Very high accuracy temperaments - Revision history

FloraC: /* Rank-3 temperaments */ move akjaysmic here

2026-05-30T08:59:29Z

Rank-3 temperaments: move akjaysmic here

@@ Line 489: / Line 489: @@
 = Rank-3 temperaments =
 == Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
 [[Subgroup]]: 2.3.5.7

FloraC: - septimal atomic (addressed in landscape microtemps). Rework on intro to the 5-limit temp.

2026-04-24T11:42:00Z

- septimal atomic (addressed in landscape microtemps). Rework on intro to the 5-limit temp.

@@ Line 390: / Line 390: @@
 == Atomic ==
-{{See also | Kirnberger's atom }}
+: ''For extensions, see [[Landscape microtemperaments #Atomic]].''
-Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.
+Atomic tempers out [[Kirnberger's atom]], the microscopic interval separating eleven [[schisma]]s and a [[syntonic comma]], or twelfth schismas and a [[Pythagorean comma]]. It is a member of the [[schismic–commatic equivalence continuum]] with {{nowrap| ''n'' {{=}} 12 }}. In this extremely accurate temperament, the [[3/2|perfect fifth]] is one [[schisma]] sharp of its [[12edo]] value.
 [[Subgroup]]: 2.3.5
@@ Line 412: / Line 410: @@
 [[Badness]] (Sintel): 0.0892
 == Revopentic ==

Xenllium at 05:45, 14 March 2026

2026-03-14T05:45:53Z

← Older revision		Revision as of 05:45, 14 March 2026
Line 534:		Line 534:
	[[Badness]] (Sintel): 1.24		[[Badness]] (Sintel): 1.24

	== ~~Saquadtrizo~~-~~asepgu (171~~ & ~~2019~~ & ~~3566) ==~~		== Izarismic ==
			This temperament is identical to the [[izar]] in the no-twos subgroup, but has an independent generator for prime 2. It can be described as {{nowrap\| 41 & 49 & 130 }} temperament, and tempers out the [[izar comma]], {{monzo\| 0 -11 -7 12 }}.

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

	[[Comma list]]: ~~{{monzo\| 0 -11 -7 12 }} (~~13841287201/13839609375)		[[Comma list]]: 13841287201/13839609375

	{{Mapping\|legend=1\| 1 0 0 0 \| 0 1 7 5 \| 0 0 -12 -7 }}		{{Mapping\|legend=1\| 1 0 0 0 \| 0 1 7 5 \| 0 0 -12 -7 }}
			: mapping generators: ~2, ~3, ~16807/10125

	[[Optimal tuning]] ([[~~CTE~~]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.9584{{c}}, ~16807/10125 = 877.2825{{c}}		[[Optimal tuning]]s:
			* [[TE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9584{{c}}, ~16807/10125 = 877.2825{{c}}
			* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9584{{c}}, ~16807/10125 = 877.2825{{c}}

	{{Optimal ET sequence\|legend=1\| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}		{{Optimal ET sequence\|legend=1\| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}

Xenllium: /* Rank-2 temperaments */

2026-02-23T01:30:07Z

Rank-2 temperaments

← Older revision		Revision as of 01:30, 23 February 2026
Line 247:		Line 247:

	== Septarium ==		== Septarium ==
	Septarium ~~({{nowrap\| 441 & 2513 }})~~ tempers out the [[septarium comma]], {{monzo\| 73 77 -84 }}.		Septarium splits the octave in seven, and tempers out the [[septarium comma]], {{monzo\| 73 77 -84 }}. It can be described as {{nowrap\| 441 & 2513 }} temperament, which tempers out 78125000/78121827 and {{monzo\| 47 -7 -7 -7 }} ([[akjaysma]]) in the 7-limit.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

	Comma list: 78125000/78121827, ~~{{monzo\| 47 -7 -7 -7 }}~~		Comma list: 78125000/78121827, 140737488355328/140710042265625

