ON THE PHONOGRAPH. 779 



components varying separately according to the simple harmonic law. If we take as an 

 example a harmony, the variation of the air pressure of a harmony is the sum of the 

 variations of simple tones, one having a period equal to the period of the harmony, a 

 second J, a third ^, and so on.* It may be that this defect in the form of the curve 

 in the phonograph is the explanation of the fact that it does not, in many cases, repro- 

 duce absolutely the quality of tone. Further, when reversal takes place, it will be 

 evident that the reproducing point will run down the slope that corresponds to diminu- 

 tion of pressure before it runs up the slope corresponding to increase of pressure, and 

 that it will take longer time in going down than in going up the slope. This, again, 

 must affect quality. 



IX. Remarks on Discrimination of Auditory Sensations. 



27. This study of the phonograph has led to the consideration of some of the funda- 

 mental questions of physiological acoustics, but I shall briefly refer to only one of these 

 at present. It is clear that by the aid of the phonograph we can record vibrations of 

 higher number than by any other method at our disposal, and that we can see and 

 study the time relations of these vibrations. This is a direction in which research 

 should proceed. So far as I am concerned, I must leave it to others. By this method, 

 for example, direct observations might be made on the limits of the sensible discrimina- 

 tion of tones. It is well known that the lower limit of tone perception is near 16, and 

 the upper limit near 50,000 vibrations per second, and it is also well known that sensible 

 discrimination diminishes towards each end of the range, and more especially towards 

 the upper limits. By noticing the smallest changes in different determinations, and by 

 the method of computing right and wrong cases in observations of the comparison of 

 differences, experimental psychologists have shown that, between 64 and 1024 vibrations 

 per second, the least noticeable difference is so small as 0"2 vibration. It is said to 

 be 0'4 at 32 and 2048 vibrations per second. It is certainly a remarkable testimony 

 to the delicacy of the ear that, between 32 and 2048 vibrations per second, we can 

 observe a difference of less than 1. Even the most skilled ear cannot observe large 

 differences between 12,288 and 16,384, and Kulpe states that only about 23 tones 

 can be distinguished beyond 4096. From these data, we can compute, as has been 

 done by KuLPE,t the number of tones that the ear can distinguish. Thus, in the range 

 of human audibility, we can hear about 97 tones between 16 and 64 vibrations per 

 second, 4800 between 65 and 1024, 6144 between 1025 and 4096, and 23 on the high 

 side of 4097. This gives a total of 11,064 tones heard by the human ear. It is 

 interesting, in this connection, to notice the range as regards pitch of the chief instru- 



* Lord Kelvin, " On Beats of Imperfect Harmonies," Proc. Royal Society of Edinburgh, 1st April 1878 ; 

 also in Popular Lectures and Addresses, vol. ii. p. 395. 



f Oswald Kulpe, Outlines of Psychology, based upon the results of experimental investigation, p. 106, 

 trans, by E. B. Titchenek, 1895. 



