of Consonances of the Form h : 1. 435 



the fourth partials are eliminated, consist entirely of variations 

 of intensity of the lower note. 



The existence of the third combination-tone in question 

 (3p — q) is demonstrated in many cases by Konig. It is heard 

 not so easily as the lower combination-tones, in the case of 

 intervals near the twelfth high in the scale. It is also less 

 easily detected by the secondary beats which it forms with 

 the second combination-tone in the case of intervals near 

 2 : 5, at which point the second and third combination-tones 

 coincide — also much less easily by the secondary beats which 

 it forms with the fourth combination-tone in the case of inter- 

 vals near 2 : 7, at which point the third and fourth combination- 

 tones coincide. 



52. Beats of the mistuned tierce (two octaves and a major 

 third), 



n : 5n±:m. 



These beats are much less easily detected in pure notes of the 

 ordinary strength than any of the foregoing. They are re- 

 corded by Konig; but I have never heard them clearly. As 

 it is certain that Konig"' s notes were not perfectly pure, and 

 he does not analyze the beats, we cannot tell whether the 

 variations of the lower note were produced in his experi- 

 ments. If they were, they are to be accounted for in a similar 

 manner. 



Number of beats = m. 



m variations of intensity of lower note (n) are produced by 

 interference of notes n and n±m. And n±m is the fourth 

 combination-tone (difference-tone of form 4p — q) of the pri- 

 maries n and 5n±m. 



The existence of the fourth combination-tone in question 

 (4p — q) is demonstrated directly by Konig in the case of 

 intervals near the double octave d" : c v . It is also less easily 

 detected by the secondary beats which it forms with the third 

 combination-tone in the case of intervals near 2 : 7, at which 

 point the third and fourth combination-tones coincide. 



53. Beats of the mistuned consonance of the nineteenth are 

 recorded by Konig; 



n : 6n±m. 



Number of beats = m. 



m variations of intensity of lower note (n) might be pro- 

 duced by interference of n and 7i±m. And n±m is the fifth 

 combination-tone (difference-tone of form 5p — q) of the pri- 

 maries n and 6?i±?n. 



The existence of the fifth combination-tone in question 

 (5p — q) is not anywhere directly demonstrated. Secondary 

 beats, which might be produced by its interference with the 



