Diminished seventh chord: Difference between revisions

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The '''diminished seventh chord''' is a [[tetrad]] ~~that comprises~~ four identical minor thirds closing at the [[octave]]. In the 5-limit, the simplest interpretation is a [[25-odd-limit]] [[essentially tempered chord]] of the [[dimipent]] temperament, the temperament named after this chord.

The '''diminished seventh chord''' is a [[tetrad]] traditionally described as comprising a root, [[minor]] third, [[interval quality|diminished]] fifth, and diminished seventh. In contemporary [[12edo]] music, it is a stack of four identical minor thirds of [[~]][[6/5]] closing at the [[octave]], [[tempering out]] [[648/625]]. In the 5-limit, the simplest interpretation is a [[25-odd-limit]] [[essentially tempered chord]] of the [[dimipent]] temperament, the temperament named after this chord.

* (Dimipent) 1 – 6/5 – 25/18 – 5/3, with steps 6/5, 6/5, 6/5, 6/5.

== In meantone ==

Before the ubiquity of [[12edo]], a diminished seventh chord ~~was simply treated as a tetrad comprising a root, minor third, diminished fifth, and diminished seventh, and~~ did not imply an equal tuning of all four ~~intervals~~. 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.

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.

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 {{Wikipedia}}
-The '''diminished seventh chord''' is a [[tetrad]] that comprises four identical minor thirds closing at the [[octave]]. In the 5-limit, the simplest interpretation is a [[25-odd-limit]] [[essentially tempered chord]] of the [[dimipent]] temperament, the temperament named after this chord.
+The '''diminished seventh chord''' is a [[tetrad]] traditionally described as comprising a root, [[minor]] third, [[interval quality|diminished]] fifth, and diminished seventh. In contemporary [[12edo]] music, it is a stack of four identical minor thirds of [[~]][[6/5]] closing at the [[octave]], [[tempering out]] [[648/625]]. In the 5-limit, the simplest interpretation is a [[25-odd-limit]] [[essentially tempered chord]] of the [[dimipent]] temperament, the temperament named after this chord.
 * (Dimipent) 1&thinsp;–&thinsp;6/5&thinsp;–&thinsp;25/18&thinsp;–&thinsp;5/3, with steps 6/5, 6/5, 6/5, 6/5.
 == In meantone ==
-Before the ubiquity of [[12edo]], a diminished seventh chord was simply treated as a tetrad comprising a root, minor third, diminished fifth, and diminished seventh, and did not imply an equal tuning of all four intervals. 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.
+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.