400 POPULAR LECTURES AND ADDRESSES. 



example, consider a harmony of two tones. They 

 may be so related in phase that at one of the 

 instants of maximum pressure of one of the con- 

 stituents there is also maximum pressure of the 

 other constituent. The same phase-relation, if the 

 harmonic numbers of the constituent tones be both 

 odd, will give also coincident minimums. But 

 when one of the harmonic numbers is even and 

 the other odd the phase-relation of coincident 

 maximums will also be such that there is a 

 coincidence of minimum pressure due to one tone 

 with maximum pressure clue to the other ; and 

 again there will be an opposite phase in which 

 there will be coincidence of minimums, and in this 

 opposite phase there will also be a coincidence of 

 maximum and minimum. (To avoid circumlo- 

 cutions a harmony of two odd numbers will be 

 called an odd binary harmony ; a harmony of even 

 and odd numbers will be called an even binary 

 harmony.) Thus we sec that in an odd binary 

 harmony there is a phase-relation of coincident 

 maximums and coincident minimums, and again 

 an opposite phase-relation of coincident maximum 



