Marvel family - Revision history

FloraC: Decanonicalize tridecimal marvel

2026-05-19T07:47:14Z

Decanonicalize tridecimal marvel

← Older revision		Revision as of 07:47, 19 May 2026
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	Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. This extension is natural because of the factorization 225/224 = (385/384)⋅(540/539). [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.		Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. This extension is natural because of the factorization 225/224 = (385/384)⋅(540/539). [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.

	In the 13-limit, 225/224 factors as ([[351/350]])⋅([[625/624]]) or ([[325/324]])⋅([[729/728]]). Tempering out 351/350 and 625/624 leads to ~~tridecimal marvel~~, tempering out 325/324 and 729/728 leads to hecate. Tempering out all of them leads to the 13-limit version of [[catakleismic]].		In the 13-limit, 225/224 factors as ([[351/350]])⋅([[625/624]]) or ([[325/324]])⋅([[729/728]]). Tempering out 351/350 and 625/624 leads to helios, tempering out 325/324 and 729/728 leads to hecate. Tempering out all of them leads to the 13-limit version of [[catakleismic]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	}}		}}

	=== ~~13-limit~~ ===		=== Helios ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

FloraC: - interwiki (moved to Marvel)

2026-05-19T07:38:57Z

- interwiki (moved to Marvel)

← Older revision		Revision as of 07:38, 19 May 2026
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	~~{{Interwiki~~
	~~\| en = Marvel family~~
	~~\| de = Marvel~~
	~~\| es =~~
	~~\| ja =~~
	}}
	{{Technical data page}}		{{Technical data page}}
	The '''marvel family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[7-limit]] [[marvel comma]] ([[ratio]]: [[225/224]], {{monzo\|legend=1\| -5 2 2 -1 }}), also known as ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common [[equal temperament\|equal]] and [[rank-2 temperament]]s.		The '''marvel family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[7-limit]] [[marvel comma]] ([[ratio]]: [[225/224]], {{monzo\|legend=1\| -5 2 2 -1 }}), also known as ''septimal kleisma''. These temperaments hence equate [[16/15]] and [[15/14]], or equivalently they equate two [[5/4]]'s and one [[14/9]]. The marvel comma is noteworthy in that it is tempered out by many common [[equal temperament\|equal]] and [[rank-2 temperament]]s.

FloraC: Move catakleismoid to kleismic rank-3 family

2026-04-11T09:42:45Z

Move catakleismoid to kleismic rank-3 family

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
 | en = Marvel family
 | de = Marvel
@@ Line 80: / Line 80: @@
 * ''[[Marvelpine]]'' (+4000/3993) → [[Wizardharry clan #Marvelpine|Wizardharry clan]]
 * ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle|Rastmic rank-3 clan]]
 == Undecimal marvel ==
@@ Line 744: / Line 745: @@
 [[Badness]] (Sintel): 1.38
 == Subgroup extensions ==

Overthink: /* Isis */ fix mapping

2026-04-10T19:59:52Z

Isis: fix mapping

← Older revision		Revision as of 19:59, 10 April 2026
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	Comma list: 225/224, 275/273, 385/384		Comma list: 225/224, 275/273, 385/384

	Mapping: {{mapping\| 1 0 0 -5 12 17 \| 0 1 0 2 -1 4 \| 0 0 1 2 -3 -3 }}		Mapping: {{mapping\| 1 0 0 -5 12 17 \| 0 1 0 2 -1 -4 \| 0 0 1 2 -3 -3 }}

	Optimal tunings:		Optimal tunings:

FloraC: /* Undecimal marvel */

2026-02-07T09:10:28Z

Undecimal marvel

← Older revision		Revision as of 09:10, 7 February 2026
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	{{Main\| Marvel }}		{{Main\| Marvel }}

	Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.		Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. This extension is natural because of the factorization 225/224 = (385/384)⋅(540/539). [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.

	~~This extension is natural because of the factorization 225/224=(385/384)(540/539).~~ In the 13-limit, 225/224 factors as ([[351/350]])([[625/624]]) or ([[325/324]])*([[729/728]]). Tempering out 351/350 and 625/624 leads to tridecimal marvel, tempering out 325/324 and 729/728 leads to hecate. Tempering out all of them leads to the 13-limit version of [[catakleismic]].		In the 13-limit, 225/224 factors as ([[351/350]])⋅([[625/624]]) or ([[325/324]])⋅([[729/728]]). Tempering out 351/350 and 625/624 leads to tridecimal marvel, tempering out 325/324 and 729/728 leads to hecate. Tempering out all of them leads to the 13-limit version of [[catakleismic]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Xenllium: /* Marvel */

2026-02-06T23:18:37Z

Marvel

← Older revision		Revision as of 23:18, 6 February 2026
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	* ''[[Artemis]]'' (+121/120) → [[Biyatismic clan #Artemis\|Biyatismic clan]]		* ''[[Artemis]]'' (+121/120) → [[Biyatismic clan #Artemis\|Biyatismic clan]]
	* ''[[Spectacle]]'' (+243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Spectacle]]'' (+243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]
			* ''[[Marvelpine]]'' (+4000/3993) → [[Wizardharry clan #Marvelpine\|Wizardharry clan]]
	* ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Mirage]]'' (+243/242, +385/384) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]

Overthink: /* Undecimal marvel */ add info on factorizations

2026-02-06T23:07:44Z

Undecimal marvel: add info on factorizations

← Older revision		Revision as of 23:07, 6 February 2026
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	{{Main\| Marvel }}		{{Main\| Marvel }}

	Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.		Undecimal marvel tempers out [[385/384]] as well as [[540/539]], and is loosely [[associated temperament\|associated]] with [[wizard]]. [[197edo]] remains useful as a tuning, with the 197e val, but [[166edo]], which among other things has a virtually pure 7, works as well.

