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BELL SYSTEM TECHNICAL JOURNAL 



contrary to this. To make the calculated and observed results agree 

 with these two sets of data, Q was made to depend upon 



re = /3 + 30 log / - 95 

 instead of Lk. 



It was found when using this function of /3 and / as an abscissa and 

 the same ordinates as in Fig. 10, a value of Q was obtained which gives 

 just as good a fit for the data of Fig. 10 and also gives a better fit for 

 the data of Figs. 8 and 9. Other much more complicated factors were 

 tried to make the observed and calculated results shown in these two 

 figures come into better agreement but none were more satisfactory 

 than the simple procedure outlined above. For purpose of calculation 

 the values of Q are tabulated in Table VI. 



TABLE VI 



Values of Q{X) 



Note: X = ^;t + 30 log/t - 95. 



There are reasons based upon the mechanics of hearing for treating 

 components which are very close together by a separate method. 

 When they are close together the combination must act as though the 

 energy were all in a single component, since the components act upon 

 approximately the same set of nerve terminals. For this reason it 

 seems logical to combine them by the energy law and treat the com- 

 bination as a single frequency. That some such procedure is necessary 

 is shown from the absurdities into which one is led when one tries to 

 make Eq. (17) applicable to all cases. For example, if 100 components 

 were crowded into a 1000-cycle space about a 1000-cycle tone, then it 

 is obvious that the combination should sound about 20 db louder. 

 But according to Eq. (10) to make this true for values of Lk greater 

 than 45, hk must be chosen as 0.036. Similarly, for 10 tones thus 

 crowded together L — Lk must be about 10 db and therefore bk = 0.13 

 and then for two such tones L — Lk must be 3 db and the corresponding 



