Diminished seventh chord: Difference between revisions

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Since [[12edo]] is a good tuning of dimipent and supports both diminished temperament and septimal meantone, and the historically prevalent [[quarter-comma meantone]] is a good tuning of septimal meantone (although it was historically usually analyzed as a 5-limit temperament), any of the above interpretations may be relevant for diminished chords found in common-practice and contemporary music.

== In equal temperaments ==

4edo (and multiples thereof): 0-300-600-900 cents

13edo: 0-277-554-923 cents, 1/1-7/6-11/8-12/7

15edo: 0-320-640-880 cents, 1/1-6/5-16/11-5/3

17edo: 0-282-565-918 cents, 1/1-33/28-11/8-56/33

== In just intonation ==

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* [[15:18:21:25]] is a [[preimage]] of the essentially-tempered chord of diminished temperament, found in [[Euler-Fokker genus|genus]] 32{{dot}}52{{dot}}7.

* [[35:42:50:60]] is a preimage of the essentially-tempered chord of starling temperament, also found in genus 3{{dot}}52{{dot}}7.

* [[25:30:35:42]] is the result of using step pattern 6/5, 7/6, 6/5.

* [[30:35:42:49]] is the result of using step pattern 7/6, 6/5, 7/6.

In the [[5-limit]]:

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 Since [[12edo]] is a good tuning of dimipent and supports both diminished temperament and septimal meantone, and the historically prevalent [[quarter-comma meantone]] is a good tuning of septimal meantone (although it was historically usually analyzed as a 5-limit temperament), any of the above interpretations may be relevant for diminished chords found in common-practice and contemporary music.
+== In equal temperaments ==
+edo (and multiples thereof): 0-300-600-900 cents
+edo: 0-277-554-923 cents, 1/1-7/6-11/8-12/7
+edo: 0-320-640-880 cents, 1/1-6/5-16/11-5/3
+edo: 0-282-565-918 cents, 1/1-33/28-11/8-56/33
 == In just intonation ==
@@ Line 30: / Line 39: @@
 * [[15:18:21:25]] is a [[preimage]] of the essentially-tempered chord of diminished temperament, found in [[Euler-Fokker genus|genus]] 3<sup>2</sup>{{dot}}5<sup>2</sup>{{dot}}7.
 * [[35:42:50:60]] is a preimage of the essentially-tempered chord of starling temperament, also found in genus 3{{dot}}5<sup>2</sup>{{dot}}7.
+* [[25:30:35:42]] is the result of using step pattern 6/5, 7/6, 6/5.
+* [[30:35:42:49]] is the result of using step pattern 7/6, 6/5, 7/6.
 In the [[5-limit]]: