Half-diminished seventh chord: Difference between revisions
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== In temperaments == | == In temperaments == | ||
In meantone (including [[12edo]]), on which traditional tonal harmony is built, the interval of a diminished fifth [[tempering together|tempers together]] [[36/25]]~[[64/45]]~[[1024/729]], and the minor seventh tempers together [[9/5]]~[[16/9]], giving a chord with an [[intervallic odd limit]] of 25: | |||
* (Meantone) 1/1 ‒ [[6/5]] ‒ [[36/25]] ‒ [[9/5]] | |||
In [[archytas]] temperament, which [[tempering out|tempers out]] [[64/63]], a ~[[16/9]] minor seventh is equated with ~[[7/4]], a ~36/25 diminished fifth is equated with ~[[7/5]], and the ratio between ~7/4 and ~6/5 is equated with a ~[[3/2]] perfect fifth, yielding a [[9-odd-limit]] [[essentially tempered chord]]: | |||
* (Archytas) 1/1 ‒ 6/5 ‒ 7/5 ‒ 7/4, with steps 6/5, 6/5, 5/4 | |||
== In just intonation == | == In just intonation == | ||
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In the [[7-limit]]: | In the [[7-limit]]: | ||
* [[5:6:7:9]] | * [[5:6:7:9]] | ||
* [[20:24:28:35]] | |||
In the [[5-limit]]: | In the [[5-limit]]: | ||