# Augmented-fourths tuning

Among alternative tunings for guitar, each augmented-fourths tuning is a regular tuning in which the musical intervals between successive open-string notes are each augmented fourths. Because augmented fourths are alternatively called "tritones" ("tri-tones") or "diminished fifths", augmented-fourths tuning is also called tritone tuning or diminished-fifths tuning.
The standard guitar-tuning
    E-A-d-g-b'-e'
interjects exactly one major third amid four perfect fourths for the intervals between its successive open strings. In contrast, the augmented fourths tunings
    C-F♯-c-f♯-c'-f '♯ and
    B-F-b-f-b'-f'
have only augmented-fourths intervals.
The set of augmented-fourths tunings has three properties that simplify learning by beginners and improvisation by experts: Regular intervals, string repetition, and lefty-righty symmetry. These properties characterize augmented-fourths tunings among non-trivial tunings.

## Properties

The set of augmented-fourths tunings has three properties that simplify learning by beginners and improvisation by experts: Regular intervals, string repetition, and lefty-righty symmetry.
Besides the set of augmented-fourths tuning, exactly one other set of tunings has these three properties—the trivial class of one-note tunings, which contains the C-C-C-C-C-C tuning, for example.
Augmented-fourths tunings have extended range. Because each of its tritone-intervals between successive strings is wider than the perfect-fourth intervals (and one major third) of standard tuning, augmented-fourths tunings have greater range than standard tuning—six additional notes, only one less note than Robert Fripp's new standard tuning.

### Regular intervals

In each regular tuning, the musical intervals are the same for each pair of consecutive strings. Other regular tunings include major-thirds, all-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.

### Thrice repeated open-string notes

Two other regular tunings, all-fourths and all-fifths tunings, have strings with five and six distinct open-notes, respectively. Thus, they have no repetition of open-notes, and so they require that the guitarist remember five and six strings, respectively.
In contrast, augmented fourths is a repetitive tuning that begins the next octave after two strings. These tunings' repetition of open-string notes again simplifies the learning of chords and improvisation.

### Left-handed involution

For left-handed guitars, the ordering of the strings reverse the ordering of right-handed guitars. Consequently, left-handed tunings have different chords than right-handed tunings. Regular guitar-tunings have the property that their left-handed ("lefty" versions) are also regular tunings. 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 $n$ semitones is the regular tuning based on its involuted interval with $12-n$ 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.
The left-handed involute of an augmented-fourth tuning is the augmented-fourths tuning with the same open-string notes. "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."

## Examples

The "standard tuning" consists of perfect fourths and a single major-third between the G (g) and B (b') strings:
    E-A-d-g-b'-e'

### C-F♯-C-F♯-C-F♯

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:
Augmented-fourths tuning C-F♯ :
| | open (0th fret) | 1st fret | 2nd fret | 3rd fret | 4th fret | 5th fret |
| 1st string | f '♯ | g' | g'♯ | a" | a"♯ | b" |
| 2nd string | c' | c'♯ | d' | d'♯ | e' | f ' |
| 3rd string | f♯ | g | g♯ | a' | a'♯ | b' |
| 4th string | c | c♯ | d | d♯ | e | f |
| 5th string | F♯ | G | G♯ | a | a♯ | b |
| 6th string | C | C♯ | D | D♯ | E | F |
Each fret displays the open strings of exactly one augmented-fourths tuning.

### B-F-B-F-B-F

There are no sharps or flats in the open strings of exactly one augmented-fourths tuning, that with only B and F notes (B-F-b-f-b'-f'). This tuning would appear, for the C-F♯ augmented-fourths tuning displayed above, to the left of the open strings, at the negative-first fret.
Augmented-fourths B-F tuning :
| | open (0th fret) | 1st fret | 2nd fret | 3rd fret | 4th fret | 5th fret |
| 1st string | f ' | f '♯ | g' | g'♯ | a" | a"♯ |
| 2nd string | b' | c' | c'♯ | d' | d'♯ | e' |
| 3rd string | f | f♯ | g | g♯ | a' | a'♯ |
| 4th string | b | c | c♯ | d | d♯ | e |
| 5th string | F | F♯ | G | G♯ | a | a♯ |
| 6th string | B | C | C♯ | D | D♯ | E |
This tuning "makes it very easy for playing half-whole scales, diminished 7 licks, and whole tone scales," stated guitarist Ron Jarzombek, who has used it on two albums. This tuning was used in "Tri 7/5" by Shawn Lane (The Tri-Tone Fascination and Powers of Ten; Live!).