View source for String harmonic

{{Short description|String instrument technique}}
{{More citations needed|date=August 2016}}
[[Image:Flageolette.svg|thumb|280px|Playing a harmonic on a string. Here, "+7" indicates that the string is held down at the position for raising the pitch by 7 semitones.]]

Playing a '''string harmonic''' (a '''flageolet''') is a [[string instrument]] [[musical technique|technique]] that uses the [[node (physics)|nodes]] of natural [[harmonic]]s of a musical [[string (music)|string]] to isolate [[overtone]]s. Playing string harmonics produces high pitched tones, often compared in timbre to a whistle or flute.<ref>[[Roger Kamien|Kamien, Roger]] (2008). ''Music: An Appreciation'', p.13. Sixth "brief" edition. McGraw Hill. {{ISBN|978-0-07-340134-8}}.</ref><ref name="Claude V 1996 p.601">[[Claude V. Palisca|Palisca, Claude V.]]; ed. (1996). ''Norton Anthology of Western Music, Volume 1: Ancient to Baroque'', glossary, p.601. Third edition. W. W. Norton. {{ISBN|0-393-96906-1}}.</ref> Overtones can be isolated "by lightly touching the string with the finger instead of pressing it down" against the [[fingerboard]] (without [[fingering (music)|stopping]]).<ref name="Claude V 1996 p.601"/> For some instruments this is a fundamental technique, such as the Chinese [[guqin]], where it is known as ''fan yin'' ([[wiktionary:泛音|泛音]], lit. "floating sound"), and the Vietnamese [[đàn bầu]].

==Overtones==
{{main|Harmonic}}
When a [[Strings (music)|string]] is plucked or bowed normally, the ear hears the [[fundamental frequency]] most prominently, but the overall sound is also colored by the presence of various [[overtone]]s (frequencies greater than the fundamental frequency). The fundamental frequency and its overtones are perceived by the listener as a single note; however, different combinations of overtones give rise to noticeably different overall tones (see [[timbre]]).<ref>{{Cite web|title = The Physics of Everyday Stuff - The Guitar|url = http://www.bsharp.org/physics/guitar|website = www.bsharp.org|access-date = 2015-08-03|archive-date = 2010-12-09|archive-url = https://web.archive.org/web/20101209191707/http://www.bsharp.org/physics/guitar|url-status = dead}}</ref> A harmonic overtone has evenly spaced nodes along the string, where the string does not move from its resting position.

{{clear}}

==Nodes==
{{Unsourced section|date=November 2024}}[[Image:Table of Harmonics.svg|thumb|700px|Table of harmonics, indicating in colors on which positions the same overtones occur|alt=|none]]

The nodes of natural harmonics are located at the following points along the string:

