Biyatismic clan - Revision history

FloraC: /* Aphrodite */ fix heading levels

2026-04-25T03:43:09Z

Aphrodite: fix heading levels

← Older revision		Revision as of 03:43, 25 April 2026
Line 291:		Line 291:
	[[Badness]] (Sintel): 0.701		[[Badness]] (Sintel): 0.701

	==== Eros ====		=== Eros ===
	Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.		Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.

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	Badness (Sintel): 1.08		Badness (Sintel): 1.08

	===== 17-limit =====		==== 17-limit ====
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

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	Badness (Sintel): 0.931		Badness (Sintel): 0.931

	===== 19-limit =====		==== 19-limit ====
	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

Line 342:		Line 342:
	Badness (Sintel): 1.16		Badness (Sintel): 1.16

	===== 23-limit =====		==== 23-limit ====
	Subgroup: 2.3.5.7.11.13.17.19.23		Subgroup: 2.3.5.7.11.13.17.19.23

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	Badness (Sintel): 1.08		Badness (Sintel): 1.08

	==== Astarte ====		=== Astarte ===
	This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder.		This extension is catalogued as tridecimal aphrodite in [[Graham Breed]]'s temperament finder.

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	Badness (Sintel): 1.36		Badness (Sintel): 1.36

	==== Inanna ====		=== Inanna ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Line 389:		Line 389:
	Badness (Sintel): 1.01		Badness (Sintel): 1.01

	==== Ishtar ====		=== Ishtar ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

FloraC: /* Aphrodite */ 13-limit aphrodite -> astarte

2026-04-25T03:42:01Z

Aphrodite: 13-limit aphrodite -> astarte

@@ Line 290: / Line 290: @@
 [[Badness]] (Sintel): 0.701
 ==== Eros ====
@@ Line 371: / Line 356: @@
 Badness (Sintel): 1.08
 ==== Inanna ====

FloraC: /* Aphrodite */ rework

2025-12-01T14:35:14Z

Aphrodite: rework

← Older revision		Revision as of 14:35, 1 December 2025
Line 307:		Line 307:

	==== Eros ====		==== Eros ====
	Eros fairs impressively into the 23-limit as a rank 3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but ~~all the generators are positive (or only 1 into the negatives in the case of the fifth) meaning it's even simpler than it might appear and~~ has the pleasing property of all harmonics ~~and subharmonics being "~~on the ~~same~~ side~~"; specifically:~~ -3 to 1 fifths ~~([[2L 3s]])~~ and -5 to 0 ~[[23/22]]'s will ~~get you every prime,~~ up to octave equivalence; you can think of this as a ~~5 by 6~~ grid ~~if you like and~~ is a recommendable place to start looking at its structure. Tempering the less accurate comma [[121/120~~\|S11]]~~ can be seen as ~~a consequence~~ of tempering {[[441/440~~\|S21~~]], [[484/483~~\|S22~~]], [[529/528~~\|S23~~]]} ~~so is very natural and given its properties certainly excusable~~. Therefore characteristic of any good tuning is the ~11 being the ~~most flat~~ prime, with other primes having strictly less than 5{{cent}} of error. This temperament was ~~first logged on x31eq~~ by [[Scott Dakota]].		Eros fairs impressively into the 23-limit as a rank-3 temperament; not only is it fairly simple (considering this is a subgroup as complex as the full 23-limit, with many challenges) but has the pleasing property that all the harmonics are on the negative side of the last generator. Specifically, -3 to 2 fifths and -5 to 0 [[~]][[23/22]]'s will provide odd harmonics 1–23 up to octave equivalence; you can think of this as a 6×6 grid, which is a recommendable place to start looking at its structure.

			Tempering out the less accurate comma 121/120 can be seen as an implication of tempering out [[441/440]] ({{S\|21}}), [[484/483]] ({{S\|22}}), and [[529/528]] ({{S\|23}}). Therefore, characteristic of any good tuning is the prime [[11/1\|11]] being the flattest prime, with other primes having strictly less than 5{{cent}} of error.

