PHYSIOLOGICAL ACOUSTICS 289 



In the case of the Fifth eg we have 



c = 132, 264, 396, 528, 660, 792, ..., 



g= 198, 396, 594, 792, ..., 



and if this be mistuned the second tone of g beats with the 

 third tone of c, and so on. When the ratio of the vibration 

 numbers of the fundamentals is less simple, the harmonics 

 which can interfere are of higher order. Thus in the case of 

 the Major Third, where the ratio is 4:5, the first pair of 

 interfering overtones consists of the fifth tone of the lower note, 

 and the fourth of the higher. Since in many musical instruments 

 the fifth tone is very feeble, this consonance is less well defined 

 than the preceding ones. On the other hand the fundamentals 

 may fall, in the lower parts of the scale, within beating distance 

 (for example c= 132, e 165), so that this consonance is to be 

 reckoned also as less perfect than the former ones. Similar 

 remarks apply with greater force to such cases as the Minor 

 Third (5 : 6) and the Minor Sixth (5 : 8). 



94. Helmholtz Theory of Audition. 



The connection between primary sensations and simple- 

 harmonic vibrations has still to be accounted for. The problem 

 is a physiological one; but the theory which Helmholtz has 

 framed to explain Ohm's law, so far as it holds, and the various 

 deviations from it, is in its essentials so simple, and is so 

 successful in binding together the facts of audition into a 

 coherent system, that a brief statement of it may be attempted. 



In its simplest form the theory postulates the existence, 

 somewhere in the internal ear, of a series of structures each 

 of which has a natural period of vibration, and is connected 

 with a distinct nerve-ending. For brevity we will speak of 

 these structures as "resonators," since that is their proper 

 function. A particular resonator is excited whenever a 

 vibration of suitable frequency impinges on the ear; the 

 appropriate nerve is stimulated ; and the sensation is com- 

 municated to the brain. In this way the resolution of a 

 musical note into its constituent tones is at once accounted 

 for. 



It is necessary to suppose that the resonators are subject 



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