Olympic clan - Revision history

FloraC: /* Orthoschismic */ there's a problem here

2026-05-29T09:01:04Z

Orthoschismic: there's a problem here

← Older revision		Revision as of 09:01, 29 May 2026
Line 38:		Line 38:
	Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval\|prime]] [[7/1\|7]], extended to the 11-limit in one of the most efficient ways possible.		Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval\|prime]] [[7/1\|7]], extended to the 11-limit in one of the most efficient ways possible.

	Orthoschismic can be ~~easily~~ notated with [[chain-of-fifths notation]] with two additional set of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[garischisma]] and the [[aberschisma]].		Orthoschismic can be notated with [[chain-of-fifths notation]] with two additional set of accidentals, one for the generic comma step (one should choose whether this step represents the syntonic comma, which is more characteristic in schismic, or the septimal comma, which is more characteristic in [[olympic]]), and the other for the generic aberschisma step which stands in for the [[garischisma]] and the [[aberschisma]].

	It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English\|ortho-]] to signify the additional rank.		It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English\|ortho-]] to signify the additional rank.

FloraC: /* Orthoschismic */ same notation as cassaschismic

2026-05-29T08:09:15Z

Orthoschismic: same notation as cassaschismic

← Older revision		Revision as of 08:09, 29 May 2026
Line 37:		Line 37:
	== Orthoschismic ==		== Orthoschismic ==
	Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval\|prime]] [[7/1\|7]], extended to the 11-limit in one of the most efficient ways possible.		Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval\|prime]] [[7/1\|7]], extended to the 11-limit in one of the most efficient ways possible.

			Orthoschismic can be easily notated with [[chain-of-fifths notation]] with two additional set of accidentals, one for the generic comma step, and the other for the generic aberschisma step which stands in for the [[garischisma]] and the [[aberschisma]].

	It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English\|ortho-]] to signify the additional rank.		It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English\|ortho-]] to signify the additional rank.

FloraC: Update

2026-05-18T08:30:23Z

Update

← Older revision		Revision as of 08:30, 18 May 2026
Line 27:		Line 27:
	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea\|Hemifamity family]]		* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea\|Hemifamity family]]
	* ''[[Cassaschismic]]'' (+19712/19683) → [[Garischismic family #Cassaschismic\|Garischismic family]]		* [[Cassaschismic]] (+19712/19683) → [[Garischismic family #Cassaschismic\|Garischismic family]]
	* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal\|Kalismic temperaments]]		* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal\|Kalismic temperaments]]
	* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif\|Breed family]]		* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif\|Breed family]]

FloraC: Intro to all three entries here

2026-03-14T09:11:02Z

Intro to all three entries here

← Older revision		Revision as of 09:11, 14 March 2026
Line 36:		Line 36:

	== Orthoschismic ==		== Orthoschismic ==
			Orthoschismic is related to [[schismic]], but with an additional generator for [[prime interval\|prime]] [[7/1\|7]], extended to the 11-limit in one of the most efficient ways possible.

			It was named by [[Flora Canou]] in 2023, using the Greek prefix [[wiktionary: ortho- #English\|ortho-]] to signify the additional rank.

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

Line 69:		Line 73:
	== Baffin ==		== Baffin ==
	: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Decovulture]].''		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Decovulture]].''

			Baffin tempers out [[5632/5625]] and [[160083/160000]] in addition to the olympia, so that the [[3/1\|3rd]] [[harmonic]] is split in halves. This leads naturally to a [[13-limit]] temperament where [[676/675]], [[1001/1000]], [[2080/2079]] and [[4096/4095]] are all tempered out.

