Dominant seventh sharp five chord: Difference between revisions

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* (Augmented) 1/1 ‒ [[5/4]] ‒ [[8/5]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~9/8.

In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]], giving another 25-odd essentially tempered chord:

* (Archytas) 1/1 ‒ [[5/4]] ‒ [[25/16]] ‒ [[7/4]], with steps ~5/4, ~5/4, ~8/7.

In [[marvel]] temperament, which tempers out [[225/224]], ~25/16 is equated with ~[[14/9]], and the ~[[64/45]] tritone between a ~5/4 major third a ~[[16/9]] minor seventh is equated with ~[[10/7]], yielding a [[9-odd-limit]] [[essentially tempered chord]]:

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* (Marvel) 1/1 ‒ [[5/4]] ‒ [[14/9]] ‒ [[16/9]], with steps ~5/4, ~5/4, ~8/7.

[[12edo]] is a good tuning of augmented temperament, and [[septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], ~~tempers out the marvel comma;~~ so any of the above interpretations may be relevant for seventh sharp five chords found in contemporary and common-practice music.

[[12edo]] is a good tuning of augmented temperament and supports all of the above temperaments to varying degrees, and [[septimal meantone]] — which is well-represented by the historically prevalent [[quarter-comma meantone]] — supports marvel, so any of the above interpretations may be relevant for seventh sharp five chords found in contemporary and common-practice music.

== In just intonation ==

@@ Line 12: / Line 12: @@
 * (Augmented) 1/1 ‒ [[5/4]] ‒ [[8/5]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~9/8.
+In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]], giving another 25-odd essentially tempered chord:
+* (Archytas) 1/1 ‒ [[5/4]] ‒ [[25/16]] ‒ [[7/4]], with steps ~5/4, ~5/4, ~8/7.
 In [[marvel]] temperament, which tempers out [[225/224]], ~25/16 is equated with ~[[14/9]], and the ~[[64/45]] tritone between a ~5/4 major third a ~[[16/9]] minor seventh is equated with ~[[10/7]], yielding a [[9-odd-limit]] [[essentially tempered chord]]:
@@ Line 17: / Line 21: @@
 * (Marvel) 1/1 ‒ [[5/4]] ‒ [[14/9]] ‒ [[16/9]], with steps ~5/4, ~5/4, ~8/7.
-[[12edo]] is a good tuning of augmented temperament, and [[septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]], tempers out the marvel comma; so any of the above interpretations may be relevant for seventh sharp five chords found in contemporary and common-practice music.
+[[12edo]] is a good tuning of augmented temperament and supports all of the above temperaments to varying degrees, and [[septimal meantone]] — which is well-represented by the historically prevalent [[quarter-comma meantone]] — supports marvel, so any of the above interpretations may be relevant for seventh sharp five chords found in contemporary and common-practice music.
 == In just intonation ==