Lehmerismic temperaments - Revision history

FloraC: Update

2026-06-06T12:15:35Z

Update

← Older revision		Revision as of 12:15, 6 June 2026
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	* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]
	* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]		* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]
	* ''[[Indra]]'' (+540/539) → [[~~Mirkwai family~~ #Indra\|~~Mirkwai family~~]]		* ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra\|Swetismic temperaments]]
	* ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant\|Pentacircle clan]]		* ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant\|Pentacircle clan]]
	* ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya\|Breed family]]		* ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya\|Breed family]]

FloraC: And the reason

2026-04-20T15:05:15Z

And the reason

← Older revision		Revision as of 15:05, 20 April 2026
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	The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].		The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].

	This temperament was first considered by [[Flora Canou]] in 2021. After a few attempts to come up with a memorable name, ''lux'', suggested by [[Godtone]], who associated certain intervals of 13 with light, was adopted.		This ultra-efficient full 13-limit temperament was first considered by [[Flora Canou]] in 2021. After a few attempts to come up with a memorable name, ''lux'', suggested by [[Godtone]], who associated certain intervals of 13 with light, was adopted.

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

FloraC: Name of lux

2026-04-20T15:03:33Z

Name of lux

← Older revision		Revision as of 15:03, 20 April 2026
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	== Lux ==		== Lux ==
	The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].		The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].

			This temperament was first considered by [[Flora Canou]] in 2021. After a few attempts to come up with a memorable name, ''lux'', suggested by [[Godtone]], who associated certain intervals of 13 with light, was adopted.

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

FloraC: + link to tyr and others

2026-04-20T14:57:11Z

+ link to tyr and others

← Older revision		Revision as of 14:57, 20 April 2026
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	* ''[[Thor]]'' (+4375/4374) → [[Ragismic family #Thor\|Ragismic family]]		* ''[[Thor]]'' (+4375/4374) → [[Ragismic family #Thor\|Ragismic family]]
	* ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo\|Hemifamity family]]		* ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo\|Hemifamity family]]
			* ''[[Tyr]]'' (+102487/102400) → [[Landscape family #Tyr\|Landscape family]]

	Considered below are skadi, ganesha, hanuman, lux, and galaxy, in the order of increasing badness. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].		Considered below are skadi, ganesha, hanuman, lux, and galaxy, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].

	== Skadi ==		== Skadi ==
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	== Lux ==		== Lux ==
	The last generator of lux, represented by 55/48, exceeds 8/7 by 385/384, which is equated with a number of important superparticular ~~ratios~~ in the 13-limit: 325/324, 352/351, 364/363, and 441/440.		The last generator of lux, represented by [[55/48]], exceeds [[8/7]] by [[385/384]], which is equated with a number of important [[superparticular ratio]]s in the [[13-limit]]: [[325/324]], [[352/351]], [[364/363]], and [[441/440]].

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

FloraC: - tyr (moved to landscape family)

2026-04-20T13:26:04Z

- tyr (moved to landscape family)

@@ Line 14: / Line 14: @@
 * ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo|Hemifamity family]]
-Considered below are tyr, skadi, ganesha, hanuman, lux, and galaxy. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].
+Considered below are skadi, ganesha, hanuman, lux, and galaxy, in the order of increasing badness. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].
 == Skadi ==

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

2026-04-19T15:36:47Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup. - redundant category

2026-04-19T15:06:44Z

Units & misc. cleanup. - redundant category

← Older revision		Revision as of 15:06, 19 April 2026
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	{{Mapping\|legend=1\| 3 0 0 4 8 \| 0 2 0 -4 1 \| 0 0 1 2 0 }}		{{Mapping\|legend=1\| 3 0 0 4 8 \| 0 2 0 -4 1 \| 0 0 1 2 0 }}

	: mapping generators: ~63/50, ~400/231, ~5		: mapping generators: ~63/50, ~400/231, ~5

	{{Optimal ET sequence\|legend=1\| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}		{{Optimal ET sequence\|legend=1\| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}

	[[Badness]]: 0.259 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.259 × 10<sup>-3</sup>

	=== Borneo ===		=== Borneo ===
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	Mapping: {{mapping\| 3 0 0 4 8 -3 \| 0 2 0 -4 1 3 \| 0 0 1 2 0 1 }}		Mapping: {{mapping\| 3 0 0 4 8 -3 \| 0 2 0 -4 1 3 \| 0 0 1 2 0 1 }}

	{{Optimal ET sequence\|legend=1\| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}		{{Optimal ET sequence\|legend=0\| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}

