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BELL SYSTEM TECHNICAL JOURNAL 



Having these values, the masking component can be found either by 

 inspection or better by trial in Eq. (21). That component whose 

 values of Lm, fm and 7' introduced into this equation gives the smallest 

 value of hk is the masking component. 



The values of G and Q can be found from Tables III and VI from 

 the corresponding values of Lk, i3k, and/t. If all these values are now 

 introduced into Eq. (10), the resulting value of the summation is the 

 loudness of the complex tone. The loudness level L corresponding to 

 it is found from Table III. 



If it is desired to know the loudness obtained if the typical listener 

 used only one ear, the result will be obtained if the summation indicated 

 in Eq. (10) is divided by 2. Practically the same result will be ob- 

 tained in most instances if the loudness level Lk for each component 

 when listened to with one ear instead of both ears is inserted in Eq. (10). 

 {G{Lk) for one ear listening is equal to one half G{Lk) for listening with 

 both ears for the same value of the intensity level of the component.) 

 If two complex tones are listened to, one in one ear and one in the 

 other, it would be expected that the combined loudness would be 

 the sum of the two loudness values calculated for each ear as though 

 no sound were in the opposite ear, although this has not been confirmed 

 by experimental trial. In fact, the loudness reduction factor hk has 

 been derived from data taken with both ears only, so strictly speaking, 

 its use is limited to this type of listening. 



To illustrate the method of using the formula the loudness of two 

 complex tones will be calculated. The first may represent the hum 

 from a dynamo. Its components are given in the table of com- 

 putations. 



Computations 



The first step is to find from Fig. 5 the values of Lk from fk and ^k- 

 Then the loudness values Gk are found from Table III. Since the 

 values of L are low and the frequency separation fairly large, one 

 familiar with these functions would readily see that the values of h 

 would be unity and. a computation would verify it so that the sum of 

 the G values gives the total loudness 1009. This corresponds to a 

 loudness level of 40. 



