Editing Harmonic (section)

==On stringed instruments==
[[Image:Flageolette.svg|thumb|200px|Playing a harmonic on a string]]{{Main|String harmonic}}
{{Quote|Harmonics may be singly produced [on stringed instruments] (1) by varying the point of contact with the bow, or (2) by slightly pressing the string at the nodes, or divisions of its aliquot parts (<math>\tfrac{ 1 }{ 2 }</math>, <math>\tfrac{ 1 }{ 3 }</math>, <math>\tfrac{ 1 }{ 4 }</math>, etc.). {{nobr|(1) In the first}} case, advancing the bow from the usual place where the fundamental note is produced, towards the bridge, the whole scale of harmonics may be produced in succession, on an old and highly resonant instrument. The employment of this means produces the effect called '[[sul ponticello]].' {{nobr|(2) The production}} of harmonics by the slight pressure of the finger on the open string is more useful. When produced by pressing slightly on the various nodes of the open strings they are called 'natural harmonics'. ... Violinists are well aware that the longer the string in proportion to its thickness, the greater the number of upper harmonics it can be made to yield.|''[[Grove's Dictionary of Music and Musicians]]'' (1879)<ref>[[George Grove|Grove, George]] (1879). ''[https://books.google.com/books?id=EP8PAAAAYAAJ&pg=PA665&dq=%22artificial+harmonic%22&hl=en&sa=X&ved=0ahUKEwjd3uOetcDYAhVDw2MKHZ2yCQE4ChDoAQgyMAI#v=onepage&q=%22artificial%20harmonic%22&f=false A Dictionary of Music and Musicians (A.D. 1450–1889)]'', Vol. 2, p. 665. Macmillan. {{pre-ISBN}}.</ref>|source=}}

The following table displays the stop points on a stringed instrument at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics (flageolet tones) are described as having a "flutelike, silvery quality" that can be highly effective as a special color or tone color ([[timbre]]) when used and heard in [[orchestration]].<ref name=Marroco-2001>{{cite dictionary |last=Marrocco |first=W. Thomas |chapter=Kennan, Kent |date=2001 |dictionary=Oxford Music Online |publisher=Oxford University Press |doi=10.1093/gmo/9781561592630.article.14882 |chapter-url=http://dx.doi.org/10.1093/gmo/9781561592630.article.14882 |access-date=2020-12-21}}</ref> It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.<ref name=Marroco-2001/>

