Guitar tunings

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The range of a guitar with standard tuning
Standard tuning (listen)

Guitar tunings assign pitches to the open strings of guitars. Tunings can be described by the particular pitches that are denoted by notes in Western music. By convention, the notes are ordered from lowest to highest.[1]

The phrase "guitar tuning" also refers to the adjusting of the string-pitches to their desired tuning, which is described in how-to manuals for guitarists.[2]

Standard tuning defines the string pitches as E, A, D, G, B, and E, from lowest (low E) to highest (high E). Standard tuning is used by most guitarists, and frequently used tunings can be understood as variations on standard tuning.

"Nonstandard" tunings are also called "alternative" or "alternate". Some tunings are used for particular songs by professional musicians, and may be called after the song's title. There are hundreds of such tunings, which are often minor variants of established tunings. Fewer alternative tunings are used regularly by communities of guitarists who share a musical tradition.

The hundreds of alternative tunings have been classified into a smaller number of categories: "open", both major and minor ("crossnote"), and "modal"; "dropped"; "instrumental" (based on other stringed instruments); and "regular". Modal, dropped, and many other tunings are mentioned in the supplementary list of guitar tunings.

Standard and alternatives[edit]

In standard tuning, the C-major chord has three shapes because of the irregular major-third between the G- and B-strings.

Standard[edit]

Guitar tunings have evolved over the years. Standard tuning is the tuning most frequently used on a 6-string guitar and musicians assume this tuning by default if a specific alternate or scordatura is not mentioned. It consists of the following notes:

E2-A2-D3-G3-B3-E4.

The letter gives the pitch name of each note, and the number indicates in which octave the pitch lies. This system is known as scientific pitch notation, and also ties each letter/number combination to a specific frequency:[3]

String Frequency Scientific pitch notation
1 (E) 329.63 Hz E4
2 (B) 246.94 Hz B3
3 (G) 196.00 Hz G3
4 (D) 146.83 Hz D3
5 (A) 110.00 Hz A2
6 (E) 82.41 Hz E2

In regions of Europe where classical musicians use the German system, the B natural is indicated with the letter H: in this system, H is B (B natural), and B is B (B flat). The guitar is a transposing instrument—music for it is notated one octave higher than actual sounding pitch, to reduce the need for ledger lines in music written for the instrument, and simplify reading.

The fifth string (A2) is tuned to 110 Hz, exactly two octaves below the standard orchestral reference pitch of 440 Hz (A440). Tuning forks and electronic tuners that match these frequencies are commonly available, so a properly tuned fifth string can provide a reference to tune the remaining strings by ear. Tuning forks which provide the pitch of the high E string (329.63 Hz) are also common.

The guitar is conventionally an equal-tempered instrument. The frets are positioned logarithmically, creating equally-tempered pitches along each string. However, guitarists who tune by ear will typically tune "clean" so that dissonant beating between particular strings is minimized. In this way, open intervals can be more consonant. This is known as just intonation, which is at variance with equal temperament. When the guitar is tuned in this way, open tunings theoretically allow for certain chords to be more consonant.

Standard tuning provides reasonably simple fingering (left hand movement) for playing standard scales and basic chords in all major and minor keys. The separation of the first (e') and second (b) string, as well as the separation between the third (g), fourth (d), fifth (A), and sixth (E) strings by a five-semitone interval (a perfect fourth) allows notes of the chromatic scale to be played with each of the four fingers of the left hand controlling one of the first four frets (index finger on fret 1, little finger on fret 4, etc.) only when the hand is in the first position; otherwise, the four fingers must stretch to cover five frets.

The separation of the second (b), and third (g) string is by a four-semitone interval (a major third). The irregular major-third provides B and E as open notes, which is convenient for many chords. On the other hand, the irregular major-third breaks the fingering patterns of scales and chords, so that guitarists have to memorize multiple chord-shapes for each chord. Scales and chords are simplified by major thirds tuning and all-fourths tuning, which are regular tunings maintaining the same musical interval between consecutive open-string notes.