			This temperament was discovered by [[Scott Dakota]]. Note that the 17-limit extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13
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	===== 17-limit =====		===== 17-limit =====
	~~Note that this extension requires the 29g val for 29edo, which has the sizes of 17/16 and 18/17 swapped.~~

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

FloraC at 13:51, 1 December 2025

2025-12-01T13:51:39Z

FloraC: Move kahoupokane here

2025-12-01T12:45:19Z

Move kahoupokane here

@@ Line 7: / Line 7: @@
 * ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector|Sensamagic family]]
-Considered below are zeus, artemis, oxpecker, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
+Considered below are zeus, artemis, oxpecker, kahoupokane, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].
 == Protomere ==
@@ Line 199: / Line 199: @@
 Badness (Sintel): 1.02
 == Big brother ==

FloraC: - redundant category

2025-12-01T12:40:13Z

- redundant category

← Older revision		Revision as of 12:40, 1 December 2025
Line 370:		Line 370:
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Biyatismic clan\| ]] <!-- main article -->		[[Category:Biyatismic clan\| ]] <!-- main article -->
	~~[[Category:Biyatismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - CTE & POTE tunings

2025-12-01T12:37:37Z

- CTE & POTE tunings

← Older revision		Revision as of 12:37, 1 December 2025
Line 22:		Line 22:
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11/10 = 157.6099{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11/10 = 157.6099{{c}}
	: error map: {{val\| 0.000 +0.030 +0.451 -6.943 }}		: error map: {{val\| 0.000 +0.030 +0.451 -6.943 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4578{{c}}, ~11/10 = 157.7466{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}		{{Optimal ET sequence\|legend=1\| 7, 15, 22, 31, 46, 53, 137e, 183ee, 190ee }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~11/10 = 157.1265{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~11/10 = 157.1265{{c}}
	: error map: {{val\| 0.000 +0.293 +1.681 +0.306 -6.197 }}		: error map: {{val\| 0.000 +0.293 +1.681 +0.306 -6.197 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1530{{c}}, ~11/10 = 157.0881{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
Line 88:		Line 86:
	* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~11/10 = 156.9897{{c}}		* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~11/10 = 156.9897{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~11/10 = 156.9568{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~11/10 = 156.9568{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8679{{c}}, ~11/10 = 156.9582{{c}} -->~~

