Archytas chords: Difference between revisions

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In the 9-odd-limit, we have an additional palindromic pentad, which also happens to be the [[2L 3s|pentic]] scale [[archy5|Archy[5]]]:  
In the 9-odd-limit, we have an additional palindromic pentad, which also happens to be the [[2L 3s|pentic]] scale [[archy5|Archy[5]]]:  
* 1–7/6–4/3–3/2–7/4 with steps 7/6, 8/7, 8/7, 7/6, 8/7.  
* 1–7/6–4/3–3/2–7/4 with steps 7/6, 8/7, 8/7, 7/6, 8/7.  
There is also an archytas tetrad involving [[prime interval|prime]] [[5/1|5]]:
* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.
For a list of equal temperaments with archytas chords, see the optimal ET sequence in [[Archytas family #Archytas]].
== Ares chords ==
'''Ares chords''' are [[essentially tempered chord]]s tempered by any two of 64/63, [[100/99]], and [[176/175]]. There are exactly two ares chords in the [[11-odd-limit]], both being palindromic pentads:
* 1–10/9–5/4–10/7–11/7 with steps 10/9, 8/7, 8/7, 10/9, 14/11.
* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.
For a list of equal temperaments with ares chords, see the optimal ET sequence in [[Archytas family #Ares]].


[[Category:7-odd-limit chords]]
[[Category:7-odd-limit chords]]
[[Category:9-odd-limit chords]]
[[Category:9-odd-limit chords]]
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]
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[[Category:Pentads]]
[[Category:Pentads]]
[[Category:Archytas]]
[[Category:Archytas]]
[[Category:Ares]]