			It was named by [[Gene Ward Smith]] some time before 2011 for {{w\|Baffin Island}}, as part of a series of island-themed names<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96550.html#96556 Yahoo! Tuning Group \| ''Madagascar<nowiki>[</nowiki>19<nowiki>]</nowiki>'']</ref>.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
Line 105:		Line 113:

	== Sophia ==		== Sophia ==
			Named by [[Scott Dakota]] in 2022, sophia tempers out [[42875/42768]], and by virtue of the identity 42875/42768 = ([[595/594]])⋅([[1225/1224]]), it is naturally a [[17-limit]] temperament.

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

Line 151:		Line 161:

	Badness (Sintel): 0.940		Badness (Sintel): 0.940

			== References ==

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Olympic clan\| ]] <!-- main article -->		[[Category:Olympic clan\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2026-02-06T12:42:18Z

Move 7-limit parents to a dedicated collection page

← Older revision		Revision as of 12:42, 6 February 2026
Line 68:		Line 68:

	== Baffin ==		== Baffin ==
	~~===~~ 7-limit ~~(decovulture) ===~~		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Decovulture]].''
	[[~~Subgroup~~]]~~: 2.3.5~~.7

	~~[[Comma list]]: 67108864/66976875~~

	~~{{Mapping\|legend=1\| 1 0 0 13 \| 0 2 0 -7 \| 0 0 1 -2 }}~~
	~~: mapping generators: ~2, ~8192/4725, ~5~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1199.9033{{c}}, ~8192/4725 = 951.0102{{c}}, ~5/4 = 386.5872{{c}}
	~~: [[error map]]: {{val\| -0.097 +0.065 +0.080 +0.059 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8192/4725 = 951.0899{{c}}, ~5/4 = 386.6184{{c}}
	~~: error map: {{val\| 0.000 +0.225 +0.305 +0.308 }}~~

	~~{{Optimal ET sequence\|legend=1\| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }}~~

	~~[[Badness]] (Sintel): 3.82~~

	~~=== 11-limit ===~~
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

Line 100:		Line 83:
	: error map: {{val\| 0.000 +0.172 +0.463 +0.176 +0.044 }}		: error map: {{val\| 0.000 +0.172 +0.463 +0.176 +0.044 }}

	{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}		{{Optimal ET sequence\|legend=1\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}

	[[Badness]] (Sintel): 1.17		[[Badness]] (Sintel): 1.17

FloraC: - redundant category

2026-02-06T12:38:36Z

- redundant category

← Older revision		Revision as of 12:38, 6 February 2026
Line 171:		Line 171:
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Olympic clan\| ]] <!-- main article -->		[[Category:Olympic clan\| ]] <!-- main article -->
	~~[[Category:Olympic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - CTE & POTE tunings

