HARMONY IN MUSIC. 87 



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 perpetually 

 destroy each other. Biit if the two tones have only approxi 

 matively 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 advanc- 

 ing elevations of the one will have again reached the elevations 

 of the other. These alternations become sensible by that alter- 

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

 These beats may pften be heard when two instruments which 

 are not exactly in unison 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 tremor 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 of the tone. If the 

 beats are more rapid the tone grates on the ear, or, if it is high, 

 becomes cutting. A grating tone is one interrupted by rapid 

 breaks, like that of the letter R, which is produced by inter- 

 rupting the tone of the voice by a tremor of the tongue or 

 uvula. 1 



1 The trill of the uvula is called the Northumbrian burr, and is not 