0 I II III IV
open 1st fret (index) 2nd fret (middle) 3rd fret (ring) 4th fret (little)
6th string E F F/G G G/A
5th string A A/B B C C/D
4th string D D/E E F F/G
3rd string G G/A A A/B B
2nd string B C C/D D D/E
1st string E F F/G G G/A
Chromatic note progression

Alternative[edit]

Alternative ("alternate") tuning refers to any open-string note-arrangement other than standard tuning. Such alternative tuning arrangements offer different sonorities, chord voicings, and fingerings. Alternative tunings are common in folk music, where the guitar may emulates various ethnic instruments and tunings, and may be called upon to produce drones. Alternative tunings necessarily change the fingering shapes of common chords associated with standard tuning, which eases the playing of some non-standard chords at the cost of increasing the difficulty of some standard chords.

Some tunings are used for particular songs by professional musicians, and may be called after the song's title. There are hundreds of such tunings, which are often minor variants of other alternate tunings.[4] A few alternative tunings are used regularly by communities of guitarists who share a musical tradition, such as American folk or Celtic folk music.

The hundreds of alternative tunings have been classified into a smaller number of categories:[5] dropped,[6][7] open,[8] both major and minor (cross note),[9][7][10] modal,[7][11] instrumental (based on other stringed instruments), and miscellaneous ("special").[7][10][12]

String gauges[edit]

Some alternative tunings are difficult or even impossible to achieve with conventional sets of guitar strings, which have gauges optimized for standard tuning. With conventional sets, some higher tunings increase string-tension until playing requires more finger-strength and stamina or even until a string snaps or the guitar is warped; with lower tunings, strings may be loose and buzz. Therefore, many alternative tunings benefit from re-stringing of the guitar with string gauges chosen to optimize particular tunings.[13]

Dropped tunings[edit]

A dropped tuning starts with standard tuning and typically lowers the pitch ("drops") of only a single string, or (rarely) two strings. This is almost always the lowest pitched (E) string on the guitar, although occasionally the A string may be lowered. The dropped D tuning, for example, is extremely common in classical guitar music. For it, the low E string is tuned down one whole step, to a low D, and the rest of the guitar remains in standard tuning.

Open tunings[edit]

Ry Cooder plays the guitar.
Ry Cooder plays slide-guitar with open tunings.

An open tuning allows a chord to be played by strumming the strings when "open" (no strings fretted). Open tunings may be either chordal or modal. In chordal open tunings the base chord consists of at least three different pitch classes, and may include all the strings or a subset. The tuning is named for the base chord when played open, typically a major chord, and all similar chords in the chromatic scale can then be played by barring all strings across a single fret.[14] Open tunings are common in blues and folk music.[15] These tunings are frequently used in the playing of slide and lap-slide ("Hawaiian") guitars, and Hawaiian slack key music.[14][16] Ry Cooder uses open tunings when he plays slide guitar.[15]

Equal temperament is used in modern music because it facilitates the playing of music in any key, as compared to just intonation which favors only a few certain keys, all other keys sounding more or less "out of tune".[17]

Relative to the "pure" thirds in the overtone series, equal-temperament widens the major third by an all-too audible 14 cents, and it narrows the minor third by an even more horrifying 16 cents (1 cent is one hundredth (1 percent) of a semitone). So, the 3 note (F#) of a D-major chord, and the b3 note (F) of a D-minor chord, may well sound a lot better / more pleasing to the ear if they are adjusted downward or upward, respectively. Unfortunately, making such an adjustment in standard tuning—and in most other tunings—is inadmissible, because it's not possible to tune the notes sounded on a particular string individually; adjusting the intonation of a string affects the intonation of all of the notes which lie "under" it ... some of which will be the 1, 4, and 5 notes of other chords. Since these notes are not displaced (or are only slightly displaced) by even-temperament, any adjustment to "improve" the intonation of a 3 note in one chord will just throw other chords badly out-of-tune.

