406 DISCORD. 



by plucking in the middle the even-numbered overtones are ex- 

 cluded. It is owing to the overtones that the sound is never quite 

 silenced between two successive beats, for their numbers of vibrations 

 are multiples by 2, 3, 4, &c., of those of the fundamental note ; they 

 produce, therefore, 2, 3, 4, &c. times as many beats. The overtone 

 which is usually most perceptible the octave of the fundamental note 

 gives two beats for every one of the latter ; hence every alternate 

 beat of the octave coincides with a rest of the fundamental note. A 

 delicate ear is capable of perceiving the octave during the rests of 

 the fundamental note, if the beats are slow and the strings are 

 plucked near the ends. In any case, however, there is never com- 

 plete silence during the rest of any sound which contains overtones 

 of appreciable intensity. The plucking of the strings in the middle 

 excludes all the even-numbered overtones, as well as the octave, 

 which has a comparatively loud sound ; hence the rests are rendered 

 more distinct. They become still more perfect if, instead of strings, 

 tuning-forks are used, for the sounds of these are free from overtones. 

 Two common tuning- forks (a'), as usually purchased, produce almost 

 always fine long beats, because it is very rare that such tuning-forks 

 are precisely equal. They should be sounded by striking them as 

 nearly as possible with equal force, and placing them side by side 

 upon the table or on a sounding-box. If the two tuning-forks should 

 happen to be precisely alike, their notes may be rendered slightly 

 different by placing small india-rubber rings, cut by the scissors 

 from a tube which is about l mm thick in the sides, upon one of the 

 prongs. 



Beats which are so slow that they may be counted are 

 not unpleasant to the ear ; but if they succeed so rapidly 

 that twenty or more take place in one second, the sound 

 is rendered harsh and grating. Such rapid beats are the 

 cause of the ' discord ' (dissonance), which is produced by 

 combinations of certain notes. Two notes which differ 

 by a semitone, for example V and c n ', produce together 

 a very unpleasant sound; V makes 495, d' makes 528 

 vibrations in one second; hence they produce 528 495- 

 = 33 beats. If B and C be sounded together upon the 

 piano, or better still upon a harmonium, nearly four 

 beats per second may be counted distinctly (the numbers 



