PHYSICAL MEASUREMENTS OP AUDITION 



151 



sponding to the intensity at the threshold of audibility. For in- 

 tensities greater than 10 4 times the threshold of audibility, the Fechner 

 ratio has the constant value of approximately one-tenth. It was 

 found that this ratio is approximately the same for all frequencies. 

 In Fig. 3 is shown the results taken from Knudsen's article on the 



Minimum Perceptible Difference in Frequency 



.011 



.010 



.009 



.008 



.001 



.006 



.005 



.004 



.003 



.002 



.001 



32 



64 



128 



256 



512 1024 

 Frequency 



Fig. 3 



2048 4096 8192 16384 



pitch sensibility. The ordinates give the fractional change in the 

 frequency which is just perceptible and the abscissae give the fre- 

 quency on a logarithmic scale. The meaning of the pitch scale at 

 the bottom of this figure will be discussed later. For frequencies 

 above 400 this fractional change is a constant equal to .003. This 

 ratio probably becomes larger again for the very high frequencies. It 

 was found that it varied with intensity in approximately the same 

 way as that given for the energy ratio. 



Using these values in connection with the auditory-sensation area, 

 it is possible to calculate the number of pure tones which the ear 

 can perceive as being different. For example, if, starting at the 

 minimum audibility curve, ordinate increments are laid off along a 

 constant pitch line, that are successively equal to the value of AE 

 at the intensity position above the threshold, then the number of 

 such increments between the upper and lower curves in Fig. 1 is 

 equal to the number of pure tones of constant pitch that can be per- 