2026-02-06T12:37:54Z

- CTE & POTE tunings

← Older revision		Revision as of 12:37, 6 February 2026
Line 17:		Line 17:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0853{{c}}, ~7/4 = 969.0242{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0853{{c}}, ~7/4 = 969.0242{{c}}
	: error map: {{val\| 0.000 +0.130 +0.198 +0.207 }}		: error map: {{val\| 0.000 +0.130 +0.198 +0.207 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0805{{c}}, ~7/4 = 969.0275{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }}		{{Optimal ET sequence\|legend=1\| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }}
Line 48:		Line 47:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7248{{c}}, ~7/4 = 969.6728{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7248{{c}}, ~7/4 = 969.6728{{c}}
	: error map: {{val\| 0.000 -0.230 -0.112 +0.847 +0.713 }}		: error map: {{val\| 0.000 -0.230 -0.112 +0.847 +0.713 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7405{{c}}, ~7/4 = 969.6950{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}		{{Optimal ET sequence\|legend=1\| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}
Line 64:		Line 62:
	* WE: ~2 = 1199.9399{{c}}, ~3/2 = 701.6899{{c}}, ~7/4 = 969.6107{{c}}		* WE: ~2 = 1199.9399{{c}}, ~3/2 = 701.6899{{c}}, ~7/4 = 969.6107{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7264{{c}}, ~7/4 = 969.6672{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7264{{c}}, ~7/4 = 969.6672{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7333{{c}}, ~7/4 = 969.7085{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}		{{Optimal ET sequence\|legend=0\| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}
Line 84:		Line 81:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~8192/4725 = 951.0899{{c}}, ~5/4 = 386.6184{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~8192/4725 = 951.0899{{c}}, ~5/4 = 386.6184{{c}}
	: error map: {{val\| 0.000 +0.225 +0.305 +0.308 }}		: error map: {{val\| 0.000 +0.225 +0.305 +0.308 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8192/4725 = 951.0868{{c}}, ~5/4 = 386.6183{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }}		{{Optimal ET sequence\|legend=1\| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }}
Line 103:		Line 99:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.0635{{c}}, ~5/4 = 386.7769{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.0635{{c}}, ~5/4 = 386.7769{{c}}
	: error map: {{val\| 0.000 +0.172 +0.463 +0.176 +0.044 }}		: error map: {{val\| 0.000 +0.172 +0.463 +0.176 +0.044 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~400/231 = 951.0585{{c}}, ~5/4 = 386.7912{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}		{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}
Line 119:		Line 114:
	* WE: ~2 = 1199.9633{{c}}, ~400/231 = 951.0591{{c}}, ~5/4 = 386.7388{{c}}		* WE: ~2 = 1199.9633{{c}}, ~400/231 = 951.0591{{c}}, ~5/4 = 386.7388{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.0896{{c}}, ~5/4 = 386.7451{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~400/231 = 951.0896{{c}}, ~5/4 = 386.7451{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~26/15 = 951.0882{{c}}, ~5/4 = 386.7507{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}		{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}
Line 140:		Line 134:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3025{{c}}, ~256/245 = 77.1949{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3025{{c}}, ~256/245 = 77.1949{{c}}
	: error map: {{val\| 0.000 +0.347 -0.339 -0.411 +0.339 }}		: error map: {{val\| 0.000 +0.347 -0.339 -0.411 +0.339 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3024{{c}}, ~256/245 = 77.1952{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 46, 94, 140, 171, 217, 311, 979, 1290 }}		{{Optimal ET sequence\|legend=1\| 46, 94, 140, 171, 217, 311, 979, 1290 }}
Line 156:		Line 149:
	* WE: ~2 = 1199.9732{{c}}, ~3/2 = 702.3162{{c}}, ~117/112 = 77.2135{{c}}		* WE: ~2 = 1199.9732{{c}}, ~3/2 = 702.3162{{c}}, ~117/112 = 77.2135{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3335{{c}}, ~117/112 = 77.2145{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3335{{c}}, ~117/112 = 77.2145{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3319{{c}}, ~117/112 = 77.2152{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }}		{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }}
Line 172:		Line 164:
	* WE: ~2 = 1199.9956{{c}}, ~3/2 = 702.3179{{c}}, ~68/65 = 77.2252{{c}}		* WE: ~2 = 1199.9956{{c}}, ~3/2 = 702.3179{{c}}, ~68/65 = 77.2252{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3207{{c}}, ~68/65 = 77.2254{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3207{{c}}, ~68/65 = 77.2254{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3205{{c}}, ~68/65 = 77.2255{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g }}		{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g }}

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

2026-02-06T12:36:53Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-02-05T19:40:02Z

Units & misc. cleanup

← Older revision		Revision as of 19:40, 5 February 2026
Line 10:		Line 10:

	{{Mapping\|legend=2\| 1 0 0 17 \| 0 1 0 -5 \| 0 0 1 -2 }}		{{Mapping\|legend=2\| 1 0 0 17 \| 0 1 0 -5 \| 0 0 1 -2 }}
			: mapping generators: ~2, ~3, ~7

	~~: sval mapping generators: ~2, ~3, ~7~~		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0805{{c}}, ~7/4 = 969.0275{{c}}

