Mr. S. Taylor o?i Variations of Fitch in Beats. 



of two different degrees of pitch at 

 the moments when it is loudest and 

 weakest respectively. In order to as- 

 certain what happens at intermediate 

 points of time, we have only to deter- 

 mine the resultant curve for a suffi- 

 cient number of wave-lengths. This is 

 done in fig. 5, which is constructed 

 for the interval of a semitone (16 : 15), 

 and represents completely the state of 

 things from a maximum of intensity 

 to the adjacent minimum. The higher 

 tone is taken as the louder of the two. 

 The wave-lengths here gradually di- 

 minish as we advance from the maxi- 

 mum to the minimum of intensity ; 

 and, accordingly, the pitch of the va- 

 rying tone rises continuously, passing 

 through every gradation which sepa- 

 rates its gravest value, at the maxi- 

 mum of intensity, from its acutest 

 value, at the minimum of intensity. 

 After the latter moment the same in- 

 terval is again traversed in the same 

 manner, but in the opposite direction, 

 the pitch falling continuously, until, 

 at the next maximum of intensity, it 

 once more reaches its lower limit. 

 Thus in every beat there is a regular 

 oscillation of pitch, as well as of inten- 

 sity, each taking place between fixed 

 limits. When, as in the case repre- 

 sented by the figure, the more acute 

 primary is the louder of the two, the 

 variable tone sinks in pitch as its power 

 strengthens, and rises in pitch as its 

 power weakens. AVhen the lower pri- 

 mary is the louder the reverse is the 

 case, as can be shown by a suitable 

 figure. The effects of these two kinds 

 of beats may be indicated in musical 

 notation thus, 



59 



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