1 1 84 THE EAR. ' 



to the syren, as its disc revolves faster and faster, our sensations go on 

 not by leaps and bounds but continuously. Since the time when Helm- 

 holtz wrote the " Tonemptindungen," histological evidence has accumu- 

 lated, and now we can give more ample data on which to form an 

 opinion on this question. 1 



Suppose we take the lower limit of perception of tone to be that 

 corresponding to nearly 16, and the upper limit nearly 50,000 vibs. per 

 second, sensible discrimination of pitch diminishes towards each end 

 of the range, more especially towards the upper limits. By noticing the 

 smallest changes in different determinations, and by the method of com- 

 puting right and wrong cases, in observations on the comparison of 

 differences, experiments have shown that between 64 and 1024 vibs. per 

 second the least noticeable difference is so small as 0*2 vibs. Kiilpe 

 gives 0*4 at 32 and 03 at 2048 vibs. per second. It is a striking testi- 

 mony to the delicacy of the ear that between 32 and 2048 vibs. per second 

 we can observe a difference of less than 1 vib. per second. Even the most 

 skilled ear cannot observe large differences between 12,288 and 16,384, 

 and it may be safely stated that only about 23 tones can be distinguished 

 beyond a vibration frequency of 4096. 2 From these data we can com- 

 pute the number of tones the human ear can distinguish. Thus, within 

 the range of human audition, we can hear about 97 tones between 16 and 

 64 vibs. per sec, 4800 between 65 and 1024, 6144 between 1025 and 

 4096, and 23 on the upper side of 4097. This gives a total of 11,064 

 tones heard by the human ear. It is interesting to notice in this con- 

 nection that the pitch of the highest tone of the piccolo stop of the organ 

 is 4096 vibs. per sec, while the deepest tone of the contra-bassoon is 27. 

 These are the highest and the lowest tones used in music 



The dimensions of the ductus cochlearis, the number of the rods of 

 Corti, and the number of hair cells have been determined by competent 

 observers. At my request, Dr. William Snodgrass made transverse 

 sections of the cochlear division of the auditory nerve of an adult who 

 was not deaf and who did not die of a disease affecting the ear, and he 

 carefully counted the number of nerve filaments. 3 These were found 

 to be about 14,000. It is obvious that all such estimations must be 

 approximate. 



The following shows the general result of computations relating to this 

 question : — 



1. Audible Sounds, the Pitch of which can be Discriminated . 11,064 

 Less those below 64 and above 4096 ..<... 110 



Leaving , 10,954 



Say . ^ . . . . . 11,000 



2. Distribution of Sounds in Six Octaves used in Music — 



— =1833 for each octave : =153 for each semitone. 



6 12 



3. Musician's Ear can detect Difference of fa Semitone— 



1 ft) 



— —2 "4 for each T V semitone. 

 64 oT 



1 M'Kendrick, Trans. Roy. Soc. Edinburgh, 1896, vol. xxxviii. p. 780. 



2 Kiilpe, " Outlines of Psychology," translated by Titchener, 1895, p. 106. 



3 Result not hitherto published. 





