String harmonic

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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. Flageolette.svg
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 is a string instrument technique that uses the nodes of natural harmonics of a musical string to isolate overtones. Playing string harmonics produces high pitched tones, often compared in timbre to a whistle or flute. [1] [2] Overtones can be isolated "by lightly touching the string with the finger instead of pressing it down" against the fingerboard (without stopping). [3]

Contents

Overtones

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). [4] A harmonic overtone has evenly spaced nodes along the string, where the string does not move from its resting position.

Nodes

Table of harmonics, indicating in colors on which positions the same overtones occur Table of Harmonics.svg
Table of harmonics, indicating in colors on which positions the same overtones occur

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

Harmonic Stop note Sounded note relative to open string Cents above open stringCents reduced to one octaveLength fractionAudio
2octave octave (P8)1,200.00.012 Loudspeaker.svg Play  
3just perfect fifthP8 + just perfect fifth (P5)1,902.0702.013, 23 Loudspeaker.svg Play  
4just perfect fourth 2P82,400.00.014, 34 Loudspeaker.svg Play  
5just major third2P8 + just major third (M3)2,786.3386.315 to 45 Loudspeaker.svg Play  
6just minor third 2P8 + P53,102.0702.016, 56
7septimal minor third2P8 + septimal minor seventh (m7)3,368.8968.817 to 67 Loudspeaker.svg Play  
8 septimal major second 3P83,600.00.018, 38, 58, 78
9Pythagorean major second3P8 + Pythagorean major second (M2)3,803.9203.919, 29, 49, 59, 79, 89 Loudspeaker.svg Play  
10just minor whole tone 3P8 + just M33,986.3386.3110, 310, 710, 910
11greater undecimal neutral second 3P8 + lesser undecimal tritone 4,151.3551.3111 to 1011 Loudspeaker.svg Play  
12lesser undecimal neutral second3P8 + P54,302.0702.0112, 512, 712, 1112
13tridecimal 2/3-tone3P8 + tridecimal neutral sixth (n6)4,440.5840.5113 to 1213 Loudspeaker.svg Play  
142/3-tone3P8 + P5 + septimal minor third (m3)4,568.8968.8114, 314, 514, 914, 1114, 1314
15septimal (or major) diatonic semitone 3P8 + just major seventh (M7)4,688.31,088.3115, 215, 415, 715, 815, 1115, 1315, 1415 Loudspeaker.svg Play  
16just (or minor) diatonic semitone4P84,800.00.0116, 316, 516, 716, 916, 1116, 1316, 1516

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 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 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:

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

Artificial harmonics

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.
Play (help*info) Artificial harmonic.png
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. Loudspeaker.svg Play  
Natural versus artificial harmonic Natural versus artificial harmonic.png
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. 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.

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.

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. [6]

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. [7]

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.)," [8] 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.)," [8] 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.)" [8] [9]

Guitar

The fundamental and the double- and triple-frequency overtones of a guitar string. Harmonic motion4.PNG
The fundamental and the double- and triple-frequency overtones of a guitar string.

There are a few harmonic techniques unique to guitar.

Pinch harmonics

Pinch harmonics performed on an acoustic guitar

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, [10] 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".

Tapped harmonics

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 12 + 3 = 15.

String harmonics driven by a magnetic field

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 guitar build 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

Related Research Articles

Fundamental frequency Lowest frequency of a periodic waveform, such as sound

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as f0, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f1, the first harmonic.

Harmonic series (music) Sequence of frequencies

A harmonic series is the sequence of frequencies, musical tones, or pure tones in which each frequency is an integer multiple of a fundamental.

Musical tuning

In music, there are two common meanings for tuning:

Violin Wooden bowed string instrument

The violin, sometimes known as a fiddle, is a wooden chordophone in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument (soprano) in the family in regular use. The violin typically has four strings, usually tuned in perfect fifths with notes G3, D4, A4, E5, and is most commonly played by drawing a bow across its strings. It can also be played by plucking the strings with the fingers (pizzicato) and, in specialized cases, by striking the strings with the wooden side of the bow.

Harmonic

A harmonic is any member of the harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as sinusoidal waves. A harmonic of such a wave is a wave with a frequency that is a positive integer multiple of the frequency of the original wave, known as the fundamental frequency. The original wave is also called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. For example, if the fundamental frequency is 50 Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz, 150 Hz, 200 Hz and any addition of waves with these frequencies is periodic at 50 Hz.

An nth characteristic mode, for n > 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at L and L, where L is the length of the string. In fact, each nth characteristic mode, for n not a multiple of 3, will not have nodes at these points. These other characteristic modes will be vibrating at the positions L and L. If the player gently touches one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the nth characteristic modes, where n is a multiple of 3, will be made relatively more prominent.

Overtone

An overtone is any frequency greater than the fundamental frequency of a sound. Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental. These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental.

