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Half-diminished seventh chord: Difference between revisions

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Copypaste information from dominant seventh chord page. As this is the inverse of the dominant seventh chord, all that applies to the dominant seventh chord applies here too
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* (Starling) 1/1 ‒ [[6/5]] ‒ [[10/7]] ‒ [[9/5]], with steps 6/5, 6/5, 5/4
* (Starling) 1/1 ‒ [[6/5]] ‒ [[10/7]] ‒ [[9/5]], with steps 6/5, 6/5, 5/4
Similarly, in [[marvel]] temperament, which tempers out [[225/224]] and tempers together 16/9~25/14 (but ''not'' 9/5), the ~64/45 tritone is tempered together with ~10/7, again resulting in a 9-odd-limit essentially tempered chord:
* (Marvel) 1/1 ‒ [[6/5]] ‒ [[10/7]] ‒ [[16/9]], with steps 6/5, 6/5, 5/4
[[Septimal meantone]], which is well-represented by the historically prevalent [[quarter-comma meantone]]), tempers together all three of these sevenths (9/5~16/9~25/14), so any of the above interpretations may be relevant for half-diminished seventh chords found in common-practice music. (→ [[Didymic chords #Dominant seventh chord]])


In [[archytas]] temperament, which tempers out [[64/63]], a ~[[16/9]] minor seventh is equated with ~[[7/4]], a ~64/45 diminished fifth is equated with ~[[7/5]], and the ~[[35/24]] ratio between ~7/4 and ~6/5 is equated with a ~[[3/2]] perfect fifth, yielding another 7-odd-limit essentially tempered chord:
In [[archytas]] temperament, which tempers out [[64/63]], a ~[[16/9]] minor seventh is equated with ~[[7/4]], a ~64/45 diminished fifth is equated with ~[[7/5]], and the ~[[35/24]] ratio between ~7/4 and ~6/5 is equated with a ~[[3/2]] perfect fifth, yielding another 7-odd-limit essentially tempered chord:
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