Guitar chord

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Ry Cooder plays slide guitar using an open tuning that allows major chords to be played by barring the strings anywhere along their length. Ry Cooder playing.jpg
Ry Cooder plays slide guitar using an open tuning that allows major chords to be played by barring the strings anywhere along their length.

In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E–A–D–G–B–E' (from the lowest pitched string to the highest); in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.

Contents

There are separate chord-forms for chords having their root note on the third, fourth, fifth, and sixth strings. For a six-string guitar in standard tuning, it may be necessary to drop or omit one or more tones from the chord; this is typically the root or fifth. The layout of notes on the fretboard in standard tuning often forces guitarists to permute the tonal order of notes in a chord.

The playing of conventional chords is simplified by open tunings, which are especially popular in folk, blues guitar and non-Spanish classical guitar (such as English and Russian guitar). For example, the typical twelve-bar blues uses only three chords, each of which can be played (in every open tuning) by fretting six strings with one finger. Open tunings are used especially for steel guitar and slide guitar. Open tunings allow one-finger chords to be played with greater consonance than do other tunings, which use equal temperament, at the cost of increasing the dissonance in other chords.

The playing of (3 to 5 string) guitar chords is simplified by the class of alternative tunings called regular tunings , in which the musical intervals are the same for each pair of consecutive strings. Regular tunings include major-thirds tuning, all-fourths, and all-fifths tunings. For each regular tuning, chord patterns may be diagonally shifted down the fretboard, a property that simplifies beginners' learning of chords and that simplifies advanced players' improvisation. On the other hand, in regular tunings 6-string chords (in the keys of C, G, and D) are more difficult to play.

Conventionally, guitarists double notes in a chord to increase its volume, an important technique for players without amplification; doubling notes and changing the order of notes also changes the timbre of chords. It can make possible a "chord" which is composed of the all same note on different strings. Many chords can be played with the same notes in more than one place on the fretboard.

Musical fundamentals

The theory of guitar-chords respects harmonic conventions of Western music. Discussions of basic guitar-chords rely on fundamental concepts in music theory: the twelve notes of the octave, musical intervals, chords, and chord progressions.

Intervals

The chromatic circle lists the twelve notes of the octave, which differ by exactly one semitone. Pitch class space.svg
The chromatic circle lists the twelve notes of the octave, which differ by exactly one semitone.
One-octave C major scale
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C major scale
One octave played up and down in the c major scale on the piano
Problems playing this file? See media help. C Major scale (up and down).svg
One-octave C major scale
Initial eight harmonics on C, namely (C,C,G,C,E,G,B,C)
Play simultaneously First eight harmonics vertical.png
Initial eight harmonics on C, namely (C,C,G,C,E,G,B,C)
Play simultaneously

The octave consists of twelve notes. Its natural notes constitute the C major scale, (C, D, E, F, G, A, B, and C).

The intervals between the notes of a chromatic scale are listed in a table, in which only the emboldened intervals are discussed in this article's section on fundamental chords; those intervals and other seventh-intervals are discussed in the section on intermediate chords. The unison and octave intervals have perfect consonance. Octave intervals were popularized by the jazz playing of Wes Montgomery. The perfect-fifth interval is highly consonant, which means that the successive playing of the two notes from the perfect fifth sounds harmonious.

A semitone is the distance between two adjacent notes on the chromatic circle, which displays the twelve notes of an octave. [lower-alpha 1]

Intervals
Number of
semitones
Minor, major, or perfect
intervals
Audio Harmoniousness [1] [2]
0 Perfect unison Play Open consonance
1 Minor second Play Sharp dissonance
2 Major second Play Mild dissonance
3 Minor third Play Soft consonance
4 Major third Play Soft consonance
5 Perfect fourth Play Ambivalence
6 Augmented fourth Play Ambiguous
7 Perfect fifth Play Open consonance
8 Minor sixth Play Soft consonance
9 Major sixth Play Soft consonance
10 Minor seventh Play Mild dissonance
11 Major seventh Play Sharp dissonance
12 Octave Play Open consonance

As indicated by their having been emboldened in the table, a handful of intervals—thirds (minor and major), perfect fifths, and minor sevenths—are used in the following discussion of fundamental guitar-chords.

As already stated, the perfect-fifths (P5) interval is the most harmonious, after the unison and octave intervals. An explanation of human perception of harmony relates the mechanics of a vibrating string to the musical acoustics of sound waves using the harmonic analysis of Fourier series. When a string is struck with a finger or pick (plectrum), it vibrates according to its harmonic series. When an open-note C-string is struck, its harmonic series begins with the terms (C,C,G,C,E,G,B,C). The root note is associated with a sequence of intervals, beginning with the unison interval (C,C), the octave interval (C,C), the perfect fifth (C,G), the perfect fourth (G,C), and the major third (C,E). In particular, this sequence of intervals contains the thirds of the C-major chord {(C,E),(E,G)}. [3]

With a note of music, one strikes the fundamental, and, in addition to the root note, other notes are generated: these are the harmonic series.... As one fundamental note contains within it other notes in the octave, two fundamentals produce a remarkable array of harmonics, and the number of possible combinations between all the notes increases phenomenally. With a triad, affairs stand a good chance of getting severely out of hand.

Perfect fifths

The perfect-fifth interval is featured in guitar playing and in sequences of chords. The sequence of fifth intervals built on the C-major scale is used in the construction of triads, which is discussed below. [lower-alpha 2]

Guitar chord
Cycle of fifths

Concatenating the perfect fifths ((F,C), (C,G), (G,D), (D,A), (A,E), (E,B),...) yields the sequence of fifths (F,C,G,D,A,E,B,...); this sequence of fifths displays all the notes of the octave. [lower-alpha 3] This sequence of fifths shall be used in the discussions of chord progressions, below.

Power chord
The Who's Peter Townshend often used a theatrical "windmill" strum to play "power chords"--a root, fifth, and octave. Pete Townshend Windmill-(jha).jpg
The Who's Peter Townshend often used a theatrical "windmill" strum to play "power chords"—a root, fifth, and octave.

