Sympathetic resonance or sympathetic vibration is a

harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...

phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similarly-tuned

tuning forks A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...

. 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 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 A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', ...

, integer multiples of the inducing frequency), as there is the greatest similarity in vibrational frequency. Sympathetic resonance is an example of

injection locking Injection locking and injection pulling are the frequency effects that can occur when a harmonic oscillator is disturbed by a second oscillator operating at a nearby frequency. When the coupling is strong enough and the frequencies near enough, th ...

occurring between

coupled oscillator Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

s, 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 ''The New Grove Dictionary of Music and Musicians'' is an encyclopedic dictionary of music and musicians. Along with the German-language '' Die Musik in Geschichte und Gegenwart'', it is one of the largest reference works on the history and t ...

'': This is the online edition of ''

'', Second Edition, with newer revisions.

Sympathetic resonance in music instruments

Sympathetic resonance has been applied to musical instruments from many cultures and time periods, and to

string instrument String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner. Musicians play some string instruments by plucking the s ...

s in particular. In instruments with undamped strings (e.g.

harp The harp is a stringed musical instrument that has a number of individual strings running at an angle to its soundboard; the strings are plucked with the fingers. Harps can be made and played in various ways, standing or sitting, and in orc ...

guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected string ...

s and kotos), strings will resonate at their fundamental or

overtone An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...

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 In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...

of a string instrument. Tailed bridge guitars like the

Fender Jaguar The Fender Jaguar is an electric guitar by Fender Musical Instruments characterized by an offset-waist body, a relatively unusual switching system with two separate circuits for lead and rhythm, and a short-scale 24" neck. Owing some roots to ...

differ in timbre from guitars with short bridges, due to the resonance that occurs in their extended floating bridge. Certain instruments are built with

sympathetic string Sympathetic strings or resonance strings are auxiliary strings found on many Indian musical instruments, as well as some Western Baroque instruments and a variety of folk instruments. They are typically not played directly by the performer (excep ...

s, 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 The sitar ( or ; ) is a plucked stringed instrument, originating from the Indian subcontinent, used in Hindustani classical music. The instrument was invented in medieval India, flourished in the 18th century, and arrived at its present form ...

, Western Baroque instruments such as the

viola d'amore The viola d'amore (; Italian for " viol of love") is a 7- or 6- stringed musical instrument with sympathetic strings used chiefly in the baroque period. It is played under the chin in the same manner as the violin. Structure and sound The ...

and folk instruments such as the

hurdy-gurdy The hurdy-gurdy is a string instrument that produces sound by a hand-crank-turned, rosined wheel rubbing against the strings. The wheel functions much like a violin bow, and single notes played on the instrument sound similar to those of a vi ...

. Some

pianos The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

are built with sympathetic strings, a practice known as

aliquot stringing Aliquot stringing is the use of extra, un-struck strings in the piano for the purpose of enriching the tone. Aliquot systems use an additional (hence fourth) string in each note of the top three piano octaves. This string is positioned slightly abo ...

. 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 guitar An electric guitar is a guitar that requires external amplification in order to be heard at typical performance volumes, unlike a standard acoustic guitar (however combinations of the two - a semi-acoustic guitar and an electric acoustic gu ...

s use string trees near their tuning pegs. Similarly, the string length behind the

bridge A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually someth ...

must be made as short as possible to dampen resonance.

References

{{Acoustics Acoustics Resonance