String harmonic#Pinch harmonics

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When a 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 overtones (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).{{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}} A harmonic overtone has evenly spaced nodes along the string, where the string does not move from its resting position.

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

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:

:$F\; =\; \backslash log\_s\; \backslash frac\{m\}\{m-n\}$

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

File:Artificial_harmonic.png

File:Natural_versus_artificial_harmonic.png

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.{{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}} 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. 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,' 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)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}}.}}

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.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}}.

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 noteheads in one 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.Potter, Louis (1995). The Art of Cello Playing, p.194. Alfred Music. {{ISBN|9781457400353}}.

The most commonly used artificial harmonic, due to its relatively easy and natural 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.),"Grimson, Samuel B. and 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}}. 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.)," 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.)"Hurwitz (2006), p.87.

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}}

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There are a few harmonic techniques unique to guitar.

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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,{{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}} canceling (silencing) the fundamental frequency of the string, and letting one of the overtones dominate. This results in a high-pitched sound which is particularly discernible on an electrically amplified guitar as a "squeal".

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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}}.

{{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.

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Category:Harmonic series (music)

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