HEARING 419 



if either rod with a hair-cell, or hair-cells, is the analytical 

 element, 9,438. Counting gives 3,487 inner, 11,700 outer, 

 hair-cells. The fibres of the basilar membrane are estimated 

 at 24,000 ; the fibres of the cochlear nerve at 14,000. It will be 

 understood that the counting of structures as minute as these 

 yields results which cannot be more than approximately 

 accurate. Helmholtz, assuming that each arc of Corti indi- 

 cates an analytical element, accounted for the apparent 

 deficiency in their number by assuming that a tone of which the 

 pitch fell between two arches set both in sympathetic vibra- 

 tion, the arch which was nearest in pitch to the tone vibrating 

 the more strongly. In this way he anticipated an objection 

 which has often been brought against his theory of a long 

 series of resonators. 



In opposition to Helmholtz 's theory it is pointed out that 

 when a violinist runs his finger up a bowed string, the pitch 

 rises with perfect smoothness ; it does not bump along from 

 resonator to resonator. Especially in the case of very high 

 tones given out by a siren, it is urged that at the rare intervals 

 at which a resonator in the ear is tuned for the tone which the 

 siren is emitting it should sound much louder than when the tone 

 falls midway between two resonators. But the whole question 

 of the nature of the response of the analytical elements is too 

 obscure at present for the discussion of points so nice as this. 



Many who think that Helmholtz's theory of resonators is 

 based upon principles of physics and of physiology which must 

 be regarded as the starting-points of any explanation of the 

 analysis of sounds by the ear and the mind, hold that it goes 

 too far in searching for a separate resonator for every dis- 

 tinguishable tone. The cochlea, as we have already said, does 

 not offer anything like so extensive a choice as this, if regard 

 be had to the tension or length of its elements, and not to their 

 numbers. Those who accept it as an axiom that the cochlea 

 contains a series of responding instruments but a series far 

 more limited in range than the gamut of our sound-percep- 

 tions seek to discover in musical tones qualities which unite 

 them in groups. Just as in the case of colour-sensations they 

 recognize four (or six) elementary qualities which excite four 

 (or six) pieces of responding apparatus, so also in the case of 

 hearing they seek for a limited number of tone-qualities and 



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