Diminished seventh chord
The diminished seventh chord is a tetrad comprising a root, minor third, diminished fifth, and diminished seventh, conventionally formed by stacking three minor thirds.
In temperaments
In diminished temperament, which is named for this chord and tempers out both 648/625 and 36/35, the ~36/25 diminished fifth is equivalent to ~7/5, and the ~216/125 diminished seventh is equivalent to a ~5/3 major sixth, giving rise to a 7-odd-limit essentially tempered chord:
- (Diminished) 1 – 6/5 – 7/5 – 5/3
(Note that the interval between ~6/5 and ~5/3 tempers to ~10/7.)
In the 5-limit, the simplest interpretation as a stack of ~6/5 is a 25-odd-limit essentially tempered chord of the dimipent temperament, another temperament named after this chord.
- (Dimipent) 1 – 6/5 – 25/18 – 5/3
In meantone
Before the ubiquity of 12edo, a diminished seventh chord did not imply an equal tuning of all four thirds (technically three minor thirds and an augmented second). It can be viewed as a 9-odd-limit essentially tempered chord of starling. See starling chords. This is still compatible with 12edo and is perhaps as authentic as the 25-odd-limit interpretation above.
In just intonation
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