The perfect-fifth interval is called a power chord by guitarists, who play them especially in blues and rock music. [7] [8] The Who's guitarist, Peter Townshend, performed power chords with a theatrical windmill-strum. [7] [9] Power chords are often played with the notes repeated in higher octaves. [7]

Although established, the term "power chord" is inconsistent with the usual definition of a chord in musical theory, which requires three (or more) distinct notes in each chord. [7]

Chords in music theory

A brief overview
Major chord in the chromatic circle.png
C Major (C,E,G) begins with the major third (C,E).
Minor chord in the chromatic circle.png
C Minor (C,E,G) begins with minor third (C,E).
Major and minor triads contain major-third and minor-third intervals in different orders.

The musical theory of chords is reviewed, to provide terminology for a discussion of guitar chords. Three kinds of chords, which are emphasized in introductions to guitar-playing, [10] [lower-alpha 4] are discussed. These basic chords arise in chord-triples that are conventional in Western music, triples that are called three-chord progressions. After each type of chord is introduced, its role in three-chord progressions is noted.

Intermediate discussions of chords derive both chords and their progressions simultaneously from the harmonization of scales. The basic guitar-chords can be constructed by "stacking thirds", that is, by concatenating two or three third-intervals, where all of the lowest notes come from the scale. [12] [13]

Triads

Major

Both major and minor chords are examples of musical triads , which contain three distinct notes. Triads are often introduced as an ordered triplet:

  • the root ;
  • the third , which is above the root by either a major third (for a major chord) or a minor third (for a minor chord);
  • the fifth, which is a perfect fifth above the root; consequently, the fifth is a third above the third—either a minor third above a major third or a major third above a minor third. [14] [15] The major triad has a root, a major third, and a fifth. (The major chord's major-third interval is replaced by a minor-third interval in the minor chord, which shall be discussed in the next subsection.)
Major chords
ChordRootMajor thirdFifth
CCEG
DDFA
EEGB
FFAC
GGBD
AACE
B [lower-alpha 5] BDF

For example, a C-major triad consists of the (root, third, fifth)-notes (C, E, G).

The three notes of a major triad have been introduced as an ordered triplet, namely (root, third, fifth), where the major third is four semitones above the root and where the perfect fifth is seven semitones above the root. This type of triad is in closed position. Triads are quite commonly played in open position: For example, the C-major triad is often played with the third (E) and fifth (G) an octave higher, respectively sixteen and nineteen semitones above the root. Another variation of the major triad changes the order of the notes: For example, the C-major triad is often played as (C,G,E), where (C,G) is a perfect fifth and E is raised an octave above the perfect third (C,E). Alternative orderings of the notes in a triad are discussed below (in the discussions of chord inversions and drop-2 chords).

In popular music, a subset of triads is emphasized—those with notes from the three major-keys (C, G, D), which also contain the notes of their relative minor keys (Am, Em, Bm). [16]

Progressions
Stacking the C-major scale with thirds creates a chord progression,
traditionally enumerated with the Roman numerals I, ii, iii, IV, V, vi, vii. Its major-key sub-progression C-F-G (I-IV-V) is conventional in popular music. In this progression, the minor triads ii-iii-vi appear in the relative minor key (Am)'s corresponding chord progression. Scale degree numbers.png
Stacking the C-major scale with thirds creates a chord progression, traditionally enumerated with the Roman numerals I, ii, iii, IV, V, vi, vii. Its major-key sub-progression C–F–G (I–IV–V) is conventional in popular music. In this progression, the minor triads ii–iii–vi appear in the relative minor key (Am)'s corresponding chord progression.

The major chords are highlighted by the three-chord theory of chord progressions, which describes the three-chord song that is archetypal in popular music. When played sequentially (in any order), the chords from a three-chord progression sound harmonious ("good together"). [lower-alpha 6]

The most basic three-chord progressions of Western harmony have only major chords. In each key, three chords are designated with the Roman numerals (of musical notation): The tonic (I), the subdominant (IV), and the dominant (V). While the chords of each three-chord progression are numbered (I, IV, and V), they appear in other orders. [lower-alpha 6] [18]

Basic three-chord progressions [lower-alpha 6] [19]
KeyTonic (I)Subdominant (IV)Dominant (V)
C CFG
D DGA
E EAB
G GCD
A ADE

In the 1950s the I–IV–V chord progression was used in "Hound Dog" (Elvis Presley) and in "Chantilly Lace" (The Big Bopper). [20]

Major-chord progressions are constructed in the harmonization of major scales in triads. [21] For example, stacking the C-major scale with thirds creates a chord progression, which is traditionally enumerated with the Roman numerals I, ii, iii, IV, V, vi, viio; its sub-progression C–F–G (I–IV–V) is used in popular music, [22] as already discussed. Further chords are constructed by stacking additional thirds. Stacking the dominant major-triad with a minor third creates the dominant seventh chord, which shall be discussed after minor chords.

Minor
An A-minor scale has the same pitches as the C major scale, because the C major and A minor keys are relative major and minor keys. A natural minor scale ascending and descending.png
An A-minor scale has the same pitches as the C major scale, because the C major and A minor keys are relative major and minor keys.

A minor chord has the root and the fifth of the corresponding major chord, but its first interval is a minor third rather than a major third:

Minor chords
ChordRootMinor thirdPerfect fifth
Cm [lower-alpha 5] CEG
DmDFA
EmEGB
Fm [lower-alpha 5] FAC
Gm [lower-alpha 5] GBD
AmACE
Bm [lower-alpha 5] BDF

Minor chords arise in the harmonization of the major scale in thirds, which was already discussed: The minor chords have the degree positions ii, iii, and vi.

Minor three-chord progressions [18] [23]
KeyTonic (I)Subdominant (IV)Dominant (V)
CmCmFmG7
Dm DmGmA7
Em EmAmB7
GmGmCmD7
Am AmDmE7
Major and minor keys that share the same key signature are paired as relative-minor and relative-major keys. Circle of fifths deluxe 4.svg
Major and minor keys that share the same key signature are paired as relative-minor and relative-major keys.

