Sounding of two Notes, 525 



interval n : n + m, but also of the interval nihn + m (Ji = 2, 3, 4), 

 when the intensity of the primary notes and their number are 

 sufficient, change into beat-notes. 



II. (4) When the two beat-notes m and mf are near the 

 unison, the octave, and twelfth, the same beats may be heard as 

 would be produced by two equal primary notes. I have 

 named these beats arising from beat-notes secondary beats, in 

 order to distinguish them from the beats arising from primary 

 notes. 



(5) When the intensity of the beat-notes by which they 

 are formed and their number are sufficient, these secondary 

 beats change to a secondary beat-note, as primary beats change 

 to a primary beat-note. 



III. (6) The difference-notes and summation-notes, which 

 are produced by the clang of two loud notes (the vibrations of 

 the latter not being infinitesimal), produce a phenomenon 

 which is independent of the beats and beat-notes : they are 

 very much weaker than the beat-notes. 



IY. (7) The beat-notes cannot be explained by reason of 

 the difference-notes and summation-notes, because the number 

 of their vibrations is in many cases different from what this 

 cause might produce. 



(8) The audibility of the beats depends solely upon their 

 number and upon the intensity of the primary notes, and is 

 independent of the distance of the interval. 



(9) The number of the beats and of the primary impulses 

 in which both may be perceived as separate impulses is the 

 game. 



(10) With the beats perceived as separate impulses, as 

 with the primary impulses perceived in the same manner, the 

 note which approaches them in number is audible. 



(11) The number at which beats and primary impulses can 

 change into one note is the same. 



(12) As with beats and primary impulses, the intermissions 

 of a note can also change into one note. 



(13) When the vibrations of a note vary periodically in 

 intensity, the periodical maxima of vibration change into one 

 note, if their number is sufficient. 



(14) The beat-note which is formed by two primary notes 

 must always be weaker than the latter, although single beats 

 are stronger than the notes which form them. 



Paris, December 1875. 



