ON BEATS OF IMPERFECT HARMONIES. 399 



period of its constituent tones. The number of 

 times that the period of the harmony contains the 

 period of any one of its constituent tones I call 

 the harmonic number of that tone. This ex- 

 pression is only applicable to any particular tone 

 when viewed as one constituent of a harmony. 

 Following the usage of Lord Rayleigh and Pro- 

 fessor Everett, I shall employ the word " fre- 

 quency " to denote the number of periods per unit 

 of time, per second let us say generally in 

 acoustical reckonings. Thus the " frequency " of 

 a tone or of a harmony means the number of its 

 periods per second. Similarly the frequency of any 

 set of beats, according to the definitions and 

 descriptions below, will mean the number of the 

 beats per second, and in this application of the 

 term it will designate sometimes a proper fraction, 

 and sometimes a small whole number plus 

 a proper fraction. 



The quality of a harmony, when the periods of 

 its several constituent tones are given, depends 

 upon the amplitudes of the different constituents, 

 and on the relation of their phases. Thus, for 



