Koenig has also found out the laws of the resultant sounds produced by other intervals than the octave, and has extended his researches 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.
Koenig also made a very ingenious modification of the siren for the purpose of enabling Seebeck to sound simultaneously notes whose vibrations had any given ratio. It is furnished for this purpose with eight disks, each of which contains a given number of circles of holes arranged at different angular distances. A description of this instrument, which is also the property of the Stevens Institute, and of Seebeck's experiments is thus given in a letter by Koenig himself.

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