Miscellaneous 5-limit temperaments - Revision history

FloraC: /* Leapday */ update

2026-08-08T10:07:52Z

Leapday: update

← Older revision		Revision as of 10:07, 8 August 2026
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	== Leapday ==		== Leapday ==
	: ''For extensions, see [[~~Hemifamity~~ temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''		: ''For extensions, see [[Sengic temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

2026-08-06T21:37:42Z

Aluminium

← Older revision		Revision as of 21:37, 6 August 2026
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	[[Badness]] (Sintel): 2.88		[[Badness]] (Sintel): 2.88

	~~== Aluminium ==~~
	~~: ''For extensions, see [[Ragismic microtemperaments #Aluminium]].''~~

	~~Aluminium tempers out {{monzo\| 92 -39 -13 }} in the 5-limit, and sets [[135/128]] to 1/13 of an [[octave]].~~

	~~[[Subgroup]]: 2.3.5~~

	~~[[Comma list]]: {{monzo\| 92 -39 -13 }}~~

	~~{{Mapping\|legend=1\| 13 0 92 \| 0 1 -3 }}~~
	~~: mapping generators: ~135/128, ~3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~135/128 = 92.3068{{c}}, ~3/2 = 701.9791{{c}}
	~~: [[error map]]: {{val\| -0.012 +0.012 +0.009 }}~~
	* [[CWE]]: ~135/128 = 92.3077{{c}}, ~3/2 = 701.9897{{c}}
	~~: error map: {{val\| 0.000 +0.032 +0.033 }}~~

	~~{{Optimal ET sequence\|legend=1\| 65, 299, 364, 429, 494, 559, 1053, 1612, 5889, 7501, 9113, 10725, 23062bc, 33787bcc, 44512bbcc }}~~

	~~[[Badness]] (Sintel): 2.89~~

	== Avila ==		== Avila ==

2026-08-01T19:07:02Z

neon is of importance to 10edo

← Older revision		Revision as of 19:07, 1 August 2026
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	[[Badness]] (Sintel): 4.70		[[Badness]] (Sintel): 4.70

	~~== Neon ==~~
	~~: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''~~
	~~{{See also\| Neon comma }}~~

	~~Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of [[10edo]]. It was named by [[Eliora]] in 2023 after the 10th element.~~

	~~[[Subgroup]]: 2.3.5~~

	~~[[Comma list]]: {{monzo\| 21 60 -50 }}~~

	~~{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}~~
	~~: mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo\| 10 29 -24 }} = 284.3890{{c}}
	~~: [[error map]]: {{val\| -0.001 -0.011 +0.019 }}~~
	* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo\| 10 29 -24 }} = 284.3891{{c}}
	~~: error map: {{val\| 0.000 -0.010 +0.021 }}~~

	~~{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}~~

	~~[[Badness]] (Sintel): 4.85~~

	== Dodifo ==		== Dodifo ==

2026-07-22T19:09:43Z

Shibboleth

← Older revision		Revision as of 19:09, 22 July 2026
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	== Shibboleth ==		== Shibboleth ==
	: ''For extensions, see [[Gamelismic clan #Superkleismic]]~~, [[Starling temperaments #Gilead]],~~ and [[Sensamagic clan #Superthird]].''		: ''For extensions, see [[Gamelismic clan #Superkleismic]] and [[Sensamagic clan #Superthird]].''

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

2026-07-21T03:48:42Z

Move aluminium, tridecatonic, and triskaidekic here

@@ Line 89: / Line 89: @@
 [[Badness]] (Sintel): 2.88
 == Avila ==
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 Scales (Scala files): [[wizard22]]
 == Merman ==
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 [[Badness]] (Sintel): 52.3
 == Satin ==

2026-07-14T14:15:08Z

Text replacement - "octave" to "octave"

← Older revision		Revision as of 14:15, 14 July 2026
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	: ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].''		: ''For extensions, see [[Porwell temperaments #Hendecatonic]] and [[Marvel temperaments #Hendeca]].''