Minor chords arise as the tonic notes of minor keys that share the same key signature with major keys. From the major key's I–ii–iii–IV–V–vi–viio progression, the "secondary" (minor) triads ii–iii–vi appear in the relative minor key's corresponding chord progression as i–iv–v (or i–iv–V or i–iv–V7): For example, from C's vi–ii–iii progression Am–Dm–Em, the chord Em is often played as E or E7 in a minor chord progression. [24] Among basic chords, the minor chords (D,E,A) are the tonic chords of the relative minors of the three major keys (F,G,C):

Key signatureMajor keyMinor key
B F major D minor
C major A minor
F G major E minor

The technique of changing among relative keys (pairs of relative majors and relative minors) is a form of modulation. [25] Minor chords are constructed by the harmonization of minor scales in triads. [26]

Seventh chords: major–minor chords with dominant function

The previously noted chord progression with a dominant seventh Play. The dominant seventh (V7) chord G7=(G,B,D,F) increases the tension with the tonic (I) chord C. Harmonized scale.png
The previously noted chord progression with a dominant seventh Play . The dominant seventh (V7) chord G7=(G,B,D,F) increases the tension with the tonic (I) chord C.

Adding a minor seventh to a major triad creates a dominant seventh (denoted V7). In music theory, the "dominant seventh" described here is called a major-minor seventh, emphasizing the chord's construction rather than its usual function. [27] Dominant sevenths are often the dominant chords in three-chord progressions, [18] in which they increase the tension with the tonic "already inherent in the dominant triad". [28]

Dominant seventh chords
ChordRootMajor thirdPerfect fifthMinor seventh
C7CEGB
D7DFAC
E7EGBD
F7 [lower-alpha 5] FACE
G7GBDF
A7ACEG
B7BDFA

The dominant seventh discussed is the most commonly played seventh chord. [29] [30]

Paul McCartney used an A-major I-IV-V7 chord progression in "3 Legs", which is also an example of the twelve-bar blues. Paul McCartney during a Wings concert, 1976.jpg
Paul McCartney used an A-major I–IV–V7 chord progression in "3 Legs", which is also an example of the twelve-bar blues.
Three-chord progressions [18] [31]
KeyTonic (I)Subdominant (IV)Dominant (V)
C CFG7
D DGA7
E EAB7
G GCD7
A ADE7

An A-major I–IV–V7 chord progression A–D–E7 was used by Paul McCartney in the song "3 Legs" on his album Ram . [32]

These progressions with seventh chords arise in the harmonization of major scales in seventh chords. [33] [lower-alpha 7]

Twelve-bar blues

Be they in major key or minor key, such I–IV–V chord progressions are extended over twelve bars in popular music—especially in jazz, blues, and rock music. [36] [37] For example, a twelve-bar blues progression of chords in the key of E has three sets of four bars:

E–E–E–E7
A–A–E–E
B7–A–E–B7;

this progression is simplified by playing the sevenths as major chords. [36] The twelve-bar blues structure is used by McCartney's "3 Legs", [32] which was noted earlier.

Playing chords: open strings, inversion, and note doubling

The implementation of musical chords on guitars depends on the tuning. Since standard tuning is most commonly used, expositions of guitar chords emphasize the implementation of musical chords on guitars with standard tuning. The implementation of chords using particular tunings is a defining part of the literature on guitar chords, which is omitted in the abstract musical-theory of chords for all instruments.

For example, in the guitar (like other stringed instruments but unlike the piano), open-string notes are not fretted and so require less hand-motion. Thus chords that contain open notes are more easily played and hence more frequently played in popular music, such as folk music. Many of the most popular tunings—standard tuning, open tunings, and new standard tuning—are rich in the open notes used by popular chords. Open tunings allow major triads to be played by barring one fret with only one finger, using the finger like a capo. On guitars without a zeroth fret (after the nut), the intonation of an open note may differ from then note when fretted on other strings; consequently, on some guitars, the sound of an open note may be inferior to that of a fretted note. [38]

Unlike the piano, the guitar has the same notes on different strings. Consequently, guitar players often double notes in chord, so increasing the volume of sound. Doubled notes also changes the chordal timbre: Having different "string widths, tensions and tunings, the doubled notes reinforce each other, like the doubled strings of a twelve-string guitar add chorusing and depth". [39] Notes can be doubled at identical pitches or in different octaves. For triadic chords, doubling the third interval, which is either a major third or a minor third, clarifies whether the chord is major or minor. [40]

Unlike a piano or the voices of a choir, the guitar (in standard tuning) has difficulty playing the chords as stacks of thirds, which would require the left hand to span too many frets, [41] particularly for dominant seventh chords, as explained below. If in a particular tuning chords cannot be played in closed position, then they often can be played in open position; similarly, if in a particular tuning chords cannot be played in root position, they can often be played in inverted positions. A chord is inverted when the bass note is not the root note. Additional chords can be generated with drop-2 (or drop-3) voicing, which are discussed for standard tuning's implementation of dominant seventh chords (below).

Johnny Marr is known for providing harmony by playing arpeggiated chords. Johnny Marr with The Cribs at the 9-30 Club.jpg
Johnny Marr is known for providing harmony by playing arpeggiated chords.

When providing harmony in accompanying a melody, guitarists may play chords all-at-once or as arpeggios. Arpeggiation was the traditional method of playing chords for guitarists for example in the time of Mozart. Contemporary guitarists using arpeggios include Johnny Marr of The Smiths.

Fundamental chords

Standard tuning

In the standard guitar tuning, one major third interval is interjected amid four perfect fourth intervals. Tuning ADGBE5 ADGBE0.svg
In the standard guitar tuning, one major third interval is interjected amid four perfect fourth intervals.
Standard diagonal shifting of C major chord.png
In standard tuning, the C-major chord has three shapes because of the irregular major-third between the G- and B-strings.

A six-string guitar has five musical-intervals between its consecutive strings. In standard tuning, the intervals are four perfect fourths and one major third, the comparatively irregular interval for the (G,B) pair. Consequently, standard tuning requires four chord shapes for the major chords. There are separate chord forms for chords having their root note on the third, fourth, fifth, and sixth strings. [42] Of course, a beginner learns guitar by learning notes and chords, [43] and irregularities make learning the guitar difficult [44] —even more difficult than learning the formation of plural nouns in German, according to Gary Marcus. [45] Nonetheless, most beginners use standard tuning. [46]

Another feature of standard tuning is that the ordering of notes often differs from root position. Notes are often inverted or otherwise permuted, particularly with seventh chords in standard tuning, [47] as discussed below.

Power chords: fingerings

As previously discussed, each power chord has only one interval, a perfect fifth between the root note and the fifth. [7] In standard tuning, the following fingerings are conventional:

Triads

Triads are usually played with doubled notes, [48] as the following examples illustrate.

Major

Commonly used major chords are convenient to play in standard tuning, in which fundamental chords are available in open position , that is, the first three frets and additional open strings.

