German sixth chord: Difference between revisions
Restore the comment on its dissonance. This is dissonant becuz of its position and voice-leading properties, and possibly lack of awareness of septimal intervals |
Per discussion, list the 5-limit chord separately. |
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== In meantone == | == 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. | 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 | ||
* 1 – 5/4 – 3/2 – 7/4 with steps 5/4, 6/5, 7/6. | * (Meantone) 1 – 5/4 – 3/2 – 125/72 with steps 5/4, 6/5, 75/64 | ||
Note the ~125/72 is simultaneously ~225/128. | |||
However, most [[meantone]] tunings has 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 == | == 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 15:58, 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
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.
However, most meantone tunings has 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.