ON BEATS OF IMPERFECT HARMONIES. 411 



>ut I find that the number of beats is quite dis- 

 tinctly equal to the error of frequency of the 

 higher note. I have found that the beats on the 

 i : 2 harmony are most easily perceived when the 

 intensity of the higher note is comparatively faint, 

 as would be the case if they were explained by 

 Helmholtz's theory that they are the beats on the 

 approximation to unison which there is between 

 the higher note and the first overtone of the lower 

 note. But the simple-harmonic character of the 

 two constituent tones at the entrance of the ear 

 precludes the acceptance of this theory unless 

 extended, as it has actually been by its author, 

 to the interior mechanism of the ear. 



Whatever may be the physiological theory by 

 which the beats are to be explained, it is an inter- 

 esting fact that the ear does distinguish, as it 

 were, between push and pull on the tympanum in 

 the manner illustrated by the preceding curves, not 

 only for the case of approximation to the harmony 

 I : 2, but for every other even binary harmony. 

 I have heard distinctly the beats on approxima- 

 tions to each of the harmonies 2:3, 3:4, 4 : 5> 