{| class="wikitable"
|-
!width="20"| {{small|Harmonic}} order
! [[Stop note]]
! Note sounded<br/><small>(relative to<br/>open string)</small>
!width="50"| [[Audio frequency]] ([[Hertz (unit)|Hz]])
!width="50"| [[Cent (music)|Cents]] {{small|above}}<br/>{{small|fundamental}} {{small|(offset by octave)}}
! Audio<br/> <small>(octave shifted)</small>
|-
|style="text-align:center;"| 1{{sup|st}}
| [[fundamental frequency|fundamental]],<br/> perfect [[unison]] 
|style="text-align:center;"| {{small|{{sc|P}} }}1
| style="text-align:right;"| {{gaps|600|Hz}}
| style="text-align:right;"| 0.0{{math| ¢ }}
| {{audio|Unison on C.mid|Play}}
|-
|style="text-align:center;"| 2{{sup|nd}}
| first perfect [[octave]] 
|style="text-align:center;"| {{small|{{sc|P}} }}8 
| style="text-align:right;"| {{gaps|1|200|Hz}}
| style="text-align:right;"| 0.0{{math| ¢ }}
| {{audio|Perfect octave on C.mid|Play}}
|-
|style="text-align:center;"| 3{{sup|rd}}
| [[perfect fifth]]
|style="text-align:center;"| {{small|{{sc|P}} }}8 + {{small|{{sc|P}} }}5 
| style="text-align:right;"| {{gaps|1|800|Hz}}
| style="text-align:right;"| 702.0{{math| ¢ }}
| {{audio|Just perfect fifth on C.mid|Play}}
|-
|style="text-align:center;"| 4{{sup|th}}
| doubled perfect [[octave]]
|style="text-align:center;"| 2{{small| · {{sc|P}} }}8
| style="text-align:right;"| {{gaps|2|400|Hz}}
| style="text-align:right;"| 0.0{{math| ¢ }}
| {{audio|Just perfect fourth on C.mid|Play}}
|-
|style="text-align:center;"| 5{{sup|th}}
| [[just major third]],<br/> [[major third]]
|style="text-align:center;"| 2{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}3 
| style="text-align:right;"| {{gaps|3|000|Hz}}
| style="text-align:right;"| 386.3{{math| ¢ }}
| {{audio|Just major third on C.mid|Play}}
|-
|style="text-align:center;"| 6{{sup|th}}
| [[perfect fifth]]
|style="text-align:center;"| 2{{small| · {{sc|P}} }}8 + {{small|{{sc|P}} }}5
| style="text-align:right;"| {{gaps|3|600|Hz}}
| style="text-align:right;"| 702.0{{math| ¢ }}
| {{audio|Just perfect fifth on C.mid|Play}}
|-
|style="text-align:center;"| 7{{sup|th}}
| [[harmonic seventh]],<br/> [[harmonic seventh|septimal minor seventh]] <br/> <small>(‘the lost chord’)</small>
|style="text-align:center;"| 2{{small| · {{sc|P}} }}8 + {{small|m }}7{{sup|↓}}
| style="text-align:right;"| {{gaps|4|200|Hz}}
| style="text-align:right;"| 968.8{{math| ¢ }}
| {{audio|Harmonic seventh on C.mid|Play}}
|-
|style="text-align:center;"| 8{{sup|th}}
| third perfect [[octave]] 
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8
| style="text-align:right;"| {{gaps|4|800|Hz}}
| style="text-align:right;"| 0.0{{math| ¢ }}
| {{audio|Perfect octave on C.mid|Play}}
|-
|style="text-align:center;"| 9{{sup|th}}
| [[Pythagorean interval|Pythagorean]] [[major second]] <br/> harmonic ninth
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}2 
| style="text-align:right;"| {{gaps|5|400|Hz}}
| style="text-align:right;"| 203.9{{math| ¢ }}
| {{audio|Major tone on C.mid|Play}}
|-
|style="text-align:center;"| 10{{sup|th}}
| [[just major third]]
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}3 
| style="text-align:right;"| {{gaps|6|000|Hz}}
| style="text-align:right;"| 386.3{{math| ¢ }}
| {{audio|Just major third on C.mid|Play}}
|-
|style="text-align:center;"| 11{{sup|th}}
| lesser undecimal [[tritone]],<br/> undecimal semi-[[augmented fourth]]
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{sup|{{sc|A}} }}4{{sup|{{music|d}}}}
| style="text-align:right;"| {{gaps|6|600|Hz}}
| style="text-align:right;"| 551.3{{math| ¢ }}
| {{audio|Eleventh harmonic on C.mid|Play}}
|-
|style="text-align:center;"| 12{{sup|th}}
| [[perfect fifth]] 
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{small|{{sc|P}} }}5
| style="text-align:right;"| {{gaps|7|200|Hz}}
| style="text-align:right;"| 702.0{{math| ¢ }}
| {{audio|Just perfect fifth on C.mid|Play}}
|-
|style="text-align:center;"| 13{{sup|th}}
| tridecimal [[neutral sixth]]
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{small|n }}6{{sup|{{music|d}}↓}}
| style="text-align:right;"| {{gaps|7|800|Hz}}
| style="text-align:right;"| 840.5{{math| ¢ }}
| {{audio|Tridecimal neutral sixth on C.mid|Play}}
|-
|style="text-align:center;"| 14{{sup|th}}
| [[harmonic seventh]],<br/> septimal [[minor seventh]] <br/> <small>(‘the lost chord’)</small>
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{small|m }}7{{sup|⤈}}
| style="text-align:right;"| {{gaps|8|400|Hz}}
| style="text-align:right;"| 968.8{{math| ¢ }}
| {{audio|Harmonic seventh on C.mid|Play}}
|-
|style="text-align:center;"| 15{{sup|th}}
| [[just intonation|just]] [[major seventh]]
|style="text-align:center;"| 3{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}7
| style="text-align:right;"| {{gaps|9|000|Hz}}
| style="text-align:right;"| {{gaps|1|088.3}}{{math| ¢ }}
| {{audio|Just major seventh on C.mid|Play}}
|-
|style="text-align:center;"| 16{{sup|th}}
| fourth perfect [[octave]] 
|style="text-align:center;"| 4{{small| · {{sc|P}} }}8
| style="text-align:right;"| {{gaps|9|600|Hz}}
| style="text-align:right;"| 0.0{{math| ¢ }}
| {{audio|Perfect octave on C.mid|Play}}
|-
|style="text-align:center;"| 17{{sup|th}}
| septidecimal [[semitone]]
|style="text-align:center;"| 4{{small| · {{sc|P}} }}8 + {{small|m }}2{{sup|⇟}}
| style="text-align:right;"| {{gaps|10|200|Hz}}
| style="text-align:right;"| 105.0{{math| ¢ }}
| {{audio|Just major semitone on C.mid|Play}}
|-
|style="text-align:center;"| 18{{sup|th}}
| [[Pythagorean interval|Pythagorean]] [[major second]]
|style="text-align:center;"| 4{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}2
| style="text-align:right;"| {{gaps|10|800|Hz}}
| style="text-align:right;"| 203.9{{math| ¢ }}
| {{audio|Major tone on C.mid|Play}}
|-
|style="text-align:center;"| 19{{sup|th}}
| nanodecimal [[minor third]]
|style="text-align:center;"| 4{{small| · {{sc|P}} }}8 + {{small|m }}3{{sup|{{music|d}}}}
| style="text-align:right;"| {{gaps|11|400|Hz}}
| style="text-align:right;"| 297.5{{math| ¢ }}
| {{audio|19th harmonic on C.mid|Play}}
|-
|style="text-align:center;"| 20{{sup|th}}
| just [[major third]]
|style="text-align:center;"| 4{{small| · {{sc|P}} }}8 + {{sup|{{sc|M}} }}3
| style="text-align:right;"| {{gaps|12|000|Hz}}
| style="text-align:right;"| 386.3{{math| ¢ }}
| {{audio|Just major third on C.mid|Play}}
|}