Our "open" tunings (ones whose open strings form a simple chord) are the one exception to this rule. To the extent that we play with a slide (like the Delta blues players) or with one barred finger or some other grip (Keith Richards) that is essentially just moved up and down the neck, ... then the 3 of the chord can be tuned more or less "pure", as in the holy overtone series. In open-G tuning (G,G,D,G,B,D), the 3 (B) of the open-G major-triad is on string 2. If we barre or use a slide to play the IV chord (C) at fret 5, the 3 of that chord (E) is still on string 2 ... as it will be when we slide up to the V chord, or the bVII chord, or the octave. As long as we don't wantonly introduce other chord shapes, our adjustment to string 2 won't break anything. If we're playing with a slide, this is more or less guaranteed.[18]

—Warren Allen

Open tunings allow "better" intonation of certain chords than do non-open tunings, because they allow the open strings to be places in just intonation, reducing the "error" of thirds in equal temperaments tuning. 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. Of all the intervals in equal temperament, the thirds have the largest deviation in comparison to those of just intonation:

"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."[19]

Repetitive open-tunings are used for two classical non-Spanish guitars. For the English guitar, the open chord is C major (C-E-G-C-E-G);[20] for the Russian guitar, which has seven strings, G major (G-B-D-G-B-D-G).[21] 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.[22]

When the open strings constitute a minor chord, the open tuning is called a cross-note tuning.

Major key tunings[edit]

C's first 8 harmonics (C,C,G,C,E,G,B,C) About this sound Play simultaneously 
Open D tuning.
Open D tuning (listen)
Open G tuning (listen)

Major open-tunings give a major chord with the open strings.

Open tunings
Major triad Repetitive Overtones Other

(often most popular)

Open A (A,C,E) A-C-E-A-C-E A-A-E-A-C-E E-A-C♯-E-A-E
Open B (B,D,F) B-D-F-B-D-F B-B-F-B-D-F B-F-B-F-B-D
Open C (C,E,G) C-E-G-C-E-G C-C-G-C-E-G C-G-C-G-C-E
Open D (D,F,A) D-F-A-D-F-A D-D-A-D-F-A D-A-D-F♯-A-D
Open E (E,G,B) E-G-B-E-G-B E-E-B-E-G-B E-B-E-G-B-E
Open F (F,A,C) F-A-C-F-A-C F-F-C-F-A-C C-F-C-F-A-F
Open G (G,B,D) G-B-D-G-B-D G-G-D-G-B-D D-G-D-G-B-D

Open tunings often tune the lowest open-note to C, D, or E and they often tune the highest open-note to D or E; tuning down the open-string from E to D or C avoids the risk of breaking strings, which is associated with tuning up strings. The most popular open-tunings have the open-string patterns

R-5-R-5-R-3 (Open C),
R-5-R-3-5-R (Open D and E),
5-R-5-R-3-5 (Open G)

where R, 3, and 5 represent the major triad's root, major third, or perfect fifth. In these tunings, the root is repeated thrice or twice, and the perfect fifth twice or thrice; the major third once.[15] In repetitive open-tunings, the open major-triad's major third is doubled; in non-repetitive open-tunings, the major third is not doubled. A seventh chord is often played by omitting the highest perfect-fifth; when a perfect fifth or other notes are omitted from a chord, the major-third note is retained.

