298 



AUDITORY BIOPHYSICS 



frequency of the source is less marked than at high frequencies; there- 

 fore, the range of any experienced musical interval is greater at higher 

 than at lower pitches. For example, the octave 256 to 512 cycles is 



experienced as a pitch range varying 

 from 250 to 400 mels, but the high- 

 frequency-range octave 1024 to 2048 

 cycles extends from a pitch of 700 to 

 one of 1000 mels. 



£000 



4000 



^3 3000 



E 



£2000 



1000 





100 200 500 1M 2M 

 Frequency 



5M 10M 



Fig. VII-22. The pitch func- 

 tion. This shows how the experi- 

 enced pitch of a tone (mels) 

 changes as a function of the fre- 

 quency of the stimulus. This 

 graph was developed at a loudness 

 level of 60 db. (Stevens, Volk- 

 mann, and Newman [1937].) (By- 

 courtesy of Stevens and Davis, 

 Hearing, John Wiley & Sons, New 

 York.) 



Resolving Power of the Ear 



If two equally intense tones are suffi- 

 ciently close together in frequency so 

 that the ear is able to experience them 

 as two just-differentiable pitches, the 

 limits of pitch resolution of the ear is 

 attained. The sensitivity of the ear to 

 small changes in pitch at very low inten- 

 sities of stimulation (just above the 

 threshold of sensitivity) is comparatively 

 small. As the intensity increases, the 

 ear becomes more sensitive to small 

 changes in frequency until, at 80 db, 

 a 1000-cycle stimulus (Shower and 

 Biddulph [1931]) can be distinguished 

 from an equally intense source of 1003 



cj^cles as a difference in pitch. 



Such a minimum detectable change in frequency is called by psycholo- 

 gists the difference limen (DL). The size of a difference limen not only 

 is a function of the frequency of the tone presented to the ear but also 

 depends on its intensity. The difference limens have been found to 

 differ greatly not only among different observers but also under differ- 

 ent experimental conditions for the same observer. 



The ability to resolve two neighboring pitches, or the resolving power, 

 is equal to the reciprocal of the difference limen. It has been found 

 that the resolving power increases with increase in intensity. It should 

 follow that for binaural listening, through which the loudness is doubled, 

 the resolving power should be greater than for monaural listening proces- 

 ses. This difference is verifiable from the experiments by Shower and 

 Biddulph [1931], who also found that at frequencies below 500 cycles the 

 difference limens are approximately constant except for frequencies 

 below 45 cycles, where aural subjective harmonics are introduced, espe- 