			This extension is natural because of the factorization 225/224=(385/384)(540/539). In the 13-limit, 225/224 factors as ([[351/350]])([[625/624]]) or ([[325/324]])*([[729/728]]). Tempering out 351/350 and 625/624 leads to tridecimal marvel, tempering out 325/324 and 729/728 leads to hecate. Tempering out all of them leads to the 13-limit version of [[catakleismic]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: /* Apollo */

2025-12-13T13:52:03Z

Apollo

← Older revision		Revision as of 13:52, 13 December 2025
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	Apollo tempers out not only [[100/99]] but [[896/891]]. Note that marvel tempers together [[25/24]] and [[28/27]], and apollo further equates it with [[33/32]] via the vanishing of 100/99. This makes it a weak extension of [[parapyth]], and [[associated temperament\|associates]] it with [[magic]]. The lattice structure is very compact, comparable to that of [[ares]], from which apollo only differs in the mapping of [[prime interval\|prime]] [[7/1\|7]].		Apollo tempers out not only [[100/99]] but [[896/891]]. Note that marvel tempers together [[25/24]] and [[28/27]], and apollo further equates it with [[33/32]] via the vanishing of 100/99. This makes it a weak extension of [[parapyth]], and [[associated temperament\|associates]] it with [[magic]]. The lattice structure is very compact, comparable to that of [[ares]], from which apollo only differs in the mapping of [[prime interval\|prime]] [[7/1\|7]].

	The canonical [[13-limit]] extension is implied by parapyth, tempering out [[352/351]] and [[364/363]], but there are a number of other extenions to consider, these being called phoebus and musagetes, after epithets of Apollo. Phoebus tempers out [[105/104]] and finds ~[[13/8]] as a stack of three [[secor]]s. Musagetes tempers out [[144/143]] and conflates 16/13 and [[11/9]], which in this case is simply a stack of two ~[[10/9]]'s. These extensions are [[support]]ed by 13-limit [[magic]], unlike the canonical one.		The canonical [[13-limit]] extension is implied by parapyth, tempering out [[352/351]] and [[364/363]], but there are a number of other extenions to consider, these being called phoebus and musagetes, after epithets of Apollo. Phoebus tempers out [[105/104]] and finds ~[[16/13]] as a stack of three [[secor]]s. Musagetes tempers out [[144/143]] and conflates 16/13 and [[11/9]], which in this case is simply a stack of two ~[[10/9]]'s. These extensions are [[support]]ed by 13-limit [[magic]], unlike the canonical one.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: /* Apollo */ - typo

2025-12-13T13:48:34Z

Apollo: - typo

← Older revision		Revision as of 13:48, 13 December 2025
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	Apollo tempers out not only [[100/99]] but [[896/891]]. Note that marvel tempers together [[25/24]] and [[28/27]], and apollo further equates it with [[33/32]] via the vanishing of 100/99. This makes it a weak extension of [[parapyth]], and [[associated temperament\|associates]] it with [[magic]]. The lattice structure is very compact, comparable to that of [[ares]], from which apollo only differs in the mapping of [[prime interval\|prime]] [[7/1\|7]].		Apollo tempers out not only [[100/99]] but [[896/891]]. Note that marvel tempers together [[25/24]] and [[28/27]], and apollo further equates it with [[33/32]] via the vanishing of 100/99. This makes it a weak extension of [[parapyth]], and [[associated temperament\|associates]] it with [[magic]]. The lattice structure is very compact, comparable to that of [[ares]], from which apollo only differs in the mapping of [[prime interval\|prime]] [[7/1\|7]].

	The canonical [[13-limit]] extension is implied by parapyth, tempering out [[352/351]] and [[364/363]], but there are a number of other extenions to consider, these being called phoebus and musagetes, after epithets of Apollo. Phoebus tempers out [[105/104]] and finds ~[[13/8]] as a stack of three [[secor]]s. Musagetes tempers out [[144/143]] and ~~finds~~ conflates 16/13 and [[11/9]], which in this case is simply a stack of two ~[[10/9]]'s. These extensions are [[support]]ed by 13-limit [[magic]], unlike the canonical one.		The canonical [[13-limit]] extension is implied by parapyth, tempering out [[352/351]] and [[364/363]], but there are a number of other extenions to consider, these being called phoebus and musagetes, after epithets of Apollo. Phoebus tempers out [[105/104]] and finds ~[[13/8]] as a stack of three [[secor]]s. Musagetes tempers out [[144/143]] and conflates 16/13 and [[11/9]], which in this case is simply a stack of two ~[[10/9]]'s. These extensions are [[support]]ed by 13-limit [[magic]], unlike the canonical one.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: /* Apollo */ expand and document two other extensions

2025-12-13T13:47:58Z

Apollo: expand and document two other extensions

@@ Line 514: / Line 514: @@
 {{See also| Ptolemismic clan #Apollo }}
-Apollo tempers out not only [[100/99]] but [[896/891]]. It is notably [[associated temperament|associated]] with [[magic]].
+[[File:Lattice Apollo.png|thumb|Lattice for apollo.]]
 [[Subgroup]]: 2.3.5.7.11
@@ Line 556: / Line 560: @@
 Projection pairs: <code>7 225/32 11 100/9 13 3200/243</code>
 == Potassium ==