Marvel temperaments - Revision history

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:58Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

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FloraC: - wizard (moved to stearnsmic clan)

2026-09-15T09:04:30Z

- wizard (moved to stearnsmic clan)

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FloraC: Recategorize

2026-08-15T07:57:54Z

Recategorize

← Older revision		Revision as of 07:57, 15 August 2026
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	== References ==		== References ==

			[[Category:Marvel temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Marvel temperaments\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

Overthink: /* Gracecordial */ fix

2026-07-28T03:35:33Z

Gracecordial: fix

← Older revision		Revision as of 03:35, 28 July 2026
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	* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}		* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
	: [[error map]]: {{val\| +0.490 -0.354 -1.655 +1.241 }}		: [[error map]]: {{val\| +0.490 -0.354 -1.655 +1.241 }}
	* [[CWE]]: ~2 = 1200.~~3333~~{{c}}, ~3/2 = 700.8112{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8112{{c}}
	: error map: {{val\| 0.000 -1.144 -2.537 +0.349 }}		: error map: {{val\| 0.000 -1.144 -2.537 +0.349 }}

Overthink: /* Septimin */ extend the optimal et sequence

2026-07-24T18:42:05Z

Septimin: extend the optimal et sequence

← Older revision		Revision as of 18:42, 24 July 2026
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	: error map: {{val\| 0.000 -1.516 -4.735 -4.790 }}		: error map: {{val\| 0.000 -1.516 -4.735 -4.790 }}

	{{Optimal ET sequence\|legend=1\| 41, 91, 132d }}		{{Optimal ET sequence\|legend=1\| 9, 23, 32, 41, 91, 132d }}

	[[Badness]] (Sintel): 1.38		[[Badness]] (Sintel): 1.38
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	* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}

	{{Optimal ET sequence\|legend=0\| 41, 91, 223cdef }}		{{Optimal ET sequence\|legend=0\| 9, 23, 32, 41, 91, 223cdef }}

	Badness (Sintel): 1.04		Badness (Sintel): 1.04
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	* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}

	{{Optimal ET sequence\|legend=0\| 41, 91 }}		{{Optimal ET sequence\|legend=0\| 9, 32f, 41, 91 }}

	Badness (Sintel): 0.955		Badness (Sintel): 0.955

FloraC: /* Hendeca */ + history

2026-07-05T11:09:01Z

Hendeca: + history

← Older revision		Revision as of 11:09, 5 July 2026
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''

	Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic\|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka\|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val.		Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic\|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka\|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val. It was named by [[Xenllium]] in 2025 as a low-accuracy variant of hendecatonic.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: /* Hendeca */ + link and note the relation to septimal hendecatonic

2026-07-05T11:02:57Z

Hendeca: + link and note the relation to septimal hendecatonic

← Older revision		Revision as of 11:02, 5 July 2026
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	== Hendeca ==		== Hendeca ==
	{{Distinguish\| Hendec }}		{{Distinguish\| Hendec }}
			: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''

	Hendeca has a period of 1/11 octave, nine ~~of them~~ represent [[7/4]] ~~in the 7-limit~~, the same as [[keemic temperaments #Undeka\|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val.		Hendeca tempers out the same 5-limit comma as [[porwell temperaments #Hendecatonic\|hendecatonic]], and has a period of 1/11 octave. However, in this temperament, nine periods represent [[7/4]], the same as [[keemic temperaments #Undeka\|undeka]]. It can be tuned to [[22edo]] or [[33edo]] using the [[patent val]], or [[55edo]] using the 55d val.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Move hendeca here

2026-07-05T10:34:55Z

Move hendeca here

@@ Line 26: / Line 26: @@
 * ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
 * ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
 * [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
 * ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
@@ Line 32: / Line 31: @@
 * ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
-Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, decic, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]].
+Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, decic, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, hendeca, gwazy, and tertiosec, in the order of increasing [[badness]].
 Since {{nowrap|(5/4)<sup>2</sup> {{=}} (225/224)⋅(14/9)}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
@@ Line 1,273: / Line 1,272: @@
 Badness (Sintel): 1.17
 == Gwazy ==

FloraC: /* Decic */ make it explicit that it's a 10th-octave temp

2026-06-25T11:59:11Z

Decic: make it explicit that it's a 10th-octave temp

← Older revision		Revision as of 11:59, 25 June 2026
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	{{Main\| Decic }}		{{Main\| Decic }}

	Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo\| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma~~, and~~ may be described as the {{nowrap\| 50 & 60 }} temperament, [[support]]ed by [[10edo\|10-]], [[50edo\|50-]], and [[60edo]]. It can be extended ~~naturally~~ to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.		Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo\| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap\| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo\|10-]], [[50edo\|50-]], and [[60edo]].

			It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: Move decic here

2026-06-25T10:15:11Z

Move decic here

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