German sixth chord: Difference between revisions
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Per discussion, the 7-limit interpretation shouldn't be presented as historical. Copypaste some information from the 7/4 page |
Give the reason for the choice of 128:160:192:225 over 72:90:108:125 in the 5-limit; clarify that the meantone interpretation can include that chord as well; remove discussion of “rare and special dissonance” in the meantone section, since the 4:5:6:7 interpretation is actually consonant. |
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{{Wikipedia|Augmented sixth chord #German sixth}} | {{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 | == 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]]. | |||
== 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]]. | |||
Revision as of 04:20, 16 August 2024
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 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.
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.