88 ON THE PHYSIOLOGICAL CAUSES OF 



When the beats become more rapid, the ear finds a con- 

 tinually increasing difficulty when attempting to hear them sepa- 

 rately, even though there is a sensible roughness of the tone. 

 At last they become entirely undistinguishable, and, like the 

 separate puffs which compose a tone, dissolve as it were into a 

 continuous sensation of tone. 1 



Hence, while every separate musical tone excites in the 

 auditory nerve a uniform sustained sensation, two tones of dif- 

 ferent pitches mutually disturb one another, and split up into 

 separable beats, which excite a feeling of discontinuity as dis- 

 agreeable to the ear as similar intermittent but rapidly repeated 

 sources of excitement are unpleasant to the other organs of 

 sense; for example, nickering and glittering light to the eye, 

 scratching with a brush to the skin. This roughness of tone is 

 the essential character of dissonance. It is most unpleasant to 

 the ear when the two tones differ by about a semitone, in which 

 case, In the middle portions of the scale, from twenty to forty 

 beats ensue in a second. When the difference is a whole tone, 

 the roughness is less; and when it reaches a third it usually 

 disappears, at least in the higher parts of the scale. The (minor 

 or major) third may in consequence pass as a consonance. Even 

 when the fundamental tones have such widely different pitches 

 that they cannot produce audible beats, the upper partial tones 

 may beat and make the tone rough. Thus, if two tones form a 

 fifth (that is, one makes two vibrations in the same time as the 

 other makes three), there is one upper partial in both tones 

 which makes six vibrations in the same time. Now, if the ratio 

 of the pitches of the fundamental tones is exactly as 2 to 3, the 

 two upper partial tones of six vibrations are precisely alike, and 

 do not destroy the harmony of the fundamental tones. But if 

 this ratio is only approximatively as 2 to 3, then these two upper 



known out of Northumberland, in England. In France it is called the r 

 grasseye or provenyai, and is the commonest Parisian sound of r. The 

 uvula trill is also very common in Germany, but it is quite unknown in 

 Italy. TK. 



1 The transition of beats into a harsh dissonance was displayed by means of 

 two organ pipes, of which one was gradually put more and more out of tune 

 with the other. 



