Starling temperaments - Revision history

FloraC: Recategorize

2026-08-15T08:01:29Z

Recategorize

← Older revision		Revision as of 08:01, 15 August 2026
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	== References ==		== References ==

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

FloraC: - "paraguay" (addressed in parakleismic family)

2026-08-09T13:49:01Z

- "paraguay" (addressed in parakleismic family)

@@ Line 22: / Line 22: @@
 * ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]
 * ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja|Buzzardsmic clan]]
 * ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton|Ditonmic family]]
 * ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean|Vishnu family]]
 * ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]]
-Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].
+Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, supersensi, and cobalt, sorted by increasing [[badness]].
 Since {{nowrap|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.
@@ Line 471: / Line 472: @@
 Badness (Sintel): 1.19
 == Bisemidim ==

Hkm: /* Uruguay */

2026-07-23T05:17:06Z

Uruguay

← Older revision		Revision as of 05:17, 23 July 2026
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	Badness (Sintel): 1.86		Badness (Sintel): 1.86

	~~==== Uruguay ====~~
	~~Subgroup: 2.3.5.7.11.13~~

	~~Comma list: 56/55, 78/77, 100/99, 1183/1152~~

	~~Mapping: {{mapping\| 1 -8 -8 -9 2 0 \| 0 13 14 16 2 5 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1199.6132{{c}}, ~5/3 = 884.7325{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.0005{{c}}

	~~{{Optimal ET sequence\|legend=0\| 19, 42e }}~~

	~~Badness (Sintel): 2.51~~

	== Bisemidim ==		== Bisemidim ==

Hkm: /* Gilead */

2026-07-22T17:40:42Z

Gilead

← Older revision		Revision as of 17:40, 22 July 2026
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	Badness (Sintel): 1.27		Badness (Sintel): 1.27

	~~== Gilead ==~~
	~~: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].''~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 126/125, 343/324~~

	~~{{Mapping\|legend=1\| 1 -5 -5 -6 \| 0 9 10 12 }}~~
	~~: mapping generators: ~2, ~5/3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1201.4516{{c}}, ~5/3 = 879.6394{{c}}
	~~: [[error map]]: {{val\| +1.452 +7.542 +2.823 -21.862 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 878.7223{{c}}
	~~: error map: {{val\| 0.000 +6.545 +0.909 -24.159 }}~~

	~~{{Optimal ET sequence\|legend=1\| 11cd, 15, 41dd }}~~

	~~[[Badness]] (Sintel): 2.92~~

	== Supersensi ==		== Supersensi ==

FloraC: Text replacement - "octave" to "octave"

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 the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Xenial]].''

	Named by [[User:Xenllium\|Xenllium]] in 2026, xenial may be described as the {{nowrap\| 19 & 70 }} temperament, splitting the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2\|perfect fifth]] above 7 [[~~2/1\|~~octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.		Named by [[User:Xenllium\|Xenllium]] in 2026, xenial may be described as the {{nowrap\| 19 & 70 }} temperament, splitting the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. Equivalently, a stack of nine [[9/5]]s is equated with the [[3/2\|perfect fifth]] above 7 [[octave]]s, so the [[ploidacot]] for the temperament is zeta-enneacot, and from this it derives its name.

