Wizmic microtemperaments - Revision history

FloraC: - witcher (more properly addressed in amity family)

2026-06-03T14:59:05Z

- witcher (more properly addressed in amity family)

FloraC: - gariwizmic (more properly addressed in the garischismic clan)

2026-05-16T09:02:47Z

- gariwizmic (more properly addressed in the garischismic clan)

@@ Line 4: / Line 4: @@
 Temperaments discussed elsewhere are:
 * [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]]
 * ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
 * [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]]
@@ Line 19: / Line 20: @@
 * ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]]
-Considered below are qak, tokko, tertiathirds, witcher, and gariwizmic.
+Considered below are qak, tokko, tertiathirds, and witcher.
 == Qak ==
@@ Line 271: / Line 272: @@
 Badness (Sintel): 2.46
 [[Category:Temperament collections]]
 [[Category:Wizmic microtemperaments| ]] <!-- main article -->
 [[Category:Rank 2]]

FloraC: Sorting. Fix grammar. - redundant categories

2026-05-11T19:14:09Z

Sorting. Fix grammar. - redundant categories

← Older revision		Revision as of 19:14, 11 May 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|~~tempers~~ out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).		This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|temper out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).

	~~Discussed~~ elsewhere are:		Temperaments discussed elsewhere are:
	* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth\|Archytas clan]]		* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth\|Archytas clan]]
	* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone\|Meantone family]]		* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone\|Meantone family]]
	* [[~~Oolong~~]] (+~~126~~/~~125~~) → [[~~Starling temperaments~~ #~~Oolong~~\|~~Starling temperaments]]~~		* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]
	* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]		* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
	* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
	* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]		* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]
	* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]		* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]
	* ''[[~~Sqrtphi~~]]'' (+~~15625~~/~~15552 or 16875~~/~~16807~~) → [[~~Kleismic family~~ #~~Sqrtphi~~\|~~Kleismic family~~]]		* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* [[~~Tsaharuk~~]] (+~~32805~~/~~32768~~) → [[~~Schismatic family~~ #~~Tsaharuk~~\|~~Schismatic family~~]]		* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong\|Starling temperaments]]
	* ''[[Fifthplus]]'' (+~~5625~~/65536) → [[Horwell temperaments #Fifthplus\|Horwell temperaments]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
			* ''[[Fifthplus]]'' (+65625/65536) → [[Horwell temperaments #Fifthplus\|Horwell temperaments]]
	* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]		* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]
			* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
			* [[Sqrtphi]] (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]
	* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell\|Semicomma family]]		* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell\|Semicomma family]]
	* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish\|Vishnuzmic family]]		* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish\|Vishnuzmic family]]
Line 345:		Line 345:
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Wizmic microtemperaments\| ]] <!-- main article -->		[[Category:Wizmic microtemperaments\| ]] <!-- main article -->
	~~[[Category:Wizmic\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]
	~~[[Category:Microtemperaments]]~~

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-05-11T19:09:12Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

Overthink: /* Gariwizmic */ fix errors

2026-05-06T23:26:55Z

Gariwizmic: fix errors

← Older revision		Revision as of 23:26, 6 May 2026
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	[[Optimal tuning\|Optimal tunings]]:		[[Optimal tuning\|Optimal tunings]]:

	* [[WE]]: ~2 = 599.996{{c}}, ~3/2 = 702.177{{c}}		* [[WE]]: ~46305/32768 = 599.996{{c}}, ~3/2 = 702.177{{c}}

	: [[error map]]: {{val\|-0.069, 0.153, -0.021, -0.053}}		: [[error map]]: {{val\|-0.069, 0.153, -0.021, -0.053}}

	* [[CWE]]: ~2 = ~~1200~~.~~0000~~{{c}}, ~3/2 = 702.216{{c}}		* [[CWE]]: ~46305/32768 = 600.000{{c}}, ~3/2 = 702.216{{c}}

	: error map: {{val\|0.000 0.261 0.114 0.149}}		: error map: {{val\|0.000 0.261 0.114 0.149}}

FloraC: Update

2026-04-05T12:17:43Z

Update

← Older revision		Revision as of 12:17, 5 April 2026
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	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[~~Rank~~-2 temperament\|rank-2]] [[microtemperament]]s which [[~~Tempering~~ out\|tempers out]] the [[wizma]], {{monzo\|-6 -8 2 5}} = 420175/419904.		This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|tempers out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).