	Badness: 0.549 × 10<sup>-3</sup>		Badness (Smith): 0.549 × 10<sup>-3</sup>

	Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7		Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
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	{{Mapping\|legend=1\| 1 0 5 8 1 \| 0 1 1 3 2 \| 0 0 -6 -14 -1 }}		{{Mapping\|legend=1\| 1 0 5 8 1 \| 0 1 1 3 2 \| 0 0 -6 -14 -1 }}

	: mapping generators: ~2, ~3, ~18/11		: mapping generators: ~2, ~3, ~18/11

	{{Optimal ET sequence\|legend=1\| 31, 90e, 114de, 121, 152, 311, 342, 836, 1178, 2014, 3192ce, 5206ce }}		{{Optimal ET sequence\|legend=1\| 31, 90e, 114de, 121, 152, 311, 342, 836, 1178, 2014, 3192ce, 5206ce }}

	[[Badness]]: 0.349 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.349 × 10<sup>-3</sup>

	== Ganesha ==		== Ganesha ==
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	{{Mapping\|legend=1\| 1 0 0 -22 -9 \| 0 1 0 1 2 \| 0 0 1 10 4 }}		{{Mapping\|legend=1\| 1 0 0 -22 -9 \| 0 1 0 1 2 \| 0 0 1 10 4 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 702.2251, ~5/4 = 386.6908		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.2251{{c}}, ~5/4 = 386.6908{{c}}

	{{Optimal ET sequence\|legend=1\| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}		{{Optimal ET sequence\|legend=1\| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }}

	[[Badness]]: 0.390 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.390 × 10<sup>-3</sup>

	== Hanuman ==		== Hanuman ==
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	{{Mapping\|legend=1\| 1 2 0 -8 1 \| 0 -3 0 11 1 \| 0 0 1 4 1 }}		{{Mapping\|legend=1\| 1 2 0 -8 1 \| 0 -3 0 11 1 \| 0 0 1 4 1 }}

	: mapping generators: ~2, ~11/10, ~5		: mapping generators: ~2, ~11/10, ~5

	{{Optimal ET sequence\|legend=1\| 15, 42bc, 49bcde, 50d, 57, 65d, 72, 152, 224, 311, 463, 535, 998 }}		{{Optimal ET sequence\|legend=1\| 15, 42bc, 49bcde, 50d, 57, 65d, 72, 152, 224, 311, 463, 535, 998 }}

	[[Badness]]: 0.500 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.500 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 2 0 -8 1 -6 \| 0 -3 0 11 1 3 \| 0 0 1 4 1 4 }}		Mapping: {{mapping\| 1 2 0 -8 1 -6 \| 0 -3 0 11 1 3 \| 0 0 1 4 1 4 }}

	{{Optimal ET sequence\|legend=1\| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }}		{{Optimal ET sequence\|legend=0\| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }}

	Badness: 0.653 × 10<sup>-3</sup>		Badness (Smith): 0.653 × 10<sup>-3</sup>

	== Lux ==		== Lux ==
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	{{Mapping\|legend=1\| 1 0 0 6 5 \| 0 1 4 -1 -3 \| 0 0 -5 -2 4 }}		{{Mapping\|legend=1\| 1 0 0 6 5 \| 0 1 4 -1 -3 \| 0 0 -5 -2 4 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1/1~~, ~3/2 = 702.1117, ~55/48 = 235.5784		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.1117{{c}}, ~55/48 = 235.5784{{c}}

	{{Optimal ET sequence\|legend=1\| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }}		{{Optimal ET sequence\|legend=1\| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }}

	[[Badness]]: 0.508 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.508 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 6 5 6 \| 0 1 4 -1 -3 -5 \| 0 0 -5 -2 4 7 }}		Mapping: {{mapping\| 1 0 0 6 5 6 \| 0 1 4 -1 -3 -5 \| 0 0 -5 -2 4 7 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 702.0674, ~55/48 = 235.5870		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.0674{{c}}, ~55/48 = 235.5870{{c}}

	{{Optimal ET sequence\|legend=1\| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}		{{Optimal ET sequence\|legend=0\| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}

	Badness: 0.360 × 10<sup>-3</sup>		Badness (Smith): 0.360 × 10<sup>-3</sup>

	== Galaxy ==		== Galaxy ==
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	{{Mapping\|legend=1\| 1 0 5 -4 -5 \| 0 1 3 -3 -3 \| 0 0 -9 14 16 }}		{{Mapping\|legend=1\| 1 0 5 -4 -5 \| 0 1 3 -3 -3 \| 0 0 -9 14 16 }}

	: mapping generators: ~2, ~3, ~6125/3456		: mapping generators: ~2, ~3, ~6125/3456

