Dominant seventh sharp five chord: Difference between revisions
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In [[meantone]], , on which traditional tonal harmony is built, the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 125: | In [[meantone]], , on which traditional tonal harmony is built, the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 125: | ||
* (Meantone) 1/1 ‒ [[5/4]] ‒ [[25/16]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~144/125 | * (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]] (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. | ||
* (Augmented) 1/1 ‒ [[5/4]] ‒ [[8/5]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~9/8 | * (Augmented) 1/1 ‒ [[5/4]] ‒ [[8/5]] ‒ [[9/5]], with steps ~5/4, ~5/4, ~9/8. | ||
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In [[marvel]] temperament, which tempers out [[225/224]], ~25/16 is equated with ~[[14/9]], and the ~[[64/45]] tritone between the 5/4 major third and 16/9 minor seventh is equated with ~[[10/7]], yielding a [[9-odd-limit]] [[essentially tempered chord]]: | |||
* (Marvel) 1/1 ‒ [[5/4]] ‒ [[14/9]] ‒ [[16/9]], with steps ~5/4, ~5/4, ~8/7. | |||
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== In just intonation == | == In just intonation == | ||
Revision as of 00:43, 16 September 2024
A dominant seventh sharp five chord, or augmented seventh chord, is a tetrad comprising a root, major third, augmented fifth, and minor seventh.
In temperaments
In meantone, , on which traditional tonal harmony is built, the minor seventh tempers together 9/5~16/9, giving a chord with an intervallic odd limit of 125:
In 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 marvel temperament, which tempers out 225/224, ~25/16 is equated with ~14/9, and the ~64/45 tritone between the 5/4 major third and 16/9 minor seventh is equated with ~10/7, yielding a 9-odd-limit essentially tempered chord:
In just intonation
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