732 SPECIAL SENSES 



The sounds produced by two tuning-forks giving precisely the same 

 number of vibrations in a second are in unison. If one of the forks is 

 loaded with a bit of wax, so that its vibrations are slightly reduced, and 

 if both are put in vibration at the same instant, there is discord. Taking 

 the illustration given by Tyndall, it may be assumed that one fork has 

 256, and the other, 255 vibrations in a second. While these two forks 

 are vibrating, one is gradually gaining on the other ; but at the end of 

 half a second, one will have made 128 vibrations, while the other will 

 have made 127^. At this point the two waves are moving in exactly 

 opposite directions ; and as a consequence, the sounds neutralize each 

 other and there is an instant of silence. The perfect sounds, as the 

 two forks continue to vibrate, are thus alternately reenforced and dimin- 

 ished, and this produces what is known in music as beats. As the 

 difference in the number of vibrations in a second is one, the instants 

 of silence occur 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 perfectly ; and discord or 

 dissonance is marked by successive beats, or pulses. If the forks are 

 loaded so that one will vibrate 240 times in a second, and the other 234, 

 there will be six instants in a second when the interference will be mani- 

 fest ; or in other words in ^ of a second, one fork will make 40 vibra- 

 tions, while the other is making 39. This will give 6 beats in a second. 

 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. An analogous interference of 

 undulations is observed in optics, when waves of light are made to 

 interfere and produce darkness. 



It is evident that the number of beats will increase as two discord- 

 ant notes are produced higher and higher in the scale. According to 

 Helmholtz, beats can be recognized up to 132 in a second. Beyond 

 that point they become confused and there is only a general sensation 

 of discord. Beats, then, are due to interference of sound-waves. There 

 is no interference of the waves of notes in unison, provided waves start 

 at the same instant ; the intensity of the sound being increased by 

 reenforcement. The differences between the ist and 8th, the ist and 

 5th, the ist and 3d, and other harmonious combinations, is so great that 

 there are no beats and no discord, the more rapid waves reenforcing 

 the harmonics of the primary sound. It is important to remember, in 

 this connection that resultant tones are equal to the difference in the 

 rates of vibration of two harmonious notes. Taking a note of 240 

 vibrations, and its 5th, with 360 vibrations, these two have a difference 

 of 120, which is the lower octave of the ist and is an harmonious tone. 