	Discussed elsewhere are:		Discussed elsewhere are:
Line 8:		Line 8:
	* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]		* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]		* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[~~Ragismic microtemperaments~~ #Ennealimmal\|~~Ragismic microtemperaments~~]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
	* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]		* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
	* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]		* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]
	* ''[[Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]		* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]
	* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]		* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]
	* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]		* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]

Eufalesio: Tredekisma

2026-03-29T11:19:04Z

Tredekisma

← Older revision		Revision as of 11:19, 29 March 2026
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	== Gariwizmic ==		== Gariwizmic ==
	Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just. Unlike schismic, it finds 5/4 at the ''trans''diminished fourth (+45 fifths) minus a half pythagorean comma, or equivalently, at the ''trans''diminished octave (+39 fifths) minus a semioctave.		Gariwizmic (94&176) tempers out the wizma (420175/419904) and the garischisma (33554432/33480783). It assumes a semioctave period and a perfect fifth generator that is slightly sharp of just. Unlike schismic, it finds 5/4 at the ''trans''diminished fourth (+45 fifths) minus a half pythagorean comma, or equivalently, at the ''trans''diminished octave (+39 fifths) minus a semioctave.

			It is bad in the 5-limit but extends extremely well to other subgroups, notably the 2.3.5.7.11.13.19 subgroup, as it also indirectly tempers out the [[tredekisma]], the smallest superparticular ratio in the 19- and 23-limit.

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

Yourmusic Productions: /* Gariwizmic */ Fix math error.

2026-03-20T17:38:54Z

Gariwizmic: Fix math error.

← Older revision		Revision as of 17:38, 20 March 2026
Line 252:		Line 252:
	: [[error map]]: {{val\|-0.069, 0.153, -0.021, -0.053}}		: [[error map]]: {{val\|-0.069, 0.153, -0.021, -0.053}}

	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = ~~696~~.~~6512~~{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.216{{c}}

	: error map: {{val\|0.000 0.261 0.114 0.149}}		: error map: {{val\|0.000 0.261 0.114 0.149}}

Eufalesio: No need for cassawizmic because there is no canon androwizmic

2026-03-20T16:45:25Z

No need for cassawizmic because there is no canon androwizmic

← Older revision		Revision as of 16:45, 20 March 2026
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	[[Badness]]: 2.225 (Sintel)		[[Badness]]: 2.225 (Sintel)

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

Xenllium at 10:39, 26 February 2026

2026-02-26T10:39:48Z

← Older revision		Revision as of 10:39, 26 February 2026
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	== Tokko ==		== Tokko ==
			: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Tokko]].''

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

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	[[Badness]]: 2.225 (Sintel)		[[Badness]]: 2.225 (Sintel)

	==== Cassawizmic ====		=== Cassawizmic ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	* mapping generators: ~99/70, ~3		* mapping generators: ~99/70, ~3

	* WE: ~99/70 = 599.979, ~3/2 = 702.194 [[error map]]: {{val\|-0.042 0.197 0.106 -0.001 -0.440}}		* WE: ~99/70 = 599.979, ~3/2 = 702.194
	* CWE: ~99/70 = 1\2, ~3/2 = 702.218 [[error map]]: {{val\|0.000 0.263 0.185 0.123 -0.306}}		: error map: {{val\|-0.042 0.197 0.106 -0.001 -0.440}}
			* CWE: ~99/70 = 1\2, ~3/2 = 702.218
			: error map: {{val\|0.000 0.263 0.185 0.123 -0.306}}

	{{Optimal ET sequence\|legend=1\|94, 176, 270, 364, 446, 634, 904}}		{{Optimal ET sequence\|legend=0\|94, 176, 270, 364, 446, 634, 904}}

	[[Badness]]: 1.008 (Sintel)		[[Badness]]: 1.008 (Sintel)
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	[[Optimal tuning\|Optimal tunings]]:		[[Optimal tuning\|Optimal tunings]]:
	* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val\|-0.008 0.246 0.035 0.146 -0.412 -0.353}}		* WE: ~99/70 = 599.996, ~3/2 = 702.210
			: error map: {{val\|-0.008 0.246 0.035 0.146 -0.412 -0.353}}
	* CWE: ~99/70 = 1\2, ~3/2 = 702.215		* CWE: ~99/70 = 1\2, ~3/2 = 702.215
	* [[error map]]: {{val\|-0.000 0.260 0.054 0.170 -0.383 -0.321}}		: error map: {{val\|-0.000 0.260 0.054 0.170 -0.383 -0.321}}

	{{Optimal ET sequence\|legend=1\|94, 176, 270, 364, 446, 634, 904}}		{{Optimal ET sequence\|legend=0\|94, 176, 270, 364, 446, 634, 904}}

	[[Badness]]: 0.822 (Sintel)		[[Badness]]: 0.822 (Sintel)
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	Comma list: [[2080/2079]], [[1540/1539]], [[1216/1215]], [[1716/1715]], [[1729/1728]]		Comma list: [[2080/2079]], [[1540/1539]], [[1216/1215]], [[1716/1715]], [[1729/1728]]

	{{Mapping\|legend=1\| 2 2 -41 22 -20 39\|0 1 39 -14 23 -27}}		{{Mapping\|legend=1\| 2 2 -41 22 -20 39 -43\|0 1 39 -14 23 -27 44}}