Power chord

A power chordPlay  is a colloquial name for a chord in guitar music, especially electric guitar, that consists of the root note and the fifth, as well as possibly octaves of those notes. Power chords are commonly played on amplified guitars, especially on electric guitar with intentionally added distortion or overdrive effects. Power chords are a key element of many styles of rock, especially heavy metal and punk rock.

Inharmonicity

In music, inharmonicity is the degree to which the frequencies of overtones depart from whole multiples of the fundamental frequency.

Sympathetic string

Sympathetic strings or resonance strings are auxiliary strings found on many Indian musical instruments, as well as some Western Baroque instruments and a variety of folk instruments. They are typically not played directly by the performer, only indirectly through the tones that are played on the main strings, based on the principle of sympathetic resonance. The resonance is most often heard when the fundamental frequency of the string is in unison or an octave lower or higher than the catalyst note, although it can occur for other intervals, such as a fifth, with less effect.

Node (physics)

A node is a point along a standing wave where the wave has minimum amplitude. For the instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes.

Violin technique

Playing the violin entails holding the instrument between the jaw and the collar bone.. The strings are sounded either by drawing the bow across them (arco), or by plucking them (pizzicato). The left hand regulates the sounding length of the strings by stopping them against the fingerboard with the fingers, producing different pitches.

Jivari

Javārī, in Indian classical music refers to the overtone-rich "buzzing" sound characteristic of classical Indian string instruments such as the tanpura, sitar, surbahar, rudra veena and Sarasvati veena. Javari can refer to the acoustic phenomenon itself and to the meticulously carved bone, ivory or wooden bridges that support the strings on the sounding board and produce this particular effect. A similar sort of bridge is used on traditional Ethiopian lyres, as well as on the ancient Greek kithara, and the "bray pins" of some early European harps operated on the same principle. A similar sound effect, called in Japanese sawari, is used on some traditional Japanese instruments as well.

A person who is specialized in the making of stringed instruments such as guitars, lutes and violins is called a luthier.

Harmonic usually refers to the frequency components of a time-varying signal, such as a musical note.

In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must be produced in unusual ways. While the overtone series is based upon arithmetic multiplication of frequencies, resulting in a harmonic series, the undertone series is based on arithmetic division.

Moodswinger

The Moodswinger is a twelve-string electric zither with an additional third bridge designed by Yuri Landman. The rod which functions as the third bridge divides the strings into two sections to cause an overtone multiphonic sound. One of the copies of the instrument is part of the collection of the Musical Instrument Museum in Phoenix, Arizona.

3rd bridge

The 3rd bridge is an extended playing technique used on the electric guitar and other string instruments that allows a musician to produce distinctive timbres and overtones that are unavailable on a conventional string instrument with two bridges. The timbre created with this technique is close to that of gamelan instruments like the bonang and similar Indonesian types of pitched gongs.

A third bridge can be devised by inserting a rigid preparation object between the strings and the body or neck of the instrument, effectively diving the string into distinct vibrating segments.

Scale of harmonics

The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale. Most fret positions appearing on Non-Western string instruments (lutes) are equal to positions of this scale. Unexpectedly, these fret positions are actually the corresponding undertones of the overtones from the harmonic series. The distance from the nut to the fret is an integer number lower than the distance from the fret to the bridge.

Playing the cello is done while seated with the instrument supported on the floor. The fingertips of the left hand stop the strings on the fingerboard to determine the pitch of the fingered note. The right hand plucks or bows the strings to sound the notes.

Overtones tuning

Among alternative tunings for the guitar, an overtones tuning selects its open-string notes from the overtone sequence of a fundamental note. An example is the open tuning constituted by the first six overtones of the fundamental note C, namely C2-C3-G3-C4-E4-G4.

References

  1. Kamien, Roger (2008). Music: An Appreciation, p.13. Sixth "brief" edition. McGraw Hill. ISBN   978-0-07-340134-8.
  2. 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.
  3. 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.
  4. "The Physics of Everyday Stuff - The Guitar". www.bsharp.org. Retrieved 2015-08-03.
  5. Grove, George (1879). A Dictionary of Music and Musicians (A.D. 1450-1889) , Vol. 2, p.665. Macmillan. [ISBN unspecified].
  6. Sevsay, Ertuğrul (2013). The Cambridge Guide to Orchestration , unpaginated. Cambridge. ISBN   9781107067486.
  7. Potter, Louis (1995). The Art of Cello Playing, p.194. Alfred Music. ISBN   9781457400353.
  8. 1 2 3 Grimson, Samuel B. and Forsyth, Cecil (1920). Modern Violin-Playing , p.79-80. New York: H. W. Gray (Novello). [ISBN unspecified].
  9. Hurwitz (2006), p.87.
  10. "Guitar Techniques: Pick Harmonic", XtremeMusician.com. Accessed: December 19, 2017.