Augmented-fourths tuning

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Augmented fourths
Tritone in the chromatic circle.png
For every augmented-fourths tuning, the interval between successive open-strings is six semitones, half the circumference of the chromatic circle.
Basic information
AliasesAll-tritone tuning, Diminished-fifth tuning
Interval Augmented fourth
Semitones 6
Example(s)C-F-c-f-c'-f '
B-F-b-f-b'-f'
Advanced information
Repetition After 2 strings
AdvantagesSimplified fretboard
DisadvantagesOnly two open-string notes
Left-handed tuning Augmented-fourths tuning
Associated musician
Guitarist Shawn Lane
ShawnLane.jpg
Shawn Lane used the B-F-B-F-B-F augmented-fourths tuning for "Tri 7/5" on his The Tri-Tone Fascination.
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
In the standard guitar-tuning, one major-third interval is interjected amid four perfect-fourth intervals. Tuning ADGBE5 ADGBE0.svg
In the standard guitar-tuning, one major-third interval is interjected amid four perfect-fourth intervals.
Standard tuning (listen)

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 . [1] Because augmented fourths are alternatively called "tritones" ("tri-tones") or "diminished fifths", augmented-fourths tuning is also called tritone tuning or diminished-fifths tuning.

Contents

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

In modern music, the twelve notes of the octave are equally space around the chromatic circle. On this circle, there are six pairs of antipodal notes, each representing an augmented-fourth interval. Each such pair specifies the successive open-strings of an augmented-fourths tuning. Pitch class space.svg
In modern music, the twelve notes of the octave are equally space around the chromatic circle. On this circle, there are six pairs of antipodal notes, each representing an augmented-fourth interval. Each such pair specifies the successive open-strings of an augmented-fourths tuning.

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. [2]

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. [2]

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. [3] [4]

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. [4]

In contrast, augmented fourths is a repetitive tuning that begins the next octave after two strings. [5] These tunings' repetition of open-string notes again simplifies the learning of chords and improvisation. [4]

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   semitones is the regular tuning based on its involuted interval with  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. [6]

The left-handed involute of an augmented-fourth tuning is the augmented-fourths tuning with the same open-string notes. [7] "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." [2]

Examples

The "standard tuning" consists of perfect fourths and a single major-third between the G (g) and B (b') strings: [8]

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, [7] and its fretboard is displayed next:

Augmented-fourths tuning C-F [2]
open
(0th fret)
1st fret2nd fret3rd fret4th fret5th fret
1st stringf 'g'g'a"a"b"
2nd stringc'c'd'd'e'f '
3rd stringfgga'a'b'
4th stringccddef
5th stringFGGaab
6th stringCCDDEF

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 fret2nd fret3rd fret4th fret5th fret
1st stringf 'f 'g'g'a"a"
2nd stringb'c'c'd'd'e'
3rd stringffgga'a'
4th stringbccdde
5th stringFFGGaa
6th stringBCCDDE

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. [9] This tuning was used in "Tri 7/5" by Shawn Lane ( The Tri-Tone Fascination and Powers of Ten; Live! ).[ citation needed ]

See also


Notes

  1. Sethares (2001 , p. 56)
  2. 1 2 3 4 Sethares (2001 , "The augmented fourths tuning", p. 60 )
  3. Sethares (2001 , p. 52):
    Sethares, Bill (2001). "Regular tunings". Alternate tuning guide (PDF). Madison, Wisconsin: University of Wisconsin; Department of Electrical Engineering. pp. 52–67. 2010 Alternate tuning guide, including a revised chapter on regular tunings . Retrieved 19 May 2012.
  4. 1 2 3 Kirkeby, Ole (1 March 2012). "Major thirds tuning". m3guitar.com. cited by Sethares (2011). Archived from the original on 29 May 2012. Retrieved 10 June 2012.
  5. Sethares (2001 , pp. 56 and 60)
  6. Sethares (2001 , p. 53)
  7. 1 2 Sethares (2001 , "The augmented fourths tuning" 60–61)
  8. Denyer (1992)
  9. Turner, Steve (30 December 2005). "Interview with Ron Jarzombek". RonJarzombek.com. Retrieved 23 May 2012.
    In this interview, Ron Jarzombek states that he has used the augmented-fourths BF tuning for "Two Thirds Of Satan" and "A Chaotic Realization Of Nothing Yet Misunderstood (ACRONYM)".