	Mapping: {{Mapping\| 7 1 7 39 \| 0 12 11 -23 }}		Mapping: {{Mapping\| 7 1 7 39 \| 0 12 11 -23 }}

Xenllium at 00:43, 23 February 2026

2026-02-23T00:43:44Z

Show changes

FloraC: - CTE & POTE tunings

2026-01-17T15:32:22Z

- CTE & POTE tunings

Show changes

FloraC: Switch to WE & CWE tunings (5/5), at least for rank-2 temps

2026-01-17T15:30:27Z

Switch to WE & CWE tunings (5/5), at least for rank-2 temps

← Older revision		Revision as of 15:30, 17 January 2026
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	Badness (Sintel): 0.530		Badness (Sintel): 0.530

	== Revopentic ~~(2.3.7)~~ ==		== Revopentic ==
	{{See also\| Revopentisma }}		{{See also\| Revopentisma }}

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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957820{{c}}		* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957784{{c}}		: [[error map]]: {{val\| -0.0009 +0.0014 +0.0001 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957796{{c}}
			: error map: {{val\| 0.0000 +0.0028 +0.0018 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957820{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957784{{c}} -->

	{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}		{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
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	[[Comma list]]: {{monzo\| -32 -64 71 }}		[[Comma list]]: {{monzo\| -32 -64 71 }}

	{{Mapping\|legend=1\| 1 35 32 \| 0 -71 -64 }}		{{Mapping\|legend=2\| 1 -36 -32 \| 0 71 64 }}
			: mapping generators: ~3, ~{{monzo\| -4 -9 10 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~3 = 1901.~~955~~{{c}}, ~{{monzo\| 5 9 -10 }} = ~~898~~.~~340~~{{c}}		* [[WE]]: ~3 = 1901.955003{{c}}, ~{{monzo\| -4 -9 10 }} = 1003.615406{{c}}
	* [[~~CWE~~]]: ~3 = 1901.955{{c}}, ~{{monzo\| 5 9 -10 }} = 898.340{{c}}		: [[error map]]: {{val\| +0.0000 +0.0000 -0.0000 }}
			* [[CWE]]: ~3 = 1901.955001{{c}}, ~{{monzo\| -4 -9 10 }} = 1003.615405{{c}}
			: error map: {{val\| 0.0000 -0.0000 -0.0000 }}
			<!-- * [[CTE]]: ~3 = 1901.955{{c}}, ~{{monzo\| 5 9 -10 }} = 898.340{{c}} -->

	[[Optimal ET sequence]]: [[163edt\|b163cd]], [[199edt\|b199c]], [[235edt\|b235]], [[271edt\|b271]], [[4643edt\|b4643]], [[4914edt\|b4914]], …, [[8708edt\|b8708]], [[8979edt\|b8979]], [[18229edt\|b18229]], [[27208edt\|b27208]], [[99853edt\|b99853]], [[127061edt\|b127061]], [[154269edt\|b154269]], [[181477edt\|b181477]], [[208685edt\|b208685]], [[390162edt\|b390162]]		[[Optimal ET sequence]]: [[163edt\|b163cd]], [[199edt\|b199c]], [[235edt\|b235]], [[271edt\|b271]], [[4643edt\|b4643]], [[4914edt\|b4914]], …, [[8708edt\|b8708]], [[8979edt\|b8979]], [[18229edt\|b18229]], [[27208edt\|b27208]], [[99853edt\|b99853]], [[127061edt\|b127061]], [[154269edt\|b154269]], [[181477edt\|b181477]], [[208685edt\|b208685]], [[390162edt\|b390162]]

FloraC: Switch to WE & CWE tunings (4/)

2026-01-17T15:17:11Z

Switch to WE & CWE tunings (4/)

← Older revision		Revision as of 15:17, 17 January 2026
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	[[Comma list]]: {{monzo\| 71 -99 37 }}		[[Comma list]]: {{monzo\| 71 -99 37 }}

