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{{Infobox Regular tuning
| regular_tuning_name = Regular tunings
|image_top =Pitch class space.svg
|caption_top=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.
|other_names =  Uniform tunings<br />All-''[[interval (music)|interval]]'' tunings
|interval=
|semitones =
|examples =
|advanced = TRUE
|repetition =
|other_instruments =
|advantages = Simplifies learning by beginners and improvisation by advanced guitarists
|disadvantages = Makes it difficult to play music written for standard tuning.
|lefty =
|guitarist =
|guitarist_image=
|guitarist_alt=
|guitarist_caption=
}}
 
Among [[guitar tunings#Alternative|alternative]] [[guitar tunings|guitar-tunings]], '''regular&nbsp;tunings''' have equal [[interval (music)|musical intervals]] between the paired [[note (music)|note]]s of their successive [[open string]]s. Regular tunings help beginning students to learn the [[fretboard]]'s notes and [[guitar chord|chord]]s. Regular tunings also facilitate [[improvisation]] by advanced guitarists.
 
''Guitar&nbsp;[[tuning (music)|tuning]]s'' assign [[pitch (music)|pitches]] to the [[open&nbsp;string]]s of [[guitar]]s.  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. The ''standard tuning'' defines the string pitches as E, A, D, G, B, and E. Between the open-strings of the standard tuning are three [[perfect fourth|perfect-fourth]]s (E-A, A-D, D-G), then the [[major third]] G-B, and the fourth perfect-fourth B-E.
 
In contrast, regular tunings have constant intervals between their successive open-strings:
* 4 semi-tones (major third): [[Major-thirds tuning]],
* 5 semi-tones (perfect fourth): [[All-fourths tuning]],
* 6 semi-tones ([[augmented fourth]], [[tritone]], or [[diminished fifth]]): [[Augmented-fourths tuning]],
* 7 semi-tones ([[perfect fifth]]): [[All-fifths tuning]]
 
For the regular tunings, chords may be moved ''diagonally'' around the fretboard, indeed ''vertically'' for the repetitive regular tunings (minor thirds, major thirds, and augmented fourths). Regular tunings thus appeal to new guitarists and also to jazz-guitarists, whose improvisation is simplified. On the other hand, some conventional chords are easier to play in standard tuning than in regular tuning than in standard tuning.<ref name="Regular"><!-- This refers to the 2001 chapter, not the 2010 pdf file of the whole guide,  or the 2011 webpage. Please do NOT remove merge this with the 2011 reference! -->{{harvtxt|Sethares|2001}}</ref> Left-handed guitarists may use the chord charts from one class of regular tunings for its left-handed tuning; for example, the chord charts for all-fifths tuning may be used for guitars strung with left-handed all-fourths tuning.
 
The class of regular tunings has been named and described by Professor [[William Sethares]]. Sethares's 2001 chapter ''Regular tunings'' (in his revised 2010-2011 ''Alternate&nbsp;tuning guide'') is the leading source for this article.<ref name="Regular"/> This article's descriptions of particular regular-tunings use other sources also.
 
==Standard and alternative guitar-tunings: A review==
{{Tall image|Standard diagonal shifting of C major chord.png|200|600|In standard tuning, the C-major chord has three shapes because of the irregular major-third between the G- and B-strings.|right}}
 
This summary of standard tuning also introduces the terms for discussing alternative tunings
 
===Standard===
<score vorbis="1"> {
\clef "treble_8"
\time 6/4
< e, a, d g b e' >1.
e,4 a, d g b e'
< e, a, d g b e' >1.}
</score>
{{Main|Standard guitar-tuning}}
 
Standard tuning has the following open-string [[note]]s:
:E-A-d-g-b-e'.
In standard tuning, the separation of the second (b), and third (g) string is by a [[major-third]] [[interval (music)|interval]], which has a width of four [[semitone]]s.
 
{| class="wikitable"
! Standard tuning !! open !! 1st fret (index) !! 2nd fret (middle) !! 3rd fret (ring) !! 4th fret (little)
|-
| 1st string
! e'
|| f' || f{{Music|♯}}' || g' || a{{Music|♭}}'
|-
| 2nd string
! b
| c' || c{{Music|♯}}' || d' || e{{Music|♭}}'
|-
| 3rd string
! g
| a{{Music|♭}} || a || b{{Music|♭}} || b
|-
| 4th string
! d
| e{{Music|♭}} || e || f || f{{Music|♯}}
|-
| 5th string
! A
| B{{Music|♭}} || B || c || c{{Music|♯}}
|-
| 6th string
! E
| F || F{{Music|♯}} || G || A{{Music|♭}}
|-
| align="center" colspan="6" | ''Chromatic note progression''
|}
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.<ref>{{harvtxt|Denyer|1992|p=119}}</ref>
 
=== Alternative ===
{{Main|Alternative guitar-tunings}}
 
[[Scordatura|''Alternative ("alternate")'' tuning]] refers to any open-string note-arrangement other than standard tuning. Such alternative tuning arrangements offer different chord voicing and sonorities. Alternative tunings necessarily change the chord shapes associated with standard tuning, which eases the playing of some non-standard chords at the cost of increasing the difficulty of some standard chords. Regular tunings benefit from re-stringing of the guitar with different gauges. In particular, [[all-fifths tuning]] has been difficult to implement on conventional guitars; even an approximation to all-fifths tuning, [[new standard tuning]], has required special sets of strings.
 
