German sixth chord
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.