	[[Optimal tuning]] ([[POTE]]): ~3/2 = 702.0805, ~7/4 = 969.0275

	{{Optimal ET sequence\|legend=1\| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }}		{{Optimal ET sequence\|legend=1\| 41, 87, 89, 94, 130, 135, 359, 400, 494, 535, 670, 805, 1164, 1299, 1834, 1969, 5102bde, 5237bde, 7206bddee, 10339bbdddeee }}

	[[Badness]]: 0.0183 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.0183 × 10<sup>-3</sup>

	=== Overview to extensions ===		=== Overview to extensions ===
Line 39:		Line 38:
	{{Mapping\|legend=1\| 1 0 15 0 17 \| 0 1 -8 0 -5 \| 0 0 0 1 -2 }}		{{Mapping\|legend=1\| 1 0 15 0 17 \| 0 1 -8 0 -5 \| 0 0 0 1 -2 }}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.7405, ~7/4 = 969.6950		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.7405{{c}}, ~7/4 = 969.6950{{c}}

	{{Optimal ET sequence\|legend=1\| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}		{{Optimal ET sequence\|legend=1\| 41, 53, 89, 94, 130, 183, 224, 354, 537, 578, 761d, 985d, 1115de }}

	[[Badness]]: 1.18 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.18 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 52:		Line 51:
	Mapping: {{mapping\| 1 0 15 0 17 -3 \| 0 1 -8 0 -5 6 \| 0 0 0 1 -2 -1 }}		Mapping: {{mapping\| 1 0 15 0 17 -3 \| 0 1 -8 0 -5 6 \| 0 0 0 1 -2 -1 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~3/2 = 701.7333, ~7/4 = 969.7085		Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.7333{{c}}, ~7/4 = 969.7085{{c}}

	{{Optimal ET sequence\|legend=1\| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}		{{Optimal ET sequence\|legend=0\| 41, 53, 89, 94, 130, 183, 224, 354, 578, 985d }}

	Badness: 0.833 × 10<sup>-3</sup>		Badness (Smith): 0.833 × 10<sup>-3</sup>

	== Baffin ==		== Baffin ==
Line 65:		Line 64:

	{{Mapping\|legend=1\| 1 0 0 13 \| 0 2 0 -7 \| 0 0 1 -2 }}		{{Mapping\|legend=1\| 1 0 0 13 \| 0 2 0 -7 \| 0 0 1 -2 }}

	: mapping generators: ~2, ~8192/4725, ~5		: mapping generators: ~2, ~8192/4725, ~5

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~8192/4725 = 951.0868, ~5/4 = 386.6183		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8192/4725 = 951.0868{{c}}, ~5/4 = 386.6183{{c}}

	{{Optimal ET sequence\|legend=1\| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }}		{{Optimal ET sequence\|legend=1\| 10, 19d, 24, 34, 43, 53, 87, 130, 183, 217, 270, 593, 863, 1133, 1856cd, 2126cd, 2719cd, 2989bcd }}

	[[Badness]]: 0.865 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.865 × 10<sup>-3</sup>

	=== 11-limit ===		=== 11-limit ===
Line 81:		Line 79:
	{{Mapping\|legend=1\| 1 0 0 13 -9 \| 0 2 0 -7 4 \| 0 0 1 -2 4 }}		{{Mapping\|legend=1\| 1 0 0 13 -9 \| 0 2 0 -7 4 \| 0 0 1 -2 4 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~400/231 = 951.0585, ~5/4 = 386.7912		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~400/231 = 951.0585{{c}}, ~5/4 = 386.7912{{c}}

	{{Optimal ET sequence\|legend=1\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}		{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 270, 670, 940, 1210, 2063c }}