	{{Mapping\|legend=1\| 1 ~~28 73~~ \| 0 -37 -99 }}		{{Mapping\|legend=1\| 1 -9 -26 \| 0 37 99 }}
	: mapping generators: ~2, ~6561~~/4000~~		: mapping generators: ~2, ~8000/6561

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~8000/6561 = 343.296094{{c}}		* [[WE]]: ~2 = 1199.999880537{{c}}, ~8000/6561 = 343.296063356{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~8000/6561 = 343.296098{{c}}		: [[error map]]: {{val\| -0.000119 +0.000418 -0.000336 }}
			* [[CWE]]: ~2 = 1200.000000000{{c}}, ~8000/6561 = 343.296095985{{c}}
			: error map: {{val\| 0.000000 +0.000551 -0.000211 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~8000/6561 = 343.296094{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~8000/6561 = 343.296098{{c}} -->

	{{Optimal ET sequence\|legend=1\| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}		{{Optimal ET sequence\|legend=1\| 7, …, 381, 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}

	[[Badness]] (Sintel): TBD		[[Badness]] (Sintel): TBD
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	[[Comma list]]: {{monzo\| -90 -15 49 }}		[[Comma list]]: {{monzo\| -90 -15 49 }}

	{{Mapping\|legend=1\| 1 ~~43 15~~ \| 0 -49 -15 }}		{{Mapping\|legend=1\| 1 -6 0 \| 0 49 15 }}
	: ~~Mapping~~ generators: ~2, ~{{monzo\| -~~23 -4~~ 13 }}		: mapping generators: ~2, ~{{monzo\| 24 4 -13 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754186{{c}}		* [[WE]]: ~2 = 1200.000195604{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754209314{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754179{{c}}		: [[error map]]: {{val\| -0.000196 +0.000418 -0.000336 }}
			* [[CWE]]: ~2 = 1200.000000000{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754209314{{c}}
			: error map: {{val\| 0.000000 +0.000082 -0.000574 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754186{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 24 4 -13 }} = 185.754179{{c}} -->

	{{Optimal ET sequence\|legend=1\| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}		{{Optimal ET sequence\|legend=1\| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
Line 386:		Line 394:
	Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.		Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.

	Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments#Hafnium\|hafnium]].		Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments #Hafnium\|hafnium]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
Line 396:		Line 404:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~{{monzo\| -67 35 5 }} = 100.000000{{c}}, ~3/2 = 701.955176{{c}} (~32805/32768 = 1.955176{{c}})		* [[WE]]: ~{{monzo\| -67 35 5 }} = 99.999995361{{c}}, ~3/2 = 701.955129505{{c}} (~32805/32768 = 1.955161980{{c}})
	* [[POTE]]: ~{{monzo\| -67 35 5 }} = 100.000000{{c}}, ~3/2 = 701.955162{{c}} (~32805/32768 = 1.955162{{c}})		: [[error map]]: {{val\| -0.000056 +0.000072 +0.000022 }}
			* [[CWE]]: ~{{monzo\| -67 35 5 }} = 100.000000000{{c}}, ~3/2 = 701.955166184{{c}} (~32805/32768 = 1.955166184{{c}})
			: error map: {{val\| 0.000000 +0.000165 +0.000123 }}
			<!-- * [[CTE]]: ~{{monzo\| -67 35 5 }} = 100.000000{{c}}, ~3/2 = 701.955176{{c}} (~32805/32768 = 1.955176{{c}})
			* [[POTE]]: ~{{monzo\| -67 35 5 }} = 100.000000{{c}}, ~3/2 = 701.955162{{c}} (~32805/32768 = 1.955162{{c}}) -->