==Properties==
[[File:Tuning ADGBE5 ADGBE0.svg|left|thumb|alt=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.]]
{{Tall image|Diagonal shift of C-major chord in major-thirds tuning.png|200|350|alt=A C-major chord in four positions.|Chords can be shifted diagonally in regular tunings, such as major-thirds (M3) tuning.|right}}
[[File:Chords in major-thirds tuning C, D, G, minor, major, dominant seventh.png|thumb|In regular tunings like M3 tuning, chords maintain the same shape, unlike the chords of standard tuning.]]
[[File:Segmented fretboard of major thirds tuning for six-string guitar.png|right|thumb|width=300px|alt=The fretboard of major-thirds tuning is segmented into four-fret intervals, frets 0-3, 4-7, and 8-11; the natural notes are labeled.|The fretboard of major-thirds tuning is segmented into four-fret intervals, which simplifies its learning and also reduces the need for shifting the left hand.]]
{{See also|Interval (music)}}
 
With standard tuning, and with all tunings, chord patterns can be moved twelve frets down, where the notes repeat in a higher octave.
 
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. Working around the irregular third of standard tuning, guitarists have to memorize chord-patterns for at least three regions: The first four strings tuned in perfect fourths; two or more fourths and the third; and one or more initial fourths, the third, and the last fourth.
 
In contrast, ''regular''&nbsp;tunings have equal intervals between the strings.<ref name="Regular"/>
In contrast, regular tunings have constant intervals between their successive open-strings. In fact, the class of each regular tuning is characterized by its musical interval as shown by the following list:
* 3 semi-tones ([[minor third]]): Minor-thirds tuning,
* 4 semi-tones ([[major third]]): [[Major-thirds tuning]],
* 5 semi-tones ([[perfect fourth]]): [[All-fourths tuning]],
* 6 semi-tones ([[augmented fourth]], [[tritone]], or [[diminished fifth]]): [[Augmented-fourths tuning]],
* 7 semi-tones ([[perfect fifth]]): [[All-fifths tuning]]
 
The regular tunings whose number of semi-tones ''s'' divides 12 (the number of notes in the [[octave]]) repeat their open-string notes (raised one octave) after 12/''s'' strings: For example,
* having three semi-tones in its interval, minor-thirds tuning repeats its open-notes after four (12/3) strings;
* having four semi-tones in its interval, major-thirds tuning repeats its open-notes after three (12/4) strings;
* having six semi-tones in its interval, augmented-fourths tuning repeats its notes after two (12/6) strings.<!--  This explanation is so trivial that mathematicians and music-theorists would be ashamed to write it---likewise, guitar-players and those familiar with 12-hour clocks. But, it provides some context and framework for the exposition. Such calculations, not OR, are allowed by the WP policy on exposition in mathematics.-->
 
Regular tunings 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 shifting of chords is especially simple for the regular tunings that repeat their open strings, in which case chords can be moved vertically: Chords can be moved three strings up (or down) in major-thirds tuning,<ref name="Griewank3">{{harvtxt|Griewank|2010|p=3}}</ref> 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.
 
===Particular conventional-chords are more difficult to play===
On the other hand, particular chords are more difficult to play in a regular tuning than in standard tuning. It can be difficult to play conventional chords especially in augmented-fourths tuning and all-fifths tuning,<ref name="Regular">{{cite book|chapter=Regular tunings|title=Alternate tuning guide|first=Bill|last=Sethares|authorlink=William Sethares|year=2001|pages=52–67|url=http://sethares.engr.wisc.edu/alternatetunings/regulartunings.pdf|format=pdf|publisher=University of Wisconsin; Department of Electrical Engineering|location=Madison, Wisconsin|ref=harv|accessdate=19 May 2012|id=[http://sethares.engr.wisc.edu/alternatetunings/alltunings.pdf 2010 ''Alternate tuning guide'', including a revised chapter on regular tunings]}}</ref>
in which the wide ([[tritone]] and [[perfect-fifth]]) intervals require hand stretching. Some chords, which are conventional in folk music, are difficult to play even in all-fourths and major-thirds tunings, which do not require more hand-stretching than standard tuning.<ref name="Patt"/>
On the other hand,
minor-thirds tuning
features many [[barre chord]]s with repeated notes,<ref name=Sethares5455>{{harvtxt|Sethares|2001|pp=54–55}}</ref> properties that appeal to acoustic guitarists and to beginners.
 
===Frets covered by the hand===
 
The [[chromatic scale]] climbs from one string to the next after a number of frets that is specific to each regular tuning. The chromatic scale climbs after exactly four frets in major-thirds tuning, so reducing the extensions of the little and index fingers ("hand stretching").<ref>{{harvtxt|Griewank|2010|p=9}}</ref> For other regular tunings, the successive strings have intervals that are minor&nbsp;thirds, perfect&nbsp;fourths, augmented&nbsp;fourths, or perfect&nbsp;fifths; thus,  the fretting hand covers three, five, six, or seven frets respectively to play a chromatic scale. (Of course, the highest chromatic-scale uses the open strings and so requires one less fret to be covered.)
 
{{clear}}
 
==Examples==
[[File:Diminished seventh chord in the chromatic circle.png|right|thumb|Every minor-thirds tuning repeats its open notes after four strings.]]
 
The following regular-tunings are discussed by Sethares, who also mentions other regular tunings that are  difficult to play or have little musical interest.
 
