String Resonance in Music Instruments
String resonance occurs on string instruments. Strings or parts of strings may resonate at their fundamental or overtone frequencies when other strings are sounded. For example, an A string at 440 Hz will cause an E string at 330 Hz to resonate, because they share an overtone of 1320 Hz (3rd harmonic of A and 4th harmonic of E).
According to Grove Music Online (2007) article on Duplex Scaling, Steinway progressed a system of aliquot scaling to provide sympathetic resonance with the intention of enriching the treble register of the pianoforte. In the 'octave duplex' piano by Hoerr of Toronto, each note had four strings, of which two, three or four could potentially be struck by the hammer depending on the depression of one of four pedals. Steinway’s duplex scale was precipitated a half century earlier by an experiment conducted by the German piano maker Wilhelm Leberecht Petzoldt, in which a small bridge was placed behind the standard larger one with the intention of maximizing the potential additional resonance of a sympathetically vibrating additional length of string.
Read more about this topic: Sympathetic Resonance
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