DISCOKUS. 191 



as the two forks continue to vibrate, are thus alternately re- 

 enforced and diminished, and we have what are known in 

 music as beats. As the difference in the number of vibra- 

 tions in a second is one, we have the instants of silence occur- 

 ring once in a second ; and, in this illustration, the beats 

 occur once a second. Unison takes place when two sounds 

 can follow each other indefinitely, their waves blending per- 

 fectly ; dissonance is marked by successive beats, or pulses. 

 If we now load forks so that one will vibrate 240 times in a 

 second, and the other 234, there will be six times in a second 

 when the interference will be manifest ; or, to make it plain- 

 er, in of a second, one fork will make 40 vibrations, while 

 the other is making 39. "We shall then have 6 beats in a sec- 

 ond. From these experiments, the law may be deduced, that 

 the number of beats produced by two tones not in harmony 

 is equal to the difference between the two rates of vibration. 1 

 An analogous interference of undulations is observed in 

 optics, when waves of light are made to interfere and pro- 

 duce darkness. 



It is evident that the number of beats will increase as we 

 sound two discordant tones higher and higher in the scale. 

 According to Helmholtz, the beats can be recognized up to 

 132 in a second. Beyond that point, they become confused, 

 and we have only a sensation of dissonance, or roughness. 3 

 "We can illustrate this point very satisfactorily by a simple 

 experiment upon the piano. Let us take two tones, the high- 

 est on the scale, separated from each other by a semitone. 

 When we strike these two notes together, we have a disa- 

 greeable sensation of dissonance, but no appreciable beats, 

 because, the rate of vibration of each note being high, the 

 difference is great and the beats are too rapid to be appre- 

 ciated as such. We strike, now, the two notes an octave be- 



rushing of the air." (HELMHOLTZ, Theorie pkysiologique de la musique, Paris, 

 1868, p. 201.) 



1 TYNDALL, Sound, London, 1867, p. 263. 



3 HELMHOLTZ, op. cit., p. 217. 

 143 