Open D[edit]

The Open D tuning D-A-D-F-A-D, also called "Vestopol" tuning,[23] is one of the most common open tunings used by European and American guitarists working with alternate tunings. There are countless recorded examples, including Joni Mitchell ("Big Yellow Taxi"), Bruce Cockburn ("Sunwheel Dance), Leo Kottke (many of his slide tunes), John Fahey (multiple tunes) and many others. The popular Allman Brothers instrumental "Little Martha" used an open D tuning raised one half step, giving an open Eb tuning with the same intervalic relationships as open D.[24]

Open C[edit]

The English guitar used a repetitive open-C tuning (with distinct open-notes C-E-G-C-E-G) that approximated a major-thirds tuning.[25] The C-G-C-G-C-E tuning was used by William Ackerman for his "Townsend Shuffle" and by John Fahey for his tribute to Mississippi John Hurt.[26][27]

The C-C-G-C-E-G tuning uses some of the harmonic sequence (overtones) of the note C. When an open-note C-string is struck, its harmonic sequence begins with the notes (C,C,G,C,E,G,B,C).[28][29] This overtone-series tuning was modified by Mick Ralphs, who used a high C rather than the high G for "Can't get enough" on Bad Company. Ralphs said, "It needs the open C to have that ring," and "it never really sounds right in standard tuning". Ralphs wrote these songs in the key of G on a guitar in Open-G tuning.[30]

Open G[edit]

Mick Ralphs' Open-C tuning was originally an open-G tuning, which listed the initial six overtones of the G note, namely G-G-D-G-B-D; Ralphs used this open-G tuning for "Hey Hey" and while writing the demo of "Can't Get Enough".[30]

The open G tuning G-G-D-G-B-D was used by Joni Mitchell for "Electricity", "For the Roses" and "Hunter (The Good Samaritan)".[31] Truncating this tuning to G-D-G-B-D for his five-string guitar, Keith Richards plays this overtones-tuning on The Rolling Stones's "Honky Tonk Women", "Brown Sugar" and "Start Me Up".[32]

The Russian guitar uses the open-G tuning D-G-B-D-G-B-D, which is approximately in major thirds.[33][34]

Minor or "cross-note" tunings[edit]

Cross-note tunings include a minor third, so giving a minor chord with open strings. Fretting the minor-third string at the first fret produces a major-third, so allowing a one-finger fretting of a major chord.[35] By contrast, it is more difficult to fret a minor chord using an open major-chord tuning.

Cross-note E-minor was used by Bukka White and Skip James.[36]

Other open chordal tunings[edit]

Some guitarists have opted for open tunings which use more complex chords, which give them more available intervals on the open strings. C6, E6, E7, E6/9 and other such tunings are common among lap-steel players such as Hawaiian slack-key guitarists and country guitarists, and are also sometimes applied to the regular guitar by bottleneck players striving to emulate these styles. A common C6 tuning, for example, is C E G A C E, which provides open major and minor thirds, open major and minor sixths, fifths, and octaves. By contrast, most open major or open minor tunings provide only octaves, fifths, and either a major third/sixth or a minor third/sixth—but not both. Don Helms of Hank Williams band favored C6 tuning; slack-key artist Henry Kaleialoha Allen uses a modified C6/7 (C6 tuning with a Bb on the bottom); Harmon Davis favored E7 tuning; David Gilmour has used an open G6 tuning.

Modal tunings[edit]

Modal tunings are open tunings in which the open strings of the guitar do not produce a tertian (i.e., major or minor, or variants thereof) chord. The strings may be tuned to exclusively present a single interval (all fourths; all fifths; etc.) Or they may be tuned to a non-tertian chord (unresolved suspensions such as E A B E A E, for example). Modal open tunings may use only one or two pitch classes across all strings (as, for example, some metal guitarists who tune each string to either E or B, effecting the playing of "power chords" of ambiguous major/minor tonality).