Related Research Articles

Guitar Fretted string instrument

The guitar is a fretted musical instrument that typically has six strings. It is held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing the strings against frets with the fingers of the opposite hand. A plectrum or individual finger picks may be used to strike the strings. The sound of the guitar is projected either acoustically, by means of a resonant chamber on the instrument, or amplified by an electronic pickup and an amplifier.

Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, which is ≈702 cents wide.

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1200 cents.

Perfect fifth musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

All fifths tuning Guitar tuning

Among guitar tunings, all-fifths tuning refers to the set of tunings in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is also called fifths, perfect fifths, or mandoguitar. The conventional "standard tuning" consists of perfect fourths and a single major third between the g and b strings:

Guitar chord

In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.

Guitar tunings

Guitar tunings are the assignment of pitches to the open strings of guitars, including acoustic guitars, electric guitars, and classical guitars. Tunings are described by the particular pitches that are made by notes in Western music. By convention, the notes are ordered and arranged from the lowest-pitched string to the highest-pitched string, or the thickest string to thinnest, or the lowest frequency to the highest. This sometimes confuses beginner guitarists, since the highest-pitched string is referred to as the 1st string, and the lowest-pitched is the 6th string.

Jazz chords refer to chords, chord voicings and chord symbols that jazz musicians commonly use in composition, improvisation, and harmony. In jazz chords and theory, most triads that appear in lead sheets or fake books can have sevenths added to them, using the performer's discretion and ear. For example, if a tune is in the key of C, if there is a G chord, the chord-playing performer usually voices this chord as G7. While the notes of a G7 chord are G–B–D–F, jazz often omits the fifth of the chord—and even the root if playing in a group. However, not all jazz pianists leave out the root when they play voicings: Bud Powell, one of the best-known of the bebop pianists, and Horace Silver, whose quintet included many of jazz's biggest names from the 1950s to the 1970s, included the root note in their voicings.

New standard tuning Alternative guitar tuning

New standard tuning (NST) is an alternative tuning for the guitar that approximates all-fifths tuning. The guitar's strings are assigned the notes C2-G2-D3-A3-E4-G4 ; the five lowest open strings are each tuned to an interval of a perfect fifth {(C,G),(G,D),(D,A),(A,E)}; the two highest strings are a minor third apart (E,G).

Open G tuning

Among alternative tunings for the guitar, an open G tuning is an open tuning that features the G-major chord; its open notes are selected from the notes of a G-major chord, such as the G-major triad (G,B,D). For example, a popular open-G tuning is

Open C tuning

Open C tuning is an open tuning for guitar. The open-string notes form a C major chord, which is the triad (C,E,G) having the root note C, the major third (C,E), and the perfect fifth (C,G). When the guitar is strummed without fretting any strings, a C-major chord is sounded. By barring all of the strings for one fret, one finger suffices to fret the other eleven major-chords.

All fourths tuning

Among alternative tunings for the guitar, all-fourths tuning is a regular tuning. In contrast, the standard tuning has one irregularity—a major third between the third and second strings—while having perfect fourths between the other successive strings. The standard tuning's irregular major-third is replaced by a perfect fourth in all-fourths tuning, which has the open notes E2-A2-D3-G3-C4-F4.

Regular diatonic tuning

A regular diatonic tuning is any musical scale consisting of "tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size which makes it a Linear temperament with the tempered fifth as a generator.

Major thirds tuning

Among alternative tunings for guitar, a major-thirds tuning is a regular tuning in which each interval between successive open strings is a major third. Other names for major-thirds tuning include major-third tuning, M3 tuning, all-thirds tuning, and augmented tuning. By definition, a major-third interval separates two notes that differ by exactly four semitones.

Regular tuning

Among alternative guitar-tunings, regular tunings have equal musical intervals between the paired notes of their successive open strings.

Repetitive tuning

Repetitive tunings are alternative tunings for the guitar. A repetitive tuning begins with a list of notes that is duplicated, either at unison or at higher octaves.

Overtones tuning

Among alternative tunings for the guitar, an overtones tuning selects its open-string notes from the overtone sequence of a fundamental note. An example is the open tuning constituted by the first six overtones of the fundamental note C, namely C2-C3-G3-C4-E4-G4.

References