Dominant seventh sharp five chord: Difference between revisions

Line 9:

* (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.

In [[augmented (temperament)|augmented temperament]], which tempers out [[128/125]], 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.

Line 16:

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

<!-- ~~TODO: starling~~, and~~/or archytas? -~~->

[[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.

== In just intonation ==

@@ Line 9: / Line 9: @@
 * (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.
+In [[augmented (temperament)|augmented temperament]], which tempers out [[128/125]], 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.
@@ Line 16: / Line 16: @@
 * (Marvel) 1/1 ‒ [[5/4]] ‒ [[14/9]] ‒ [[16/9]], with steps ~5/4, ~5/4, ~8/7.
-<!-- TODO: starling, and/or archytas? -->
+[[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.
 == In just intonation ==