	Minimax tuning:		Minimax tuning:
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	* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~11/10 = 155.3569{{c}}		* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~11/10 = 155.3569{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~11/10 = 155.3484{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~11/10 = 155.3484{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 699.3420{{c}}, ~11/10 = 155.3666{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 7, 9, 15, 22f, 24, 31 }}		{{Optimal ET sequence\|legend=0\| 7, 9, 15, 22f, 24, 31 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.2777{{c}}, ~11/10 = 158.3100{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.2777{{c}}, ~11/10 = 158.3100{{c}}
	: error map: {{val\| 0.000 -1.677 -2.656 -0.955 -9.350 }}		: error map: {{val\| 0.000 -1.677 -2.656 -0.955 -9.350 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.8719{{c}}, ~11/10 = 158.3232{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee }}		{{Optimal ET sequence\|legend=1\| 9, 15d, 16d, 20, 22, 31, 53, 60e, 84e, 91e, 113e, 144ee }}
Line 153:		Line 148:
	* WE: ~2 = 1201.7896{{c}}, ~3/2 = 699.7509{{c}}, ~11/10 = 158.9484{{c}}		* WE: ~2 = 1201.7896{{c}}, ~3/2 = 699.7509{{c}}, ~11/10 = 158.9484{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.1687{{c}}, ~11/10 = 158.7345{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.1687{{c}}, ~11/10 = 158.7345{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 698.7090{{c}}, ~11/10 = 158.7117{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 9, 20, 22f, 29, 31, 60e, 129cddee }}		{{Optimal ET sequence\|legend=0\| 9, 20, 22f, 29, 31, 60e, 129cddee }}
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	* WE: ~2 = 1200.9110{{c}}, ~3/2 = 701.5110{{c}}, ~11/10 = 159.1256{{c}}		* WE: ~2 = 1200.9110{{c}}, ~3/2 = 701.5110{{c}}, ~11/10 = 159.1256{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9717{{c}}, ~11/10 = 158.7903{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9717{{c}}, ~11/10 = 158.7903{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.9789{{c}}, ~11/10 = 159.0048{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 22, 29, 31, 53, 82e, 84e, 113e }}		{{Optimal ET sequence\|legend=0\| 22, 29, 31, 53, 82e, 84e, 113e }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~11/10 = 155.7399{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~11/10 = 155.7399{{c}}
	: error map: {{val\| 0.000 -0.719 +3.442 -2.029 -5.822 }}		: error map: {{val\| 0.000 -0.719 +3.442 -2.029 -5.822 }}
	~~<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 700.8882{{c}}, ~11/10 = 155.7756{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}		{{Optimal ET sequence\|legend=1\| 7d, 8d, 15, 23de, 24d, 31, 46, 77 }}
Line 203:		Line 195:
	* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~11/10 = 154.7247{{c}}		* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~11/10 = 154.7247{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~11/10 = 154.9115{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~11/10 = 154.9115{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5946{{c}}, ~11/10 = 154.8652{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 7d, 8d, 15, 23de, 24d, 31 }}		{{Optimal ET sequence\|legend=0\| 7d, 8d, 15, 23de, 24d, 31 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8990{{c}}, ~22/21 = 78.4412{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.8990{{c}}, ~22/21 = 78.4412{{c}}
	: error map: {{val\| 0.000 -1.056 +0.820 -4.150 -7.301 }}		: error map: {{val\| 0.000 -1.056 +0.820 -4.150 -7.301 }}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.3200{{c}}, ~22/21 = 78.6421{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}		{{Optimal ET sequence\|legend=1\| 14c, 15, 29, 31, 46, 60e, 77, 91e, 137de, 168dee }}
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	* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}		* WE: ~2 = 1201.0656{{c}}, ~3/2 = 700.7374{{c}}, ~22/21 = 78.5908{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.7005{{c}}, ~22/21 = 78.3253{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 700.1158{{c}}, ~21/20 = 78.5211{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}		{{Optimal ET sequence\|legend=0\| 14cf, 29ff, 31, 45ef, 46, 77, 122ee, 137def, 168deef }}
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	* WE: ~2 = 1200.6419{{c}}, ~3/2 = 701.8766{{c}}, ~22/21 = 78.6564{{c}}		* WE: ~2 = 1200.6419{{c}}, ~3/2 = 701.8766{{c}}, ~22/21 = 78.6564{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5612{{c}}, ~22/21 = 78.4778{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5612{{c}}, ~22/21 = 78.4778{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5014{{c}}, ~21/20 = 78.6143{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}		{{Optimal ET sequence\|legend=0\| 17c, 29, 31, 46, 60e, 77, 106de, 183dee }}
Line 313:		Line 301:
	* WE: ~2 = 1200.6172{{c}}, ~3/2 = 702.1026{{c}}, ~22/21 = 78.7963{{c}}		* WE: ~2 = 1200.6172{{c}}, ~3/2 = 702.1026{{c}}, ~22/21 = 78.7963{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7925{{c}}, ~22/21 = 78.6203{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7925{{c}}, ~22/21 = 78.6203{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9299{{c}}, ~22/21 = 78.2539{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 77, 106de }}		{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 77, 106de }}
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	* WE: ~2 = 1200.6224{{c}}, ~3/2 = 702.0959{{c}}, ~22/21 = 78.8004{{c}}		* WE: ~2 = 1200.6224{{c}}, ~3/2 = 702.0959{{c}}, ~22/21 = 78.8004{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6963{{c}}, ~22/21 = 78.6479{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6963{{c}}, ~22/21 = 78.6479{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5642{{c}}, ~22/21 = 78.2353{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}		{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
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	* WE: ~2 = 1200.7268{{c}}, ~3/2 = 702.2463{{c}}, ~22/21 = 78.8824{{c}}		* WE: ~2 = 1200.7268{{c}}, ~3/2 = 702.2463{{c}}, ~22/21 = 78.8824{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8010{{c}}, ~23/22 = 78.7188{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8010{{c}}, ~23/22 = 78.7188{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7115{{c}}, ~23/22 = 78.2054{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}		{{Optimal ET sequence\|legend=0\| 17cg, 29g, 31, 46, 60e, 75dfgh, 77, 106de }}
Line 361:		Line 346:
	* WE: ~2 = 1201.7881{{c}}, ~3/2 = 699.8166{{c}}, ~22/21 = 79.7282{{c}}		* WE: ~2 = 1201.7881{{c}}, ~3/2 = 699.8166{{c}}, ~22/21 = 79.7282{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5926{{c}}, ~22/21 = 79.3822{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5926{{c}}, ~22/21 = 79.3822{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 698.7754{{c}}, ~21/20 = 79.6096{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14cf, 15, 29, 31, 45ef, 60e }}		{{Optimal ET sequence\|legend=0\| 14cf, 15, 29, 31, 45ef, 60e }}
Line 377:		Line 361:
	* WE: ~2 = 1200.7875{{c}}, ~3/2 = 703.8568{{c}}, ~22/21 = 79.0096{{c}}		* WE: ~2 = 1200.7875{{c}}, ~3/2 = 703.8568{{c}}, ~22/21 = 79.0096{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7640{{c}}, ~22/21 = 78.8025{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7640{{c}}, ~22/21 = 78.8025{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3952{{c}}, ~21/20 = 78.9578{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}		{{Optimal ET sequence\|legend=0\| 14cf, 15, 17c, 29, 31f, 46, 106deff, 121def }}