<!-- Deleted image removed: [[Image:Guitar harmonic nodes.svg|600px|Harmonic mode shapes and their corresponding node locations on a guitar]] -->{| class="wikitable"
!Harmonic
![[Stop note]]
!Sounded note relative to open string
! width="50" |[[Cent (music)|Cents]] above open string
! width="50" |Cents reduced to one octave
!Length fraction
!Audio
|-
|2
|octave
|[[octave]] (P8)
| style="text-align:right;" |1,200.0
| style="text-align:right;" |0.0
|{{1/2}}
|{{audio|Perfect octave on C.mid|Play}}
|-
|3
|just perfect fifth
|P8 + just [[perfect fifth]] (P5)
| style="text-align:right;" |1,902.0
| style="text-align:right;" |702.0
|{{1/3}}, {{2/3}}
|{{audio|Just perfect fifth on C.mid|Play}}
|-
|4
|just [[perfect fourth]]
|2P8
| style="text-align:right;" |2,400.0
| style="text-align:right;" |0.0
|{{1/4}}, {{3/4}}
|{{audio|Perfect fifteenth on C.mid|Play}}
|-
|5
|just major third
|2P8 + [[just major third]] (M3)
| style="text-align:right;" |2,786.3
| style="text-align:right;" |386.3
|{{frac|1|5}} to {{frac|4|5}}
|{{audio|Just major third on C.mid|Play}}
|-
|6
|just [[minor third]]
|2P8 + P5
| style="text-align:right;" |3,102.0
| style="text-align:right;" |702.0
|{{frac|1|6}}, {{frac|5|6}}
|
|-
|7
|septimal minor third
|2P8 + [[Harmonic seventh|septimal minor seventh]] (m7)
| style="text-align:right;" |3,368.8
| style="text-align:right;" |968.8
|{{frac|1|7}} to {{frac|6|7}}
|{{audio|Harmonic seventh on C.mid|Play}}
|-
|8
|[[septimal major second]]
|3P8
| style="text-align:right;" |3,600.0
| style="text-align:right;" |0.0
|{{frac|1|8}}, {{frac|3|8}}, {{frac|5|8}}, {{frac|7|8}}
|
|-
|9
|Pythagorean major second
|3P8 + [[Pythagorean interval|Pythagorean major second]] (M2)
| style="text-align:right;" |3,803.9
| style="text-align:right;" |203.9
|{{frac|1|9}}, {{frac|2|9}}, {{frac|4|9}}, {{frac|5|9}}, {{frac|7|9}}, {{frac|8|9}}
|{{audio|Major tone on C.mid|Play}}
|-
|10
|just minor [[whole tone]]
|3P8 + just M3
| style="text-align:right;" |3,986.3
| style="text-align:right;" |386.3
|{{frac|1|10}}, {{frac|3|10}}, {{frac|7|10}}, {{frac|9|10}}
|
|-
|11
|greater undecimal [[neutral second]]
|3P8 + lesser undecimal [[tritone]]
| style="text-align:right;" |4,151.3
| style="text-align:right;" |551.3
|{{frac|1|11}} to {{frac|10|11}}
|{{audio|Eleventh harmonic on C.mid|Play}}
|-
|12
|lesser undecimal neutral second
|3P8 + P5
| style="text-align:right;" |4,302.0
| style="text-align:right;" |702.0
|{{frac|1|12}}, {{frac|5|12}}, {{frac|7|12}}, {{frac|11|12}}
|
|-
|13
|tridecimal 2/3-tone
|3P8 + tridecimal [[neutral sixth]] (n6)
| style="text-align:right;" |4,440.5
| style="text-align:right;" |840.5
|{{frac|1|13}} to {{frac|12|13}}
|{{audio|Tridecimal neutral sixth on C.mid|Play}}
|-
|14
|2/3-tone
|3P8 + P5 + [[septimal minor third]] (m3)
| style="text-align:right;" |4,568.8
| style="text-align:right;" |968.8
|{{frac|1|14}}, {{frac|3|14}}, {{frac|5|14}}, {{frac|9|14}}, {{frac|11|14}}, {{frac|13|14}}
|
|-
|15
|septimal (or major) [[diatonic semitone]]
|3P8 + just [[major seventh]] (M7)
| style="text-align:right;" |4,688.3
| style="text-align:right;" |1,088.3
|{{frac|1|15}}, {{frac|2|15}}, {{frac|4|15}}, {{frac|7|15}}, {{frac|8|15}}, {{frac|11|15}}, {{frac|13|15}}, {{frac|14|15}}
|{{audio|Just major seventh on C.mid|Play}}
|-
|16
|just (or minor) diatonic semitone
|4P8
| style="text-align:right;" |4,800.0
| style="text-align:right;" |0.0
|{{frac|1|16}}, {{frac|3|16}}, {{frac|5|16}}, {{frac|7|16}}, {{frac|9|16}}, {{frac|11|16}}, {{frac|13|16}}, {{frac|15|16}}
|
|}
Above, the length fraction is the point, with respect to the length of the whole string, the string is lightly touched. It is expressed as a fraction {{math|{{sfrac|n|m}}}}, where ''m'' is the mode (2 through 16 are given above), and ''n'' the node number. The node number for a given mode can be any integer from 1 to {{nowrap|''m'' − 1}}. However, certain nodes of higher harmonics are coincident with nodes of lower harmonics, and the lower sounds overpower the higher ones. For example, mode number 4 can be fingered at nodes 1 and 3; it will occur at node 2 but will not be heard over the stronger first harmonic. Ineffective nodes to finger are not listed above.

