German sixth chord: Difference between revisions
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Note the ~125/72 is simultaneously ~225/128, and the ~75/64 is simultaneously ~125/108. | Note the ~125/72 is simultaneously ~225/128, and the ~75/64 is simultaneously ~125/108. | ||
However, most [[meantone]] tunings | However, most [[meantone]] tunings have the augmented sixth 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]]: | ||
* (Meantone) 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6. | * (Meantone) 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6. | ||
Revision as of 02:26, 18 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
If we stick to the 5-limit, which traditional tonal harmony mainly concerns, the augmented sixth represents both 125/72 and 225/128. It is treated as a rare and special dissonance, especially when used on the sixth degree. The chord is
- (Meantone) 1 – 5/4 – 3/2 – 125/72 with steps 5/4, 6/5, 75/64.
Note the ~125/72 is simultaneously ~225/128, and the ~75/64 is simultaneously ~125/108.
However, most meantone tunings have the augmented sixth 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:
- (Meantone) 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.