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

2025-12-01T12:36:45Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

FloraC: Update the catalog

2025-11-30T13:47:20Z

Update the catalog

← Older revision		Revision as of 13:47, 30 November 2025
Line 5:		Line 5:
	* ''[[Sonic]]'' (+55/54 or 100/99) → [[Porcupine rank-3 family #Sonic\|Porcupine rank-3 family]]		* ''[[Sonic]]'' (+55/54 or 100/99) → [[Porcupine rank-3 family #Sonic\|Porcupine rank-3 family]]
	* ''[[Urania]]'' (+81/80) → [[Rastmic rank-3 clan #Urania\|Rastmic rank-3 clan]]		* ''[[Urania]]'' (+81/80) → [[Rastmic rank-3 clan #Urania\|Rastmic rank-3 clan]]
	* ''[[Big brother]]'' (+99/98) → [[Nuwell family #big Brother\|Nuwell family]]
	* ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector\|Sensamagic family]]		* ''[[Bisector]]'' (+245/243) → [[Sensamagic family #Bisector\|Sensamagic family]]

	Considered below are zeus, artemis, oxpecker, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].		Considered below are zeus, artemis, oxpecker, big brother, aphrodite, and the no-7 subgroup temperament, protomere. For the rank-4 biyatismic temperament, see [[Rank-4 temperament #Biyatismic (121/120)]].

	== Protomere ==		== Protomere ==

FloraC: Move big brother here and move squalentine to the misc. page.

2025-11-30T13:15:08Z

Move big brother here and move squalentine to the misc. page.

← Older revision		Revision as of 13:15, 30 November 2025
Line 169:		Line 169:
	Badness (Smith): 1.093 × 10<sup>-3</sup>		Badness (Smith): 1.093 × 10<sup>-3</sup>

	== ~~Aphrodite~~ ==		== Big brother ==
	~~Aphrodite tempers out~~ the ~~squalentine comma, 64827/64000~~, ~~in the~~ 7-limit. ~~Its generators can be taken to be~~ 2, 3~~, and 21~~/20, ~~and it equates (21~~/~~20)<sup>~~3~~</sup> with 8/7.~~		: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Nuwell]].''

			[[Subgroup]]: 2.3.5.7.11

			[[Comma list]]: 99/98, 121/120

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

			{{Optimal ET sequence\|legend=1\| 8d, 9, 22, 31, 53 }}

	~~=== 7-limit (squalentine) ===~~		[[Badness]]: 0.507 × 10<sup>-3</sup>
	[[~~Subgroup~~]]: 2.3~~.5.7~~

	[[~~Comma list~~]]: ~~64827~~/~~64000~~		[[Projection pair]]s: 5 2401/486 11 98/9 to 2.3.7

	~~{{Mapping\|legend~~=~~1\| 1 0 1 3 \| 0 1 1 0 \| 0 0~~ -~~4 -3 }}~~		=== 13-limit ===
	: ~~mapping generators: ~~~2~~, ~~~3~~, ~21/20~~		Subgroup: 2.3.5.7.11.13

	~~[[Optimal tuning]] ([[POTE]])~~: ~~~2 = 1200.0000{{c}}~~, ~3/~~2 = 700.2144{{c}}~~, ~~~21~~/~~20 = 78.5694{{c}}~~		Comma list: 66/65, 99/98, 121/120

