Tutonic hexad - Revision history

FloraC at 13:45, 23 October 2026

2026-10-23T13:45:05Z

← Older revision		Revision as of 13:45, 23 October 2026
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	A '''tutonic hexad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] (also called as [[~~Huygens~~]], tempered by [[81/80]], [[99/98]] and [[126/125]]).		A '''tutonic hexad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] (also called [[huygens]], tempered by [[81/80]], [[99/98]] and [[126/125]]).

	There are eight hexads as [[11-odd-limit]] essentially tempered chords of the 11-limit meantone, all of them are available in the tutone temperament; in other words, all of the essentially tempered hexads of the 11-limit meantone are tutonic hexads.		There are eight hexads as [[11-odd-limit]] essentially tempered chords of the 11-limit meantone, all of them are available in the tutone temperament; in other words, all of the essentially tempered hexads of the 11-limit meantone are tutonic hexads.

	The palindromic hexads are		The palindromic hexads are
	* 1–9/8–5/4–7/5–14/9–7/4 with steps of 9/8, 9/8, 9/8, 9/8, 9/8, 8/7 ([[~~Didymic~~ chords\|erato hexad]], tempered by 81/80 and 126/125);		* 1–9/8–5/4–7/5–14/9–7/4 with steps of 9/8, 9/8, 9/8, 9/8, 9/8, 8/7 ([[didymus chords #Septimal meantone chords\|erato hexad]], tempered by 81/80 and 126/125);
	* 1–9/8–9/7–10/7–11/7–7/4 with steps of 9/8, 8/7, 9/8, 11/10, 9/8, 8/7 (euterpe hexad, tempered by 81/80 and 99/98);		* 1–9/8–9/7–10/7–11/7–7/4 with steps of 9/8, 8/7, 9/8, 11/10, 9/8, 8/7 (euterpe hexad, tempered by 81/80 and 99/98);
	* 1–9/8–9/7–7/5–8/5–7/4 with steps of 9/8, 8/7, 11/10, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175);		* 1–9/8–9/7–7/5–8/5–7/4 with steps of 9/8, 8/7, 11/10, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175);

FloraC: Cleanup; recategorize

2025-01-01T13:47:30Z

Cleanup; recategorize

← Older revision		Revision as of 13:47, 1 January 2025
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	The palindromic hexads are		The palindromic hexads are
	* ~~1-9~~/~~8-5~~/~~4-7~~/~~5-14~~/~~9-7~~/4 with steps of 9/8-9/8-9/8-9/8-9/8-8/7 ([[Didymic chords\|erato hexad]], tempered by 81/80 and 126/125);		* 1–9/8–5/4–7/5–14/9–7/4 with steps of 9/8, 9/8, 9/8, 9/8, 9/8, 8/7 ([[Didymic chords\|erato hexad]], tempered by 81/80 and 126/125);
	* ~~1-9~~/~~8-9~~/~~7-10~~/~~7-11~~/~~7-7~~/4 with steps of 9/8-8/7-9/8-11/10-9/8-8/7 (euterpe hexad, tempered by 81/80 and 99/98);		* 1–9/8–9/7–10/7–11/7–7/4 with steps of 9/8, 8/7, 9/8, 11/10, 9/8, 8/7 (euterpe hexad, tempered by 81/80 and 99/98);
	* ~~1-9~~/~~8-9~~/~~7-7~~/~~5-8~~/~~5-7~~/4 with steps of 9/8-8/7-11/10-8/7-11/10-8/7 (minerva hexad, tempered by 99/98 and 176/175);		* 1–9/8–9/7–7/5–8/5–7/4 with steps of 9/8, 8/7, 11/10, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175);
	* ~~1-9~~/~~8-5~~/~~4-7~~/~~5-8~~/~~5-7~~/4 with steps of 9/8-9/8-9/8-8/7-11/10-8/7 (minerva hexad, tempered by 99/98 and 176/175).		* 1–9/8–5/4–7/5–8/5–7/4 with steps of 9/8, 9/8, 9/8, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175).

	The inversely related pairs of hexads are		The inversely related pairs of hexads are
	* ~~1-9~~/~~8-5~~/~~4-10~~/~~7-11~~/~~7-7~~/4 with steps of 9/8-9/8-8/7-11/10-9/8-8/7, and its inverse		* 1–9/8–5/4–10/7–11/7–7/4 with steps of 9/8, 9/8, 8/7, 11/10, 9/8, 8/7, and its inverse
	* ~~1-9~~/~~8-11~~/~~9-7~~/~~5-11~~/~~7-7~~/4 with steps of 9/8-11/10-8/7-9/8-9/8-8/7;		* 1–9/8–11/9–7/5–11/7–7/4 with steps of 9/8, 11/10, 8/7, 9/8, 9/8, 8/7;
	* ~~1-9~~/~~8-9~~/~~7-7~~/~~5-11~~/~~7-7~~/4 with steps of 9/8-8/7-11/10-9/8-9/8-8/7, and its inverse		* 1–9/8–9/7–7/5–11/7–7/4 with steps of 9/8, 8/7, 11/10, 9/8, 9/8, 8/7, and its inverse
	* ~~1-9~~/~~8-5~~/~~4-11~~/~~8-11~~/~~7-7~~/4 with steps of 9/8-9/8-11/10-8/7-9/8-8/7.		* 1–9/8–5/4–11/8–11/7–7/4 with steps of 9/8, 9/8, 11/10, 8/7, 9/8, 8/7.