===Minor thirds===
<!--[[Minor thirds tuning]] redirects directly here. Please do not link minor-thirds tuning in the text, which just would create a useless redirection here. -->
 
:C-E{{music|b}}-G{{music|b}}-a-c-e{{music|b}},<ref name="Sethares54"/><ref>{{cite web | url=http://www.gtdb.org/tuner/acd-sharp-f-sharp-ac/ | title= ACD#F#AC: Minor thirds (m3)| publisher=Guitar tunings database | date=3 February 2013 | accessdate=4 February 2013}}</ref>  or
:B-D-F-A{{music|b}}-b-d<ref>{{cite web | url=http://www.gtdb.org/tuner/g-sharp-bdfg-sharp-b/ | title=G#BDFG#B: Minor thirds (m3) | publisher=Guitar tunings database | date=3 February 2013 | accessdate=4 February 2013}}</ref>
 
In each minor-thirds ([[minor third|m3]]) tuning, every interval between successive strings is a [[minor third]]. Thus each [[repetitive tuning|repeats]] its open-notes after four strings.
In the minor-thirds tuning beginning with C, the open strings contain the notes (c, e{{music|b}}, g{{music|b}}) of the [[diminished triad|diminished&nbsp;C triad]].<ref name="Sethares54">{{harvtxt|Sethares|2001|pp=54}}</ref>
 
Minor-thirds tuning
features many [[barre chord]]s with repeated notes,<ref name="Sethares5455" />
properties that appeal to acoustic guitarists and to beginners.
[[Doubling (music)|Doubled note]]s
have different sounds
because of differing "string widths, tensions and tunings,
and [they<!-- the doubled notes -->] reinforce each other,
like the doubled strings of a twelve string guitar
add chorusing and depth,"
according to [[William&nbsp;Sethares]].<ref name="Sethares54"/>
{{clear}}
 
===Major thirds===
[[File:Augmented chord in the chromatic circle.png|right|thumb|The major-thirds tuning A{{music|b}}-C-E-A{{music|b}}-C-E repeats its three open-notes in the higher octave after three strings.]]
{{multiple image
  | width    =300
  | footer    = Major-thirds tuning repeats its notes after three strings.
  | image1    = Shift C-major chord three strings in major thirds tuning on six-string guitar.png
  | alt1      = The C major chord (C,E,G) on the bass (4-6) and tenor (1-3) strings of M3 tuning, on frets .  the C note and the E note have been raised 3 strings on the same fret.
  | caption1  =Chords vertically shift.
  | image2    =First and second inversions of C-major chord on six-string guitar with major-thirds tuning.png
  | alt2      =The C major chord and its first and second inversions. In the first inversion, the C note has been raised 3 strings on the same fret. In the second inversion, both the C note and the E note have been raised 3 strings on the same fret.
  | caption2  =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.<ref name="KirkebyMajor">{{harvtxt|Kirkeby|2012|loc=[http://v3p0.m3guitar.com/html/fretmaps_chords_major.html "Fretmaps, major chords: Major Triads"]}}</ref>
}}
{{Main|Major-thirds tuning}}
 
<score vorbis="1"> {
\clef "treble_8"
\time 6/4
< c, e, aes, c e aes c' e' aes' >1.
||
< c, e, aes, >2
<c,>4
<e,>4
<aes, >4
< c, e, aes, >4
||
< c e aes >2
<c >4
<e >4
<aes  >4
< c e aes >4
||
<c' e' aes' >2
<c' >4
<e' >4
<aes' >4
< c' e' aes' >4
||
<c, e, aes, c e aes c' e' aes'>1.
}
</score>
 
''Major-thirds tuning'' is a regular tuning in which the [[musical&nbsp;interval]]s between successive strings are each [[major third]]s.<ref name="Sethares56">{{harvtxt|Sethares|2001|pp=56}}</ref><ref name="Griewank">{{citation|last=Griewank|first=Andreas|authorlink=Andreas Griewank|title=Tuning guitars and reading music in major thirds|year=2010|url=http://vs24.kobv.de/opus4-matheon/frontdoor/index/index/docId/675|month=1 January|id=MSC-Classification 97M80 Arts. Music. Language. Architecture|series=Matheon preprints|volume=695|ref=harv|publisher=DFG research center "MATHEON, Mathematics for key technologies" Berlin|location=Rosestr.&nbsp;3a, 12524 Berlin, Germany|id=[http://vs24.kobv.de/opus4-matheon/files/675/7047_mathtune.ps Postscript file] and [http://vs24.kobv.de/opus4-matheon/files/675/7046_mathtune.pdf Pdf file]}}</ref> Like minor-thirds tuning (and unlike all-fourths and all-fifths tuning), major-thirds tuning is a [[repetitive tuning]]; it repeats its octave after three strings, which again simplifies the learning of chords and improvisation;<ref name="Kirkeby">{{cite web|first=Ole|last=Kirkeby|year=2012|month=1&nbsp;March|title=Major&nbsp;thirds tuning|accessdate=10 June 2012|ref=harv|url=http://v3p0.m3guitar.com/|publisher=m3guitar.com|id=cited by {{harvtxt|Sethares|2011}} and {{harvtxt|Griewank|p=1}}}}</ref> similarly, minor-thirds tuning repeats itself after four strings while augmented-fourths tuning repeats itself after two strings.
 
Neighboring the standard tuning is the all-thirds tuning that has the open strings
:E-G{{music|#}}-B{{music|#}}-e-g{{music|#}}-b{{music|#}}'(or F{{music|b}}-A{{music|b}}-C-f{{music|b}}-a{{music|b}}-c').<ref name="Patt">{{cite web|url=http://www.ralphpatt.com/Tune.html|first=Ralph|last=Patt|authorlink=Ralph Patt|publisher=ralphpatt.com|work=Ralph&nbsp;Patt's jazz web page|title=The major&nbsp;3rd tuning|ref=harv|year=2008|month=14&nbsp;April|accessdate=10 June 2012|id=cited by {{harvtxt|Sethares|2011}} and {{harvtxt|Griewank|2010|p=1}}}}</ref>
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.<ref name="Sethares56">{{harvtxt|Sethares|2001|loc=[http://sethares.engr.wisc.edu/alternatetunings/regulartunings.pdf "The major&nbsp;third tuning", p.&nbsp;56]}}</ref><ref name="Griewank"/> With the repetition of three open-string notes, each major-thirds tuning provides the guitarist with many options for fingering chords. Indeed, the fingering of two successive frets suffices to play pure major and minor chords, while the fingering of three successive frets suffices to play seconds, fourths, sevenths, and ninths.<ref name="Sethares56"/><ref name="Griewank2">{{harvtxt|Griewank|2010|p=2}}</ref>
 