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 701.9856, ~6125/3456 = 991.0688		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9856{{c}}, ~6125/3456 = 991.0688{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }}		{{Optimal ET sequence\|legend=1\| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }}

	[[Badness]]: 0.841 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.841 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 5 -4 -5 -4 \| 0 1 3 -3 -3 -4 \| 0 0 -9 14 16 17 }}		Mapping: {{mapping\| 1 0 5 -4 -5 -4 \| 0 1 3 -3 -3 -4 \| 0 0 -9 14 16 17 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 701.9368, ~484/273 = 991.0597		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.9368{{c}}, ~484/273 = 991.0597{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }}		{{Optimal ET sequence\|legend=0\| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }}

	Badness: 0.463 × 10<sup>-3</sup>		Badness (Smith): 0.463 × 10<sup>-3</sup>

	=== 17-limit ===		=== 17-limit ===
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	Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.1144, ~85/48 = 991.1035		Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.1144, ~85/48 = 991.1035

	{{Optimal ET sequence\|legend=1\| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }}		{{Optimal ET sequence\|legend=0\| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }}

	Badness: 0.933 × 10<sup>-3</sup>		Badness (Smith): 0.933 × 10<sup>-3</sup>

	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:Lehmerismic temperaments\| ]] <!-- main article -->		[[Category:Lehmerismic temperaments\| ]] <!-- main article -->
	~~[[Category:Lehmerismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Move 7-limit parents to a dedicated collection page

2025-11-29T07:11:45Z

Move 7-limit parents to a dedicated collection page

@@ Line 56: / Line 56: @@
 == Ganesha ==
-=== 7-limit (quasiorwellismic) ===
+: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Quasiorwellismic]].''
 [[Subgroup]]: 2.3.5.7.11

FloraC: Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

2025-11-27T12:29:44Z

Text replacement - "Category:Temperament collections↵Category:Pages with mostly numerical content" to "Category:Temperament collections"

← Older revision		Revision as of 12:29, 27 November 2025
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Lehmerismic temperaments\| ]] <!-- main article -->		[[Category:Lehmerismic temperaments\| ]] <!-- main article -->
	[[Category:Lehmerismic\| ]] <!-- key article -->		[[Category:Lehmerismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Fix linking

2025-08-27T13:50:19Z

Fix linking

← Older revision		Revision as of 13:50, 27 August 2025
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	* ''[[Oxpecker]]'' (+121/120 or 126/125) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]		* ''[[Oxpecker]]'' (+121/120 or 126/125) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]
	* ''[[Manwe]]'' (+176/175) → [[Valinorsmic clan #Manwe\|Valinorsmic clan]]		* ''[[Manwe]]'' (+176/175) → [[Valinorsmic clan #Manwe\|Valinorsmic clan]]
	* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank ~~three~~ clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]
	* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]		* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]
	* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Indra\|Mirkwai family]]		* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Indra\|Mirkwai family]]

← Older revision		Revision as of 12:15, 6 June 2026
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	* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]
	* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]		* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]
	* ''[[Indra]]'' (+540/539) → [[~~Mirkwai family~~ #Indra\|~~Mirkwai family~~]]		* ''[[Indra]]'' (+540/539) → [[Swetismic temperaments #Indra\|Swetismic temperaments]]
	* ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant\|Pentacircle clan]]		* ''[[Tolerant]]'' (+896/891) → [[Pentacircle clan #Tolerant\|Pentacircle clan]]
	* ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya\|Breed family]]		* ''[[Freya]]'' (+2401/2400) → [[Breed family #Freya\|Breed family]]

← Older revision		Revision as of 13:50, 27 August 2025
Line 3:		Line 3:
	* ''[[Oxpecker]]'' (+121/120 or 126/125) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]		* ''[[Oxpecker]]'' (+121/120 or 126/125) → [[Biyatismic clan #Oxpecker\|Biyatismic clan]]
	* ''[[Manwe]]'' (+176/175) → [[Valinorsmic clan #Manwe\|Valinorsmic clan]]		* ''[[Manwe]]'' (+176/175) → [[Valinorsmic clan #Manwe\|Valinorsmic clan]]
	* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank ~~three~~ clan #Spectacle\|Rastmic rank-3 clan]]		* ''[[Spectacle]]'' (+225/224 or 243/242) → [[Rastmic rank-3 clan #Spectacle\|Rastmic rank-3 clan]]
	* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]		* ''[[Portent]]'' (+385/384 or 441/440) → [[Gamelismic family #Portent\|Gamelismic family]]
	* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Indra\|Mirkwai family]]		* ''[[Indra]]'' (+540/539) → [[Mirkwai family #Indra\|Mirkwai family]]