Guitar harmonics
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[edit] Overtones
When a guitar string is plucked, the string vibrates at several frequencies. 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.
[edit] Harmonics
Nodal points of excitation are located at the points of intregal division of the string length. Harmonics are produced on the guitar by lightly touching a string, rather than fretting it, at any of these nodal points. When sounded the string can no longer vibrate at its fundamental tone, instead it is forced to vibrate at the specific overtones that correspond to the nodal point, resulting in a chimelike tone. Harmonics produced by this method that arise on an open-string are termed natural harmonics. If the string is fretted the harmonics are termed artificial harmonics. Harmonics can only be sounded at the strings' nodes. The nodes for natural harmonics fall at the following points along the guitar's neck:
| Fret | Note | |
|---|---|---|
| 1/2 | 12 | octave |
| 1/3 + 2/3 | 7, 19 | octave + perfect fifth |
| 1/4 + 3/4 | 5, 24 | 2nd octave |
| 1/5 to 4/5 | 4- (3.9), 9-, 16- and 1 more above the body | 2nd octave + just major third |
| 1/6 + 5/6 | 3.2 and 1 more above the body | 2nd octave + perfect fifth |
| 1/7 to 6/7 | 2.7, 5.9, 9.5, 14.7 and 2 more above the body | 2nd octave + septimal minor seventh |
| 1/8, 3/8, 5/8, 7/8 | 2.3 and 3 more | 3rd octave |
| 1/9, 4/9, 5/9, 8/9 | 2 and 3 more | 3rd octave + neutral second |
| 1/10, 3/10, 7/10, 9/10 | 1.8 and 3 more | 3rd octave + just major third |
A bit different described in table below:
| 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 |
[edit] 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 3-5mm), 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.
[edit] 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.
[edit] 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 wave length 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.