Regular tunings[edit]

Regular tunings
For regular guitar-tunings, the distance between consecutive open-strings is a constant musical-interval, measured by semitones on the chromatic circle. The chromatic circle lists the twelve notes of the octave.
Basic information
Aliases Uniform tunings
Advanced information
Advantages Simplifies learning by beginners and improvisation by advanced guitarists
Disadvantages Replicating the open chords ("cowboy chords") of standard tuning is difficult;
intermediate guitarists must relearn the fretboard and chords.
Regular tunings (semitones)
Trivial (0)
Minor thirds (3)
Major thirds (4)
All fourths (5)
Augmented fourths (6)
New standard (7, 3)
All fifths (7)
Minor sixths (8)
Guitar tunings
A fretboard with line-segments connecting the successive open-string notes of the standard tuning
In the standard guitar-tuning, one major-third interval is interjected amid four perfect-fourth intervals. In each regular tuning, all string successions have the same interval.
A C-major chord in four positions.
Chords can be shifted diagonally in major-thirds tuning and other regular tunings. In standard tuning, chords change their shape because of the irregular major-third G-B.
Main article: Regular tunings

For the standard tuning, there is exactly one interval of a third between the second and third strings, and all the other intervals are fourths. The irregularity has a price. Chords cannot be shifted around the fretboard in the standard tuning E-A-D-G-B-E, which 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.[37]

In contrast, regular tunings have equal intervals between the strings,[38] and so they have symmetrical scales all along the fretboard. This makes it simpler to translate chords. For the regular tunings, chords may be moved diagonally around the fretboard. The diagonal movement of chords is especially simple for the regular tunings that are repetitive, in which case chords can be moved vertically: Chords can be moved three strings up (or down) in major-thirds tuning and chords can be moved two strings up (or down) in augmented-fourths tuning. Regular tunings thus appeal to new guitarists and also to jazz-guitarists, whose improvisation is simplified by regular intervals.

On the other hand, 5-6 string open chords ("cowboy chords") are more difficult to play in a regular tuning than in standard tuning. Instructional literature uses standard tuning.[39] Traditionally a course begins with the hand in first position,[40] that is, with the left-hand covering frets 1–4.[41] Beginning players first learn open chords belonging to the major keys CG, and D. Guitarists who play mainly open chords in these three major-keys and their relative minor-keys (AmEmBm) may prefer standard tuning over many regular tunings,[42][43] On the other hand, minor-thirds tuning features many barre chords with repeated notes,[44] properties that appeal to acoustic-guitarists and beginners.

Major thirds and perfect fourths[edit]

Standard tuning mixes a major third (M3) with its perfect fourths. Regular tunings that are based on either major thirds or perfect fourths are used, for example, in jazz.

All fourths tuning E-A-d-g-c'-f' keeps the lowest four strings of standard tuning, changing the major third to a perfect fourth.[45][46] Jazz musician Stanley Jordan stated that all-fourths tuning "simplifies the fingerboard, making it logical".[47]

Major-thirds tuning (M3 tuning) is a regular tuning in which the musical intervals between successive strings are each major thirds, for example

E-G-c-e-g-c'.[22][48][49][50] Unlike all-fourths and all-fifths tuning, M3 tuning repeats its octave after three strings, which simplifies the learning of chords and improvisation.[39] This repetition provides the guitarist with many possibilities for fingering chords.[22][50] With six strings, major-thirds tuning has a smaller range than standard tuning; with seven strings, the major-thirds tuning covers the range of standard tuning on six strings.[48][49][50]

Major-thirds tunings require less hand-stretching than other tunings, because each M3 tuning packs the octave's twelve notes into four consecutive frets.[48][51] The major-third intervals allow major chords and minor chords to be played with two–three consecutive fingers on two consecutive frets.[52]

Chord inversion is especially simple in major-thirds tuning. Chords are inverted simply by raising one or two notes three strings. The raised notes are played with the same finger as the original notes. In contrast, inversions of triads in standard and all-fourths tuning require three fingers on a span of four frets,[53] in standard tuning, the shape of inversions depends on the involvement of the irregular major-third.[54]

All fifths and "new standard tuning"[edit]

New standard tuning.
New Standard Tuning's open strings.
C-G-d-a-e'-b'

All-fifths tuning is a tuning in intervals of perfect fifths like that of a mandolin or a violin; other names include "perfect fifths" and "fifths".[55] It has a wide range. Its implementation has been impossible with nylon strings and has been difficult with conventional steel strings. The high b makes the first string very taut, and consequently a conventionally gauged string would easily break.

