Dominant seventh flat five chord: Difference between revisions

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A '''dominant seventh flat five chord''' is a [[tetrad]] comprising a root, a [[major]] third, a [[interval quality|diminished]] fifth, and a [[minor]] seventh.

== In temperaments ==

In meantone (including [[12edo]]), on which traditional tonal harmony is built, the interval of a diminished fifth [[tempering together|tempers together]] [[36/25]]~[[64/45]]~[[1024/729]], and the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 125:

* (Meantone) 1/1 ‒ [[5/4]] ‒ [[36/25]] ‒ [[9/5]]

In [[marvel]] temperament, which [[tempering out|tempers out]] [[225/224]], a ~[[16/9]] minor seventh is equated with ~[[25/14]], which combines with a [[10/7]]~[[64/45]] diminished fifth to give a [[9-odd-limit]] [[essentially tempered chord]]:

* (Marvel) 1/1 ‒ 5/4 ‒ 10/7 ‒ 16/9, with steps 5/4, [[8/7]], 5/4

Similarly, in [[starling]] temperament, which tempers out [[126/125]] a ~[[9/5]] minor seventh is equated with ~25/14, which combines with a 10/7~[[36/25]] diminished fifth to give a 9-odd-limit essentially tempered chord:

* (Starling) 1/1 ‒ 5/4 ‒ 10/7 ‒ 9/5, with steps 5/4, 8/7, 5/4

[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all of the above chords, so any of the those interpretations may be relevant for dominant seventh flat five chords found in common-practice music.

== In just intonation ==

In the [[7-limit]]:

* [[28:35:40:50]] corresponds to a just interpretation of the essentially-tempered chords of marvel and starling temperament.

In the [[5-limit]]:

* [[180:225:256:320]] is a found rooted on V ({{Frac|3|2}}) and II ({{Frac|9|8}}) in the [[duodene]].

* [[100:125:144:180]] is another interpretation of the chord from meantone temperament, found in genus 3<sup>2</sup>{{dot}}5<sup>3</sup>.

== See also ==

* [[French sixth chord]], a chord that is enharmonically equivalent to a dominant seventh flat five chord in [[12edo]].

[[Category:Just intonation chords]]

[[Category:Dominant seventh flat five chords| ]]

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 {{Wikipedia}}
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+A '''dominant seventh flat five chord''' is a [[tetrad]] comprising a root, a [[major]] third, a [[interval quality|diminished]] fifth, and a [[minor]] seventh.
+== In temperaments ==
+In meantone (including [[12edo]]), on which traditional tonal harmony is built, the interval of a diminished fifth [[tempering together|tempers together]] [[36/25]]~[[64/45]]~[[1024/729]], and the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 125:
+* (Meantone) 1/1 ‒ [[5/4]] ‒ [[36/25]] ‒ [[9/5]]
+In [[marvel]] temperament, which [[tempering out|tempers out]] [[225/224]], a ~[[16/9]] minor seventh is equated with ~[[25/14]], which combines with a [[10/7]]~[[64/45]] diminished fifth to give a [[9-odd-limit]] [[essentially tempered chord]]:
+* (Marvel) 1/1 ‒ 5/4 ‒ 10/7 ‒ 16/9, with steps 5/4, [[8/7]], 5/4
+Similarly, in [[starling]] temperament, which tempers out [[126/125]] a ~[[9/5]] minor seventh is equated with ~25/14, which combines with a 10/7~[[36/25]] diminished fifth to give a 9-odd-limit essentially tempered chord:
+* (Starling) 1/1 ‒ 5/4 ‒ 10/7 ‒ 9/5, with steps 5/4, 8/7, 5/4
+[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all of the above chords, so any of the those interpretations may be relevant for dominant seventh flat five chords found in common-practice music.
+== In just intonation ==
+In the [[7-limit]]:
+* [[28:35:40:50]] corresponds to a just interpretation of the essentially-tempered chords of marvel and starling temperament.
+In the [[5-limit]]:
+* [[180:225:256:320]] is a found rooted on V ({{Frac|3|2}}) and II ({{Frac|9|8}}) in the [[duodene]].
+* [[100:125:144:180]] is another interpretation of the chord from meantone temperament, found in genus 3<sup>2</sup>{{dot}}5<sup>3</sup>.
+== See also ==
+* [[French sixth chord]], a chord that is enharmonically equivalent to a dominant seventh flat five chord in [[12edo]].
 [[Category:Just intonation chords]]
 [[Category:Dominant seventh flat five chords| ]]