4i2 POPULAR LECTURES AND ADDRESSES. 



5:6, 6:7, 7:8, 1:3, and 3 : 5. The two last 

 mentioned, though sometimes less easily heard 

 than the beats on most of the others, are unmis- 

 takably distinct ; and by counting the numbers of 

 them in ten seconds or in twenty seconds, I have 

 ascertained that they, as do all the others, fulfil 

 the condition of having the whole period of the 

 imperfection, and not any sub-multiple of it, for 

 their period of audible beat. They are interesting 

 as being cases of odd binary harmonies. Before 

 making the experiments, I thought it possible that 

 what is heard in the beat might not make 

 distinction between the configurations II. and IV. 

 (first quarter phase and third quarter phase) : but 

 a revolving cJiaracter which I perceive in the beat 

 is to me certainly distinct enough to prove that 

 the ear docs distinguish between these configura- 

 tions, which are one of them the same as the other 

 taken in the reverse order of time. 



In every instance except the octave, the beat on 

 the approximation to a binary harmony is less 

 distinct than the beat <>n an approximation t<> .1 

 ternary or higher multiple harmony with only one 



