Transwiki:Regular tuning



Among alternative guitar-tunings, regular tunings have equal musical intervals between the paired notes of their successive open strings. Regular tunings simplify the learning of the fretboard of the guitar and of chords by beginning students. Regular tunings also facilitate improvisation by advanced guitarists.

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 highest to lowest. The standard tuning defines the string pitches as E, A, D, G, B, and E, from lowest (low E) to highest (high E). Between the open-strings of the standard tuning are three fourths (E-A, A-D, D-G), then one major third (D-G), and the fourth perfect-fourth (B-E).

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: 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,
 * 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
 * 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.

Regular tunings have symmetrical scales all along the fretboard. This makes it simpler to translate chords. For the regular tunings, chords may be be moved diagonally around the fretboard. Regular tunings thus appeal to new guitarists and also to jazz-guitarists, whose improvisation is simplified by regular intervals. On the other hand, some 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, in which the large spacings require hand stretching.

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.

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 tuning guide) is the leading source for this article. This article's descriptions of particular regular-tunings use other sources also.

Review of standard and alternative guitar-tunings
This summary of standard tuning also introduces the terms for discussing alternative tunings

Standard


Standard tuning has the following open-string notes:
 * 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, which has a width of four semitones.

Alternative
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.

Regular intervals between successive open-strings


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 tunings have equal intervals between the strings. 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, The regular-tunings with either zero semi-tones (unison), one semi-tone (minor second), two semi-tones (major second), or twelve semitones (octave) as their intervals have little musical-interest, because it is very difficult to play chords in those tunings. Similarly, the regular tunings with minor seventh or major seventh would make chord-playing very difficult.
 * 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.

Regular tunings have symmetrical scales all along the fretboard. This makes it simpler to translate chords. For the regular tunings, chords may be 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.

Some conventional chords may be more difficult to play
On the other hand, some 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, in which the large spacings 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.

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"). For other regular 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.)

Examples
The following regular-tunings are discussed by Sethares, who also mentions other regular tunings that may be difficult to play or of little musical interest.

Minor thirds

 * C-D♯-F♯-a-c-d♯

In the minor-thirds tuning, every interval between successive strings is a minor third. In the minor-thirds tuning beginning with C, the open strings contain the notes (c, d♯, f♯) of the diminished C chord.

Major thirds
Major-thirds tuning is a regular tuning in which the musical intervals between successive strings are each major thirds. Unlike all-fourths and all-fifths tuning, major-thirds tuning repeats its octave after three strings, which again simplifies the learning of chords and improvisation; similarly, augmented-fourths tuning repeats itself after two strings.

Neighboring the standard tuning is the all-thirds tuning that has the open strings
 * E-G♯-c-e-g♯-c'.

A lower all-thirds tuning has the open strings
 * C-E-G♯-c-e-g♯,

which "contains two octaves of a C augmented chord". With the repetition of three open-string notes, this tuning provides the guitarist with many possibilities for fingering chords. 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.

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.

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:

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 in has been suggested; for other strings (of steel and of nylon), gauges have been tabulated.

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.

All fourths



 * E-A-d-g-c'-f'

This tuning is like that of the lowest four strings in standard tuning. 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 musician Stanley Jordan plays guitar in all-fourths tuning; he has stated that all-fourths tuning "simplifies the fingerboard, making it logical".

For all-fourths tuning, all twelve major chords (in the first or open positions) are generated by two chords, the open F major chord and the D major chord. The regularity of chord-patterns reduces the number of finger positions that need to be memorized.

Augmented fourths



 * C-F♯-c-f♯-c'-f♯' and B-F-b-f-b'-f' etc.

Between the all-fifths and all-fourths tunings are augmented-fourth tunings, which are also called "diminished-fifths" or "tritone" tunings. With augmented-fourths tunings, the fretboard has greatest symmetry. 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 "The augmented-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 C-C-C-C-C-C) for which all chords-forms remain unchanged when the strings are reversed. Thus the augmented-fourths tuning is its own 'lefty' tuning." Of all the augmented-fourths tunings, the C-F♯-c-f♯-c'-f '♯ tuning is the closest approximation to the standard tuning, and its fretboard is displayed next: An augmented-fourths tuning "makes it very easy for playing half-whole scales, diminished 7 licks, and whole tone scales," stated guitarist Ron Jarzombek.

All fifths: "Mandoguitar"

 * 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". 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.

New standard tuning


All-fifths tuning has been approximated with tunings that avoid the high b' or the low C. The b' has been approximated with a g' in the New Standard Tuning (NST) of King Crimson's Robert Fripp. The original version of NST was all fifths tuning. However, in the 1980s, Fripp never attained the all fifth's high B. While he could attain A, the string's lifetime distribution was too short. Experimenting with a G string, Fripp succeeded. "Originally, seen in 5ths. all the way, the top string would not go to B. so, as on a tenor banjo, I adopted an A on the first string. These kept breaking, so G was adopted." In 2012, Fripp experimented with A String (0.007);  if successful, the experiment could lead to "the NST 1.2", CGDAE-A, according to Fripp. Fripp's NST has been taught in Guitar Craft courses. Guitar Craft, which has been succeeded by Guitar Circle, has taught Fripp's tuning to three-thousand students. After studying with Fripp's Guitar Craft, The California Guitar Trio commissioned a luthier to build them guitars for all-fifths tuning.

Summary
The principal regular-tunings have their properties summarized in the following table:

Major thirds

 * Professors Andreas Griewank and William Sethares each recommend discussions of major-thirds tuning by two jazz-guitarists, and :
 * 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.

All fourths

 * Yahoo group for all-fourths tuning

New standard tuning

 * Courses in New Standard Tuning are offered by Guitar Circle, the successor of Guitar Craft:
 * Guitar Circle of Europe
 * Guitar Circle of Latin America
 * Guitar Circle of North America

Wikipedia in other languages

 * Guitarstemning
 * Offene Stimmung
 * Gitarstemming
 * Гитарный строй