For the standard Western guitar, which has six strings, major-thirds tuning has a smaller range than standard tuning; on a guitar with [[seven-string guitar|''seven''&nbsp;strings]], the major-thirds tuning covers the range of standard tuning on ''six''&nbsp;strings. Even greater range is possible with guitars with [[eight-string guitar|''eight''&nbsp;strings]].<!-- This statement is trivial. Patt is cited because he discusses 8-string guitars. --><ref name="Patt"/><ref>In the table, the last row is labeled the "7th string" so that the low C tuning can be displayed without needing another table; the term "7th string" does not appear in the sources.<p>Similarly, the terms "-1st string" and "0th string" do not appear in the sources, which do discuss guitars having seven-eight strings.</ref>
 
Major-thirds tuning was introduced in 1964 by the American jazz-guitarist [[Ralph&nbsp;Patt]] to facilitate [[improvisation]].<ref name="Patt"/><ref name="Griewank1">{{harvtxt|Griewank|2010|p=1}}</ref>
 
{{clear}}
 
===All fourths===
[[File:All fourths tuning in the chromatic circle.png|right|thumb|The consecutive notes of all-fourths tuning are spaced apart by five semi-tones on the chromatic circle.]]
[[File:All fourths tuning.png|thumb|right|All fourths tuning.]]
{{main|All fourths tuning}}
{{see also|Perfect fourth}}
 
:E-A-d-g-c'-f'
This tuning is like that of the lowest four strings in standard tuning.<ref>{{harvtxt|Sethares|2001|pp=58–59}}</ref><ref>{{Cite book |first=Bob |last=Bianco |title=Guitar in Fourths |publisher=Calliope Music |location=[[New York City]] |year=1987 |pages= |isbn=0-9605912-2-2 |oclc=16526869}}</ref> Consequently, of all the regular tunings, it is the closest approximation to standard tuning, and thus it best allows the transfer of a knowledge of chords from standard tuning to a regular tuning. Jazz&nbsp;musician [[Stanley&nbsp;Jordan]] plays guitar in all-fourths tuning; he has stated that all-fourths tuning "simplifies the fingerboard, making it logical".<ref>
{{harvtxt|Ferguson|1986|p=76}}:<br />
{{cite book|chapter=Stanley Jordan|first=Jim |last=Ferguson|authorlink=Jim Ferguson|pages=68–76|title=New directions in modern guitar|series=''[[Guitar&nbsp;Player]]'' basic library|editor1-first=Helen|editor1-last=Casabona|editor2-first=Adrian|editor2-last=Belew|editor2-link=Adrian Belew|publisher=Hal&nbsp;Leonard Publishing Corporation|year=1986|ref=harv|url=http://books.google.se/books?id=3idLAAAAYAAJ&q=%22Stanley+Jordan%22,+%22all+fourth%22+OR+%22perfect+fourth%22,+guitar+tuning&dq=%22Stanley+Jordan%22,+%22all+fourth%22+OR+%22perfect+fourth%22,+guitar+tuning&hl=en&sa=X&ei=BfzgT_XgKILetAaampnyDg&ved=0CDEQ6AEwAA|id=ISBN 0881884235; ISBN 9780881884234}}</ref>
 
For all-fourths tuning, all twelve [[major&nbsp;chord]]s (in the first or open positions) are generated by two chords, the open F&nbsp;major chord and the D&nbsp;major chord. The regularity of  chord-patterns reduces the number of finger&nbsp;positions that need to be memorized.<ref name="Sethares52">{{harvtxt|Sethares|2001|p=52}}</ref>
 
The left-handed involute of an all-fourths tuning is an all-fifths tuning. All-fourths tuning is based on the [[perfect fourth]] (five semitones), and all-fifths tuning is based on the [[perfect fifth]] (seven semitones). Consequently, chord charts for all-fifths tunings may be used for left-handed all-fourths tuning.<ref name="Sethares53"/>
{{clear}}
 
===Augmented fourths===
[[File:Tritone in the chromatic circle.png|right|thumb|A line segment bisecting the chromatic circle specifies an augmented-fourths (tritone) tuning.]]
{{Main|Augmented-fourths tuning}}
 
:C-F{{music|#}}-c-f{{music|#}}-c'-f{{music|#}}' and B-F-b-f-b'-f' etc.
 
