Sympathetic resonance has been applied to musical instruments from many cultures and time periods, and to
string instruments in particular. In instruments with undamped strings (e.g.
harps,
guitars and
kotos), strings will resonate at their
fundamental or
overtone frequencies when other nearby 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 (the third harmonic of A and fourth harmonic of E). Sympathetic resonance is a factor in the
timbre of a string instrument. Certain instruments are built with
sympathetic strings, auxiliary strings which are not directly played but sympathetically produce sound in response to tones played on the main strings. Sympathetic strings can be found on Indian musical instruments such as the
sitar, Western Baroque instruments such as the
viola d'amore and folk instruments such as the
hurdy-gurdy and
Hardanger fiddle. Some
pianos are built with sympathetic strings, a practice known as
aliquot stringing. Sympathetic resonance is sometimes an unwanted effect that must be mitigated when designing an instrument. For example, to dampen resonance in the headstock, some
electric guitars use
string trees near their tuning pegs. Similarly, the string length behind the
bridge must be made as short as possible to dampen resonance.
Piano Sustain When the
sustain pedal is pressed on a piano, sympathetic resonance occurs, becoming more noticeable as more notes (nearby in frequency values) are played while the pedal is held active (pressed down). This resonance causes a "muddying" of sound when the sustain pedal is held too long, blurring the sound from crisp audible note endings to a sort of inseparable watercolor of mixed sound. For example, pressing one key on a piano with the sustain pedal pressed causes multiple harmonic notes to gradually and spontaneously "appear" to the listener, though the harmonics are often far quieter than the original note's strength.
Arbitrarily assuming that playing a single note on a piano will cause 4 more harmonics to play, continuing to press 9 more keys (with the sustain pedal held down throughout the duration of playing) would cause up to 10 \times ~5 = ~ 50 notes to become audible to the player, rather than just the 10 directly played notes. ==References==