Augmented triad: Difference between revisions
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The definition of P1-M3-A5 is a meantone-centrist definition. This is a chord of the augmented temp. Quick rework to reveal the implications of this chord. |
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{{Wikipedia|Augmented triad}} | {{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. | |||
* (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. | |||
== In just intonation == | == In just intonation == | ||
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[[Category:Augmented triads| ]] <!-- main article --> | [[Category:Augmented triads| ]] <!-- main article --> | ||
[[Category:Augmented]] | |||
[[Category:5-odd-limit chords]] | |||
[[Category:Essentially tempered chords]] | |||
[[Category:Just intonation chords]] | [[Category:Just intonation chords]] | ||
Revision as of 10:42, 21 August 2024
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, 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 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.
In just intonation
In the 5-limit:
In the 3-limit:
- 4096:5184:6561 may be considered a 3-limit approximation of 16:20:25.