58 Mr. S. Taylor on Variations of Pitch in Beats. 



half wave-lengths of the constituents ; C the point in X where 

 the ordinates C D and C E are equal in length but opposite in 



Fig. 2. 



direction^ and where^ accordingly^ the resultant curve meets the 

 axis. 



In fig. 1 C is greater than A and less than O B, while in 

 fig. 2 C is less than either A or OB. But C is in each 

 case the half wave-length of the resultant tone^ A and B 

 those of the primary tones. Hence, when the two sets of waves 

 are in complete accordance, and the intensity of the resultant 

 tone therefore a maximum, its pitch will lie between the two pri- 

 maries. In the opposite case, where the intensity is a minimum, 

 the pitch of the resultant tone will be more acute than the higher 

 of the primaries. 



Figs. 3 and 4 represent the state of things when the lower of 

 the two original tones is the more powerful. 



Fig. 3. 



Fig. 4. 



Here, when the intensity is a maximum, the pitch will be, as 

 in the first case, intermediate between the primaries ; when a mi- 

 nimum, lower than the more grave of the primaries. 



Thus, in both the cases under consideration, each beat will be 