The fret number, which shows the position of the node in terms of half tones (or frets on a fretted instrument) then is given by:
:<math>F = \log_s \frac{m}{m-n}</math>

With ''s'' equal to the [[twelfth root of two]], notated ''s'' because it's the first letter of the word "semitone".

== Artificial harmonics ==
[[File:Artificial_harmonic.png|thumb|Artificial harmonics on a G fundamental, as written (below) and as sounding (top). The round note (below) is pressed with one finger, and the square note is lightly touched with another one. {{audio|Artificial harmonic.mid|Play}}]]
[[File:Natural_versus_artificial_harmonic.png|thumb|256x256px|Natural versus artificial harmonic]]

When a string is only lightly pressed by one finger (that is, isolating overtones of the open string), the resulting harmonics are called '''natural harmonics'''.<ref name=":0">{{Cite web |last=MasterClass |date=Jun 7, 2021 |title=Learn How to Play Natural Harmonics on Guitar |url=https://www.masterclass.com/articles/learn-how-to-play-natural-harmonics-on-guitar |access-date=May 14, 2024 |website=[[MasterClass]]}}</ref> However, when a string is held down on the neck in addition to being lightly pressed on a node, the resulting harmonics are called '''artificial harmonics'''.<ref name=":0" /> In this case, as the total length of the string is shortened, the fundamental frequency is raised, and the positions of the nodes shift accordingly (that is, by the same number of frets), thereby raising the frequency of the overtone by the same interval as the fundamental frequency.

{{Blockquote|Artificial harmonics are produced by stopping the string with the first or second finger, and thus making an artificial '[[nut (string instrument)|nut]],' and then slightly pressing the node with the fourth finger. By this means harmonics in perfect intonation can be produced in all scales.|''[[Grove's Dictionary of Music and Musicians]]'' (1879)<ref>[[George Grove|Grove, George]] (1879). ''[https://books.google.com/books?id=EP8PAAAAYAAJ&dq=%22artificial+harmonic%22&pg=PA665 A Dictionary of Music and Musicians (A.D. 1450-1889)]'', Vol. 2, p.665. Macmillan. {{pre-ISBN}}.</ref>}}

Artificial harmonics are more difficult to play than natural harmonics, but they are not limited to the overtone series of the open strings, meaning they have much greater flexibility to play chromatic passages. Unlike natural harmonics, they can be played with [[vibrato]].<ref>Sevsay, Ertuğrul (2013). ''[https://books.google.com/books?id=yBwu2t_5ZVIC&dq=%22artificial+harmonic%22&pg=PT128 The Cambridge Guide to Orchestration]'', unpaginated. Cambridge. {{ISBN|9781107067486}}.</ref>

This technique, like natural harmonics, works by canceling out the fundamental tone and one or more partial tones by deadening their modes of vibration. It is traditionally notated using two or three simultaneous [[notehead]]s in one [[Staff (music)|staff]]: a normal notehead for the position of the firmly held finger, a square notehead for the position of the lightly pressed finger, and sometimes, a small notehead for the resulting pitch.<ref>Potter, Louis (1995). ''The Art of Cello Playing'', p.194. Alfred Music. {{ISBN|9781457400353}}.</ref>

