German sixth chord: Difference between revisions

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A '''German sixth chord''' is a [[tetrad]] comprising a root, major third, fifth, and augmented sixth.

A '''German sixth chord''' is a [[tetrad]] comprising a root, major third, perfect fifth, and augmented sixth, often built on the sixth degree of the minor scale.

In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the augmented sixth is treated as a rare and special dissonance. It is approximately the size of a [[7/4|harmonic seventh (7/4)]], so the chord approximates the [[harmonic seventh chord]]:

== In just intonation ==

* 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6.

In 5-limit ~~just intonation~~, ~~this~~ augmented sixth ~~is likely to be~~ [[225/128]] – the ~~Neapolitan augmented sixth~~, so ~~if we stick~~ to ~~the~~ 5~~-limit, one possible tuning is given as~~ [[128:160:192:225]].

Because the German sixth chord is often built on the sixth degree of a minor scale, the [[128:160:192:225]] found on the ♭VI of the [[duodene]] is a good candidate for its interpretation in the [[5-limit]].

== In meantone ==

In [[meantone]], the augmented sixth represents both [[125/72]] and [[225/128]]. In the historically-prevalent [[quarter-comma meantone]] it is tuned only a few cents shy of a just [[7/4]], and in the closely related [[septimal meantone]] it explicitly represents [[7/4]] as well, so the meantone German sixth chord can be considered to approximate both [[4:5:6:7]] and [[128:160:192:225]].

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 {{Wikipedia|Augmented sixth chord #German sixth}}
-A '''German sixth chord''' is a [[tetrad]] comprising a root, major third, fifth, and augmented sixth.
+A '''German sixth chord''' is a [[tetrad]] comprising a root, major third, perfect fifth, and augmented sixth, often built on the sixth degree of the minor scale.
-In [[meantone]] (including [[12edo]]), on which traditional tonal harmony is built, the augmented sixth is treated as a rare and special dissonance. It is approximately the size of a [[7/4|harmonic seventh (7/4)]], so the chord approximates the [[harmonic seventh chord]]:
+== In just intonation ==
-* 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;3/2&thinsp;–&thinsp;7/4 with steps 5/4, 6/5, 7/6.
-In 5-limit just intonation, this augmented sixth is likely to be [[225/128]] – the Neapolitan augmented sixth, so if we stick to the 5-limit, one possible tuning is given as [[128:160:192:225]].
+Because the German sixth chord is often built on the sixth degree of a minor scale, the [[128:160:192:225]] found on the ♭VI of the [[duodene]] is a good candidate for its interpretation in the [[5-limit]].
+== In meantone ==
+In [[meantone]], the augmented sixth represents both [[125/72]] and [[225/128]]. In the historically-prevalent [[quarter-comma meantone]] it is tuned only a few cents shy of a just [[7/4]], and in the closely related [[septimal meantone]] it explicitly represents [[7/4]] as well, so the meantone German sixth chord can be considered to approximate both [[4:5:6:7]] and [[128:160:192:225]].