C major chord in open position C major chord for guitar (open).png
C major chord in open position

For the C major chord (C,E,G), the conventional left-hand fingering doubles the C and E notes in the next octave; this fingering uses two open notes, E and G:

  • E on the first string
  • C on the second string
  • G on the third string
  • E on the fourth string
  • C on the fifth string
  • Sixth string is not played. [49]

Major Chords (Guide for Guitar Chord Charts)

  • A: 002220
  • B: x24442
  • C: 032010
  • D: xx0232
  • E: 022100
  • F: 133211
  • F#: 244322 (movable – remember that no sharps or flats are between BC and EF)
  • Normal G: 320003
  • Nashville style G: 3×0033

For the other commonly used chords, the conventional fingerings also double notes and feature open-string notes:

Besides doubling the fifth note, the conventional E-major chord features a tripled bass note. [48]

A barre chord ("E Major shape"), with the index finger used to bar the strings Guitar barre chord.jpg
A barre chord ("E Major shape"), with the index finger used to bar the strings

The B major and F major chords are commonly played as barre chords, with the first finger depressing five–six strings.

B major chord has the same shape as the A major chord but it is located two frets further up the fretboard. The F major chord is the same shape as E major but it is located one fret further up the fretboard.

Minor

Minor chords (commonly notated as C-, Cm, Cmi or Cmin) are the same as major chords except that they have a minor third instead of a major third. This is a difference of one semitone.

To create F minor from the F major chord (in E major shape), the second finger should be lifted so that the third string plays onto the barre. Compare the F major to F minor:

The other shapes can be modified as well:

Chord nameFret numbers
E minor[0 2 2 0 0 0]
A minor[X 0 2 2 1 0]
D minor[X X 0 2 3 1]
Suspended

Movable Suspended Chords Guide (for chord charts)

(in standard tuning)

Sus2

  • A Sus2 x02200
  • B Sus2 x24422
  • C Sus2 x35533
  • D Sus2 x00230

Sus4

  • E SUS4 022200
  • F SUS4 133311
  • G SUS4 355533

These chords are used extensively by My Bloody Valentine, on the album Loveless. They are also used on the Who song "Pinball Wizard" and many, many more songs.

Dominant sevenths: drop two

In standard tuning, the C7 chord has notes on frets 3-8. Covering six frets is difficult, and so C7 is rarely played. Instead, an "alternative voicing" is substituted. C7 chord and alternative voicing for EADG (standard and all-fourths) tuning for six string guitar.png
In standard tuning, the C7 chord has notes on frets 3–8. Covering six frets is difficult, and so C7 is rarely played. Instead, an "alternative voicing" is substituted.
Dominant seventh chord on C guitar.png
Dominant seventh chord on C guitar barre.png
Dominant seventh chord on C, played on guitar in open position Play and as a barre chord Play .

As previously stated, a dominant seventh is a four-note chord combining a major chord and a minor seventh. For example, the C7 dominant seventh chord adds B to the C-major chord (C,E,G). The naive chord (C,E,G,B) spans six frets from fret 3 to fret 8; [50] such seventh chords "contain some pretty serious stretches in the left hand". [47] An illustration shows a naive C7 chord, which would be extremely difficult to play, [50] besides the open-position C7 chord that is conventional in standard tuning. [50] [lower-alpha 8] The standard-tuning implementation of a C7 chord is a second-inversion C7 drop 2 chord, in which the second highest note in a second inversion of the C7 chord is lowered by an octave. [50] [52] [53] Drop-two chords are used for sevenths chords besides the major–minor seventh with dominant function, [54] which are discussed in the section on intermediate chords, below. Drop-two chords are used particularly in jazz guitar. [55] Drop-two second-inversions are examples of openly voiced chords, which are typical of standard tuning and other popular guitar tunings. [lower-alpha 9]

"Alternatively voiced" seventh chords are commonly played with standard tuning. A list of fret number configurations for some common chords follows:

  • E7:[020100]
  • G7:[320001]
  • A7:[X02020]
  • B7:[X21202] (This B7 requires no barre, unlike the B major.)
  • D7:[XX0212]

Other chord inversions

Already in basic guitar playing, inversion is important for sevenths chords in standard tuning. It is also important for playing major chords.

In standard tuning, chord inversion depends on the bass note's string, and so there are three different forms for the inversion of each major chord, depending on the position of the irregular major thirds interval between the G and B strings.

For example, if the note E (the open sixth string) is played over the A minor chord, then the chord would be [0 0 2 2 1 0]. This has the note E as its lowest tone instead of A. It is often written as Am/E, where the letter following the slash indicates the new bass note. However, in popular music it is usual to play inverted chords on the guitar when they are not part of the harmony, since the bass guitar can play the root pitch.

Alternate tunings

Chords have consistent shapes everywhere on the fretboard for each regular tuning, for example, major-thirds (M3) tuning. Chords in major-thirds tuning C, D, G, minor, major, dominant seventh.png
Chords have consistent shapes everywhere on the fretboard for each regular tuning, for example, major-thirds (M3) tuning.
Diagonal shift of C-major chord in major-thirds tuning.png
Chords can be shifted diagonally in regular tunings.

There are many alternate tunings. These change the way chords are played, making some chords easier to play and others harder.

Open tunings

An open tuning allows a chord to be played by strumming the strings when "open", or while fretting no strings. The base chord consists of at least three notes and may include all the strings or a subset. The tuning is named for the base chord when played open, typically a major triad, and each major triad can be played by barring exactly one fret. [60] Open tunings are common in blues and folk music, [59] and they are used in the playing of slide and lap-slide ("Hawaiian") guitars. [60] [61] Ry Cooder uses open tunings when he plays slide guitar. [59]

Open tunings improve the intonation of major chords by reducing the error of third intervals in equal temperaments. For example, in the open-G overtones tuning G–G–D–G–B–D, the (G,B) interval is a major third, and of course each successive pair of notes on the G- and B-strings is also a major third; similarly, the open-string minor-third (B,D) induces minor thirds among all the frets of the B-D strings. The thirds of equal temperament have audible deviations from the thirds of just intonation: Equal temperament is used in modern music because it facilitates music in all keys, while (on a piano and other instruments) just intonation provided better-sounding major-third intervals for only a subset of keys. [65] "Sonny Landreth, Keith Richards and other open-G masters often lower the second string slightly so the major third is in tune with the overtone series. This adjustment dials out the dissonance, and makes those big one-finger major-chords come alive." [66]

