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Augmented sixth - Wikipedia

From Wikipedia, the free encyclopedia

augmented sixth
Name
Inverse	diminished third
Abbreviation	A6^[1], ^A6
Size
Semitones	10
Interval class	2
Just interval	125:72,^[2] 225:128,^[3] 7:4^{[citation needed]}, 59049:32768^{[citation needed]}
Cents
12-Tone equal temperament	1000
Just intonation	955, 977, 969, 1020

In music, an augmented sixth (Play^ⓘ), ^A6, is an interval produced by widening a major sixth by a chromatic semitone.^[1]^[4] For instance, the interval from C to A is a major sixth, nine semitones wide in 12 TET, and both the intervals from C^♭ to A, and from C to A^♯ are augmented sixths, spanning ten semitones (in 12 TET).

Being augmented, it is nominally considered a dissonant interval, even though it renders a perceptibly consonant harmonic seventh in some tuning systems:^[5] In septimal meantone temperament, an augmented sixth is specifically assigned to the harmonic seventh (a consonant just interval of 7:4) and very nearly so in quarter comma meantone and 31 TET. In 12 TET, the augmented sixth is equal to ten semitones, and is both nominally and audibly dissonant.

An augmented sixth (^A6) is enharmonicly equivalent to a minor seventh (m7). An inverted ^A6 is a diminished third.

Description

The augmented sixth is relatively rare. Its most common occurrence is built on the lowered submediant of the prevailing key, in which position the interval assumes a natural tendency to resolve by expanding to an octave built on the dominant tonal degree. In its most common and expected resolution, the lower note of the interval moves downwards by a minor second to the dominant while the upper note, being chromatically inflected, is heard as the leading note of the dominant key, naturally tending to rise by a minor second. It is the strong tendency to resolve in this way that properly identifies an interval as functioning harmonically as an augmented sixth rather than a minor seventh, its more common enharmonic equivalent: The minor seventh has a contrary tendency to resolve to a lower pitch.

As the augmented sixth is correctly named only in certain specific contexts, and the notational distinction between ^A6 and the minor seventh (m7) is often ignored. Regardless of the true diatonic context, and despite the augmented sixth being harmonically consonant in several tuning systems, many composers and annotators to the contrary favor the more familiar but dissonant minor seventh – especially in chord notation, which is biased towards rendering chords as chains of major and / or minor thirds, in which chords containing a nominal ^A6 are conventionally written as the near-equivalent flattened seventh chords.

The augmented sixth interval in combination with certain other intervals forms the group of chords known collectively as augmented sixth chords.

The just augmented sixth arises in the extended C major scale between A^♭ and F^♯.^[6] Play^ⓘ

References

^ ^a ^b Benward; Saker (2003). Music: In theory and practice. Vol. I. p. 54. ISBN 978-0-07-294262-0. — ^A6 not specificly given, but general example of augmenting major intervals described.
^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems. p. $xxvi$ . ISBN 0-8247-4714-3. — "Classic" augmented sixth.
^ Haluska (2003), "Augmented sixth"
^ Hoffmann, F.A. (1881). Music: Its theory & practice. Thurgate & Sons. pp. 89–90. — Digitized 16 Aug 2007. Uses archaic terms superfluous sixth or extreme sharp sixth.
^ Benward & Saker (2003), p. 92.
^ Paul, Oscar (1885). ""Pythagorean major third" (musical interval)". A Manual of Harmony. Translated by Schirmer, G. Theodore Baker. p. 165 – via Google. for use in music-schools and seminaries, and for self-instruction

Perfect	unison (0) fourth (5) fifth (7) octave (12)
Major	second (2) third (4) sixth (9) seventh (11)
Minor	second (1) third (3) sixth (8) seventh (10)
Augmented	unison (1) second (3) third (5) fourth (6) fifth (8) sixth (10) seventh (12)
Diminished	second (0) third (2) fourth (4) fifth (6) sixth (7) seventh (9) octave (11)
Compound	ninth (13 or 14) tenth (15 or 16) eleventh (17 or 18) twelfth (18 or 19) thirteenth (20 or 21) fourteenth (22 or 23) fifteenth (24)

Other
tuning
systems

24-tone equal temperament
(Numbers in brackets refer
to fractional semitones.)

Neutral	quarter tone (1⁄2) second (1+1⁄2) third (3+1⁄2) major fourth (5+1⁄2) minor fifth (6+1⁄2) sixth (8+1⁄2) seventh (10+1⁄2)

Just intonations
(Numbers in brackets
refer to pitch ratios.)

7-limit	septimal quarter tone (36:35) septimal third tone (28:27) septimal chromatic semitone (21:20) septimal diatonic semitone (15:14) supermajor second (8:7) subminor third (7:6) supermajor third (9:7) subminor fifth (7:5) supermajor fourth (10:7) subminor seventh (7:4)
Higher-limit	minor diatonic semitone (17-limit)

Other
intervals

Groups	Microtone 5-limit Comma Pseudo-octave Pythagorean interval Subminor and supermajor
Semitones	Pythagorean limma Pythagorean apotome Major limma
Quarter tones	Quarter tone Septimal quarter tone Undecimal quarter tone
Commas	Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma (27.3 cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma (13.8 cents) Kleisma (8.1 cents) Septimal kleisma (7.7 cents) Schisma (1.95 cents) Breedsma (0.72 cents) Ragisma (0.4 cents)
Measurement	Cent Centitone Millioctave Savart
Others	Wolf Ditone Semiditone Secor Incomposite interval

List of pitch intervals

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Hidden categories:

Description

See also

References

Further reading