Between the all-fifths and all-fourths tunings are ''[[tritone|augmented-fourth]]'' tunings, which are also called "''[[diminished fifth|diminished-fifth]]s''" or "''[[tritone]]''" tunings. It is a [[repetitive tuning]] that repeats its notes after two strings. With  augmented-fourths tunings, the fretboard has greatest symmetry.<ref name="60Sethares61"/> In fact, every augmented-fourths tuning lists the notes of all the  other augmented-fourths tunings on the frets of its fretboard. Professor Sethares wrote that<blockquote>
"The augmented-<!-- inserted dash, here and elsewhere per WP:MOS and consistency -->fourth interval is the only
interval whose inverse is the same as itself. The
augmented-fourths tuning is the only tuning (other
than the 'trivial' tuning <!-- notation changed from original "CCCCCC", per WP:MOS -->C-C-C-C-C-C) for which all
chords-<!-- inserted dash, here and elsewhere per WP:MOS. Hyphen prevents  "All chord" modifying "form", on first reading-->forms remain unchanged when the strings
are reversed. Thus the augmented-fourths tuning is
its own 'lefty' tuning."<ref name="Sethares60"/>
</blockquote>
Of all the augmented-fourths tunings, the C-F{{music|#}}-c-f{{music|#}}-c'-f&nbsp;'{{music|#}} tuning is the closest approximation to the standard tuning, and its fretboard is displayed next:
{| class="wikitable"
|-
| align="center" colspan="7" | ''Tritone'':<ref name="Sethares60">{{harvtxt|Sethares|2001|loc=[http://sethares.engr.wisc.edu/alternatetunings/regulartunings.pdf "The augmented fourths tuning", p.&nbsp;60]}}</ref> Each fret displays the open strings of <!-- exactly one -->an augmented-fourths tuning
|-
!  !! open<br />(0th&nbsp;fret) !! 1st fret !! 2nd fret !! 3rd fret !! 4th fret !! 5th fret !!
|-
| 1st string
! f '{{music|#}}
|| g' || g'{{music|#}} || a"||a"{{music|#}}||b"
|-
| 2nd string
! c'
| c'{{music|#}} || d' || d'{{music|#}}||e'||f '
|-
| 3rd string
! f{{music|#}}
|| g || g{{music|#}} || a'||a{{music|#}}'||b'
|-
| 4th string
! c
| c{{music|#}} || d || d{{music|#}}||e||f
|-
| 5th string
! F{{music|#}}
|| G || G{{music|#}} || a||a{{music|#}}||b
|-
| 6th string
! C
| C{{music|#}} || D || D{{music|#}}||E||F
|}
An augmented-fourths tuning "makes it very&nbsp;easy for playing half-whole scales, diminished&nbsp;7 licks, and whole&nbsp;tone scales," stated guitarist [[Ron&nbsp;Jarzombek]].<ref>{{cite web|title=Interview with Ron&nbsp;Jarzombek|first=Steve|last=Turner|authorlink=Steve Turner (guitarist)|url=http://www.ronjarzombek.com/stevet.html|ref=harv|accessdate=23 May 2012|publisher=[http://www.ronjarzombek.com/ RonJarzombek.com]|month=30&nbsp;December|year=2005}}.</ref>
{{clear}}
 
===All fifths: "Mandoguitar"===
[[File:All fifths tuning in the chromatic circle.png|left|thumb|The consecutive open-notes of all-fifths tuning are spaced seven semi-tones apart on the chromatic circle. While the notes of the open-notes of the all-fifths and all-fourths tunings agree, their orderings are reversed.]]
[[File:New standard tuning in the chromatic circle.png|right|thumb|New standard tuning substitutes a G for the high B of all-fifths tuning.]]
{{main|All fifths}}
{{See also|Quartal and quintal harmony}}
 
:C-G-d-a-e'-b'
 
All-fifths tuning is a tuning in intervals of [[perfect fifth]]s like that of a [[mandolin]], [[cello]] or [[violin]]; other names include "perfect fifths" and "fifths".<ref>{{harvtxt|Sethares|2001|loc="The mandoguitar tuning" 62–63}}</ref> Consequently, classical compositions written for violin or guitar may be adapted to all-fifths tuning more easily than to standard tuning.
 
When he was asked whether tuning in fifths  facilitates "new intervals or harmonies that aren't readily available in standard  tuning", [[Robert Fripp]] responded, "It's a more rational system, but it's also better sounding—better for chords, better for single notes." To build chords, Fripp uses "perfect intervals in fourths, fifths and octaves", so avoiding [[minor third]]s and especially [[major third]]s,<ref name="Mulhern" >{{harvtxt|Mulhern|1986}}: {{cite journal|first=Tom|last=Mulhern|date=January 1986|title=On the discipline of craft and art: An interview with Robert Fripp|journal=Guitar Player|ref=harv|url=http://www.mulhern.com/articles/Fripp.html|accessdate=8 January 2013|volume=20|pages=88–103}}</ref> 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.<ref name="Tamm10" >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]]. {{harv|Tamm|2003|loc=[http://www.progressiveears.com/frippbook/ch10.htm Chapter&nbsp;10: Postscript]}}
<br />{{citation|title=Robert&nbsp;Fripp: From crimson&nbsp;king to crafty&nbsp;master
|first=Eric|last=Tamm|url=http://www.progressiveears.com/frippbook/ch10.htm|ref=harv|year=2003|origyear=1990|publisher=Faber and Faber (1990)|isbn=0-571-16289-4
|edition=Progressive Ears|id=[http://www.erictamm.com/rf.zip Zipped Microsoft Word Document]
|accessdate=25 March 2012}}</ref> Some closely voiced [[jazz chords]] become impractical in NST and all-fifths tuning.<ref name="Mandoguitar">{{harvtxt|Sethares|2001|loc="The mandoguitar tuning", pp.&nbsp;62–63}}</ref>
 
It has a wide range, thus its implementation can be difficult. The high ''b'' requires a taut, thin string, and consequently is prone to breaking. This can be ameliorated by using a shorter [[Scale length (string instruments)|scale length]] guitar, by shifting to a different [[Key (music)|key]], or by shifting down a fifth.
 