Repetitive open-tunings are used for two non-Spanish classical-guitars. For the English guitar the open chord is C major (C–E–G–C–E–G); [67] for the Russian guitar which has seven strings, G major (G–B–D–G–B–D–G). [68] [69] [70] Mixing a perfect fourth and a minor third along with a major third, these tunings are on-average major-thirds regular-tunings. While on-average major-thirds tunings are conventional open tunings, properly major-thirds tunings are unconventional open-tunings, because they have augmented triads as their open chords. [71]

Regular tunings

Guitar chords are dramatically simplified by the class of alternative tunings called regular tunings. In each regular tuning, the musical intervals are the same for each pair of consecutive strings. Regular tunings include major-thirds (M3), all-fourths, augmented-fourths, and all-fifths tunings. For each regular tuning, chord patterns may be diagonally shifted down the fretboard, a property that simplifies beginners' learning of chords and that simplifies advanced players' improvisation. [72] [73] [74] The diagonal shifting of a C major chord in M3 tuning appears in a diagram.

Major-thirds tuning repeats its notes after three strings. Shift C-major chord three strings in major thirds tuning on six-string guitar.png
Major-thirds tuning repeats its notes after three strings.

Further simplifications occur for the regular tunings that are repetitive , that is, which repeat their strings. For example, the E–G–c–e–g–c' M3 tuning repeats its octave after every two strings. Such repetition further simplifies the learning of chords and improvisation; [73] This repetition results in two copies of the three open-strings' notes, each in a different octave. Similarly, the B–F–B–F–B–F augmented-fourths tuning repeats itself after one string. [75]

In major-thirds tuning, chords are inverted by raising notes by three strings on the same frets. The inversions of a C major chord are shown. First and second inversions of C-major chord on six-string guitar with major-thirds tuning.png
In major-thirds tuning, chords are inverted by raising notes by three strings on the same frets. The inversions of a C major chord are shown.

A chord is inverted when the bass note is not the root note. Chord inversion is especially simple in M3 tuning. Chords are inverted simply by raising one or two notes by three strings; each raised note is played with the same finger as the original note. Inverted major and minor chords can be played on two frets in M3 tuning. [76] [77] In standard tuning, the shape of inversions depends on the involvement of the irregular major third, and can involve four frets. [78]

It is a challenge to adapt conventional guitar chords to new standard tuning, which is based on all-fifths tuning. [lower-alpha 10]

Intermediate chords

After major and minor triads are learned, intermediate guitarists play seventh chords.

Tertian harmonization

Types of triads: I, i, i, I Type of triads-2.png
Types of triads: I , i , i , I
Stacking of third intervals

The fundamental guitar-chords—major and minor triads and dominant sevenths—are tertian chords, which concatenate third intervals, with each such third being either major (M3) or minor (m3).

More triads: diminished and augmented

As discussed above, major and minor triads are constructed by stacking thirds:

  • The major triad concatenates (M3,m3), supplementing M3 with a perfect-fifth (P5) interval, and
  • the minor triad concatenates (m3, M3), supplementing m3 with a P5 interval.

Similar tertian harmonization yields the remaining two triads:

More sevenths: major, minor, and (half-)diminished

Sevenths chords are constructed by stacking third intervals on the C-major scale. Fretboard diagrams for major-thirds tuning are shown. Sevenths via tertian harmonization of major scale on C.mid Sevenths via tertian harmonization of major scale on C minor on A.svg
Sevenths chords are constructed by stacking third intervals on the C-major scale. Fretboard diagrams for major-thirds tuning are shown. Sevenths via tertian harmonization of major scale on C.mid

Stacking thirds also constructs the most used seventh-chords. The most important seventh-chords concatenate a major triad with a third interval, supplementing it with a seventh interval:

  1. The (dominant) major-minor seventh concatenates a major triad with another minor third, supplementing it with a minor-seventh interval.
  2. The major seventh concatenates a major triad with a major third, supplementing it with a major-seventh interval.
  3. The minor seventh concatenates a minor triad with a minor third, supplementing it with a minor-seventh interval.
  4. The half-diminished seventh concatenates a diminished triad with a major third, supplementing it with a diminished-seventh interval.
  5. The (fully) diminished seventh concatenates a diminished triad with a minor third, supplementing it with a diminished-seventh interval. [80]

Four of these five seventh-chords—all but the diminished seventh—are constructed via the tertian harmonization of a major scale. [81] As already stated,

  1. The major-minor seventh has the dominant V7 function.
  2. The major seventh plays the tonic (I7) and subdominant (IV7) roles;
  3. The minor seventh plays the ii7, iii7, and vi7 roles.
  4. The half-diminished seventh plays the viiø7 role.

While absent from the tertian harmonization of the major scale,

Besides these five types there are many more seventh-chords, which are less used in the tonal harmony of the common-practice period. [80]

An approximate "ranking by frequency of the seventh chords in major".
V (dominant), ii (minor), vii (half-diminished), IVM (major), vi, IM, or iii Seventh chords frequency.png
An approximate "ranking by frequency of the seventh chords in major".
V (dominant), ii (minor), vii (half-diminished), IVM (major), vi , IM , or iii

When playing seventh chords, guitarists often play only a subset of notes from the chord. The fifth is often omitted. When a guitar is accompanied by a bass, the guitarist may omit the bass note from a chord. As discussed earlier, the third of a triad is doubled to emphasize its major or minor quality; similarly, the third of a seventh is doubled to emphasize its major or minor quality. The most frequent seventh is the dominant seventh; the minor, half-diminished, and major sevenths are also popular. [82]

Chord progression: circle of fifths

Sevenths chords arising in the tertian harmonization of the C-major scale, arranged by the circle of perfect fifths (perfect fourths). Fretboard diagrams for major-thirds tuning are shown. FifthsC.mid FifthsCSevenths.svg
Sevenths chords arising in the tertian harmonization of the C-major scale, arranged by the circle of perfect fifths (perfect fourths). Fretboard diagrams for major-thirds tuning are shown. FifthsC.mid

The previously discussed I–IV–V chord progressions of major triads is are a subsequence of the circle progression, which ascends by perfect fourths and descends by perfect fifths: Perfect fifths and perfect fourths are inverse intervals, because one reaches the same pitch class by either ascending by a perfect fourth (five semitones) or descending by a perfect fifth (seven semitones). For example, the jazz standard "Autumn Leaves" contains the iv7–VII7–VIM7–iiø7–i circle-of-fifths chord progression; [83] its sevenths occur in the tertian harmonization in sevenths of the minor scale. [84] Other subsequences of the fifths-circle chord progression are used in music. In particular, the ii–V–I progression is the most important chord progression in jazz music.

