String resonance

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 overtone of A and 4th overtone of E).

Electric guitars can have string trees near the tuning pegs to mute this type of reverberation. The string length behind the bridge also must be as short as possible to prevent the resonance. String resonance is a factor in the timbre of a string instrument. Tailed bridge guitars like the Fender Jaguar differ in timbre from guitars with short bridges, because of their (extended) floating bridge. The Japanese Koto is also an example of an instrument with occurring string resonance.

String resonance in instrument building[edit]

Sometimes string resonance is used in the construction of the instrument, like for instance the Sympathetic strings in many Eastern instruments.

Piano[edit]

According to a 2007 Grove Music Online article on "duplex scaling", Steinway developed a system of Aliquot stringing to provide sympathetic resonance, with the intention of enriching the treble register of the piano. In the "octave duplex" piano by Hoerr of Toronto, each note had four strings, of which two, three or four could be struck by the hammer depending on the depression of any of four pedals. Steinway’s duplex scale was inspired 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.

Overtones due to string resonance on the koto[edit]

The following table^[1] ^[2] shows the created resonating overtones on the koto for various positions on a stopped string (the proportion being between the "played" portion of the string and resonant portion, the remaining length of the string).

Resonating string length/Played string	resonating harmonic	cents	reduced cents
1/1	P0	0.0	0.0
8/9	Just major tone	203.9	203.9
7/8	Septimal major second	231.2	231.2
6/7	Septimal minor third	266.9	266.9
5/6	Just minor third	315.6	315.6
4/5	Just major third	386.3	386.3
3/4	perfect fourth	498.0	498.0
2/3	P5	702.0	702.0
3/5	Just major sixth	884.4	884.4
1/2	P8	1200.0	0.0
2/5	P8 + just M3	1586.3	386.3
1/3	P8 + P5	1902.0	702.0
1/4	2P8	2400.0	0.0
1/5	2P8 + just M3	2786.3	386.3
1/6	2P8 + P5	3102.0	702.0
1/7	2P8 + septimal m7	3368.8	968.8
1/8	3P8	3600.0	0.0
1/9	3P8 + pyth M2	3803.9	203.9
1/10	3P8 + just M3	3986.3	386.3
1/11	3P8 + just M3 + GUN2	4151.3	551.3
1/12	3P8 + P5	4302.0	702.0
1/13	3P8 + P5 + T23T	4440.5	840.5
1/14	3P8 + P5 + septimal m3	4568.8	968.8
1/15	3P8 + P5 + just M3	4688.3	1088.3
1/16	4P8	4800.0	0.0

v t e Acoustics
Engineering	Architectural acoustics Monochord Reverberation Soundproofing String vibration string resonance	Spectrogram
Psychoacoustics	Bark scale Combination tone Equal-loudness contour Fletcher–Munson curves Mel scale Missing fundamental
Frequency and pitch	Beat Formant Fundamental frequency Frequency spectrum harmonic spectrum Harmonic series inharmonicity Mersenne's laws Overtone Resonance Standing wave Node Subharmonic
Acousticians	John Backus Jens Blauert Ernst Chladni Hermann von Helmholtz Franz Melde Marin Mersenne Werner Meyer-Eppler Lord Rayleigh Joseph Sauveur D. Van Holliday Thomas Young
Related topics	Echo Infrasound Sound Ultrasound Musical acoustics piano violin
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