	[[Badness]]: 0.976 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.976 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 94:		Line 92:
	Mapping: {{mapping\| 1 0 0 13 -9 1 \| 0 2 0 -7 4 3 \| 0 0 1 -2 4 1 }}		Mapping: {{mapping\| 1 0 0 13 -9 1 \| 0 2 0 -7 4 3 \| 0 0 1 -2 4 1 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~26/15 = 951.0882, ~5/4 = 386.7507		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~26/15 = 951.0882{{c}}, ~5/4 = 386.7507{{c}}

	{{Optimal ET sequence\|legend=1\| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}		{{Optimal ET sequence\|legend=0\| 34, 43, 53, 87, 130, 183, 217, 270, 940, 1210f }}

	Badness: 0.604 × 10<sup>-3</sup>		Badness (Smith): 0.604 × 10<sup>-3</sup>

	Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11		Complexity spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11
Line 109:		Line 107:
	{{Mapping\|legend=1\| 1 0 2 3 11 \| 0 1 0 0 -5 \| 0 0 5 -3 6 }}		{{Mapping\|legend=1\| 1 0 2 3 11 \| 0 1 0 0 -5 \| 0 0 5 -3 6 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 702.3024, ~256/245 = 77.1952		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.3024{{c}}, ~256/245 = 77.1952{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 94, 140, 171, 217, 311, 979, 1290 }}		{{Optimal ET sequence\|legend=1\| 46, 94, 140, 171, 217, 311, 979, 1290 }}

	[[Badness]]: 3.78 × 10<sup>-3</sup>		[[Badness]] (Smith): 3.78 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
Line 122:		Line 120:
	Mapping: {{mapping\| 1 0 2 3 11 7 \| 0 1 0 0 -5 -2 \| 0 0 5 -3 6 -2 }}		Mapping: {{mapping\| 1 0 2 3 11 7 \| 0 1 0 0 -5 -2 \| 0 0 5 -3 6 -2 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 702.3319, ~117/112 = 77.2152		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.3319{{c}}, ~117/112 = 77.2152{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }}		{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 979, 1290 }}

	Badness: 1.67 × 10<sup>-3</sup>		Badness (Smith): 1.67 × 10<sup>-3</sup>

	=== 17-limit ===		=== 17-limit ===
Line 135:		Line 133:
	Mapping: {{mapping\| 1 0 2 3 11 7 7 \| 0 1 0 0 -5 -2 -2 \| 0 0 5 -3 6 -2 4 }}		Mapping: {{mapping\| 1 0 2 3 11 7 7 \| 0 1 0 0 -5 -2 -2 \| 0 0 5 -3 6 -2 4 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 702.3205, ~68/65 = 77.2255		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.3205{{c}}, ~68/65 = 77.2255{{c}}

	{{Optimal ET sequence\|legend=1\| 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g }}		{{Optimal ET sequence\|legend=0\| 46, 77e, 94, 140, 171, 217, 311, 668, 839e, 979g }}

	Badness: 0.989 × 10<sup>-3</sup>		Badness (Smith): 0.989 × 10<sup>-3</sup>

	[[Category:Temperament clans]]		[[Category:Temperament clans]]

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

2025-11-27T12:27:09Z

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

← Older revision		Revision as of 12:27, 27 November 2025
Line 142:		Line 142:

	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Olympic clan\| ]] <!-- main article -->		[[Category:Olympic clan\| ]] <!-- main article -->
	[[Category:Olympic\| ]] <!-- key article -->		[[Category:Olympic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

← Older revision		Revision as of 08:30, 18 May 2026
Line 27:		Line 27:
	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea\|Hemifamity family]]		* ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea\|Hemifamity family]]
	* ''[[Cassaschismic]]'' (+19712/19683) → [[Garischismic family #Cassaschismic\|Garischismic family]]		* [[Cassaschismic]] (+19712/19683) → [[Garischismic family #Cassaschismic\|Garischismic family]]
	* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal\|Kalismic temperaments]]		* ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal\|Kalismic temperaments]]
	* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif\|Breed family]]		* ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif\|Breed family]]