German sixth chord: Difference between revisions
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simultaneously represents both [[72:90:108:125]] (with steps 5/4, 6/5, and [[125/108]]) and [[128:160:192:225]] (with steps 5/4, 6/5, and [[75/64]]). | simultaneously represents both [[72:90:108:125]] (with steps 5/4, 6/5, and [[125/108]]) and [[128:160:192:225]] (with steps 5/4, 6/5, and [[75/64]]). | ||
However, in the historically prevalent [[quarter-comma meantone]], the augmented | However, in the historically prevalent [[quarter-comma meantone]], the augmented sixth 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'' as in [[septimal meantone]]: | ||
* ( | * (Septimal meantone) 1 – 5/4 – 3/2 – 7/4 | ||
representing [[4:5:6:7]] (with steps 5/4, 6/5, and 7/6). | representing [[4:5:6:7]] (with steps 5/4, 6/5, and 7/6). | ||
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In the [[5-limit]]: | In the [[5-limit]]: | ||
* [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted | * [[128:160:192:225]], one of the possible 5-limit interpretations of the meantone chord, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]]. | ||
[[Category:Just intonation chords]] | [[Category:Just intonation chords]] | ||
[[Category: | [[Category:German sixth chords| ]] <!-- main article --> | ||
Latest revision as of 05:31, 24 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 5-limit meantone, the traditional foundation of tonal harmony, the augmented sixth represents both 225/128 and 125/72. It is treated as a rare and special dissonance, especially when used on the sixth degree. The 5-limit meantone German sixth chord,
- (Meantone) 1 – 5/4 – 3/2 – 125/72
simultaneously represents both 72:90:108:125 (with steps 5/4, 6/5, and 125/108) and 128:160:192:225 (with steps 5/4, 6/5, and 75/64).
However, in the historically prevalent quarter-comma meantone, the augmented sixth 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 as in septimal meantone:
- (Septimal meantone) 1 – 5/4 – 3/2 – 7/4
representing 4:5:6:7 (with steps 5/4, 6/5, and 7/6).
In just intonation
In the 5-limit:
- 128:160:192:225, one of the possible 5-limit interpretations of the meantone chord, is found rooted at the ♭II (16⁄15) and ♭VI (8⁄5) of the duodene.