Dominant (temperament): Difference between revisions

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-#redirect [[Meantone#Dominant]]
+'''Dominant''' is a [[regular temperament|temperament]] [[tempering out]] the [[81/80|syntonic comma (81/80)]] and [[64/63|septimal comma (64/63)]] in the 7-limit. It also tempers out the [[36/35|septimal quartertone (36/35)]], as 36/35 = (64/63)(81/80). It is the unique temperament that identifies the [[harmonic seventh chord]] with the [[dominant seventh chord]], which is a familiar feature from [[12edo]].
+Other possible tunings include [[17edo]] (17c val), [[29edo]] (29cd val), [[41edo]] (41cd val), [[53edo]] (53cdd val), as well as [[Pythagorean tuning]].
+== Interval chain ==
+In the following table, odd harmonics 1–9 are in '''bold'''.
+{| class="wikitable center-1 right-2"
+|-
+! # !! Cents* !! Approximate Ratios
+|-
+| 0 || 0.0 || '''1/1'''
+|-
+| 1 || 701.1 || '''3/2'''
+|-
+| 2 || 202.2 || '''8/7''', '''9/8''', 10/9
+|-
+| 3 || 903.3 || 5/3, 12/7
+|-
+| 4 || 404.5 || '''5/4''', 9/7
+|-
+| 5 || 1105.6 || 15/8, 27/14, 40/21
+|-
+| 6 || 606.7 || 10/7
+|-
+| 7 || 107.8 || 15/14
+|}
+<nowiki>*</nowiki> in 7-limit [[CWE]] tuning
+== Chords and harmony ==
+Much of 12edo harmony can be used. Dominant enables chords of [[didymic chords|didymic]] and [[archytas chords|archytas]].
 [[Category:Temperaments]]
+[[Category:Dominant (temperament)| ]] <!-- main article -->
 [[Category:Meantone family]]
+[[Category:Archytas clan]]
+[[Category:Mint temperaments]]