	The 5-limit version of hendecatonic simply equates a stack of eleven [[16/15]]'s with the [[~~2/1\|~~octave]].		The 5-limit version of hendecatonic simply equates a stack of eleven [[16/15]]'s with the [[octave]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	: ''For extensions, see [[Keemic temperaments #Undeka]].''		: ''For extensions, see [[Keemic temperaments #Undeka]].''

	Undeka has a period of 1/11 octave, like [[#Hendecatonic\|hendecatonic]], but this temperament equates a stack of eleven 6/5's and three [[~~2/1\|~~octave]]s, so that three periods represent [[6/5]].		Undeka has a period of 1/11 octave, like [[#Hendecatonic\|hendecatonic]], but this temperament equates a stack of eleven 6/5's and three [[octave]]s, so that three periods represent [[6/5]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

2026-07-05T10:54:42Z

Move hendecatonic, undeka, and elven here

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 [[Badness]] (Sintel): 10.6
 == Nusecond ==
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 [[Badness]] (Sintel): 17.0
 == Kumonga ==
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 [[Badness]] (Sintel): 203
 == References ==
 [[Category:Temperament collections]]

2026-07-05T07:42:02Z

Neon: + see also

← Older revision		Revision as of 07:42, 5 July 2026
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	== Neon ==		== Neon ==
	: For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''		: ''For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''
			{{See also\| Neon comma }}

	Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of [[10edo]]. It was named by [[Eliora]] in 2023 after the 10th element.		Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of [[10edo]]. It was named by [[Eliora]] in 2023 after the 10th element.

2026-07-05T07:37:15Z

Move neon here

← Older revision		Revision as of 07:37, 5 July 2026
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	[[Badness]] (Sintel): 4.70		[[Badness]] (Sintel): 4.70

			== Neon ==
			: For extensions, see [[Ragismic microtemperaments #Deca]], [[Landscape microtemperaments #Zinc]], and [[20th-octave temperaments #Calcium]].''

			Neon tempers out {{monzo\| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of [[10edo]]. It was named by [[Eliora]] in 2023 after the 10th element.

			[[Subgroup]]: 2.3.5

			[[Comma list]]: {{monzo\| 21 60 -50 }}

			{{Mapping\|legend=1\| 10 4 9 \| 0 5 6 }}
			: mapping generators: ~3125/2916, {{monzo\| 10 29 -24 }}

			[[Optimal tuning]]s:
			* [[WE]]: ~3125/2916 = 119.9999{{c}}, {{monzo\| 10 29 -24 }} = 284.3890{{c}}
			: [[error map]]: {{val\| -0.001 -0.011 +0.019 }}
			* [[CWE]]: ~3125/2916 = 120.0000{{c}}, {{monzo\| 10 29 -24 }} = 284.3891{{c}}
			: error map: {{val\| 0.000 -0.010 +0.021 }}

			{{Optimal ET sequence\|legend=1\| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }}

			[[Badness]] (Sintel): 4.85

	== Dodifo ==		== Dodifo ==

2026-07-03T16:49:44Z

Move 5-limit octoid here

← Older revision		Revision as of 16:49, 3 July 2026
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	[[Badness]] (Sintel): 6.65		[[Badness]] (Sintel): 6.65

			== Octoid ==
			: ''For extensions, see [[Ragismic microtemperaments #Octoid]].''

			[[Subgroup]]: 2.3.5

			[[Comma list]]: {{monzo\| -5 -32 24 }}

			{{Mapping\|legend=1\| 8 1 3 \| 0 3 4 }}
			: Mapping generators: ~2125764/1953125, ~4374/3125

			[[Optimal tuning]]s:
			* [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
			* [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}

			{{Optimal ET sequence\|legend=1\| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}

			[[Badness]] (Sintel): 6.69

	== Kangaroo ==		== Kangaroo ==