HARMONY IN MUSIC. 99 



we obtain the fundamental tone of the corresponding 

 tone of the siren very full and strong. But on arranging 

 the boxes so that the upper puffs escape when the lower 

 series of holes is covered, and conversely, the fundamental 

 tone vanishes, and we only hear a faint sound of the first 

 upper partial, which is an octave higher, and which is not 

 destroyed by interference under these circumstances. 



Interference leads us to the so-called musical beats, 

 If two tones of exactly the same pitch are produced 

 simultaneously, and their elevations coincide at first, they 

 will never cease to coincide, and if they did not coincide 

 at first they never will coincide. 



The two tones will either perpetually reinforce, or per- 

 petually destroy each other. But if the two tones have only 

 approximatively equal pitches, and their elevations at 

 first coincide, so that they mutually reinforce each other, 

 the elevations of one will gradually outstrip the elevations 

 of the other. Times will come when the elevations of the 

 one fall upon the depressions of the other, and then other 

 times when the more rapidly advancing elevations of the 

 one will have again reached the elevations of the other. 

 These alternations become oensible by that alternate 

 increase and decrease of loudness, which we call a beat. 

 These beats may often be heard when two instruments 

 which are not exactly in uuison play a note of the same 

 name. When the two or three strings which are struck 

 by the same hammer on a piano are out of tune, the beats 

 may be distinctly heard. Very slow and regular beats 

 often produce a fine effect in sostenuto passages, as in 

 sacred part-songs, by pealing through the lofty aisles like 

 majestic waves, or by a gentle tremour giving the tone a 

 character of enthusiasm and emotion. The greater the 

 difference of the pitches, the quicker the beats. As long 

 as no more than four to six beats occur in a second, 

 the ear readily distinguishes the alternate reinforcements 