	[[Category:9-odd-limit]]		[[Category:9-odd-limit chords]]
	[[Category:11-odd-limit]]		[[Category:11-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Hexads]]		[[Category:Hexads]]
	[[Category:Tutone]]		[[Category:Tutone]]

Xenllium: Update the article

2023-11-11T12:20:31Z

Update the article

@@ Line 1: / Line 1: @@
-The '''tutonic hexad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.
+A '''tutonic hexad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] (also called as [[Huygens]], tempered by [[81/80]], [[99/98]] and [[126/125]]).
 [[Category:11-odd-limit]]
 [[Category:Essentially tempered chords]]
 [[Category:Hexads]]
 [[Category:Tutone]]

FloraC: Recategorize

2023-05-23T11:56:04Z

Recategorize

← Older revision		Revision as of 11:56, 23 May 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	~~[[Category:Hexad]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
			[[Category:Hexads]]
	[[Category:Tutone]]		[[Category:Tutone]]

Fredg999: Change "sextad" to "hexad", categories

2023-04-20T20:51:46Z

Change "sextad" to "hexad", categories

← Older revision		Revision as of 20:51, 20 April 2023
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			The '''tutonic hexad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Hexad]]		[[Category:Hexad]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Tutone]]		[[Category:Tutone]]
	~~[[Category:Tutonic]]~~
	The '''tutonic [[sextad]]''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

Fredg999: Fredg999 moved page Tutonic sextad to Tutonic hexad: "Sextad" isn't the usual word for a 6-note chord

2023-04-20T20:51:06Z

Fredg999 moved page Tutonic sextad to Tutonic hexad: "Sextad" isn't the usual word for a 6-note chord

← Older revision	Revision as of 20:51, 20 April 2023
(No difference)

Fredg999 category edits: Moving from Category:Sextad to Category:Hexad using Cat-a-lot

2023-04-20T20:50:25Z

Moving from Category:Sextad to Category:Hexad using Cat-a-lot

← Older revision		Revision as of 20:50, 20 April 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:~~Sextad~~]]		[[Category:Hexad]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Tutone]]		[[Category:Tutone]]
	[[Category:Tutonic]]		[[Category:Tutonic]]
	The '''tutonic [[sextad]]''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.		The '''tutonic [[sextad]]''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

BudjarnLambeth: Added links (as requested by the to:do notice)

2023-04-20T08:05:36Z

Added links (as requested by the to:do notice)

← Older revision		Revision as of 08:05, 20 April 2023
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	The '''tutonic sextad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the generator chain of 11-limit meantone (Huygens.) This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {81/80, 99/98, 126/125}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Sextad]]		[[Category:Sextad]]
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	[[Category:Tutone]]		[[Category:Tutone]]
	[[Category:Tutonic]]		[[Category:Tutonic]]
			The '''tutonic [[sextad]]''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the [[generator]] chain of [[11-limit]] [[meantone]] ([[Huygens]]). This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {[[81/80]], [[99/98]], [[126/125]]}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.
	{~~{todo\|add_links}~~}

Xenwolf: recat

2021-05-20T08:38:34Z

recat

← Older revision		Revision as of 08:38, 20 May 2021
Line 1:		Line 1:
	The '''tutonic sextad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the generator chain of 11-limit meantone (Huygens.) This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {81/80, 99/98, 126/125}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.		The '''tutonic sextad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the generator chain of 11-limit meantone (Huygens.) This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {81/80, 99/98, 126/125}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

	[[Category:11-limit]]		[[Category:11-odd-limit]]
	[[Category:Sextad]]		[[Category:Sextad]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]

Xenwolf: simplify links,+cat

2021-05-20T07:17:00Z

simplify links,+cat

← Older revision		Revision as of 07:17, 20 May 2021
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	The ''tutonic sextad'' is an [[~~Dyadic_chord\|~~essentially tempered chord]] of the [[~~Chromatic_pairs#Tutone\|~~tutone]] temperament, which is every other member of the generator chain of 11-limit meantone (Huygens.) This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {81/80, 99/98, 126/125}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.		The '''tutonic sextad''' is an [[essentially tempered chord]] of the [[tutone]] temperament, which is every other member of the generator chain of 11-limit meantone (Huygens.) This means it is 9/8-9/8-9/8-9/8-9/8-8/7 tempered by {81/80, 99/98, 126/125}, or in other words the tempering of 9/8-5/4-7/5-11/7-7/4-2.

	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:~~sextad~~]]		[[Category:Sextad]]
	[[Category:~~todo:add_links~~]]		[[Category:Essentially tempered chords]]
	[[Category:~~tutone~~]]		[[Category:Tutone]]
	[[Category:~~tutonic~~]]		[[Category:Tutonic]]

			{{todo\|add_links}}