German sixth chord: Difference between revisions
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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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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. | 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 == | |||
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 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]]. | ||
Revision as of 08:31, 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 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 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.