Chord chart guide for major inversions

Major inversions for guitar in standard tuning. The low E is on the left. The A demonstrates three of the different movable shapes.

  • A: [XXX655] | A: [XXX9(10)9] | A: [XXX220]
  • B: [XXX442]
  • C: [XXX553]
  • D: [XXX775]
  • E: [XXX997]
  • F: [XXX211]
  • G: [XXX433] [85]

Specific tunings

Standard tuning: minor and major sevenths

Guitar - Dm7 chord.png

Besides the dominant seventh chords discussed above, other seventh chords—especially minor seventh chords and major seventh chords—are used in guitar music.

Minor seventh chords have the following fingerings in standard tuning:

  • Dm7: [XX0211]
  • Em7: [020000]
  • Am7: [X02010]
  • Bm7: [X20202]
  • Fm7: [202220] or ([XX2222] Also an A/F Chord)

Major seventh chords have the following fingerings in standard tuning:

  • Cmaj7: [X32000]
  • Dmaj7: [XX0222]
  • Emaj7: [021100]
  • Fmaj7: [103210]
  • Gmaj7: [320002]
  • Amaj7: [X02120]

Major-thirds tuning

In major-thirds (M3) tuning, the chromatic scale is arranged on three consecutive strings in four consecutive frets. [86] [87] This four-fret arrangement facilitates the left-hand technique for classical (Spanish) guitar: [87] For each hand position of four frets, the hand is stationary and the fingers move, each finger being responsible for exactly one fret. [88] Consequently, three hand positions (covering frets 1–4, 5–8, and 9–12) partition the fingerboard of classical guitar, [89] which has exactly 12 frets. [lower-alpha 11]

Only two or three frets are needed for the guitar chords—major, minor, and dominant sevenths—which are emphasized in introductions to guitar-playing and to the fundamentals of music. [92] [93] Each major and minor chord can be played on exactly two successive frets on exactly three successive strings, and therefore each needs only two fingers. Other chords—seconds, fourths, sevenths, and ninths—are played on only three successive frets. [94]

Advanced chords and harmony

Sequences of thirds and seconds

The circle of fifths was discussed in the section on intermediate guitar chords. Other progressions are also based on sequences of third intervals; [95] progressions are occasionally based on sequences of second intervals. [96]

Extended chords

Ninth chord voice leading.png
Eleventh chord voice leading.png
Commonly voiced with only four notes in open position, ninth and eleventh chords often play a dominant (V) role. Play 9th (left) Play 11th

As their categorical name suggests, extended chords indeed extend seventh chords by stacking one or more additional third-intervals, successively constructing ninth, eleventh, and finally thirteenth chords; thirteenth chords contain all seven notes of the diatonic scale. In closed position, extended chords contain dissonant intervals or may sound supersaturated, particularly thirteenth chords with their seven notes. Consequently, extended chords are often played with the omission of one or more tones, especially the fifth and often the third, [97] [98] as already noted for seventh chords; similarly, eleventh chords often omit the ninth, and thirteenth chords the ninth or eleventh. Often, the third is raised an octave, mimicking its position in the root's sequence of harmonics. [97]

Dominant ninth chords were used by Beethoven, and eleventh chords appeared in Impressionist music. Thirteenth chords appeared in the twentieth century. [99] Extended chords appear in many musical genres, including jazz, funk, rhythm and blues, and progressive rock/progressive metal. [98]

Chord guide for major and minor 9 chords

(Standard tuning, read from left to right, low E to high e)

Major 9

Minor 9

Alternative harmonies

Scales and modes

Conventional music uses diatonic harmony, the major and minor keys and major and minor scales, as sketched above. Jazz guitarists must be fluent with jazz chords and also with many scales and modes; "of all the forms of music, jazz ... demands the highest level of musicianship—in terms of both theory and technique". [100]

Whole tone scales were used by King Crimson for the title track on its Red album of 1974; [101] [102] whole tone scales were also used by King Crimson guitarist Robert Fripp on "Fractured". [101]

Beyond tertian harmony

Disliking the sound of thirds (in equal-temperament tuning), Robert Fripp builds chords with perfect intervals in his new standard tuning. Robert Fripp.jpg
Disliking the sound of thirds (in equal-temperament tuning), Robert Fripp builds chords with perfect intervals in his new standard tuning.

In popular music, chords are often extended also with added tones, especially added sixths. [103]

Quartal and quintal harmony

Chords are also systematically constructed by stacking not only thirds but also fourths and fifths, supplementing tertian major–minor harmony with quartal and quintal harmonies. Quartal and quintal harmonies are used by guitarists who play jazz, folk, and rock music.

Quartal harmony has been used in jazz by guitarists such as Jim Hall (especially on Sonny Rollins's The Bridge ), George Benson ("Skydive"), Kenny Burrell ("So What"), and Wes Montgomery ("Little Sunflower"). [104]

Harmonies based on fourths and fifths also appear in folk guitar. On her 1968 debut album Song to a Seagull , Joni Mitchell used both quartal and quintal harmony in "Dawntreader", and she used quintal harmony in "Seagull". [105]

Quartal and quintal harmonies also appear in alternate tunings. It is easier to finger the chords that are based on perfect fifths in new standard tuning than in standard tuning. New standard tuning was invented by Robert Fripp, a guitarist for King Crimson. Preferring to base chords on perfect intervals—especially octaves, fifths, and fourths—Fripp often avoids minor thirds and especially major thirds, [106] which are sharp in equal temperament tuning (in comparison to thirds in just intonation).

Alternative harmonies can also be generated by stacking second intervals (major or minor). [107]

See also

Related Research Articles

<span class="mw-page-title-main">Musical tuning</span> Terms for tuning an instrument and a systems of pitches

In music, there are two common meanings for tuning:

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

<span class="mw-page-title-main">Perfect fifth</span> Musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

<span class="mw-page-title-main">Power chord</span> Type of guitar chord

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

A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.

