Archytas chords - Revision history

FloraC: Link to optimal ET sequence instead (see talk)

2025-12-16T11:33:40Z

Link to optimal ET sequence instead (see talk)

← Older revision		Revision as of 11:33, 16 December 2025
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	* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.		* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.

	~~Equal~~ temperaments with archytas chords ~~include {{Edos\|5~~, ~~10, 12, 15, 17, 22, 27, and 49}}~~.		For a list of equal temperaments with archytas chords, see the optimal ET sequence in [[Archytas family #Archytas]].

	== Ares chords ==		== 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:		'''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:
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	* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.		* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.

	~~Equal~~ temperaments with ares chords ~~include {{Edos\|12~~, ~~15, 22, and 49}}~~.		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]]

Overthink: + equal temperaments

2025-12-16T01:27:26Z

+ equal temperaments

← Older revision		Revision as of 01:27, 16 December 2025
Line 17:		Line 17:
	* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.		* 1–8/7–5/4–10/7 with steps 8/7, 10/9, 8/7, 7/5.

			Equal temperaments with archytas chords include {{Edos\|5, 10, 12, 15, 17, 22, 27, and 49}}.
	== Ares chords ==		== 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:		'''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:
Line 22:		Line 23:
	* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.		* 1–8/7–5/4–11/8–11/7 with steps 8/7, 10/9, 10/9, 8/7, 14/11.

			Equal temperaments with ares chords include {{Edos\|12, 15, 22, and 49}}.
	[[Category:7-odd-limit chords]]		[[Category:7-odd-limit chords]]
	[[Category:9-odd-limit chords]]		[[Category:9-odd-limit chords]]

FloraC: Expand

2025-12-15T08:42:26Z

Expand

← Older revision		Revision as of 08:42, 15 December 2025
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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.

			== 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.

	[[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]]

FloraC: Expand

2024-10-09T10:08:00Z

Expand

← Older revision		Revision as of 10:08, 9 October 2024
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	'''Archytas chords''' are [[essentially tempered chord]]s tempered by the archytas comma, [[64/63]].		'''Archytas chords''' are [[essentially tempered chord]]s tempered by the archytas comma, [[64/63]].

	~~These include~~ the following palindromic triad in the [[7-odd-limit]]:		The only archytas triad is the following palindromic triad in the [[7-odd-limit]], presented as a stack of two fourths here:
	* 1–4/3–7/4 with steps 4/3, 4/3, 8/7.		* 1–4/3–7/4 with steps 4/3, 4/3, 8/7.

	~~as well as~~ the following palindromic tetrad:		Note that one rotation is the sus2 chord (1–8/7–3/2) and the other is the sus4 chord (1–4/3–3/2). In any case, it becomes an essentially just chord in the [[9-odd-limit]].

			Another archytas chord is the following palindromic tetrad that could be called the archy sus4/7 chord:
	* 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.		* 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.

	In the [[9-odd-limit]], we have an additional palindromic pentad:		Unlike the triad above, this chord remains essentially tempered in the 9-odd-limit. It makes for an interesting comparison with the [[didymic chords\|meantone sus2/6 chord]].

			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.

	[[Category:7-odd-limit chords]]		[[Category:7-odd-limit chords]]
			[[Category:9-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

FloraC: Improve readability; recategorize

2024-10-09T09:46:10Z

Improve readability; recategorize

← Older revision		Revision as of 09:46, 9 October 2024
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	These include the following palindromic triad in the [[7-odd-limit]]:		These include the following palindromic triad in the [[7-odd-limit]]:
	* ~~1-4~~/~~3-7~~/4 with steps 4/3-4/3-8/7.		* 1–4/3–7/4 with steps 4/3, 4/3, 8/7.

	as well as the following palindromic tetrad:		as well as the following palindromic tetrad:
	* ~~1-4~~/~~3-3~~/~~2-7~~/4 with steps 4/3-8/7-7/6-8/7.		* 1–4/3–3/2–7/4 with steps 4/3, 8/7, 7/6, 8/7.

	In the [[9-odd-limit]], we have an additional palindromic pentad:		In the [[9-odd-limit]], we have an additional palindromic pentad:
	* ~~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.

	[[Category:7-odd-limit]]		[[Category:7-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Triads]]		[[Category:Triads]]

FloraC: Created page with "'''Archytas chords''' are essentially tempered chords tempered by the archytas comma, 64/63. These include the following palindromic triad in the 7-odd-limit: *..."

2023-06-01T08:43:32Z

Created page with "'''Archytas chords''' are essentially tempered chords tempered by the archytas comma, 64/63. These include the following palindromic triad in the 7-odd-limit: *..."

New page

'''Archytas chords''' are [[essentially tempered chord]]s tempered by the archytas comma, [[64/63]].

These include the following palindromic triad in the [[7-odd-limit]]:
* 1-4/3-7/4 with steps 4/3-4/3-8/7.

as well as the following palindromic tetrad:
* 1-4/3-3/2-7/4 with steps 4/3-8/7-7/6-8/7.

In the [[9-odd-limit]], we have an additional palindromic pentad:
* 1-7/6-4/3-3/2-7/4 with steps 7/6-8/7-8/7-7/6-8/7.

[[Category:7-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Archytas]]