{|
|+ '''Notation key'''
|-
| {{small|{{sc|P}}}} || [[perfect fifth#term_perfect_anchor|perfect]] interval
|-
| {{sup|{{sc|A}}}} || [[augmented (music)|augmented]] interval (sharpened)
|-
| {{sup|{{sc|M}}}} || [[Major and minor|major]] interval
|-
| {{small|m}} || [[Major and minor|minor]] interval (flattened major)
|-
| {{small|n}} || [[neutral interval|neutral]] interval (between major and minor)
|-
| {{sup|{{music|d}}}} || [[quarter tone|half-flattened]] (approximate) ({{math|≈ −38 ¢ }} for [[just intonation|just]], {{math| −50 ¢ }} for [[12 equal temperament|{{nobr|12 {{sc|TET}}}}]])
|-
| {{sup|↓}} || flattened by a [[syntonic comma]] (approximate) ({{math|≈ −21 ¢ }})
|-
| {{sup|⤈}} || flattened by a half-[[comma (music)|comma]] (approximate) ({{math|≈ −10 ¢ }})
|-
| {{sup|⇟}} || flattened by a quarter-[[comma (music)|comma]] (approximate) ({{math|≈ −5 ¢ }})
|}

===Artificial harmonics===

Occasionally a score will call for an [[artificial harmonic]], produced by playing an overtone on an already stopped string. As a performance technique, it is accomplished by using two fingers on the fingerboard, the first to shorten the string to the desired fundamental, with the second touching the node corresponding to the appropriate harmonic.