The left-handed involute of an all-fifths tuning is an all-fourths tuning. All-fifths tuning is based on the [[perfect fifth]] (seven semitones), and all-fourths tuning is based on the [[perfect fourth]] (five semitones). Consequently, chord charts for all-fifths tunings are used for left-handed all-fourths tuning.<ref name="Sethares53"/>
 
{{clear}}
 
====New standard tuning====
[[File:New standard tuning.png|thumb|right|New standard tuning.]]
[[File:Guitar Crafty Tuning.ogg|right|thumb|Audio file of New Standard Tuning's open notes.|New Standard Tuning's open strings.]]
{{main|New standard tuning}}
{{see also|Guitar Craft}}
 
All-fifths tuning has been approximated with tunings that avoid the high b' or the low C. The b' has been replaced with a g' in the [[new standard tuning]] (NST) of [[King&nbsp;Crimson]]'s [[Robert&nbsp;Fripp]]. The original version of NST was all-fifths tuning. However, in the 1980s, Fripp never attained the all fifth's high&nbsp;b'. While he could attain&nbsp;a', the string's [[service life|life]]-time [[empirical distribution function|distribution]] was too short. Experimenting with a g&nbsp;string, Fripp succeeded. "Originally, seen in 5ths. all the way, the top string would not go to&nbsp;B. so, as on a tenor banjo, I adopted an&nbsp;A on the first string. These kept breaking, so&nbsp;G was adopted."<ref name="Fripp2010" >{{cite journal|title=Robert Fripp's diary: Friday, 5th February 2010|date=5 February 2010|first=Robert|last=Fripp|authorlink=Robert Fripp|publisher=[[Discipline Global Mobile]], DGM&nbsp;Live!|url=http://www.dgmlive.com/diaries.htm?entry=16789|ref=harv}}</ref>  In 2012, Fripp experimented with&nbsp;A String (0.007);<ref name="Fripp2012" >{{cite journal|title=Robert&nbsp;Fripp's diary: Sunday, 22nd&nbsp;April 2012|date=22 April 2012|first=Robert|last=Fripp|publisher=[[Discipline Global Mobile]], DGM&nbsp;Live!|url=http://www.dgmlive.com/diaries.htm?entry=21688|ref=harv}}</ref><ref>[http://octave4plus.com/ Octave4Plus of Gary Goodman]</ref>  if successful, the experiment could lead to "the NST 1.2", CGDAE-A, according to Fripp.<ref name="Fripp2012"/> Fripp's NST has been taught in [[Guitar&nbsp;Craft]] courses.<ref>{{citation|title=Robert&nbsp;Fripp: From crimson&nbsp;king to crafty&nbsp;master
|first=Eric|last=Tamm|authorlink=Eric Tamm (musicologist)
|url=http://www.progressiveears.com/frippbook/ch10.htm|ref=harv|year=2003|origyear=1990|publisher=Faber and Faber (1990)|isbn=0-571-16289-4
|edition=Progressive Ears|id=[http://www.erictamm.com/rf.zip  Zipped Microsoft Word Document]  
|accessdate=25 March 2012}}</ref><ref name="Zwerdling">{{cite journal|first=Daniel|last=Zwerdling|authorlink=Daniel Zwerdling|location=Washington DC|title=California Guitar Trio|edition=NPR Weekend Edition|journal=[[All Things Considered]]|publisher=[[National Public Radio]]|accessdate=25 March 2012|ref=harv|month=5 September 5|year=1998|url=http://www.highbeam.com/doc/1P1-29111365.html|id=[http://www.highbeam.com/doc/1P1-29111365.html Html transcription (subscription required)]. [http://www.npr.org/templates/story/story.php?storyId=1006483 Audio recording (free)]}}</ref> Guitar&nbsp;Craft and its successor [[Guitar Circle]] have taught Fripp's tuning to three-thousand students.<ref name="Fripp11">{{harvtxt|Fripp|2011|p=3}}: {{cite book|last=Fripp|first=Robert|authorlink=Robert Fripp|title=Seven Guitar&nbsp;Craft themes: Definitive scores for guitar ensemble|publisher=Partitas Music|year=2011|ref=harv|editor-first=Horacio|editor-last=Pozzo|url=http://partitasmusic.com/ |id=[[International Standard Music Number|ISMN]]&nbsp;979-0-9016791-7-7. [[Discipline Global Mobile|DGM]]&nbsp;[[Stock-keeping unit|Sku]]&nbsp;partitas001|edition=First limited|others="Original transcriptions by Curt&nbsp;Golden", "Layout scores and tablatures: Ariel&nbsp;Rzezak and Theo&nbsp;Morresi"}}</ref>
 
{{clear}}
 
===Extreme intervals===
For regular tunings, intervals wider than a perfect fifth or narrower than a minor third have limited interest.
 
====Wide intervals====
{{anchor|Minor_sixths}}{{anchor|Minor_sixth}}
Two regular-tunings based on sixths, having intervals of [[minor&nbsp;sixth]]s (eight semitones) and of [[major&nbsp;sixth]]s (nine semitones), have received scholarly discussion.<ref name="SetharesMajor6Minor">{{harvtxt|Sethares|2001|pp=64–67}}</ref> The chord charts for minor-sixths tuning are useful for left-handed guitarists playing in major-thirds tuning; the chord charts for major-sixths tuning, for left-handed guitarists playing in minor-thirds tuning.<ref name="Sethares53"/>
 
The regular tunings with [[minor seventh|minor-seventh]] (ten semitones) or [[major seventh|major-seventh]] (eleven semitones) intervals would make chord-playing very difficult, as would octave intervals.<ref name="Sethares53"/>
 
====Narrow intervals====
The regular-tunings that have as their intervals either zero semi-tones ([[unison]]), one semi-tone ([[minor second]]), or two semi-tones ([[major second]]) have little musical-interest, because it is very difficult to play chords in those tunings.<ref name="Sethares53"/>
 
The "trivial" class of unison tunings (such as C-C-C-C-C-C) is its own left-handed tuning.<ref name="Sethares53"/> Unison tunings are briefly discussed in the article on [[ostrich tuning]]s. Having exactly one note, unison tunings are also ostrich tunings, which have exactly one [[pitch class]] (but may have two or more notes, for example, C, c, and c'); non-unison ostrich tunings are not regular.
 