	{{Optimal ET sequence\|legend=1\| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}		{{Optimal ET sequence\|legend=1\| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
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	Optimal tunings:		Optimal tunings:
	* CTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949917{{c}} (or ~32805/32768 = 1.949917{{c}})		* WE: ~30375/28672 = 99.999866{{c}}, ~3/2 = 701.948670{{c}} (~32805/32768 = 1.949605{{c}})
	* POTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949608{{c}} (or ~32805/32768 = 1.949608{{c}})		* CWE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949698{{c}} (~32805/32768 = 1.949698{{c}})
			<!-- * CTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949917{{c}} (~32805/32768 = 1.949917{{c}})
			* POTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.949608{{c}} (~32805/32768 = 1.949608{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}		{{Optimal ET sequence\|legend=0\| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
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	Optimal tunings:		Optimal tunings:
	* CTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.948456{{c}} (or ~32805/32768 = 1.948456{{c}})		* WE: ~30375/28672 = 99.999760{{c}}, ~3/2 = 701.946301{{c}} (~32805/32768 = 1.947983{{c}})
	* POTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.947988{{c}} (or ~32805/32768 = 1.947988{{c}})		* CWE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.948121{{c}} (~32805/32768 = 1.948121{{c}})
			<!-- * CTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.948456{{c}} (or ~32805/32768 = 1.948456{{c}})
			* POTE: ~30375/28672 = 100.000000{{c}}, ~3/2 = 701.947988{{c}} (or ~32805/32768 = 1.947988{{c}}) -->

	{{Optimal ET sequence\|legend=0\| 12, …, 600e, 612, 1236, 1848 }}		{{Optimal ET sequence\|legend=0\| 12, …, 600e, 612, 1236, 1848 }}
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	Subgroup: 2.3.7		Subgroup: 2.3.7

	Comma list: ~~11399736556781568/11398895185373143~~		Comma list: {{monzo\| 47 4 -19 }}

	{{Mapping\|legend=2\| 1 ~~12 5~~ \| 0 -19 -4 }}		{{Mapping\|legend=2\| 1 -7 1 \| 0 19 4 }}
	: mapping generators: ~2, ~~~24576~~/~~16807~~		: mapping generators: ~2, ~16807/12288

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.000000{{c}}, ~~~24576~~/~~16807~~ = ~~657~~.~~791865~~{{c}}		* [[WE]]: ~2 = 1199.998821{{c}}, ~16807/12288 = 542.207710{{c}}
	* [[~~CWE~~]]: ~2 = 1200.000000{{c}}, ~~~24576~~/~~16807~~ = ~~657~~.~~791796~~{{c}}		: [[error map]]: {{val\| -0.0012 -0.0003 +0.0038 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.208204{{c}}
			: error map: {{val\| 0.0000 +0.0009 +0.0069 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.208135{{c}} -->

	{{Optimal ET sequence\|legend=1\| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}		{{Optimal ET sequence\|legend=1\| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
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	Comma list: 645700815/645657712, {{monzo\| 51 -13 -1 -10 }}		Comma list: 645700815/645657712, {{monzo\| 51 -13 -1 -10 }}

	Mapping: {{mapping\| 1 12 -~~155 5~~ \| 0 -19 287 -4 }}		Mapping: {{mapping\| 1 -7 132 1 \| 0 19 -287 4 }}

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = 1200.~~000000~~{{c}}, ~~~24576~~/~~16807~~ = ~~657~~.~~792032~~{{c}}		* WE: ~2 = 1200.000110{{c}}, ~16807/12288 = 542.208018{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~~~24576~~/16807 = ~~657~~.~~792032~~{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.207968{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~16807/12288 = 542.207968{{c}} -->

	{{Optimal ET sequence\|legend=0\| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}		{{Optimal ET sequence\|legend=0\| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}

FloraC: Switch to Sintel's badness, WE & CWE tunings (3/)

2026-01-17T14:05:36Z

Switch to Sintel's badness, WE & CWE tunings (3/)

← Older revision		Revision as of 14:05, 17 January 2026
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	[[Comma list]]: {{monzo\| -17 62 -35 }}		[[Comma list]]: {{monzo\| -17 62 -35 }}

