String harmonic

A guitar harmonic is a musical note played by preventing or amplifying vibration of certain overtones of a guitar string.

Music using harmonics can contain very high pitch notes difficult or impossible to reach by fretting. Guitar harmonics also produce a different sound quality than fretted notes, and are one of many techniques used to create musical variety.

Technique

Harmonics are mainly generated manually by different playing techniques. Another method is sound wave feedback of a high volume guitar amplifier which causes an "infinite" vibration of certain string harmonics. As a third method magnetic string drivers like the EBow can be used for generating string harmonics.

Harmonics are most often played by lightly placing a finger on a string at a nodal point of one of the overtones at the moment when the string is driven. The finger immediately damps all overtones that do not have a node near the location touched. The lowest-pitch overtone dominates the resulting sound.

Overtones

The fundamental and the double- and triple-frequency overtones of a guitar string.

When a guitar string is plucked, the string vibrates most prominently at its fundamental frequency, but at the same time also vibrates at all integer multiples of that frequency. The vibration along the entire length of the string is known as the fundamental, while vibrations occurring between points along the string (known as nodes) are referred to as overtones. The fundamental and overtones, when sounded together, are perceived by the listener as a single tone, though the relative prominence of the frequencies varies among instruments, and contribute to its timbre.

Nodes

The nodes of natural harmonics are located at the following points along a guitar's neck. Note that for fretted strings, these locations shift up the fingerboard by the same number of frets, and resulting harmonics are called artificial harmonics.

Harmonic mode shapes and their corresponding node locations on a guitar

Mode	Length Fraction	Fret	Note
1	1	open	unison
2	1/2	12	octave
3	1/3, 2/3	7, 19	octave + perfect fifth
4	1/4, 3/4	5, 24	2nd octave
5	1/5 to 4/5	3.9, 8.8, 15.9, 27.9	2nd octave + just major third
6	1/6, 5/6	3.2, 31.0	2nd octave + perfect fifth
7	1/7 to 6/7	2.7, 5.8, 9.7, 14.7, 21.7, 33.7	2nd octave + septimal minor seventh
8	1/8, 3/8, 5/8, 7/8	2.3, 8.1, 17.0, 36.0	3rd octave
9	1/9, 2/9, 4/9, 5/9, 7/9, 8/9	2.0, 4.4, 10.2, 14.0, 26.0, 38.0	3rd octave + neutral second
10	1/10, 3/10, 7/10, 9/10	1.8, 6.2, 20.8, 39.9	3rd octave + just major third

The above fret numbers can be calculated:

$F_{1..n}=\log _{s}{m \over {m-n}}$

where $s=2^{1/12}$, the frequency ratio of one musical half-step (i.e. one fret), $m$ is the mode number (1-10 are given above), and $n$ is the node number for that mode ($1$ to $m-1$).

Note that 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.

Intervals

harmonic	stop note	harmonic note	cents	reduced cents
2	octave	P8	1200.0	0.0
3	just perfect fifth	P8 + P5	1902.0	702.0
4	just perfect fourth	2P8	2400.0	0.0
5	just major third	2P8 + just M3	2786.3	386.3
6	just minor third	2P8 + P5	3102.0	702.0
7	septimal minor third	2P8 + septimal m7	3368.8	968.8
8	septimal major second	3P8	3600.0	0.0
9	Pythagorean major second	3P8 + pyth M2	3803.9	203.9
10	just minor whole tone	3P8 + just M3	3986.3	386.3
11	greater unidecimal neutral second	3P8 + just M3 + GUN2	4151.3	551.3
12	lesser unidecimal neutral second	3P8 + P5	4302.0	702.0
13	tridecimal 2/3-tone	3P8 + P5 + T23T	4440.5	840.5
14	2/3-tone	3P8 + P5 + septimal m3	4568.8	968.8
15	septimal (or major) diatonic semitone	3P8 + P5 + just M3	4688.3	1088.3
16	just (or minor) diatonic semitone	4P8	4800.0	0.0

Advanced techniques

Pinch harmonics

See Pinch harmonic

A pinch harmonic is produced by lightly touching the thumb of the picking hand against the string immediately after it is picked. This action is sufficient to silence the fundamental and all overtones except those which have a nodes at that location. This is generally accomplished by holding the plectrum so that very little of its tip protrudes between the thumb and forefinger (roughly 3–5 mm), allowing the thumb to brush the string immediately after it is picked.

The technique must be performed at one of the appropriate harmonic nodes for the note to sound. For example, to produce a pinch harmonic which is one octave higher than the fundamental of a string which is stopped at the third fret of a guitar, the string must be plucked halfway between the third fret and the bridge (i.e., 15th fret as the neck is logarithmic). Other overtones of the same fundamental note may be produced in the same way at other nodes along the string. The point at which the string is plucked therefore varies depending on the desired note. Most harmonics have several accessible nodes evenly spaced on the string; so it is no surprise that the nodes used in practice are normally those around where the string is normally picked (around the pickups on an electric guitar), rather than those above the neck as these are the easiest to access with the picking hand from normal playing.

Overtones with a frequency of a multiple of the intended overtone (i.e., the same note in a higher octave) will share the nodes of the lower overtones, so won't be muted. They will, however, be at a much lower volume and since they are the same note in a higher octave, don't detract from the sound of the note. If the string is pinched at the antinode of the intended overtone, no higher overtones will sound.

A single harmonic overtone is far quieter than a normal note which contains many overtones. For this reason, the gain of an amplified instrument is often increased to make it more easily audible. Thicker strings, stronger pickups and adjustment to amplifier settings (increasing gain) are some ways of doing this. It is important to note that as there is only one fundamental sounding, it will have a different volume through different pickups, depending on the proximity of nodes or antinodes to the pickup. The different volumes of overtones are the reason pickups sound different. The outcome of this is that if a node is directly over a pickup, it won't sound through that pickup.

Tapped harmonics

This technique was popularized by Eddie van Halen. Tapped harmonics are 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 12+3=15.

Double attack harmonics

This technique has been attributed to J. K. Hays of Stidham-Hays, and generates the excitation of the string harmonic by forcing the shorter wavelength of a particular harmonic mode during the pluck of the string. The harmonic is generated by plucking the string "up" with the middle or ring finger of the plucking hand while holding the pick grasped between the thumb and the index finger against the string. The harmonic generated is dependent on the distance between the pick and the attack of the string by the middle or ring finger or fingernail (which establishes the nodal distance), and the distance of the application from the bridge of the guitar (which must match a multiple of the nodal distance). Using this technique, multiple harmonic modes may be generated no matter where the string is fretted on the neck, and these modes may be generated in the plucking area over the pickups of an electric guitar, or the sound hole of an acoustic guitar. These harmonics may then be modified by bending the string. According to J. K. Hays, the technique is more repeatable and reliable, and was developed out of frustration with the precision required by the pinch harmonics technique and its repeatability for live performances.

See also

• 3rd Bridge