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Scientific American Supplement, No. 401, September 8, 1883 by Various
page 68 of 136 (50%)
4024 : " 503:512 36 Re_{-1}
7936 : 8192 31:32 128 Ut_{2}
8064 : " 63:64 64 Ut_{1}
8096 : " 253:256 48 Sol_{-1}
8106.7 : " 95:96 42.7 Fa_{-1}
8112 : " 507:512 40 Mi_{-1}
8120 : " 1015:1024 36 Re_{-4}
8128 : " 127:128 32 Ut_{-4}

On sounding two forks nearly in unison, the sound heard corresponds to
a number of vibrations equal to the difference of the numbers of
vibrations of the forks.

On sounding two forks, one of which is nearly the octave of the other,
the ear perceives a sound, which is that given by vibrations whose
number equals the difference in the number of vibrations of the higher
fork and the upper octave of the lower fork.

Koenig has also found out the laws of the resultant sounds produced
by other intervals than the octave, and has extended his researces to
intervals differing by any number of vibrations, as may be seen from the
above table.

His conclusion is that beats and resultant sounds are one and the same
phenomenon.

Thus, for example, the lowest number of vibrations capable of producing
a musical sound is 32 per second; in like manner, a clear musical sound
is produced by two simple notes of sufficient intensity which produce 32
beats per second.
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