EXCITATION OF THE AUDITORY NERVE 501 



Helmholtz sought the resonators in the transverse strands of this structure. 

 In a membrane of this kind where the longitudinal tension is small as com- 

 pared with the transverse tension, the radial fibers act like a system of sepa- 

 rate strings. The membrane connecting them serves only to give the pressure 

 of the fluid a purchase on the strings and each one will therefore vibrate 

 independently of the others. 



Finally, the hair cells might serve as resonators. In short, although we 

 cannot settle definitely on a choice between these various elements, it must 

 be evident that there is no lack of structures suitable for such a function. 



B. OBJECTIONS TO THE RESONANCE THEORY 



The resonance theory of Helmholtz fits in remarkably well with the facts 

 mentioned thus far. But there are some circumstances under which the the- 

 ory cannot be applied so readily, and these circumstances must not be passed 

 over in silence. 



1. Beats. When two tones of different vibration frequencies are sounded at 

 the same time, if the difference between them is not too great, the vibrations 

 of the two will interfere with each other, producing what are called beats. Thus 

 if the difference in the number of vibrations be only one per second, and if the 

 two tones be struck at the same instant, the air waves of the deeper tone will 

 gradually fall behind those of the higher until at the end of a half second the 

 summit of one wave will coincide with the valley of the other; after another 

 half second the two summits will coincide, and so on. And in general if n 

 represent the number of vibrations of a tone per second, and n -f- 1 that of 

 another, then the loudness of the tone will be increased every second .and be 

 diminished every half second. The number of beats per second therefore will 

 always be equal to the difference in the number of vibrations per second between 

 the two tones. 



Now if each tone has only one independent resonator in the cochlea, it is 

 difficult to see how it would be possible for two tones to influence each other 

 in this way. There is, however, very good reason for believing that each tone 

 excites several neighboring resonators, and the difficulty offered by beats for 

 the resonance theory is readily disposed of by this supposition. For two tones 

 lying close together we suppose must influence several resonators in common; 

 then since the objective strength of the tone varies incessantly because of the 

 interference, the sympathetic vibrations of the resonators common to the two 

 must likewise vary in strength, and hence the subjective sensation must present 

 similar variations. Other phenomena connected with beats can be explained 

 from the same viewpoint. 



2. Combination Tones. When two tones not too close together in the scale 

 are sounded at the same time, one may hear, as was first pointed out by Sorge 

 (1740) and Tartini, a true tone, the vibration frequency of which is equal to 

 the difference in the number of vibrations per second between the two. For ex- 

 ample, striking a fundamental and its fifth at the same time (ratio 2:3), one 

 hears the lower duodecime of the fundamental. The first difference tone 

 then forms a second difference tone with the first primary tone. Under cer- 

 tain circumstances a tone may also be perceived which represents the sum 

 of the vibration frequencies of the two primary tones (Helmholtz). These 

 difference tones and summation tones are included under the term combina- 

 tion tones. 



