 

 The loudness of complex or simple tones is measured in terms of the 

 number ot loudness units a tone of 700 cycles must be raised above 

 its average threshold value before it sounds equally loud to the sound 

 measured. 