	{{Mapping\|legend=1\| 1 ~~11 19~~ \| 0 -35 -62 }}		{{Mapping\|legend=1\| 1 -24 -43 \| 0 35 62 }}
	: mapping generators: ~2, ~{{monzo\| -6 23 -13 }}		: mapping generators: ~2, ~{{monzo\| 7 -23 13 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| -6 23 -13 }} = ~~322~~.~~801349~~{{c}}		* [[WE]]: ~2 = 1200.000236{{c}}, ~{{monzo\| 7 -23 13 }} = 877.198814{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| -6 23 -13 }} = ~~322~~.~~801358~~{{c}}		: [[error map]]: {{val\| +0.0002 -0.0022 +0.0026 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 7 -23 13 }} = 877.198647{{c}}
			: error map: {{val\| 0.0000 -0.0024 -0.0024 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 7 -23 13 }} = 877.198651{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 7 -23 13 }} = 877.198642{{c}} -->

	{{Optimal ET sequence\|legend=1\| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}		{{Optimal ET sequence\|legend=1\| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
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	[[Comma list]]: {{monzo\| 144 -22 -47 }}		[[Comma list]]: {{monzo\| 144 -22 -47 }}

	{{Mapping\|legend=1\| 1 45 -18 \| 0 -47 22 }}		{{Mapping\|legend=1\| 1 -2 4 \| 0 47 -22 }}
	: mapping generators: ~2, ~{{monzo\| -45 7 15 }}		: mapping generators: ~2, ~{{monzo\| 46 -7 -15 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.530979{{c}}		* [[WE]]: ~2 = 1199.998956{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.530922{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.531001{{c}}		: [[error map]]: {{val\| -0.0010 +0.0004 +0.0018 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.530995{{c}}
			: error map: {{val\| 0.0000 +0.0018 +0.0044 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.530979{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 46 -7 -15 }} = 91.531001{{c}} -->

	{{Optimal ET sequence\|legend=1\| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}		{{Optimal ET sequence\|legend=1\| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.~~000000~~{{c}}, ~3/2 = 701.~~955310~~{{c}}		* [[WE]]: ~2 = 1199.999902567{{c}}, ~3/2 = 701.955253373{{c}}
	* [[~~CWE~~]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.955310{{c}}		: [[error map]]: {{val\| -0.000097 +0.000155 -0.000001 }}
			* [[CWE]]: ~2 = 1200.000000000{{c}}, ~3/2 = 701.955310152{{c}}
			: error map: {{val\| 0.000000 +0.000309 +0.000149 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.955310{{c}} -->

	{{Optimal ET sequence\|legend=1\| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}		{{Optimal ET sequence\|legend=1\| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
Line 289:		Line 300:

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = ~~1200~~.~~000000~~{{c}}, ~3/2 = 701.~~955371~~{{c}}		* WE: ~2 = 1199.979407{{c}}, ~3/2 = 701.943437{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.955457{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.955457{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~3/2 = 701.955371{{c}} -->

	{{Optimal ET sequence\|legend=1\| 306, 665, 1636, 2301, 2966 }}		{{Optimal ET sequence\|legend=1\| 306, 665, 1636, 2301, 2966 }}
Line 304:		Line 316:

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = 1200.~~000000~~{{c}}, ~3/2 = 701.~~954810~~{{c}}		* WE: ~2 = 1200.010750{{c}}, ~3/2 = 701.961041{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.954771{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.954771{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~3/2 = 701.954810{{c}} -->

