German sixth chord: Difference between revisions

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Rework part of the meantone section as quarter-comma meantone is a specific instance of septimal meantone. The harmonic seventh chord should remain highlighted as it's the focus nowadays.
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== In meantone ==
== 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]].
In [[meantone]], the augmented sixth represents both [[125/72]] and [[225/128]]. Most meantone tunings has this interval placed near [[7/4]]. In the historically-prevalent [[quarter-comma meantone]], for example, it is tuned only a few cents shy of a just 7/4, so the meantone German sixth chord can be considered to approximate the [[harmonic seventh chord]]:
 
* 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6.


== In just intonation ==
== In just intonation ==
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]].
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]].