Porwell temperaments - Revision history

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

2026-09-24T12:33:39Z

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

FloraC: Move majo here

2026-09-20T05:04:17Z

Move majo here

← Older revision		Revision as of 05:04, 20 September 2026
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	Badness (Sintel): 0.971		Badness (Sintel): 0.971

			== Majo ==
			: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Maja (5-limit)]].''

			Possibly named by [[Gene Ward Smith]] in 2012, majo may be described as {{nowrap\| 53 & 167 }} and is a more complex alternative to [[maja]].

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 6144/6125, 1250000/1240029

			{{Mapping\|legend=1\| 1 -9 -12 19 \| 0 17 23 -26 }}
			: mapping generators: ~2, ~125/81

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.4701{{c}}, ~125/81 = 746.9341{{c}}
			: [[error map]]: {{val\| -0.530 +0.694 -0.470 +0.819 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/81 = 747.2751{{c}}
			: error map: {{val\| 0.000 +1.721 +1.013 +2.022 }}

			{{Optimal ET sequence\|legend=1\| 53, 167, 220, 493bd, 713bdd }}

			[[Badness]] (Sintel): 3.56

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 2200/2187, 3388/3375, 6144/6125

			Mapping: {{mapping\| 1 -9 -12 19 -42 \| 0 17 23 -26 73 }}

			Optimal tunings:
			* WE: ~2 = 1199.4882{{c}}, ~77/50 = 746.9681{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~77/50 = 747.2776{{c}}

			{{Optimal ET sequence\|legend=0\| 53, 114e, 167, 220, 387bd }}

			Badness (Sintel): 2.71

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 325/324, 352/351, 1001/1000, 2704/2695

			Mapping: {{mapping\| 1 -9 -12 19 -42 -10 \| 0 17 23 -26 73 22 }}

			Optimal tunings:
			* WE: ~2 = 1199.5860{{c}}, ~20/13 = 747.0285{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 747.2789{{c}}

			{{Optimal ET sequence\|legend=0\| 53, 114e, 167, 220, 387bd }}

			Badness (Sintel): 1.78

	== Whoops ==		== Whoops ==

FloraC: Recategorize

2026-08-15T08:00:19Z

Recategorize

← Older revision		Revision as of 08:00, 15 August 2026
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	== References ==		== References ==

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

FloraC: - semaja (addressed in gariboh clan)

2026-08-08T13:01:18Z

- semaja (addressed in gariboh clan)

@@ Line 21: / Line 21: @@
 * ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
 * ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]
 * ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]
 * ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]
@@ Line 303: / Line 304: @@
 Badness (Sintel): 1.12
 == Aufo ==
 :''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
-Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
+Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
 [[Subgroup]]: 2.3.5.7

FloraC: - twothirdtonic (addressed in sengic temps)

2026-08-08T10:02:56Z

- twothirdtonic (addressed in sengic temps)

@@ Line 16: / Line 16: @@
 * ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]
 * ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
 * ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]]
 * ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee|Keegic temperaments]]
@@ Line 24: / Line 25: @@
 * ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]
-Considered below are hendecatonic, nessafof, grendel, twothirdtonic, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].
+Considered below are hendecatonic, nessafof, grendel, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].
 == Hendecatonic ==
@@ Line 302: / Line 303: @@
 Badness (Sintel): 1.12
 == Semaja ==

FloraC: /* Hendecatonic */ update

2026-07-05T11:03:25Z

Hendecatonic: update

← Older revision		Revision as of 11:03, 5 July 2026
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	== Hendecatonic ==		== Hendecatonic ==
	: ''For the 5-limit version, see [[~~11th~~-~~octave~~ temperaments #~~Hendecapent~~]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''

	The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represent [[9/7]]. It tempers out 10976/10935, the [[hemimage comma]], and may be described as the {{nowrap\| 22 & 99 }} temperament, with [[99edo]] giving an almost perfect tuning.		The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represent [[9/7]]. It tempers out 10976/10935, the [[hemimage comma]], and may be described as the {{nowrap\| 22 & 99 }} temperament, with [[99edo]] giving an almost perfect tuning.

FloraC: Update

2026-06-25T10:24:28Z

Update

← Older revision		Revision as of 10:24, 25 June 2026
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	* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]		* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]
	* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]		* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]
	* ''[[Quinkee]]'' (+1029/1000) → [[~~Cloudy clan~~ #Quinkee\|~~Cloudy clan~~]]		* ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee\|Keegic temperaments]]
	* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]		* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]
	* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]

FloraC: /* Semaja */ relate to llywelynsmic clan

2026-05-28T10:17:18Z

Semaja: relate to llywelynsmic clan

← Older revision		Revision as of 10:17, 28 May 2026
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	== Semaja ==		== Semaja ==
	Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[gariboh comma]] to the comma list, and may be described as the {{nowrap\| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot. The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>.		{{See also\| Llywelynsmic clan }}

			Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[gariboh comma]] to the comma list, and may be described as the {{nowrap\| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup\|2.5.7-subgroup]] [[restriction]]). The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>.

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

FloraC: /* Hendecatonic */ decanonicalize undecimal hendecatonic

2026-05-19T08:06:22Z

Hendecatonic: decanonicalize undecimal hendecatonic

← Older revision		Revision as of 08:06, 19 May 2026
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	[[Badness]] (Sintel): 1.04		[[Badness]] (Sintel): 1.04

	=== ~~11-limit~~ ===		=== Hendecaton ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC at 03:46, 23 April 2026

2026-04-23T03:46:20Z

← Older revision		Revision as of 03:46, 23 April 2026
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	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[regular temperament\|temperaments]] that [[tempering out\|~~tempers~~ out]] the porwell comma, {{monzo\| 11 1 -3 -2 }} ([[6144/6125]]).		This is a collection of [[regular temperament\|temperaments]] that [[tempering out\|temper out]] the [[porwell comma]] ({{monzo\|legend=1\| 11 1 -3 -2 }}, [[ratio]]: [[6144/6125]]).

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are: