Augmented triad: Difference between revisions

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The '''augmented triad''' ~~comprises~~ three identical ~~major thirds closing~~ at the [[octave]]~~. It~~ is a [[5-odd-limit]] [[essentially tempered chord]] of the [[augmented (temperament)|augmented]] temperament, the temperament named after this chord.

The '''augmented triad''' is a [[triad]] traditionally described as comprising a root, [[major]] third, and [[interval quality|augmented]] fifth. In contemporary [[12edo]] music, the augmented fifth is [[enharmonic equivalence|enharmonically equivalent]] to a minor sixth, approximating [[8/5]], with the major third approximating [[5/4]], so it is a stack of two [[~]]5/4's making up ~8/5, [[tempering out]] [[128/125]]. In other words, three identical ~5/4's close at the [[octave]], which implies it is a [[5-odd-limit]] [[essentially tempered chord]] of the [[augmented (temperament)|augmented]] temperament, the temperament named after this chord.

* (Augmented) 1 – 5/4 – 8/5, with steps 5/4, 5/4, 5/4.

== In meantone ==

Before the ubiquity of [[12edo]], an augmented triad ~~was simply treated as a [[triad]] comprising a root, [[major]] third, and [[interval quality|augmented]] fifth, and~~ did not imply an equal tuning of all three ~~intervals~~. It can be viewed as a [[9-odd-limit]] essentially tempered chord of [[marvel]]. See [[marvel chords]]. This is still compatible with 12edo and is perhaps as authentic as the 5-odd-limit interpretation above.

Before the ubiquity of [[12edo]], an augmented triad did not imply an equal tuning of all three thirds (technically, two major thirds and a diminished fourth). It can be viewed as a [[9-odd-limit]] essentially tempered chord of [[marvel]]. See [[marvel chords]]. This is still compatible with 12edo and is perhaps as authentic as the 5-odd-limit interpretation above.

== In just intonation ==

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 {{Wikipedia|Augmented triad}}
-The '''augmented triad''' comprises three identical major thirds closing at the [[octave]]. It is a [[5-odd-limit]] [[essentially tempered chord]] of the [[augmented (temperament)|augmented]] temperament, the temperament named after this chord.
+The '''augmented triad''' is a [[triad]] traditionally described as comprising a root, [[major]] third, and [[interval quality|augmented]] fifth. In contemporary [[12edo]] music, the augmented fifth is [[enharmonic equivalence|enharmonically equivalent]] to a minor sixth, approximating [[8/5]], with the major third approximating [[5/4]], so it is a stack of two [[~]]5/4's making up ~8/5, [[tempering out]] [[128/125]]. In other words, three identical ~5/4's close at the [[octave]], which implies it is a [[5-odd-limit]] [[essentially tempered chord]] of the [[augmented (temperament)|augmented]] temperament, the temperament named after this chord.
 * (Augmented) 1&thinsp;–&thinsp;5/4&thinsp;–&thinsp;8/5, with steps 5/4, 5/4, 5/4.
 == In meantone ==
-Before the ubiquity of [[12edo]], an augmented triad was simply treated as a [[triad]] comprising a root, [[major]] third, and [[interval quality|augmented]] fifth, and did not imply an equal tuning of all three intervals. It can be viewed as a [[9-odd-limit]] essentially tempered chord of [[marvel]]. See [[marvel chords]]. This is still compatible with 12edo and is perhaps as authentic as the 5-odd-limit interpretation above.
+Before the ubiquity of [[12edo]], an augmented triad did not imply an equal tuning of all three thirds (technically, two major thirds and a diminished fourth). It can be viewed as a [[9-odd-limit]] essentially tempered chord of [[marvel]]. See [[marvel chords]]. This is still compatible with 12edo and is perhaps as authentic as the 5-odd-limit interpretation above.
 == In just intonation ==