{{clear}}
 
==Left-handed involution==
{{See also|Interval inversion|chord inversion|involution (mathematics)}}
 
The class of regular tunings is preserved under the [[involution (mathematics)|involution]] from right-handed to left-handed tunings, as observed by [[William Sethares]].<ref name="Sethares53"/> The present discussion of left-handed tunings is of interest to [[music theory|musical theorists]], mathematicians, and left-handed persons, but may be skipped by other readers.
 
For [[left handed guitar|left-handed guitar]]s, the ordering of the strings reverses the ordering of the strings for right-handed guitars. For example, the left-handed [[involution (mathematics)|involute]] of the standard tuning E-A-D-G-B-E is the "lefty" tuning  E-B-G-D-A-E. Similarly, the "left-handed" involute of the "lefty" tuning is the standard ("righty") tuning.<ref name="Sethares53"/>
 
The reordering of open-strings in left-handed tunings has an important consequence. The chord fingerings for the right-handed tunings must be changed for left-handed tunings. However, the left-handed involute of a regular tuning is easily recognized: it is another regular tuning. Thus the chords for the involuted regular-tuning may be used for the left-handed involute of a regular tuning.
 
For example, the left-handed version of [[all-fourths tuning]] is [[all-fifths tuning]], and the left-handed version of  all-fifths tuning is all-fourths tuning. In general, the left-handed involute of the regular tuning based on the interval with&nbsp;<math>n</math>&nbsp;[[semitone]]s is the regular tuning based on its [[interval inversion|involuted interval]] with&nbsp;<math>12-n</math>&nbsp;semitones: All-fourths tuning is based on the [[perfect fourth]] (five semitones), and all-fifths tuning is based on the [[perfect fifth]] (seven semitones), as mentioned previously.<ref name="Sethares53">{{harvtxt|Sethares|2001|p=53}}</ref> The following table summarizes the lefty-righty pairings discussed by Sethares.<ref name="Sethares53"/>
 
{| class="wikitable"
|+ Left-handed tunings<ref name="Sethares53"/>
|-
! Right-handed !! Left-handed
|-
| Minor thirds|| [[Major sixth]]s
|-
| Major thirds|| [[Minor sixth]]s
|-
| All fourths|| All fifths
|-
| Augmented fourths || Augmented fourths
|-
| All fifths || All fourths
|-
| Minor sixths|| Major thirds
|-
| Major sixths|| Minor thirds
|}
The left-handed involute of a left-handed involute is the original right-handed tuning. The left-handed version of the trivial tuning C-C-C-C-C-C is also C-C-C-C-C-C. Among non-trivial tunings, only the class of augmented-fourths tunings is [[fixed point (mathematics)|fixed]] under the lefty involution.<ref name="Sethares53"/><ref name="60Sethares61">{{harvtxt|Sethares|2001|loc="The augmented&nbsp;fourths tuning" 60–61}}</ref>
 
==Summary==
The principal regular-tunings have their properties summarized in the following table:
{| class="wikitable"
|-
! Regular tuning !!  [[Interval (music)|Interval]]<p>(Number of [[semitone]]s) !! [[Repetitive tuning|Repetition]] !! Advantages:<p>Each facilitates learning and improvisation. !! Disadvantages:<p>None use standard-tuning's [[open chord]]s.!! Left-handed<p>[[involution (mathematics)|involution]]<ref name="Sethares53"/> !!Guitarist(s)
<!-- |-
| [[Minor-thirds tuning|Minor thirds]]||  [[Minor third]] (3) || After 4 strings || ''not discussed'' (''nd'') || ''nd'' || ''nd'' -->
|-
|  [[Major-thirds tuning|Major thirds]]||  [[Major third]] (4) || After 3 strings ||
* Chromatic scale on four successive frets.
* Hence, reduced hand-stretching:
**Major and minor chords are played on 2 successive frets;
**others (seconds, fourths, sevenths, and ninths) on 3.<ref name="Griewank2"/>
||
* Smaller range (without [[7-string guitar|7 strings]])
* Only three open-notes.
|| [[minor sixth|Minor-sixth]] tuning
|| [[Ralph Patt]]
|-
| [[All-fourths tuning|All fourths]] ||  [[Perfect fourth]] (5) || Non-repetitive<ref name="RepetitiveFootnote" >No repetition occurs in six strings; repetition occurs after 12 strings.</ref> ||
* Uses chords from lowest 4 strings of standard tuning.
* Same tuning as [[bass guitar]]
|| Difficult to play folk chords || All-fifths tuning ||[[Stanley Jordan]]
|-
| [[Augmented-fourths tuning|Augmented fourths]]|| [[Tritone]] (6) || After 2  strings|| symmetry ("left-handed")|| Only 2 open&nbsp;notes || Augmented-fourths tuning ||
|-
| [[All-fifths tuning|All fifths]] || [[Perfect fifth]] (7) || Non-repetitive<ref name="RepetitiveFootnote"/> ||
* Wide scope facilitates ensemble playing and single-note picking (rather than conventional chords)
* Natural for all-fifths music (violin, cello)
||
* Very difficult to play conventional chords.
* Requires extreme (light and heavy) strings.
|| All-fourths tuning
||[[Robert&nbsp;Fripp]], [[Guitar&nbsp;Craft|League of Crafty Guitarists]], and [[California Guitar Trio]] ([[New&nbsp;standard&nbsp;tuning]])
|}
 
