Dominant seventh sharp five chord: Difference between revisions

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 {{Wikipedia|Augmented seventh chord}}
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+A '''dominant seventh sharp five chord''', or '''augmented seventh chord''', is a [[tetrad]] comprising a root, [[major]] third, [[interval quality|augmented]] fifth, and [[minor]] seventh.
+== In temperaments ==
+In [[meantone]], , on which traditional tonal harmony is built, the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 125:
+* (Meantone) 1/1 ‒ [[5/4]] ‒ [[25/16]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~144/125
+In [[augmented (temperament)|augmented temperament]] (including [[12edo]]), a ~[[25/16]] augmented fifth is equated with an ~[[8/5]] minor sixth. However, the chord is still [[25-odd-limit]] due to the [[36/25]]~[[45/32]] interval between the ~[[9/5]] minor seventh and ~[[5/4]] major third.
+* (Augmented) 1/1 ‒ [[5/4]] ‒ [[8/5]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~9/8
+<!-- TODO: marvel, starling, and/or archytas? -->
+== In just intonation ==
 [[Category:Just intonation chords]]
 [[Category:Dominant seventh sharp five chords| ]]
+{{stub}}