<span class="mw-page-title-main">Chord (music)</span> Harmonic set of two or more notes

In music, a chord is a group of two or more notes played simultaneously, typically consisting of a root note, a third, and a fifth. Chords are the building blocks of harmony and form the harmonic foundation of a piece of music. They can be major, minor, diminished, augmented, or extended, depending on the intervals between the notes and their arrangement. Chords provide the harmonic support and coloration that accompany melodies and contribute to the overall sound and mood of a musical composition. For many practical and theoretical purposes, arpeggios and other types of broken chords may also be considered as chords in the right musical context.

<span class="mw-page-title-main">Root (chord)</span> Musical note characterizing a chord

In the music theory of harmony, the root is a specific note that names and typifies a given chord. Chords are often spoken about in terms of their root, their quality, and their extensions. When a chord is named without reference to quality, it is assumed to be major—for example, a "C chord" refers to a C major triad, containing the notes C, E, and G. In a given harmonic context, the root of a chord need not be in the bass position, as chords may be inverted while retaining the same name, and therefore the same root.

In music, a minor seventh chord is a seventh chord composed of a root note, a minor third, a perfect fifth, and a minor seventh. In other words, one could think of it as a minor triad with a minor seventh attached to it.

<span class="mw-page-title-main">Guitar tunings</span> Adjusting pitches of guitar strings

Guitar tunings are the assignment of pitches to the open strings of guitars, including classical guitars, acoustic guitars, and electric guitars. Tunings are described by the particular pitches that are made by notes in Western music. By convention, the notes are ordered and arranged from the lowest-pitched string to the highest-pitched string, or the thickest string to thinnest, or the lowest frequency to the highest. This sometimes confuses beginner guitarists, since the highest-pitched string is referred to as the 1st string, and the lowest-pitched is the 6th string.

<span class="mw-page-title-main">New standard tuning</span> Alternative guitar tuning

New standard tuning (NST) is an alternative tuning for the guitar that approximates all-fifths tuning. The guitar's strings are assigned the notes C2-G2-D3-A3-E4-G4 ; the five lowest open strings are each tuned to an interval of a perfect fifth {(C,G),(G,D),(D,A),(A,E)}; the two highest strings are a minor third apart (E,G).

<span class="mw-page-title-main">Open C tuning</span>

Open C tuning is an open tuning for guitar. The open-string notes form a C major chord, which is the triad (C,E,G) having the root note C, the major third (C,E), and the perfect fifth (C,G). When the guitar is strummed without fretting any strings, a C-major chord is sounded. By barring all of the strings for one fret, one finger suffices to fret the other eleven major-chords.

<span class="mw-page-title-main">Diatonic and chromatic</span> Terms in music theory to characterize scales

Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.

In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".

Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:

  1. the root note,
  2. the chord quality,
  3. whether the chord is a triad, seventh chord, or an extended chord,
  4. any altered notes,
  5. any added tones, and
  6. the bass note if it is not the root.
<span class="mw-page-title-main">Major thirds tuning</span> Regular tuning among guitars

Among alternative tunings for guitar, a major-thirds tuning is a regular tuning in which each interval between successive open strings is a major third. Other names for major-thirds tuning include major-third tuning, M3 tuning, all-thirds tuning, and augmented tuning. By definition, a major-third interval separates two notes that differ by exactly four semitones.

<span class="mw-page-title-main">Regular tuning</span>

Among alternative guitar-tunings, regular tunings have equal musical intervals between the paired notes of their successive open strings.

<span class="mw-page-title-main">Ralph Patt</span> American jazz guitarist

Ralph Oliver Patt was an American jazz guitarist who introduced major-thirds tuning. Patt's tuning simplified the learning of the fretboard and chords by beginners and improvisation by advanced guitarists. He invented major-thirds tuning under the inspiration of first the atonal music of Arnold Schoenberg and second the jazz of John Coltrane and Ornette Coleman.

<span class="mw-page-title-main">Repetitive tuning</span>

Repetitive tunings are a type of alternative tunings for the guitar. A repetitive tuning begins with a list of notes that is duplicated, either at unison or at higher octaves.

<span class="mw-page-title-main">Overtones tuning</span> Tuning for a guitar

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

Footnotes

  1. An octave is the interval between one musical pitch and another with double (or half) its frequency.
  2. This sequence of fifths features the diminished fifth (b,f), which replaces the perfect fifth (b,f) containing the chromatic note f, which is not a member of the C-major key. The note f (of the C-major scale) is replaced by the note f in the Lydian chromatic scale. [5]
    Guitar chord
  3. Perfect fifths have been emphasized since the chants and hymns of medieval Christendom, according to the medieval musical-theory called the organum. [6]
  4. Denyer (1992) and Schmid & Kolb (2002) each list the same fifteen chords for beginners: Am, A, A7; B7; C, C7; Dm, D, D7; Em, E, E7; F; G, G7. [11]
  5. 1 2 3 4 5 6 This chord does not appear among the fifteen basic chords listed independently by Denyer and by Schmid and Kolb: Am, A, A7; B7; C, C7; Dm, D, D7; Em, E, E7; F; G, G7. [11]
  6. 1 2 3 Roman numeral analysis. [17]
  7. The harmony of major chords has dominated music since the Baroque era (17th and 18th centuries). [34] The Baroque period also introduced the dominant seventh. [35]
  8. The alternative voicing of the C7 chord follows the first seventh-chord diagram of (Denyer 1992). [51]
  9. Closed voicings, which are typical of minor-thirds tuning, are typical also of a keyboard or piano. [56]
  10. Musicologist Eric Tamm wrote that despite "considerable effort and search I just could not find a good set of chords whose sound I liked" for rhythm guitar. [79]
  11. Classical guitars have 12 frets, while steel-string acoustics have 14 or more. [90] Electrical guitars have more frets, for example 20. [91]

