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of the beats, as the interval between the forks increases from unison to a semitone, can doubt that the discord here arises from these beats.
Now, gradually increase the interval between the forks still more; the rapidity of the beats of course increases, but the resultant sound becomes less and less harsh ; till finally, when the beats number about 78 per second, all the harshness vanishes. At this point, the interval between the forks is rather less than a minor third. The interval at which the dissonance thus disappears, has been termed the Beating Distance.
The fact just alluded to,—that all Discord or Dissonance between musical tones arises from beats,—is one of Helmholtz's most important discoveries. In order to thoroughly convince himself of its truth, the student must proceed step by step. In the first place, as we have seen, beats are reinforcements and diminutions of intensity, which are due to the interference of two separate sound waves. Now this being the case, if such reinforcements and diminutions can be made to occur in the case of a single sound, then, not only should beats be heard, but the harsh jarring we call discord, which is supposed to be due to beats, should be heard also.
This was put to the test of experiment by Helmholtz, in the following way. A little reed pipe was substituted for the wind conduit of the upper box of his Syren (see page 33), and wind driven through this reed pipe. The tone of this pipe could be heard externally, only when the revolution of the disc brought its holes before the holes of the box, and so opened an exit for the air. Hence, allowing the disc to revolve, while air was being driven through the pipe, an intermittent sound was obtained, which sounded exactly like the beats arising from two tones sounded at once.
By means of a perforated disc and multiplying wheel, similar to that shown in fig. 19, the same thing may be still more easily demonstrated. One circle of holes on the disc is sufficient, but they should be larger than shown in the figure. One end of the india-rubber tube is held opposite to the circle of holes, just as in the figure, but the other end is to be applied to the ear. On the other side of the disc and opposite to the end of the india-rubber tube, a vibrating tuning-fork is held, the necessary intermittence of tone being brought about by the revolution of the disc.
In either of the above ways, intermittent tones may be obtained, and this intermission gives them all exactly the same kind of roughness, that is produced by two tones which beat rapidly