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

FloraC: Update & sorting

2026-07-05T07:29:13Z

Update & sorting

← Older revision		Revision as of 07:29, 5 July 2026
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	Temperaments discussed in families and clans are:		Temperaments discussed in families and clans are:
	* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]		* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]
			* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]
			* ''[[Mavling]]'' (+135/128) → [[Mavila family #Mavling\|Mavila family]]
			* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie\|Dicot family]]		* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie\|Dicot family]]
	* ''[[Opossum]]'' (+28/27) → [[Trienstonic clan #Opossum\|Trienstonic clan]]		* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic\|Diaschismic family]]
			* [[Augene]] (+64/63) → [[Augmented family #Augene\|Augmented family]]
			* [[Opossum]] (+28/27) → [[Trienstonic clan #Opossum\|Trienstonic clan]]
	* [[Diminished (temperament)\|Diminished]] (+36/35) → [[Diminished family #Septimal diminished\|Diminished family]]		* [[Diminished (temperament)\|Diminished]] (+36/35) → [[Diminished family #Septimal diminished\|Diminished family]]
			* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
			* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
			* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
	* [[Augene]] (+64/63) → [[Augmented family #Augene\|Augmented family]]
	* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]
	* [[Mavila]] (+135/128) → [[Pelogic family #Mavila\|Pelogic family]]
	* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]
	* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
	* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine\|Gamelismic clan]]
	* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic\|Diaschismic family]]
	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]
			* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine\|Gamelismic clan]]
			* ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee\|Mabila family]]
	* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja\|Buzzardsmic clan]]		* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja\|Buzzardsmic clan]]
	* ''[[~~Passionate~~]]'' (+~~131072~~/~~127575~~) → [[~~Passion~~ family #~~Passionate~~\|~~Passion~~ family]]		* ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton\|Ditonmic family]]
	* ''[[Vishnean]]'' (+540225/524288) → [[~~Vishnuzmic~~ family #Vishnean\|~~Vishnuzmic family]]~~		* ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean\|Vishnu family]]
	* ''[[Ditonic]]'' (+8751645/8388608) → [[Ditonmic family #Ditonic\|Ditonmic family]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[~~Muscogee~~]]'' (+~~33756345~~/~~33554432~~) → [[~~Mabila~~ family #~~Muscogee~~\|~~Mabila~~ family]]

	Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].		Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].

FloraC: Update

2026-06-25T11:01:21Z

Update

← Older revision		Revision as of 11:01, 25 June 2026
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	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]		* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family~~]] / [[Cloudy clan #Coblack\|cloudy clan~~]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]		* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]

Hkm at 05:55, 7 June 2026

2026-06-07T05:55:59Z

← Older revision		Revision as of 05:55, 7 June 2026
Line 28:		Line 28:
	Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].		Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].

	Since {{nowrap\|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord. 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 actually three stacked minor thirds and an augmented second, contrary to the popular belief that it is four stacked minor thirds.		Since {{nowrap\|(6/5)<sup>3</sup> {{=}} (126/125)⋅(12/7)}}, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5–6/5–6/5–7/6 versions of the diminished seventh chord.

	== Myna ==		== Myna ==

Xenllium at 10:17, 14 May 2026

2026-05-14T10:17:22Z

← Older revision		Revision as of 10:17, 14 May 2026
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	== Paraguay ==		== Paraguay ==
	: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''		: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''

			Named by [[User:Xenllium\|Xenllium]] in 2026, paraguay tempers out [[12005/11664]] and may be described as the {{nowrap\| 19 & 61 }} temperament. It is a variant of [[parakleismic]], mapping 7th harmonic to 16 generators.

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

Xenllium at 09:54, 14 May 2026

2026-05-14T09:54:08Z

← Older revision		Revision as of 09:54, 14 May 2026
Line 471:		Line 471:

	Badness (Sintel): 1.19		Badness (Sintel): 1.19

			== Paraguay ==
			: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Parakleismic]].''

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 126/125, 12005/11664

			{{Mapping\|legend=1\| 1 -8 -8 -9 \| 0 13 14 16 }}
			: mapping generators: ~2, ~5/3

			[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1200.6421{{c}}, ~5/3 = 885.3232{{c}}
			: [[error map]]: {{val\| +0.642 +2.110 +3.074 -9.434 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 884.8949{{c}}
			: error map: {{val\| 0.000 +1.678 +2.214 -10.508 }}

			{{Optimal ET sequence\|legend=1\| 19, 61, 80d, 99d }}

			[[Badness]] (Sintel): 2.47

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

			Comma list: 56/55, 100/99, 12005/11664

			Mapping: {{mapping\| 1 -8 -8 -9 2 \| 0 13 14 16 2 }}

			Optimal tunings:
			* WE: ~2 = 1197.7783{{c}}, ~5/3 = 883.6140{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1383{{c}}

			{{Optimal ET sequence\|legend=0\| 19, 42e, 61e }}

			Badness (Sintel): 2.49

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

			Comma list: 56/55, 91/90, 100/99, 343/338

			Mapping: {{mapping\| 1 -8 -8 -9 2 -14 \| 0 13 14 16 2 24 }}

			Optimal tunings:
			* WE: ~2 = 1197.7848{{c}}, ~5/3 = 883.6431{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.1623{{c}}

