# Sympathetic resonance

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Harmonic phenomenon in music

For the album by John Arch and Jim Matheos, see [Sympathetic Resonance (album)](/source/Sympathetic_Resonance_(album)).

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**Sympathetic resonance** or **sympathetic vibration** is a [harmonic](/source/Harmonic) phenomenon wherein a passive string or vibratory body [responds to external vibrations](/source/Resonance) to which it has a harmonic likeness.[1] The classic example is demonstrated with two similarly-tuned [tuning forks](/source/Tuning_forks). When one fork is struck and held near the other, vibrations are induced in the unstruck fork, even though there is no physical contact between them. In similar fashion, [strings](/source/String_(structure)) will respond to the vibrations of a tuning fork when sufficient harmonic relations exist between them. The effect is most noticeable when the two bodies are tuned in unison or an octave apart (corresponding to the first and second [harmonics](/source/Harmonic_series_(music)), integer multiples of the inducing frequency), as there is the greatest similarity in vibrational frequency. Sympathetic resonance is an example of [injection locking](/source/Injection_locking) occurring between [coupled oscillators](/source/Coupled_oscillator), in this case coupled through vibrating air. In musical instruments, sympathetic resonance can produce both desirable and undesirable effects.

According to *[The New Grove Dictionary of Music and Musicians](/source/The_New_Grove_Dictionary_of_Music_and_Musicians)*:[2]

The property of sympathetic vibration is encountered in its direct form in room acoustics in the rattling of window panes, light shades and movable panels in the presence of very loud sounds, such as may occasionally be produced by a full organ. As these things rattle (or even if they do not audibly rattle) sound energy is being converted into mechanical energy, and so the sound is absorbed. Wood paneling and anything else that is lightweight and relatively unrestrained have the same effect. Absorptivity is at its highest at the resonance frequency, usually near or below 100 Hz.

## Sympathetic resonance in music instruments

Sympathetic resonance has been applied to musical instruments from many cultures and time periods, and to [string instruments](/source/String_instrument) in particular. In instruments with undamped strings (e.g. [harps](/source/Harp), [guitars](/source/Guitar) and [kotos](/source/Koto_(musical_instrument))), strings will resonate at their [fundamental](/source/Fundamental_frequency) or [overtone](/source/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](/source/Timbre) of a string instrument.

Certain instruments are built with [sympathetic strings](/source/Sympathetic_string), 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](/source/Sitar), Western Baroque instruments such as the [viola d'amore](/source/Viola_d'amore) and folk instruments such as the [hurdy-gurdy](/source/Hurdy-gurdy) and [Hardanger fiddle](/source/Hardanger_fiddle). Some [pianos](/source/Pianos) are built with sympathetic strings, a practice known as [aliquot stringing](/source/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](/source/Electric_guitar) use [string trees](/source/String_tree_(instrument)) near their tuning pegs. Similarly, the string length behind the [bridge](/source/Bridge_(instrument)) must be made as short as possible to dampen resonance.

### Piano Sustain

When the [sustain pedal](/source/Sustain_pedal) [3] 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). [4] 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](https://en.wiktionary.org/wiki/arbitrary) 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 × {\displaystyle \times } ~5 = ~ 50 notes to become audible to the player, rather than just the 10 directly played notes.[5]

## References

1. **[^](#cite_ref-1)** von Helmholtz, Hermann (1885). *On the sensations of tone as a physiological basis for the theory of music*. [Longman](/source/Longman). p. 36.

1. **[^](#cite_ref-Lewcock_2006_2-0)** Lewcock, Ronald; et al. (2006). Sadie, Stanley; Tyrrell, John (eds.). ["Acoustics"](http://www.oxfordmusiconline.com/subscriber/article/grove/music/00134pg1). *Grove Music Online*. [Oxford University Press](/source/Oxford_University_Press). "Resonance, reverberation and absorption" section. Retrieved 17 August 2016 – via OxfordMusicOnline.com. This is the online edition of *[The New Grove Dictionary of Music and Musicians](/source/The_New_Grove_Dictionary_of_Music_and_Musicians)*, Second Edition, with newer revisions.

1. **[^](#cite_ref-3)** AKA Damper pedal, but not to be confused with the Sostenuto pedal nor Soft pedal

1. **[^](#cite_ref-4)** The effect is most noticeable with a piano that is properly tuned and has a large number of keys (rather than fewer keys). Proper tuning of the piano's strings allows the predicted frequencies of the harmonics to match the frequencies of the actual physical strings. Having more keys means there are more strings that can potentially match the played-notes harmonic frequencies.

1. **[^](#cite_ref-5)** "Up to" since some notes will have overlapping (i.e., equivalent) harmonic frequencies

v t e Acoustics Acoustical engineering Architectural acoustics Monochord Reverberation Soundproofing String vibration Sympathetic resonance Spectrogram Psychoacoustics Pitch Bark scale Mel scale Equal-loudness contour Fletcher–Munson curves Audio frequency and pitch Beat Formant Fundamental frequency Frequency spectrum harmonic spectrum Harmonic Series Inharmonicity Missing fundamental Combination tone Mersenne's laws Overtone Resonance Standing wave Node Subharmonic Acousticians John Backus Jens Blauert Ernst Chladni Hermann von Helmholtz Carleen Hutchins 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 Category

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