4 



PROCEEDINGS OF THE AMERICAN ACADEMY 



the number giving the maximum dissonance, varies greatly with 

 the pitch of the notes sounded. 



The pitch of one of the resonators was varied so as to run upward 

 and downward through the vanishing point of the heats. This pro- 

 cedure was extremely tiresome, and the values obtained were found 

 to be considerably influenced by fatigue of the ear. The following 

 table (Table II.) gives the results obtained when the ear was in 

 good condition. The first column gives the rate of vibration of 

 the lower note, the next four the rate of the upper note as found 

 in corresponding series of observations; the seventh column gives 

 the number of beats, and the last the interval between the two 

 notes. 



TABLE II. 



These figures abundantly confirm for interference beats the results 

 already reached by Mayer for interruptional beats, viz. that the ear 

 is capable of appreciating a greater number of beats as the pitch of 

 the beating notes rises. They also show very beautifully the in- 

 creasing consonance of small intervals as the pitch rises, noted by 

 Helmholtz. 



The numerical results reached by us differ, as a whole, consider- 

 ably from those given by Mayer for interruptional beats in either of 

 his papers, though the divergence is less than that between the two 

 series representing his own observations and those of Mrs. Seiler. 

 In some cases, however, the agreement is very close. Thus, for Ut 2 

 we find the last trace of beats to occur when these are 46 in number. 

 The number as observed by Mayer is 26, and as observed by Mrs. 

 Seiler 45. For Ut 3 our figure is 70, and Mrs. Seller's is 70 also. 



