French sixth chord

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Augmented sixth chord #French sixth

A French sixth chord is a tetrad comprising a root, major third, augmented fourth, and augmented sixth.

In meantone

In 5-limit meantone, the traditional foundation of tonal harmony, the augmented sixth represents both 225/128 and 125/72, and the augmented fourth represents all of 45/32, 25/18, and 729/512, so the 5-limit meantone French sixth chord,

• (Meantone) 1 – 5/4 – 25/18 – 125/72

represents a range of JI interpretations including both 72:90:100:125 and 128:160:180:225.

However, in the historically prevalent quarter-comma meantone, the augmented seventh is tuned only a few cents shy of a just 7/4, and the augmented fourth is only a few cents shy of 7/5, so the meantone French sixth chord can be considered to approximate the septimal meantone chord:

• (Meantone) 1 – 5/4 – 7/5 – 7/4

representing 20:25:28:35.

In just intonation

In the 5-limit:

• 128:160:180:225, one of the possible 5-limit interpretations of the meantone chord, is found rooted at ♭II (16⁄15) and ♭VI (8⁄5) in the duodene.