3i8 



NA TURE 



[September 2, 1922 



points H and J, with a pendulum KL with heavy bob 

 L to act as driver, and a number of light graduated 

 responders lettered C to C The latter have small 

 paper cones about 2 cm. high as bobs, with the addition 

 of split rings of copper wire resting on them to prevent 

 the damping being too great. The driving pendulum 

 has a " tightener " at M to adjust its length, which 

 must be reckoned from L up to N, since when the 

 heavy bob L swings the bridle HKJ swings about the 

 line HNJ. The lengths of the light responders, on 

 the other hand, must be reckoned only up to their 

 suspension point on the cord HK. These light re- 

 sponders have suspensions of thread which are passed 

 through the cord HK and may then be cut off and 

 the adjustment to place made so that the line of the 

 bobs CD — C passes through H. This is essential in 

 order that each responder receives an equal inclination 

 by a given displacement of the heavy bob L. In the 



diagram just one octave of responders is shown, the 

 number being thirteen and the lengths such as to 

 make their relative frequencies those of the consecutive 

 notes on the piano or organ. This allows a fineness of 

 discrimination of pitch in agreement with experience. 

 Of course to represent the whole set of aural mechan- 

 isms, seven or more octaves would be needed, but a 

 single octave on the model enables one to carry out 

 a number of interesting tests, though for some, two 

 octaves are necessary, as shown by dotted lines in 

 the figure. For the latter the lengths of the responders 

 (and also the distances from H of their points of 

 suspension) may be as follows : 57-05, 50-8, 45*25; 

 4°"3, 35'9, 32-0, 28-5, 25-4, 22-6, 20-16, 18-0, 16-0, 

 14-25, 127, n -3, io-i, 9-o, 8-o, 7-13, 6-35, 5-65, 5-04, 

 4-49, 4-0, 3-55 cm. Any consecutive thirteen values 

 will do for a single octave. 



We may now test the behaviour of such a model 

 and ascertain if in essential features it typifies the 

 mechanism in the ear, although of course it is not for 

 a moment imagined that any pendulums exist in the 

 ear. If vibratory responders exist there they must be 

 of an elastic nature. 



I! the seven octaves or more of responders were 



NO. 2757, VOL. I io] 



provided we should have the musical range of seven 

 octaves accounted for. Further, the lack of precise 

 discrimination of pitch for very high notes and for 

 very low notes is explained also. Thus, for any note 

 well within the range of the responders. when the 

 pendulum bob L is swung, thus representing by its 

 frequency a certain note, the responders vibrate in 

 response, the one best in tune vibrating most, the 

 others near it, both above and below, showing a rather 

 less response. Hence the pitch is recognised and 

 located by this behaviour. But if the pendulum LN 

 is made shorter than the shortest or longer than the 

 longest responder provided, then we have the responders 

 near the end in question responding best but no 

 maximum response with a return to quiescence beyond it. 

 Thus the exact pitch cannot be located, and this agrees 

 with experience. Consider next the discrimination of 

 pitch between notes very near in pitch, and let us 

 ascertain what is possible when the 

 adjacent responders differ in pitch by 

 a semitone or one-twelfth of an octave. 

 It will be easily ascertained that a 

 discrimination of pitch of about the 

 twentieth of this semitone is possible. 

 For by adjusting the tightener M on 

 the suspension KL, we can make the 

 response of two adjacent pendulums 

 equal, and then by repeatedly length- 

 ening the heavy or driving pendulum 

 the response of the lower of the two 

 light pendulums may be increased and 

 that of the higher one decreased till the 

 lower one just shows a maximum, the 

 adjacent ones above and below being 

 alike in their response. We should 

 then have passed over the half of a 

 semitone only and ten steps are suscep- 

 tible of discrimination in this range. 

 Without any wire rings on the paper 

 cones the responders would not succeed 

 in this test, but with the rings to weight 

 the cones there is less damping, sharper resonance, 

 and adequate discrimination. 



If two octaves of responders are provided very 

 striking experiments can be shown as to the recognition 

 of the overtones essential to notes of a certain quality 

 of tone. Thus, setting the pendulum NL to the pitch 

 of a low responder, say the third from the bottom, 

 if the pendulum swings freely we have a responsive 

 maximum at that lesponder. But if the bob L is 

 grasped in the hand and swung to and fro in the same 

 period as before, but with a " dimple " at one end of 

 the swing, it is really executing tone and octave, and 

 the responders will promptly show the corresponding 

 two resonance humps. Again, if the bob L is swung 

 to and fro, with a " dimple " at each end, it is really 

 executing tone and twelfth (frequencies 1 and 3), and 

 the responders give the corresponding two resonances. 

 Lastly, if the bob L is moved smoothly from end to 

 end in one direction, but returns with two kinks or 

 dimples, we have really a vibration consisting of 

 tone, octave and twelfth (frequencies as 1, 2 and 3). 

 and the three appropriate resonance humps are shown 

 by the set of responders. 

 Thus, without overstraining or even exhausting the 