All-fifths tuning has been approximated by the so-called "New Standard Tuning" (NST) of King Crimson's Robert Fripp, which NST replaces all-fifth's high b' with a g'. To build chords, Fripp uses "perfect intervals in fourths, fifths and octaves", so avoiding minor thirds and especially major thirds,[56] which are sharp in equal temperament tuning (in comparison to thirds in just intonation). It is a challenge to adapt conventional guitar-chords to new standard tuning, which is based on all-fifths tuning.[57] Some closely voiced jazz chords become impractical in NST and all-fifths tuning.[58]

Instrumental tunings[edit]

These are tunings in which some or all of the strings of the guitar are retuned to emulate the standard tuning of some other instrument, such as a lute, banjo, cittern, mandolin, etc. Many of these tunings will overlap other categories, especially open and model tunings.

Miscellaneous or "special" tunings[edit]

This category includes everything that doesn't fit into any of the other categories, for example (but not limited to): tunings designated only for a particular piece; non-western intervals and modes; micro- or macro-tones.

See also[edit]

Notes[edit]

  1. ^ Denyer. Chapter "Playing the guitar": 'How the guitar is tuned', pp. 68-69.
  2. ^ Denyer. Chapter "Playing the guitar": 'Tuning methods', pp. 70-71.
  3. ^ name="tgl">Online guitar tuner “Retrieved August 27, 2013”
  4. ^ Weissman (2006, Off the wall tunings: A brief inventory (Appendix A), pp. 95-96)
  5. ^ Roche (2004, "Categories of tunings", p. 153)
  6. ^ Roche (2004, pp. 153–156)
  7. ^ a b c d Denyer (1992, pp. 158–159)
  8. ^ Roche (2004, "Open tunings", pp. 156–159)
  9. ^ Roche (2004, "Cross-note tunings", p. 166)
  10. ^ a b Sethares (2011)
  11. ^ Roche (2004, "Modal tunings", pp. 160–165)
  12. ^ Roche (2004, "More radical tunings", p. 166)
  13. ^ Roche (2004, "String gauges and altered tunings", p. 169–170)
  14. ^ a b Sethares (2009, p. 16)
  15. ^ a b c Denyer (1992, p. 158)
  16. ^ Denyer (1992, p. 160)
  17. ^ Gold, Jude (1 December 1 2005). "Just desserts: Steve Kimock shares the sweet sounds of justly tuned thirds and sevenths". Guitar Player. Master class.  (subscription required)
  18. ^ Allen (2011)
  19. ^ Gold, Jude (June 2007). "Fender VG Stratocaster". Guitar Player. Gear: Bench Test (Product/service evaluation). 
  20. ^ Hannu Annala, Heiki Mätlik (2007). "Composers for other plucked instruments: Rudolf Straube (1717-1785)". Handbook of Guitar and Lute Composers (Translated by Katarina Backman ed.). Mel Bay. p. 30. ISBN 0786658444; ISBN 9780786658442. 
  21. ^
  22. ^ a b c Sethares (2001, pp. 56)
  23. ^ Grossman (1972, p. 29)
  24. ^ Sethares (2009, pp. 20–21)
  25. ^ Hannu Annala, Heiki Mätlik (2007). "Composers for other plucked instruments: Rudolf Straube (1717-1785)". Handbook of guitar and lute composers (Translated by Katarina Backman ed.). Mel Bay. p. 30. ISBN 0786658444. ISBN 9780786658442. 
  26. ^ Sethares (2009, pp. 18–19)
  27. ^ Baughman, Steve (2004). "Open C". Mel Bay Beginning Open Tunings. Pacific, Missouri: Mel Bay Publications. pp. 8–14. ISBN 978-0-7866-7093-2. 