	{{Optimal ET sequence\|legend=1\| 306d, 359cd, 665 }}		{{Optimal ET sequence\|legend=1\| 306d, 359cd, 665 }}
Line 322:		Line 335:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = 1200.~~000000~~{{c}}, ~3/2 = 701.~~954415~~{{c}}		* [[WE]]: ~2 = 1200.000184840{{c}}, ~3/2 = 701.954524421{{c}}
	* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.~~954416~~{{c}}		: [[error map]]: {{val\| +0.000185 -0.000292 -0.000002 }}
			* [[CWE]]: ~2 = 1200.000000000{{c}}, ~3/2 = 701.954415845{{c}}
			: error map: {{val\| 0.000000 -0.000585 -0.000289 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.954415{{c}} -->

	{{Optimal ET sequence\|legend=1\| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}		{{Optimal ET sequence\|legend=1\| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}

FloraC: Switch to WE & CWE tunings (2/)

2026-01-17T13:48:05Z

Switch to WE & CWE tunings (2/)

← Older revision		Revision as of 13:48, 17 January 2026
Line 103:		Line 103:

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 27 -18 1 }} = 950.981427{{c}}		* [[WE]]: ~2 = 1199.997524{{c}}, ~{{monzo\| 27 -18 1 }} = 950.979631{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 27 -18 1 }} = 950.981594{{c}}		: [[error map]]: {{val\| -0.0025 +0.0043 -0.0005 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 27 -18 1 }} = 950.981535{{c}}
			: error map: {{val\| 0.0000 +0.0081 +0.0031 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 27 -18 1 }} = 950.981427{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~{{monzo\| 27 -18 1 }} = 950.981594{{c}} -->

	{{Optimal ET sequence\|legend=1\| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}		{{Optimal ET sequence\|legend=1\| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
Line 115:		Line 119:
	[[Comma list]]: {{monzo\| -36 -52 51 }}		[[Comma list]]: {{monzo\| -36 -52 51 }}

	{{Mapping\|legend=1\| 1 ~~15 16~~ \| 0 -51 -52 }}		{{Mapping\|legend=1\| 1 -36 -36 \| 0 51 52 }}
	: mapping generators: ~2, ~6/5		: mapping generators: ~2, ~5/3

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~6/5 = ~~315~~.~~647899~~{{c}}		* [[WE]]: ~2 = 1200.000553{{c}}, ~5/3 = 884.352488{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~6/5 = ~~315~~.~~647919~~{{c}}		: [[error map]]: {{val\| +0.0006 +0.0020 -0.0042 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~5/3 = 844.352090{{c}}
			: error map: {{val\| 0.0000 +0.0016 -0.0050 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~5/3 = 884.352101{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~5/3 = 884.352081{{c}} -->

	{{Optimal ET sequence\|legend=1\| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}		{{Optimal ET sequence\|legend=1\| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
Line 131:		Line 139:
	Comma list: 78125000/78121827, {{monzo\| -48 0 11 8 }}		Comma list: 78125000/78121827, {{monzo\| -48 0 11 8 }}

	Mapping: {{mapping\| 1 ~~15 16~~ -16 \| 0 -102 -~~104~~ 143 }}		Mapping: {{mapping\| 1 -87 -88 127 \| 0 102 104 -143 }}
			: mapping generators: ~2, ~67108864/36756909

	Optimal tunings:		Optimal tunings:
	* ~~CTE~~: ~2 = 1200.~~000000~~{{c}}, ~36756909~~/33554432~~ = ~~157~~.~~823952~~{{c}}		* WE: ~2 = 1200.000308{{c}}, ~67108864/36756909 = 1042.176313{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~36756909/~~33554432~~ = ~~157~~.~~823954~~{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~67108864/36756909 = 1042.176046{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~67108864/36756909 = 1042.176048{{c}} -->

	{{Optimal ET sequence\|legend=0\| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}		{{Optimal ET sequence\|legend=0\| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
Line 146:		Line 156:
	Comma list: [[140625/140608]], {{monzo\| -4 20 -9 0 0 -4 }}		Comma list: [[140625/140608]], {{monzo\| -4 20 -9 0 0 -4 }}