Citations

  1. Persichetti 1961, p. 14.
  2. Denyer 1992, Playing the guitar: The harmonic guitarist; Intervals: Interval chart, pp. 118–119.
  3. Persichetti 1961, pp. 23–24.
  4. Denyer 1992, p. 114.
  5. Russell 2001, "The fundamental harmonic structure of the Lydian scale", Example 1:7, "The C Lydian scale", p. 5.
  6. Duarter 2008, p. 49.
  7. 1 2 3 4 5 Denyer (1992 , "The advanced guitarist; Power chords and fret tapping: Power chords", p. 156)
  8. Kolb 2005, "Chapter 7: Chord construction; Suspended chords, power chords, and 'add' chords", p. 42.
  9. Denyer 1992, "The Guitar Innovators: Pete Townshend", pp. 22–23.
  10. Mead 2002, pp. 28 and 81, compare p. 40.
  11. 1 2 Denyer (1992, The beginner, Open chords, The beginner's chord dictionary, pp. 74–75) and Schmid & Kolb (2002, Chord chart, p. 47).
  12. Denyer 1992, pp. 123–125.
  13. Kolb 2005, Chapter 6: Harmonizing the major scale, pp. 35–38; Chapter 7: Chord construction, pp. 40–48; and Chapter 8: Harmonizing the minor scale, pp. 49–51.
  14. Duckworth 2007, Chapter 11 "Triads" and Chapter 12 "Triads in a musical context".
  15. Kolb (2005 , Chapter 5: Triads, Major and minor triads, pp. 30-31)
  16. Griewank (2010 , p. 5)
  17. Denyer 1992, "The beginner: The three-chord theory, Chords built on the major scale in five common keys", p. 76.
  18. 1 2 3 4 Denyer (1992 , "The beginner: The three-chord theory, Chord progressions based on the three-chord theory", p. 77)
  19. Kolb 2005, Chapter 6: Harmonizing the major scale, Diatonic triads, Figure3, Harmonized major scales (triads), p. 38.
  20. Everett 2008, p.  35.
  21. Kolb 2005, Chapter 6: Harmonizing the major scale: Diatonic triads, pp. 35–36.
  22. Duckworth 2007, p. 239.
  23. Kolb 2005, Chapter 8: Harmonizing the major scale, Figure 4, Harmonized minor scales (triads), p. 50.
  24. Denyer 1992, pp. 77–78.
  25. Duckworth 2007, p. 156.
  26. Kolb 2005, Chapter 8: Harmonizing the minor scale, Minor scale triads, pp. 49–50.
  27. Kostka, Payne & Almén 2013, Chapter 3: Introduction to triads and seventh chords, Seventh chords, pp. 40–41, and Chapter 13: The V7 chord, p. 198.
  28. Duckworth 2007, p. 245.
  29. Kostka, Payne & Almén 2013, Chapter 3: Introduction to triads and seventh chords, Seventh chords, p. 40–41, Chapter 13: The V7 chord, p. 198, and Chapter 14, The II7 and VII7 chords, p. 217.
  30. Kolb 2005, Chapter 6: Harmonizing the major scale, Diatonic seventh chords, pp. 37–38; Chapter 7: Chord construction, Seventh chords, Diminished seventh, dominant seventh SUS4, and minor(maj7) chords, pp. 44–45; Chapter 8: Harmonizing the minor scale: Minor scale seventh chords, p. 51.
  31. Kolb 2005, Chapter 6: Figure 5, Harmonized major scales (seventh chords), p. 38.
  32. 1 2 Benitez (2010 , p.  29 )
  33. Kolb 2005, Chapter 6: Harmonizing the major scale, Diatonic seventh chords, pp. 37–38.
  34. Benward & Saker 2003, p. 100.
  35. Benward & Saker 2003, p. 201.
  36. 1 2 Denyer (1992 , "The beginner: The three-chord theory: Blues chord progressions, p. 77)
  37. Kolb 2005, Chapter 10: Blues harmony and pentatonic scales, The 12-bar blues progression", pp. 61–62.
  38. LeVan, John (December 2007). "Go Nuts!". Acoustic Guitar. String Letter Publishing.[ dead link ]
  39. Sethares (2001 , pp. 54)
  40. Denyer (1992 , "The harmonic guitarist: Interval inversions, Triad doubling", p. 123)
  41. Clendinning & Marvin 2005, p. 181.
  42. Denyer 1992, p. 119.
  43. Marcus 2012, p. 46.
  44. Marcus 2012, pp. 40–43.
  45. Marcus 2012, pp. 39–40.
  46. Marcus 2012, p. 181.
  47. 1 2 Kolb (2005 , Chapter 6: Harmonizing the major scale: Diatonic seventh chords, p. 37)
  48. 1 2 Roche (2004 , p. 104)
  49. Denyer 1992, p. 75.
  50. 1 2 3 4 Smith (2010 , pp.  92–93 )
  51. Denyer 1992, "The harmonic guitarist: Seventh chords: The dominant seventh chords", p. 127.
  52. Chapman 2000, p.  6.
  53. Fisher 2002, 'Drop voicing' and '7th chords in drop 2 and drop 3 voicings', pp. 30–33.
  54. Willmott 1994, Chapter 1: Drop 2 type voicings, pp. 8–13.
  55. Vincent 2011, pp. 2–7.
  56. Sethares 2001, "The minor third tuning", p. 54.
  57. Roche (2004 , "Open tunings", pp. 156–159)
  58. Roche (2004 , "Cross-note tunings", p. 166)
  59. 1 2 3 Denyer (1992 , p. 158)
  60. 1 2 3 Sethares (2009 , p. 16)
  61. 1 2 Denyer (1992 , p. 160)
  62. Roche (2004 , pp. 153–156)
  63. Denyer (1992 , pp. 158–159)
  64. Sethares (2009 , p. 2) "Learn a handful of chord forms in a regular tuning, and you'll know hundreds of chords!"
  65. Gold, Jude (1 December 2005). "Just desserts: Steve Kimock shares the sweet sounds of justly tuned thirds and sevenths". Master class. Guitar Player.[ dead link ]
  66. Gold, Jude (June 2007). "Fender VG Stratocaster". Gear: Bench Test (Product/service evaluation). Guitar Player. Archived from the original on 16 January 2013.
  67. Annala & Mätlik 2007, p. 30.
  68. Ophee, Matanya (ed.). 19th Century etudes for the Russian 7-string guitar in G Op. The Russian Collection. Vol. 9. Editions Orphee. PR.494028230. Archived from the original on 4 July 2013.
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Bibliography

Further reading

Berklee College of Music

Professors at the Department of Guitar at the Berklee College of Music wrote the following books, which like their colleagues' Chapman (2000) and Willmott (1994) are Berklee-course textbooks: