152 BELL SYSTEM TECHNICAL JOURNAL 



ceived as being different in volume. If the minimum and maximum 

 audibility curves were plotted on an energy scale, the increment 

 length AE near the maximum audibility curve would be a million 

 million times longer than its length in the minimum audibility curve, 

 whereas when they are plotted on a logarithmic scale, this increment 

 length remains approximately constant, changing by less than a factor 

 2 for 90 per cent, of the distance across the auditory-sensation area. 

 The calculation shows (see Appendix A) that the number of such 

 increments on the 100-cycle frequency line is 270, that is, 270 tones 

 having a frequency of vibration of 1,000 cycles can be perceived as 

 being different in loudness. 



What has been said of the intensity scale applies equally well to 

 the frequency scale. The calculation (see Appendix A) indicates 

 that the number of tones that are perceivable as being different in 

 pitch along the 10-dyne pressure line is approximately 1,300. 



If an ordinate increment corresponding to A-E and an abscissa 

 increment corresponding to AN be drawn, a small rectangle will be 

 formed which may be considered as forming the boundary lines for 

 a single pure tone. All tones which lie in this area sound alike to the 

 ear. The number of such small rectangles in the auditory-sensation 

 area corresponds to the number of pure tones which can be perceived 

 as being different. The calculation (see Appendix A) of this number 

 indicates that there are approximately 300,000 such tones. 



One might well ask the question : How many complex sounds which 

 are different can be sensed by the ear? At first thought, one might 

 say that this number is represented by all the possible combinations 

 of pure tones. Of course, such a number would be entirely too large, 

 for some of these would sound alike to the ear, since the louder tones 

 would necessarily mask the feebler ones. It is evident, however, 

 that the number of such complex sounds will be very much larger 

 than the number of pure tones. 



Scales of Loudness and Pitch 



It is seen that the use of the logarithmic scale in Fig. 1 is much 

 more convenient not only on account of the large range of values 

 necessary to represent the auditory-sensation area, but also because 

 of its scientific basis. Psychologists have recognized this since Weber 

 and Fechner formulated the relation between the sensation and the 

 stimulus. Although logarithmic units have been used by various 

 authors in measuring the amount of sensation, the numerical values 

 have been quite different. It seems inevitable that there will be a 



