264 AYERS. [Vol. VI. 



Similarly for the violoncello. At the instant when the finger 

 which makes the shake falls on the string the latter must com- 

 mence a vibration of a different periodic time, due to its length, 

 and the instant the finger is removed the vibration belonging 

 to the deeper tone must return. And yet the shake in the base 

 is as imperfect on the violoncello as on any other instrument. 



" Runs and shakes can be relatively best executed on a piano- 

 forte, because, at the moment of striking, the new tone sounds 

 with great but rapidly decreasing intensity ; hence, in addition 

 to the inharmonic noise produced by the simultaneous continu- 

 ance of the two tones, we also hear a distinct prominence given 

 to each separate tone. Now, since the difficulty of shaking in 

 the base is the same for all instruments, and for individual 

 instruments is demonstrably independent of the manner in 

 which the tones are produced, we are forced to conclude that 

 the difficulty lies in the ear itself [italics mine]. We have, 

 then, a plain indication that the vibrating parts of the ear are 

 not damped with sufficient force and rapidity to allow of success- 

 fully affecting such a rapid alteration of tones. Nay, more, this 

 fact further proves that there nmst be different parts of tJie ear 

 which are set in vibration by tones of different pitch and which 

 receive the sensation of these tones. 



"We may on the whole assume that the parts of the ear which 

 vibrate sympathetically have an amount of damping power cor- 

 responding to the third degree of our table. Of course there 

 can be no question of exact determinations, but it is important 

 for us to be able to form at least an approximate conception of 

 the influence of damping on the sympathetic vibration of the 

 ear, as it has great significance in the relations of consonance." 



Helmholtz means by the expression " sympathetic vibration " 

 the vibratory response of a given structure to a determinate 

 tone primarily, and to over and under tones secondarily. Physi- 

 cists have shown that a vibrating body is sympathetically affected 

 by tones both above and below its own proper tone, but that 

 the sympathetic susceptibility decreases very rapidly as the 

 scale is ascended or descended from the given note. 



Helmholtz materially modifies his views from time to time as 

 to the parts of the internal ear which vibrate sympathetically. 

 In the first edition of his Die Lehre von den Tonempfindnn- 

 gen, he put forward the view that it was the rods of Corti 



