HELMHOLTZ IN BONN 



major third, and so on. What he did not explain 

 is Why the sensation should be disagreeable when 

 two portions of the membrana basilaris, sufficiently 

 near, are thrown into vibration ? For some un- 

 explained reason, if two nerve filaments sufficiently 

 near are simultaneously stimulated, or if they are 

 stimulated in the intermittent manner peculiar to 

 beats, the sensation is disagreeable. Helmholtz 

 contrasts it with that caused by a flickering light 

 on the eye. There is, in listening to beats, always an 

 effort at analysis, and it may be that this effort gives 

 rise to a disagreeable sensation when the number of 

 beats reaches a certain amount. 



While the theory explains the dissonance of in- 

 tervals produced by instruments that are rich in 

 partials, how does it apply to cases in which there are 

 no partials, but only prime tones, as when the tones 

 are produced by well-bowed tuning-forks and open 

 organ pipes ? This question also was attacked by 

 Helmholtz, and led to the examination of what he 

 termed combination tones. If, for example, two 

 forks representing a fifth are properly bowed, sound- 

 ing the fork of lower pitch first and that of higher 

 pitch afterwards, we may hear a weak lower tone, 

 the pitch of which is an octave below that of the 

 first fork. This is known as a combination tone. 

 Such tones he divided into two classes differential 

 notes, in which the frequency is the difference of the 

 frequencies of the generating tones ; and summational 

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