	Mapping: {{mapping\| 1 ~~15 16~~ -16 \| 0 -51 -52 -138 }}		Mapping: {{mapping\| 1 -36 -36 -98 \| 0 51 52 138 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.0031{{c}}, ~6/5 = ~~315~~.~~6490~~{{c}}		* WE: ~2 = 1200.000308{{c}}, ~5/3 = 884.354064{{c}}
	* POTE: ~2 = 1200.0000{{c}}, ~6/5 = ~~315~~.~~6482~~{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~5/3 = 884.351835{{c}}
			<!-- * CTE: ~2 = 1200.0031{{c}}, ~5/3 = 884.3510{{c}}
			* POTE: ~2 = 1200.0000{{c}}, ~5/3 = 884.3518{{c}} -->

	{{Optimal ET sequence\|legend=0\| 19, …, 441, 460, 901, 1342 }}		{{Optimal ET sequence\|legend=0\| 19, …, 441, 460, 901, 1342 }}
Line 163:		Line 175:
	[[Comma list]]: {{monzo\| -107 47 14 }}		[[Comma list]]: {{monzo\| -107 47 14 }}

	{{Mapping\|legend=1\| 1 13 -36 \| 0 -14 47 }}		{{Mapping\|legend=1\| 1 -1 11 \| 0 14 -47 }}
	: mapping generators: ~2, 7381125~~/4194304~~		: mapping generators: ~2, ~8388608/7381125

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567861{{c}}		* [[WE]]: ~2 = 1200.000553{{c}}, ~8388608/7381125 = 221.568202{{c}}
	* [[POTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567899{{c}}		: [[error map]]: {{val\| +0.0016 -0.0018 -0.0012 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567889{{c}}
			: error map: {{val\| 0.0000 -0.0046 -0.0045 }}
			<!-- * [[CTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567861{{c}}
			* [[POTE]]: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.567899{{c}} -->

	{{Optimal ET sequence\|legend=1\| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}		{{Optimal ET sequence\|legend=1\| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
Line 179:		Line 195:
	Comma list: 78125000/78121827, {{monzo\| -52 17 12 -1 }}		Comma list: 78125000/78121827, {{monzo\| -52 17 12 -1 }}

	Mapping: {{mapping\| 1 13 -~~36 -263~~ \| 0 -14 47 326 }}		Mapping: {{mapping\| 1 -1 11 63 \| 0 14 -47 -326 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568013{{c}}		* WE: ~2 = 1200.001970{{c}}, ~8388608/7381125 = 221.568395{{c}}
	* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568031{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568026{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568013{{c}}
			* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568031{{c}} -->

	{{Optimal ET sequence\|legend=0\| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}		{{Optimal ET sequence\|legend=0\| 65d, …, 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}

	Badness (Sintel): TBD		Badness (Sintel): TBD
Line 194:		Line 212:
	Comma list: 151263/151250, 21437500/21434787, 369140625/369098752		Comma list: 151263/151250, 21437500/21434787, 369140625/369098752

	Mapping: {{mapping\| 1 13 -~~36 -263 -573~~ \| 0 -14 47 326 707 }}		Mapping: {{mapping\| 1 -1 11 63 134 \| 0 14 -47 -326 -707 }}

	Optimal tunings:		Optimal tunings:
	* CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568116{{c}}		* WE: ~2 = 1200.003854{{c}}, ~8388608/7381125 = 221.568850{{c}}
	* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568139{{c}}		* CWE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568133{{c}}
			<!-- * CTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568116{{c}}
			* POTE: ~2 = 1200.000000{{c}}, ~8388608/7381125 = 221.568139{{c}} -->

	{{Optimal ET sequence\|legend=1\| 612, 2513, 3125, 3737, 8086, 19909d }}		{{Optimal ET sequence\|legend=0\| 65dee, …, 612, 2513, 3125, 3737, 8086, 19909d }}

	Badness (Sintel): TBD		Badness (Sintel): TBD