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BELL SYSTEM TECHNICAL JOURNAL 



give the best fit. The values of b were calculated from these curves as 

 follows: 



According to the assumptions made above, the component of lowest 

 pitch in the series of components always has a value of bk equal to 

 unity. Therefore for the series of 10 components having a common 



S 80 



<n 



5 

 O 

 U 60 



-10 o 



10 20 30 40 50 60 70 



LOUDNESS LEVEL OF SINGLE COMPONENT-DB 



Fig. 10 — Loudness levels of complex tones having ten equally loud components with 

 a fundamental frequency of 1000 c.p.s. 



loudness level La-, the value of h is related to Lt by 



or by solving for bi 



G{L) = (1 + 9b,)G{U) 



b, = (1/9)[G(L)/G(L.) - 1]. 



(16) 



The values of bf. can be computed from this equation from the ob- 

 served values of L and Lk by using the values of G given in Table III. 

 Because of the difficulty in obtaining accurate values of L and Lk such 

 computed values of bk will be rather inaccurate. Consequently, con- 

 siderable freedom is left in choosing a simple formula which will 



