PHYSICAL MEASUREMENTS OP AUDITION 



175 



where j8i and fa are the points where the particular intensity line 

 cuts the boundary lines of the auditory-sensation area. For ex- 

 ample, the limits for the line corresponding to 1-dyne pressure ampli- 



Curves for Obtaining 

 Values of F(a) 



Curves show I I I ' / 



too /ipfp) f( a -°o) 



Fig. 14 



tude are 500 and 1420. Similarly the number of tones of constant 

 pitch which are perceivable as being different in loudness is given by 



logo 10 r°" da 



y = 



) r 



J OL\ 



10 J ai Ka-ca) 



where ai and a-i are determined by the intersection of the particular 

 pitch line with the boundary lines of the auditory-sensation area. 



The values of these integrals were computed graphically. Figs. 

 12 and 13 show the results of these calculations. It is seen that 

 the maximum number of tones perceivable as different in loudness 

 is in the frequency range 700 to 1,500 which is also the important 

 speech range. The number in this range is approximately 270. 



In the pressure range from 1 to 100 there are approximately 1,500 

 tones which can be perceived as being different in pitch. 



The number of tones AT in a small area d$ da situated with one 

 corner at the point (a, /3) is given by dx dy or 



log, 2 log, 10 da d^ 



AT = dx dy = 



T = 



10,000 

 log,21og e 10 



10,000 



J J tp 



<ptP)P(a-a Q y 

 d^ da 

 (P)P(a-a o y 