			{{Optimal ET sequence\|legend=0\| 19, 42ef, 61e }}

			Badness (Sintel): 1.86

			==== Uruguay ====
			Subgroup: 2.3.5.7.11.13

			Comma list: 56/55, 78/77, 100/99, 1183/1152

			Mapping: {{mapping\| 1 -8 -8 -9 2 0 \| 0 13 14 16 2 5 }}

			Optimal tunings:
			* WE: ~2 = 1199.6132{{c}}, ~5/3 = 884.7325{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 885.0005{{c}}

			{{Optimal ET sequence\|legend=0\| 19, 42e }}

			Badness (Sintel): 2.51

	== Bisemidim ==		== Bisemidim ==

← Older revision		Revision as of 07:29, 5 July 2026
Line 4:		Line 4:
	Temperaments discussed in families and clans are:		Temperaments discussed in families and clans are:
	* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]		* ''[[Pater]]'' (+16/15) → [[Father family #Pater\|Father family]]
			* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]
			* ''[[Mavling]]'' (+135/128) → [[Mavila family #Mavling\|Mavila family]]
			* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie\|Dicot family]]		* ''[[Flattie]]'' (+21/20) → [[Dicot family #Flattie\|Dicot family]]
	* ''[[Opossum]]'' (+28/27) → [[Trienstonic clan #Opossum\|Trienstonic clan]]		* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic\|Diaschismic family]]
			* [[Augene]] (+64/63) → [[Augmented family #Augene\|Augmented family]]
			* [[Opossum]] (+28/27) → [[Trienstonic clan #Opossum\|Trienstonic clan]]
	* [[Diminished (temperament)\|Diminished]] (+36/35) → [[Diminished family #Septimal diminished\|Diminished family]]		* [[Diminished (temperament)\|Diminished]] (+36/35) → [[Diminished family #Septimal diminished\|Diminished family]]
			* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
			* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
			* ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate\|Passion family]]
	* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]		* [[Keemun]] (+49/48) → [[Kleismic family #Keemun\|Kleismic family]]
	* [[Augene]] (+64/63) → [[Augmented family #Augene\|Augmented family]]
	* [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone\|Meantone family]]
	* [[Mavila]] (+135/128) → [[Pelogic family #Mavila\|Pelogic family]]
	* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]		* [[Sensi]] (+245/243), [[Sensipent family #Sensi\|Sensipent family]]
	* [[Muggles]] (+525/512) → [[Magic family #Muggles\|Magic family]]
	* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine\|Gamelismic clan]]
	* [[Diaschismic]] (+2048/2025) → [[Diaschismic family #Septimal diaschismic\|Diaschismic family]]
	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]
			* [[Valentine]] (+1029/1024) → [[Gamelismic clan #Valentine\|Gamelismic clan]]
			* ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee\|Mabila family]]
	* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja\|Buzzardsmic clan]]		* ''[[Thuja]]'' (+65536/64827) → [[Buzzardsmic clan #Thuja\|Buzzardsmic clan]]
	* ''[[~~Passionate~~]]'' (+~~131072~~/~~127575~~) → [[~~Passion~~ family #~~Passionate~~\|~~Passion~~ family]]		* ''[[Diton]]'' (+8751645/8388608) → [[Ditonmic family #Diton\|Ditonmic family]]
	* ''[[Vishnean]]'' (+540225/524288) → [[~~Vishnuzmic~~ family #Vishnean\|~~Vishnuzmic family]]~~		* ''[[Vishnean]]'' (+540225/524288) → [[Vishnu family #Vishnean\|Vishnu family]]
	* ''[[Ditonic]]'' (+8751645/8388608) → [[Ditonmic family #Ditonic\|Ditonmic family]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[~~Muscogee~~]]'' (+~~33756345~~/~~33554432~~) → [[~~Mabila~~ family #~~Muscogee~~\|~~Mabila~~ family]]

	Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].		Considered below are myna, nusecond, oolong, vines, kumonga, cypress, bisemidim, casablanca, amigo, gilead, supersensi, and cobalt, sorted by increasing [[badness]].

← Older revision		Revision as of 11:01, 25 June 2026
Line 17:		Line 17:
	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]		* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family~~]] / [[Cloudy clan #Coblack\|cloudy clan~~]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]		* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]