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 | 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]]. | ||
Revision as of 09:03, 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. 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
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.