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BELL SYSTEM TECHNICAL JOURNAL 



But the values of (3 and a are given by 



,3 = 100 log 2 2V (6) 



a = 10(log 10 £-logi £ ] ) (7) 



where E\ is the value of intensity corresponding to a pressure am- 

 plitude of 1 dyne. 



Substituting values of <LN and dE in terms of a and /? we have 



d(3 



1 N . j _ logf 2 

 dX ~ TOO A7V l0 S^ tf P " 1000 *>(/3) -/(a-« ) 



1 £ . , log, 10 (/a 



10 A.E 10 /(a — a ) 



(4') 

 (50 



The number of tones of constant intensity which are perceivable as 

 different in pitch is then 



log, 2 re* dp 





1000 ./^ <p(J3)-f(a-a ) 



340 

 320 

 300 

 280 

 260 

 240 

 220 

 i 200 

 „ '80 



| ' 60 

 S^/40 



•5 120 



100 

 80 

 60 

 40 



10 



300 400 500 600 100 800 900 1000 1100 1100 1300 HO0 1500 1600 



Values of (S 

 8 16 32 64 128 ?56 512 I0Z4 tm 4096 819? I63M 31168 65536 =aP 

 Pitch 



Fig. 13 