	* mapping generators: ~99/70, ~3		* mapping generators: ~99/70, ~3

	[[Optimal tuning\|Optimal tunings]]:		[[Optimal tuning\|Optimal tunings]]:
	* WE: ~99/70 = 599.996, ~3/2 = 702.210 [[error map]]: {{val\|-0.006 0.250 0.057 0.147 -0.394 -0.355 -0.079}}		* WE: ~99/70 = 599.996, ~3/2 = 702.210
	* CWE: ~99/70 = 1\2, ~3/2 = 702.215 [[error map]]: {{val\|-0.000 0.260 0.070 0.165 -0.374 -0.332 -0.055}}		: error map: {{val\|-0.006 0.250 0.057 0.147 -0.394 -0.355 -0.079}}
			* CWE: ~99/70 = 1\2, ~3/2 = 702.215
			: error map: {{val\|-0.000 0.260 0.070 0.165 -0.374 -0.332 -0.055}}

	{{Optimal ET sequence\|legend=1\|94, 176, 270, 364, 446, 634, 904}}		{{Optimal ET sequence\|legend=0\|94, 176, 270, 364, 446, 634, 904}}

	[[Badness]]: 0.655 (Sintel)		[[Badness]]: 0.655 (Sintel)

	~~==== Androwizmic ====~~
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Wizmic microtemperaments\| ]] <!-- main article -->		[[Category:Wizmic microtemperaments\| ]] <!-- main article -->

← Older revision		Revision as of 19:14, 11 May 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|~~tempers~~ out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).		This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|temper out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).

	~~Discussed~~ elsewhere are:		Temperaments discussed elsewhere are:
	* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth\|Archytas clan]]		* [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth\|Archytas clan]]
	* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone\|Meantone family]]		* ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone\|Meantone family]]
	* [[~~Oolong~~]] (+~~126~~/~~125~~) → [[~~Starling temperaments~~ #~~Oolong~~\|~~Starling temperaments]]~~		* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]
	* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]		* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
	* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
	* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]		* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]
	* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]		* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]
	* ''[[~~Sqrtphi~~]]'' (+~~15625~~/~~15552 or 16875~~/~~16807~~) → [[~~Kleismic family~~ #~~Sqrtphi~~\|~~Kleismic family~~]]		* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* [[~~Tsaharuk~~]] (+~~32805~~/~~32768~~) → [[~~Schismatic family~~ #~~Tsaharuk~~\|~~Schismatic family~~]]		* [[Oolong]] (+126/125) → [[Starling temperaments #Oolong\|Starling temperaments]]
	* ''[[Fifthplus]]'' (+~~5625~~/65536) → [[Horwell temperaments #Fifthplus\|Horwell temperaments]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
			* ''[[Fifthplus]]'' (+65625/65536) → [[Horwell temperaments #Fifthplus\|Horwell temperaments]]
	* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]		* ''[[Octowerck]]'' (+321489/320000) → [[Varunismic temperaments #Octowerck\|Varunismic temperaments]]
			* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
			* [[Sqrtphi]] (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]
	* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell\|Semicomma family]]		* ''[[Quinwell]]'' (+2109375/2097152) → [[Semicomma family #Quinwell\|Semicomma family]]
	* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish\|Vishnuzmic family]]		* ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish\|Vishnuzmic family]]
Line 345:		Line 345:
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Wizmic microtemperaments\| ]] <!-- main article -->		[[Category:Wizmic microtemperaments\| ]] <!-- main article -->
	~~[[Category:Wizmic\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]
	~~[[Category:Microtemperaments]]~~

← Older revision		Revision as of 12:17, 5 April 2026
Line 1:		Line 1:
	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[~~Rank~~-2 temperament\|rank-2]] [[microtemperament]]s which [[~~Tempering~~ out\|tempers out]] the [[wizma]], {{monzo\|-6 -8 2 5}} = 420175/419904.		This is a collection of [[rank-2 temperament\|rank-2]] [[microtemperament]]s which [[tempering out\|tempers out]] the [[wizma]] ({{monzo\|legend=1\| -6 -8 2 5 }}, [[ratio]]: 420175/419904).

	Discussed elsewhere are:		Discussed elsewhere are:
Line 8:		Line 8:
	* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]		* [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard\|Marvel temperaments]]
	* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]		* ''[[Hemiseven]]'' (+1029/1024) → [[Gamelismic clan #Hemiseven\|Gamelismic clan]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[~~Ragismic microtemperaments~~ #Ennealimmal\|~~Ragismic microtemperaments~~]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
	* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]		* ''[[Sengagen]]'' (+3136/3125) → [[Hemimean clan #Sengagen\|Hemimean clan]]
	* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]		* ''[[Septiquarter]]'' (+5120/5103) → [[Hemifamity temperaments #Septiquarter\|Hemifamity temperaments]]
	* ''[[Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]		* ''[[Hendecatonic (temperament)\|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic\|Porwell temperaments]]
	* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]		* ''[[Sqrtphi]]'' (+15625/15552 or 16875/16807) → [[Kleismic family #Sqrtphi\|Kleismic family]]
	* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]		* [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk\|Schismatic family]]