172 The Resonance Theory of Audition. 



yet clearly recognizable whether the note in question is 

 near the upper or lower limit of the range. And this cor- 

 responds with one of the facts (5) of audition as already 

 pointed out. 



Referring to fact (6) of audition, the test corresponding to 

 a musical shake was carried out as follows. The two driving 

 pendulums were set to what we may call the notes D and E 

 (that is the bobs third and fifth from the bottom of the 

 series). One driver was started while the other remained at 

 rest, and in a short time the maximum vibration of the corre- 

 sponding bob was elicited, the other bobs exhibiting the 

 ordered amplitudes and phases characteristic of forced 

 vibrations. Then the first driver was stopped and the 

 second started. After five or ten vibrations the new pitch 

 was clearly established, as shown by the ordered state of 

 things with the new maximum. So there is here quite 

 sufficient damping to make clear shakes possible. And we 

 have previously seen that the damping is small enough to 

 give fairly sharp resonance and so render possible a line 

 discrimination of pitch. 



Summary and Conclusion. 



1. The present position of the resonance theoiwof audition 

 is reviewed. The subject is acknowledged to be controversial. 

 But the endeavour is made to throw a side-light upon it by 

 the trial of a graduated set of pendulums used as responders 

 to other pendulums as drivers. In actual form these pen- 

 dulums make no pretensions to represent any structures to 

 be found in the ear ; but in their essential behaviour they do 

 typify such mechanisms as are postulated for the ear by the 

 resonance theory. This typical representation may be pos- 

 sible and useful, because we can apply to it the theory of 

 forced vibrations in its most essential aspects. 



2. Six facts of audition are then recognized as fundamental. 

 These include a much finer discrimination of pitch than one 

 for each responder and the failure to locate pitches quite 

 exactly when they lie near either limit of audition. 



3. Twelve photographs of the responding pendulums in 

 action are taken and here reproduced. 



4. These experimental results nowhere conflict with the 

 above six facts of audition. 



Indeed, for their explanation it suffices to have a set of 

 suitably damped responders and their associated nerves «>f 

 about twelve to the octave over a range of seven octaves, or 

 say about a hundred in all. The supposed necessity for a 



