Tlieory of Audition subjected to Experiments. 171 



to our perception of' these figures, it would be possible to 

 discriminate between successive notes differing in pitch b) r 

 only the twentieth of an equal-tempered semitone or five 

 logarithmic cents. And this is just about what a good ear 

 can accomplish. 



In the case of the six figures of Plate II. it should be noted 

 that the shorter driver is allowed to swing the whole time, 

 and in no way interferes with the discrimination of pitch of 

 the longer one as seen throughout. And this is known to be 

 the case with hearing when the other note is neither too near 

 in pitch nor too loud. 



Hence the six figures of this Plate corroborate the facts of 

 audition 1 and 2 in our list. Indeed, fact 1 was supported 

 also by photographs 1-18 on plates V. and VI. of the paper 

 on Mechanical il Resonators," &c. (Phil. Mag. April 1919). 

 Further, photographs 14 and 15 of plate VI. in that paper 

 showed by flash exposures the presence of beats, which 

 obviously allow of a finer discrimination of pitch between 

 simultaneous notes. And this constitutes our third fact of" 

 audition. 



As for fact 4 of audition, any finite set of responders would! 

 obviously accord with that experience. 



Photographs 7-12 (PI. III.) are devoted to the test of fact 5,. 

 which is the failure to recognize with precision pitches lying 

 near either limit of audition. Thus in figures 7-9 we test 

 the upper limit on the supposition that our single octave 

 represents the top of the whole set of responders in the ear.. 

 In fig. 7 the responder second from the top has maximum 

 amplitude, in fig. 8 the driving pendulum has been shortened 

 so that the shortest pendulum responds best. In fig, 9 the 

 driving pendulum was shorter than any responder, but that 

 fact can scarcely be inferred from inspection of the figure,, 

 so that the exact location of pitch is lost. Indeed, as soon as 

 the pitch of the driver passes beyond either limit of the 

 pitches of the set of responders, so that no one bob exhibits 

 a maximum vibration with a falling off above and below, the 

 exact location of pitch must be lost. 



For the lower limit of this single representative octave of 

 responders the gradual failure to locate the pitch is illustrated 

 by photographs 10-12. In fig. 10 the pitch is evidently 

 between the lowest and the second, that is between what we 

 have called and C#. In fig. 11 it is about at the lowest C, 

 and in fig. 12 it is still lower, but by an amount which cannot 

 be precisely inferred from the figure. 



It may be noted that although by a set of responders. the 

 exact pitch is not detectablo for notes near either limit, it is 