==Notes==
{{Reflist}}
 
==References==
* {{Cite book
| title = The guitar handbook
| first = Ralph
| last = Denyer
| others = Special contributors [[Isaac&nbsp;Guillory]] and <!-- NOT [[Alastair Crawford]] -->Alastair&nbsp;M.&nbsp;Crawford
| pages =65–160
| chapter=Playing the guitar ('How the guitar is tuned',  pp.&nbsp;68–69, and 'Alternative tunings', pp.&nbsp;158–159)
| isbn = 0-330-32750-X
| location = London and Sydney
| publisher = Pan Books
| edition= Fully revised and updated
| year = 1992
| ref = harv
}}
* {{citation|last=Griewank|first=Andreas|authorlink=Andreas Griewank|title=Tuning guitars and reading music in major thirds|year=2010|url=http://vs24.kobv.de/opus4-matheon/frontdoor/index/index/docId/675|month=1 January|id=MSC-Classification 97M80 Arts. Music. Language. Architecture|series=Matheon preprints|volume=695|ref=harv|publisher=DFG research center "MATHEON, Mathematics for key technologies" Berlin|location=Rosestr.&nbsp;3a, 12524 Berlin, Germany|id=[http://vs24.kobv.de/opus4-matheon/files/675/7047_mathtune.ps Postscript file] and [http://vs24.kobv.de/opus4-matheon/files/675/7046_mathtune.pdf Pdf file]}}
* {{cite book|year=2001|chapter=Regular&nbsp;tunings|title=Alternate tuning guide|first=Bill|last=Sethares|authorlink=William Sethares|pages=52–67|url=http://sethares.engr.wisc.edu/alternatetunings/regulartunings.pdf|format=pdf|publisher=University of Wisconsin; Department of Electrical Engineering|location=Madison, Wisconsin|ref=harv|accessdate=19 May 2012}}
* {{cite book|year=2009|title=Alternate tuning guide|first=Bill|last=Sethares|authorlink=William Sethares|url=http://sethares.engr.wisc.edu/alternatetunings/alltunings.pdf|format=pdf|origyear=2001|month=10&nbsp;January|publisher=University  of Wisconsin; Department of Electrical Engineering|location=Madison, Wisconsin|ref=harv|accessdate=19 May 2012}}
* {{cite web|title=Alternate tuning guide|first=William A.|last=Sethares|authorlink=William Sethares|year=2012|month=18&nbsp;May|url=http://sethares.engr.wisc.edu/alternatetunings/alternatetunings.html|publisher=University of Wisconsin; Department of Electrical Engineering|location=Madison, Wisconsin|accessdate=8 December 2012|ref=harv}}
* {{cite book|title=Guitar tunings: A comprehensive guide|first=Dick|last=Weissman|authorlink=Dick Weissman|url=http://books.google.se/books?id=-rRf8x53_1gC&dq=Dick+Weissman,+Guitar+tuning&source=bl&ots=J2gON97DvJ&sig=mUoCTUXlK-VH-HP1Nv2AjiKUd6Y&hl=sv&sa=X&ei=guoTUI_vL8mn4gScmIGwCg&ved=0CDkQ6AEwAA|publisher=Routledge|year=2006|lccn=0415974410|isbn=9780415974417|ref=harv}}
 
==External links==
 
{{wikibooks|Guitar|Alternate Tunings|Alternative tunings}}
 
* {{cite web|url=http://warrenallencom.ipage.com/waguitartunings/tunings.htm|last=Allen|first=Warren|origyear=30 December 1997|date=22 September 2011|title=WA's encyclopedia of guitar tunings|accessdate=27 June 2012|ref=harv|id=(Recommended by {{cite book|first=Gary|last=Marcus|authorlink=Gary Marcus|title=Guitar zero: The science of learning to be musical|year=2012|publisher=Oneworld|page=234|isbn=9781851689323}})}}
* {{cite web|url=http://sethares.engr.wisc.edu/alternatetunings/alternatetuningsInteractive.html|title=Alternate&nbsp;tuning guide: Interactive|first=William A.|last=Sethares|authorlink=William Sethares|accessdate=27 June 2012|date=12 May 2012|id=Uses Wolfram Cdf player|ref=harv}}
 
===Major thirds===
* Professors Andreas Griewank and [[William Sethares]] each recommend discussions of major-thirds tuning by two jazz-guitarists, {{harv|Sethares|2011|loc="[http://sethares.engr.wisc.edu/alternatetunings/alternatetunings.html Regular tunings]"}} and {{harv|Griewank|2010|p=1}}:
** [http://v3p0.m3guitar.com/  Ole&nbsp;Kirkeby for 6- and 7-string guitars]: Charts of [http://v3p0.m3guitar.com/html/fretmaps_intervals.html intervals] [http://v3p0.m3guitar.com/html/fretmaps_chords_major.html major chords], and [http://v3p0.m3guitar.com/html/fretmaps_chords_minor.html minor chords], and [http://v3p0.m3guitar.com/html/strings.html recommended gauges for strings].
** [http://www.ralphpatt.com/Tune.html  Ralph&nbsp;Patt for 6-, 7-, and 8-string guitars]: Charts of [http://www.ralphpatt.com/Tune/Scales.html scales], [http://www.ralphpatt.com/Tune/Chords.html chords], and [http://www.ralphpatt.com/Tune/Prog.html chord-progressions].
 
===All fourths===
* [http://launch.groups.yahoo.com/group/GuitarTuningIn4ths/links Yahoo group for all-fourths tuning]
 
===New standard tuning===
* Courses in New Standard Tuning are offered by [[Guitar Circle]], the successor of [http://www.guitarcraft.com/ Guitar Craft]:
** [http://www.guitarcircleofeurope.com/          Guitar Circle of Europe]
** [http://www.guitarcircleoflatinamerica.com/  Guitar Circle of Latin America]
** [http://www.guitarcircleofnorthamerica.com/ Guitar Circle of North America]
 
{{Guitar tunings|Regular}}
 
{{DEFAULTSORT:Regular tunings}}
[[Category:Regular guitar-tunings]]
[[Category:Design theory]]
[[Category:Intervals]]
 
[[da:Guitarstemning]]
[[de:Offene Stimmung]]
[[no:Gitarstemming]]
[[ru:Гитарный строй]]

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