Transwiki:Major thirds tuning

An equilateral triangle circumscribed by the chromatic circle specifies a major-thirds tuning.

Among alternative tunings for guitar, a major-thirds tuning is a regular tuning in which the intervals between successive open strings are each major thirds. Another name for major-thirds tuning is all-thirds tuning.

In the standard tuning, the successive open-strings mix two types of intervals, four perfect fourths and a single major-third between the G (g) and B (b') strings:

E-A-d-g-b'-e'

In contrast, the major-thirds tuning

D♯-G-B-D♯-G-B-D♯

has only major-third intervals between successive strings. Its open-string notes contain two copies of the augmented C chord.

For guitars with at least six strings, every major-third tuning thrice repeats open strings at different octaves. With the repetition of three open-string notes, each major-thirds tuning provides the guitarist with many options for fingering chords. By having repeated open-string notes (at different octaves) and by having uniform intervals between strings, major-thirds tuning simplifies improvisation by advanced guitarists and learning by beginners.

An alternative to standard tuning

In the standard guitar-tuning, one major-third interval is interjected amid four perfect-fourth intervals. In contrast, major-thirds tuning has five major-thirds intervals.

Standard tuning (listen)

In the standard tuning, the successive open-strings mix two types of intervals, four perfect fourths and a single major-third between the G (g) and B (b') strings:

E-A-d-g-b'-e'

In modern music, the twelve notes of the octave are equally space around the chromatic circle. This circle thus circumscribes four equilateral triangles with vertices among the notes. Each such triangle specifies the successive open-strings of a major-thirds tuning.

Neighboring the standard tuning is the major-thirds tuning that has the open strings

E-G♯-c-e-g♯-c'.

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.

The open strings of the C-E-G♯-c-e-g♯ tuning contains the augmented-C chord:

play .

A lower major-thirds tuning has the open strings

C-E-G♯-c-e-g♯,

which contain two augmented C chords in two octaves. These two major-thirds tunings share five open-strings

E-G♯-c-e-g♯,

and the tunings both appear in the following table:

Major-thirds tuning C-E-G♯
	open (0th fret)	1st fret	2nd fret	3rd fret	4th fret	5th fret
-1st string	g '♯	a"	a♯"	b"	c"	c♯"
0th string	e'	f'	f♯'	g'	g♯'	a"
1st string	c'	c♯'	d'	d♯'	e'	f '
2nd string	g♯	a'	a♯'	b'	c'	c♯'
3rd string	e	f	f♯	g	g♯	a'
4th string	c	c♯	d	d♯	e	f
5th string	G♯	a	a♯	b	c	c#
6th string	E	F	F♯	G	G♯	a
7th string	C	C♯	D	D♯	E	F

The table also displays the open-notes for guitars with more than six strings, which also are used for major-thirds tuning. For the standard Western guitar, which has six strings, major-thirds tuning has a smaller range than standard tuning; on a guitar with seven strings, the major-thirds tuning covers the range of standard tuning on six strings. Even greater range is possible with guitars with eight strings. For the highest open-string note listed in the table g'♯, a steel-string having the diameter of 0.008 inches (0.20 mm) has been suggested; for other strings (of steel and of nylon), gauges have been tabulated.

Other major-thirds tunings

In the above table, four consecutive frets display all of the major-thirds tunings. Again, the lower major-thirds tuning

C-E-G♯-c-e-g♯

assigns its initial open-strings the notes

C-E-G♯.

The other major-thirds tunings respectively assign their initial open-strings the notes

C♯-F-a,

D-F♯-a♯, and

D♯-G-b.

Russian guitar

The major-thirds tuning is approximated by the open G tuning of the Russian guitar, which has seven strings.

In the above table, the third fret displays the major-thirds tuning

D♯-G-B-D♯-G-B-D♯.

This tuning is approximated by the open G tuning

D-G-B-D-G-B-D

of the seven-string Russian guitar.

Properties

Every major-thirds tuning is regular and repetitive.

Regular musical-intervals

In each regular tuning, the musical intervals are the same for each pair of consecutive strings. Other regular tunings include all-fourths, augmented-fourths, and all-fifths tunings. For each regular tuning, chord patterns may be moved around the fretboard, a property that simplifies beginners' learning of chords and that simplifies advanced players' improvisation.

Repetition

Unlike all-fourths and all-fifths tuning, major-thirds tuning repeats its octave after every two strings, which again simplifies the learning of chords and improvisation; This repetition results in two copies of the three open-strings' notes, each in a different octave. Similarly, augmented-fourths tuning repeats itself after one string, resulting in three copies of the two open-strings' notes, each in a different octave.

