Dominant seventh chord: Difference between revisions

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[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])

In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:

* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]

[[Dominant (temperament)|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).

== In just intonation ==

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 [[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for dominant seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])
+In [[archytas]] temperament, which tempers out [[64/63]], ~16/9 is equated with ~[[7/4]] rather than 25/14, resulting in an [[essentially just]] [[7-odd-limit]] chord that tempers together [[4:5:6:7]] and [[36:45:54:64]]:
+* (Archytas) 1/1 - [[5/4]] - [[3/2]] - [[7/4]]
+[[Dominant (temperament)|Dominant temperament]] combines archytas with meantone, tempering out both 81/80 and 64/63, and as a result also tempers out [[36/35]], equating 4:5:6:7 with all of the 5-limit dominant seventh chords of meantone. Since [[12edo]] is a good tuning of Dominant temperament, this simpler septimal interpretation may also be relevant for dominant seventh chords in music originally composed for 12edo — particularly in performance styles that use more flexible intonation (such as Barbershop).
+<!-- Note: 12edo also supports Mint temperament via Dominant, but I'm intentionally omitting it here for simplicity. It's easy enough to find via [[36/35]].-->
 == In just intonation ==