The most commonly used artificial harmonic, due to its relatively easy and natural [[Fingering (music)|fingering]], is that in which, "the fourth finger lightly touches the nodal point a perfect fourth above the first finger. (Resulting harmonic sound: two octaves above the first finger or new fundamental.),"<ref name="Modern">Grimson, Samuel B. and [[Cecil Forsyth|Forsyth, Cecil]] (1920). ''[https://books.google.com/books?id=ltgrAAAAMAAJ&dq=%22artificial+harmonic%22&pg=PA81 Modern Violin-Playing]'', p.79-80. New York: H. W. Gray (Novello). {{pre-ISBN}}.</ref> followed by the artificial harmonic produced when, "the fourth finger lightly touches the nodal point a perfect fifth above the first finger (Resulting harmonic sound: a twelfth above the first finger or new fundamental.),"<ref name="Modern" /> and, "the third finger lightly touches the nodal point a major third above the first finger. (Resulting harmonic sound: two octaves and a major third above the first finger or new fundamental.)"<ref name="Modern" /><ref>Hurwitz (2006), p.87.</ref>

In some cases, especially in the electric guitar technique, it is common to refer to Pinch Harmonics as Artificial Harmonics (AH) and to refer to harmonics produced by other means as Natural Harmonics.{{citation needed|date=March 2024}}

==Guitar==
[[Image:Harmonic motion4.PNG|280px|right|thumb|The fundamental and the double- and triple-frequency overtones of a guitar string.]]

There are a few harmonic techniques unique to guitar.

===Pinch harmonics===
{{anchor|Pinch|Pinch harmonic}}<!--[[Pinch harmonic]] redirects directly here-->
[[File:Pinch harmonics.ogg|thumb|Pinch harmonics performed on an acoustic guitar]]
{{Listen|filename=Pinch harmonic1.ogg|title=Example of pinch harmonic|description=Pinch harmonic example on the 3rd fret of the G string}}

A pinch harmonic (also known as squelch picking, pick harmonic or squealy) is a guitar technique to achieve artificial harmonics in which the player's thumb or index finger on the picking hand slightly catches the string after it is picked,<ref>{{cite web |url=http://www.xtrememusician.com/info/guitar/techniques/1.html |title=Guitar Techniques: Pick Harmonic |website=XtremeMusician.com |access-date=December 19, 2017 |archive-url=https://web.archive.org/web/20160308213440if_/http://www.xtrememusician.com/info/guitar/techniques/1.html |archive-date=March 8, 2016 |url-status=usurped}}</ref> canceling (silencing) the fundamental frequency of the string, and letting one of the [[overtone]]s dominate. This results in a high-pitched sound which is particularly discernible on an electrically amplified guitar as a "squeal".

===Tapped harmonics===
{{anchor|Tap|Tap harmonic|Tap guitar harmonic}}<!--[[Tap harmonic]] redirects directly here.-->
{{Unreferenced section|auto=yes|date=December 2009}}

Tapped harmonics were popularized by [[Eddie Van Halen]]. This technique is an extension of the [[tapping]] technique. The note is fretted as usual, but instead of striking the string the excitation energy required to sound the note is achieved by tapping at a harmonic nodal point. The tapping finger bounces lightly on and off the fret. The open string technique can be extended to artificial harmonics. For instance, for an [[octave]] harmonic (12-fret nodal point) press at the third fret, and tap the fifteenth fret, as {{nowrap|12 + 3 {{=}} 15}}.

===String harmonics driven by a magnetic field===
{{Unreferenced section|auto=yes|date=December 2009}}This technique is used by effect devices producing a magnetic field that can agitate fundamentals and harmonics of steel strings. There are harmonic mode switches as provided by newer versions of the [[EBow]] and by guitars built in sustainers like the [[Fernandes Sustainer]] and the Moog Guitar. Harmonics control by harmonic mode switching and by the playing technique is applied by the [[Guitar Resonator]] where harmonics can be alternated by changing the string driver position at the fretboard while playing.

==See also==
*[[3rd bridge]]

==References==
{{Reflist}}

{{Guitars|Playing}}
{{Guitar techniques}}
{{Strings (music)}}
{{Violin family}}

{{DEFAULTSORT:String harmonic}}
[[Category:Harmonic series (music)]]
[[Category:String performance techniques]]