	{{~~Optimal ET sequence~~\|~~legend=~~1\| ~~14c, 15, 29, 31, 46, 60, 77, 91, 122, 137d, 168d~~ }}		Mapping: {{mapping\| 1 0 3 1 3 1 \| 0 1 3 2 2 0 \| 0 0 -4 -1 -2 2 }}

	~~[[Badness]] (Smith):~~ 0~~.943 × 10<sup>-3</sup>~~		{{Optimal ET sequence\|legend=0\| 8d, 9, 22f, 31 }}

	[[~~Projection pair~~]]~~s: 5 320000/64827 7 64000/9261 to 2~~.~~3.7/5~~		== Aphrodite ==
			: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Squalentine]].''

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

← Older revision		Revision as of 13:51, 1 December 2025
Line 20:		Line 20:
	* [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}		* [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}
	: [[error map]]: {{val\| +0.663 +0.553 +1.190 -5.318 }}		: [[error map]]: {{val\| +0.663 +0.553 +1.190 -5.318 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11~~/10~~ = 157.6099{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~12/11 = 157.6099{{c}}
	: error map: {{val\| 0.000 +0.030 +0.451 -6.943 }}		: error map: {{val\| 0.000 +0.030 +0.451 -6.943 }}

Line 44:		Line 44:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~11~~/10~~ = 157.1102{{c}}		* [[WE]]: ~2 = 1200.1693{{c}}, ~3/2 = 702.2521{{c}}, ~12/11 = 157.1102{{c}}
	: [[error map]]: {{val\| +0.169 +0.466 +2.057 +0.761 -5.668 }}		: [[error map]]: {{val\| +0.169 +0.466 +2.057 +0.761 -5.668 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~11~~/10~~ = 157.1265{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2478{{c}}, ~12/11 = 157.1265{{c}}
	: error map: {{val\| 0.000 +0.293 +1.681 +0.306 -6.197 }}		: error map: {{val\| 0.000 +0.293 +1.681 +0.306 -6.197 }}

Line 84:		Line 84:

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~11~~/10~~ = 156.9897{{c}}		* WE: ~2 = 1200.2411{{c}}, ~3/2 = 702.0090{{c}}, ~12/11 = 156.9897{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~11~~/10~~ = 156.9568{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8818{{c}}, ~12/11 = 156.9568{{c}}

	Minimax tuning:		Minimax tuning:
Line 112:		Line 112:

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~11~~/10~~ = 155.3569{{c}}		* WE: ~2 = 1199.9251{{c}}, ~3/2 = 699.2984{{c}}, ~12/11 = 155.3569{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~11~~/10~~ = 155.3484{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.2982{{c}}, ~12/11 = 155.3484{{c}}

	{{Optimal ET sequence\|legend=0\| 7, 9, 15, 22f, 24, 31 }}		{{Optimal ET sequence\|legend=0\| 7, 9, 15, 22f, 24, 31 }}
Line 176:		Line 176:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~11~~/10~~ = 155.8292{{c}}		* [[WE]]: ~2 = 1200.4124{{c}}, ~3/2 = 701.1291{{c}}, ~12/11 = 155.8292{{c}}
	: [[error map]]: {{val\| +0.412 -0.414 +3.982 -1.435 -4.781 }}		: [[error map]]: {{val\| +0.412 -0.414 +3.982 -1.435 -4.781 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~11~~/10~~ = 155.7399{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2359{{c}}, ~12/11 = 155.7399{{c}}
	: error map: {{val\| 0.000 -0.719 +3.442 -2.029 -5.822 }}		: error map: {{val\| 0.000 -0.719 +3.442 -2.029 -5.822 }}

Line 193:		Line 193:

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~11~~/10~~ = 154.7247{{c}}		* WE: ~2 = 1198.9113{{c}}, ~3/2 = 700.9581{{c}}, ~12/11 = 154.7247{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~11~~/10~~ = 154.9115{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.6409{{c}}, ~12/11 = 154.9115{{c}}

	{{Optimal ET sequence\|legend=0\| 7d, 8d, 15, 23de, 24d, 31 }}		{{Optimal ET sequence\|legend=0\| 7d, 8d, 15, 23de, 24d, 31 }}