On the other hand, because major-thirds tunings have only three open-notes (occurring in each of two octaves), major-thirds tunings offer fewer open-chords. Furthermore, the geometry of the chromatic circle forces every major-thirds tuning to contain one (or two) open-stings having sharp (or flat) notes; thus, each major thirds tuning has at most two natural-notes. Consequently, guitarists playing in major-third have fewer natural open-chords, that is, chords having a natural root-note on an open string. Such open chords are conventional in popular music.

In contrast, such natural open-chords can often be fingered using the natural open-notes of other tunings, of which there are exactly

• five in the standard tuning E-A-D-G-B-E,
• three in the Russian open-G tuning G-D-B-G-B-D-G,
• six in the all-fourths tuning E-A-D-G-C-F,
• five such notes for the new standard tuning C-G-D-A-E-G, which approximates the all-fifths tuning C-G-D-A-E-B, which has six such notes.

Translation of chords

For all guitar tunings, chord shapes can be shifted horizontally, up and down the fretboard. However, the regular repetition of the major-thirds tuning enable chord shapes also to be vertically shifted.

Four frets for the four fingers

Because the chromatic scale climbs from one string to the next after exactly four frets, major-thirds tuning reduces the extensions of the little and index fingers ("hand stretching"). For other tunings, the successive strings have intervals that are perfect-fourths, augmented-fourths, or perfect fifths; thus, the fretting hand must cover 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.)

See also

• Minor thirds tuning
• Scordatura, alternative tunings of stringed instruments
• Stringed instrument tunings

References

• Griewank, Andreas (2010), Tuning guitars and reading music in major thirds (html), Matheon preprints, vol. 695, Rosestr. 3a, 12524 Berlin, Germany: DFG research center "MATHEON, Mathematics for key technologies" Berlin, Postscript file and Pdf file {{citation}}: Invalid |ref=harv (help); Unknown parameter |month= ignored (help); Unknown parameter |urn= ignored (|id= suggested) (help)CS1 maint: location (link)
• Sethares, William A. (2011). "Alternate tuning guide" (html). Madison, Wisconsin: University of Wisconsin; Department of Electrical Engineering. 2010 PDF version by Bill Sethares. Retrieved 19 May 2012. {{cite web}}: Invalid |ref=harv (help)

Further reading

• Anonymous (2000). Alternate tunings guitar essentials. Acoustic Guitar Magazine's private lessons. String Letter Publishing. Hal Leonard Publishing Corporation. ISBN 9781890490249. LCCN 1890490245. {{cite book}}: Invalid |ref=harv (help)
• Denyer, Ralph (1992). "Playing the guitar: Alternative tunings". The guitar handbook. Special contributors Isaac Guillory and Alastair M. Crawford (Fully revised and updated ed.). London and Syndey: Pan Books. pp. 158–159. ISBN 0-330-32750-X. {{cite book}}: Unknown parameter |foreword= ignored (help)
• Hanson, Mark (1995). The complete book of alternate tunings. Accent on Music. ISBN 9780936799131. {{cite book}}: Invalid |ref=harv (help)
• Hanson, Mark (1997). Alternate tunings picture chords. Accent on Music. ISBN 9780936799148. LCCN 0936799145. {{cite book}}: Cite has empty unknown parameter: |1= (help); Invalid |ref=harv (help)
• Heines, Danny (2007). Mastering alternate tunings: A revolutionary system of fretboard navigation for fingerstyle guitarists. Hal Leonard. ISBN 9780634065699. LCCN 0634065696. {{cite book}}: Invalid |ref=harv (help)
• Johnson, Chad (2002). Alternate tuning chord dictionary. Hal Leonard. ISBN 9780634038570. LCCN 2005561612. {{cite book}}: Cite has empty unknown parameter: |1= (help); Invalid |ref=harv (help)
• Maloof, Richard (2007). Alternate tunings for guitar. Cherry Lane Music Company. ISBN 1575605783. {{cite book}}: Invalid |ref=harv (help); Unknown parameter |iccn= ignored (help)
• Shark, Mark (2008). The tao of tunings: A map to the world of alternate tunings. Hal Leonard Corporation. ISBN 9781423430872. LCCN 1423430875. {{cite book}}: Invalid |ref=harv (help)
• Weissman, Dick (2006). Guitar tunings: A comprehensive guide. Routledge. ISBN 9780415974417. LCCN 0415974410. {{cite book}}: Cite has empty unknown parameters: |1= and |2= (help); Invalid |ref=harv (help)

External links

• Professors Andreas Griewank and William Sethares each recommend discussions of major-thirds tuning by two jazz-guitarists, (Sethares 2011, "Regular tunings") and (Griewank 2010, p. 1):
  • Ole Kirkeby for 6- and 7-string guitars: Charts of intervals major chords, and minor chords, and recommended gauges for strings.
  • Ralph Patt for 6-, 7-, and 8-string guitars: Charts of scales, chords, and chord-progressions.
• Ole Kirkeby notes two additional sites (besides Patt's):
  • Brian Berge
  • Patrick Zemb (in French original and English translation)