  28. ^ Guitar Tunings Database (2013). "CCGCEG Guitar Tuner". CCGCEG: Open C via harmonic overtones. Retrieved 20 February 2013. 
  29. ^ Persichetti (1961, pp. 23–24): Persichetti, Vincent (1961). Twentieth-century harmony: Creative aspects and practice. New York: W. W. Norton. ISBN 0-393-09539-8. OCLC 398434. 
  30. ^ a b Sharken, Lisa (15 May 2001). "Mick Ralphs: The rock 'N' roll fantasy continues". Vintage Guitar. Retrieved 21 February 2013. 
  31. ^ "List of all Guitar and Piano Transcriptions". GGDGBD. JoniMitchell.com. Retrieved February 22, 2013. 
  32. ^ Ellis, Andy (2005). "How to play like ... Keith Richards". Guitar Player. (subscription required). Retrieved 24 March 2013. 
  33. ^ Bellow (1970, p. 164): Bellow, Alexander (1970). The illustrated history of the guitar. Colombo Publications. 
  34. ^ Timofeyev (1999): Timofeyev, Oleg V. (1999). The golden age of the Russian guitar: Repertoire, performance practice, and social function of the Russian seven-string guitar music, 1800-1850. Duke University, Department of Music. pp. 1–584. University Microfilms (UMI), Ann Arbor, Michigan, number 9928880. 
  35. ^ Sethares (2001, p. 16)
  36. ^ Cohen, Andy (22 March 2005). "Stefan Grossman- Country Blues Guitar in Open Tunings". Sing Out! 49 (1): 152. 
  37. ^ Denyer (1992, p. 119)
  38. ^ Sethares (2001, p. 52)
  39. ^ a b Kirkeby, Ole (1 March 2012). "Major thirds tuning". m3guitar.com. cited by Sethares (2011). Retrieved 10 June 2012. 
  40. ^ White, Mark (2005). "Reading skills: The guitarist's nemesis?". Berklee Today (Boston, Massachusetts: Berklee College of Music) 72. ISSN 1052-3839. 
  41. ^ Denyer (1992, p. 72)
  42. ^ Peterson (2002, p. 37)
  43. ^ Griewank (2010, p. 5)
  44. ^ Sethares (54–55)
  45. ^ Sethares (2001, pp. 58–59)
  46. ^ Bianco, Bob (1987). Guitar in Fourths. New York City: Calliope Music. ISBN 0-9605912-2-2. OCLC 16526869. 
  47. ^ Ferguson (1986, p. 76):
    Ferguson, Jim (1986). "Stanley Jordan". In Casabona, Helen; Belew, Adrian. New directions in modern guitar. Guitar Player basic library. Hal Leonard Publishing Corporation. pp. 68–76. ISBN 0881884235; ISBN 9780881884234. 
  48. ^ a b c Peterson (2002, pp. 36–37)
  49. ^ a b Griewank (2010)
  50. ^ a b c Patt, Ralph (14 April 2008). "The major 3rd tuning". Ralph Patt's jazz web page. ralphpatt.com. cited by Sethares (2011). Retrieved 10 June 2012. 
  51. ^ Griewank (2010, p. 9)
  52. ^ Griewank (2010, p. 2)
  53. ^ Griewank (2010, p. 10)
  54. ^ Denyer (1992, p. 121)
  55. ^ Sethares (2001, "The mandoguitar tuning" 62–63)
  56. ^ Mulhern (1986): Mulhern, Tom (January 1986). "On the discipline of craft and art: An interview with Robert Fripp". Guitar Player 20: 88–103. Retrieved 8 January 2013. 
  57. ^ 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. (Tamm 2003, Chapter 10: Postscript)
    Tamm, Eric (2003) [1990], Robert Fripp: From crimson king to crafty master (Progressive Ears ed.), Faber and Faber (1990), ISBN 0-571-16289-4, Zipped Microsoft Word Document, retrieved 25 March 2012 
  58. ^ Sethares (2001, "The mandoguitar tuning", pp. 62–63)

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