Augmented triad: Difference between revisions
m Mention the comma earlier in the paragraph about augmented temperament. This makes the paragraph more parallel to the septimal one, and also allows the reader to more easily understand the paragraph without already knowing what "augmented temperament" is. |
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{{Wikipedia|Augmented triad}} | {{Wikipedia|Augmented triad}} | ||
An '''augmented triad''' is a [[triad]] comprising a root, a [[major]] third, and an [[interval quality|augmented]] fifth formed by stacking another major third. | |||
== In temperaments == | == In temperaments == | ||
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* (Augmented) 1 – 5/4 – 8/5 | * (Augmented) 1 – 5/4 – 8/5 | ||
The gap remaining to close the octave is another identical | The gap remaining to close the octave is another identical third (~5/4), giving rise to the temperament's name after this chord. | ||
If [[225/224]] is tempered out, as in [[marvel]] and [[septimal meantone]], the ~25/16 augmented fifth is tempered together with ~[[14/9]]. The resulting intervals are ~5/4, ~5/4, and ~14/9, making the augmented triad a [[9-odd-limit]] essentially tempered chord (→ [[Marvel chords]]). | If [[225/224]] is tempered out, as in [[marvel]] and [[septimal meantone]], the ~25/16 augmented fifth is tempered together with ~[[14/9]]. The resulting intervals are ~5/4, ~5/4, and ~14/9, making the augmented triad a [[9-odd-limit]] essentially tempered chord (→ [[Marvel chords]]). | ||
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In the [[7-limit]]: | In the [[7-limit]]: | ||
* [[36:45:56]] is the simplest JI tuning of the 7-limit marvel augmented chord. | * [[36:45:56]] (1/1 – 5/4 – 14/9) is the simplest JI tuning of the 7-limit marvel augmented chord. | ||
* [[35:45:56]] (1/1 –  9/7 – 8/5) | |||
* [[28:35:45]] (1/1 – 5/4 – [[45/28]]) | |||
* [[28:36:45]] (1/1 – 9/7 – [[45/28]]) | |||
In the [[5-limit]]: | In the [[5-limit]]: | ||