Half-diminished seventh chord: Difference between revisions
correct Archytas diminished fifth — it's based on 64/45, not 36/25. |
add Archytas essentially-just chord |
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* (Archytas) 1/1 ‒ 6/5 ‒ 7/5 ‒ 7/4, with steps 6/5, 7/6, 5/4 | * (Archytas) 1/1 ‒ 6/5 ‒ 7/5 ‒ 7/4, with steps 6/5, 7/6, 5/4 | ||
Alternately, if we take the ~9/5 minor seventh instead, archytas gives a 9-odd-limit essentially just chord, tempering together [[5:6:7:9]] with [[45:54:64:81]]: | |||
* (Archytas) 1/1 ‒ 6/5 ‒ 7/5 ‒ 9/5, with steps 6/5, 7/6, 9/7 | |||
== In just intonation == | == In just intonation == | ||
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* [[25:30:36:45]] | * [[25:30:36:45]] | ||
* [[45:54:64:80]] | * [[45:54:64:80]] | ||
* [[45:54:64:81]], another [[preimage]] of the meantone half-diminished seventh chord, is found in [[Euler-Fokker genus|genus]] 3<sup>4</sup>{{dot}}5, and tempered together with 5:6:7:9 in archytas temperament. | |||
* [[135:160:192:240]] | * [[135:160:192:240]] | ||