Diminished (temperament): Difference between revisions

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'''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the 5-limit, and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.

'''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the 5-limit, and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned. [[12edo]] is an obvious tuning. Other possible tunings include [[16edo]] and [[28edo]].

See [[Dimipent family #Diminished]] for technical data.

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== Scales ==

* [[Diminished12]] – in [[44edo]] tuning

== Tunings ==

=== Prime-optimized tunings ===

* 7-limit [[CTE]]: ~6/5 = 1\4, ~3/2 = 696.9833

* 7-limit [[CWE]]: ~6/5 = 1\4, ~3/2 = 698.2661

=== Others ===

* 5-limit [[DKW theory|DKW]]: ~6/5 = 1\4, ~3/2 = 690.289

== See also ==

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 | de = Verminderte Temperaturen
 }}
-'''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the 5-limit, and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned.
+'''Diminished''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] that [[tempering out|tempers out]] the diminished comma, [[648/625]], in the 5-limit, and [[36/35]] and [[50/49]] in the [[7-limit]]. It has a 1/4-[[octave]] [[period]] and is [[generator|generated]] by a [[~]][[3/2]] perfect fifth. The main interest in this temperament is in its [[mos scale]]s, featuring [[tetrawood]] (4L 4s) when properly tuned. [[12edo]] is an obvious tuning. Other possible tunings include [[16edo]] and [[28edo]].
 See [[Dimipent family #Diminished]] for technical data.
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 == Scales ==
 * [[Diminished12]] – in [[44edo]] tuning
+== Tunings ==
+=== Prime-optimized tunings ===
+* 7-limit [[CTE]]: ~6/5 = 1\4, ~3/2 = 696.9833
+* 7-limit [[CWE]]: ~6/5 = 1\4, ~3/2 = 698.2661
+=== Others ===
+* 5-limit [[DKW theory|DKW]]: ~6/5 = 1\4, ~3/2 = 690.289
 == See also ==