Very high accuracy temperaments - Revision history

Eufalesio: Agh Linnaeus isn't a microbiologist choose better name

2026-10-20T16:13:16Z

Agh Linnaeus isn't a microbiologist choose better name

← Older revision		Revision as of 16:13, 20 October 2026
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	Notable temperaments not appearing in the optimal ET sequence are {{Edos\|15, 217, 311}}.		Notable temperaments not appearing in the optimal ET sequence are {{Edos\|15, 217, 311}}.

	=== ~~Linnaeus~~ ===		=== Microbiology ===
	A weak extension of microorganic adding the [[chalmersia]] and the [[insanisma]], which surfaces as a detemperament of [[vulture]].		A weak extension of microorganic adding the [[chalmersia]] and the [[insanisma]], which surfaces as a detemperament of [[vulture]].

Eufalesio: Added microorganic temperament since hosting it on the comma page is not that good

2026-10-19T16:47:10Z

Added microorganic temperament since hosting it on the comma page is not that good

← Older revision		Revision as of 16:47, 19 October 2026
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	[[Badness]] (Sintel): 1.62		[[Badness]] (Sintel): 1.62

			== Microorganic ==
			[[Subgroup]]: 2.3.7.11

			An insanely accurate [[gary]] or no-5 [[superkleismic]] detemperament. It does not have good strong extensions to the 11-limit and beyond. It splits the septischisma in 3 parts and the pythrabian comma in 5 parts, each of these parts being a tempered [[olympia]]~[[argyria]].

			[[Comma list]]: [[67110351/67108864]]

			{{Mapping\|legend=1\|1 0 7 7\|0 1 1 -2\| 0 0 3 -5}}

			[[Optimal tuning\|Optimal tunings]]:

			* [[WE]]: ~2 = 1200.001014{{c}}, ~3/2 = 1901.953889{{c}}, ~539/512 = 88.956151{{c}}

			: [[error map]]: ⟨+0.001014 -0.000098 -0.001537 -0.001401]

			* [[CWE]]: ~2 = 1200.000000 ¢, ~3/2 = 701.953627¢, ~539/512 = 88.955923 ¢

			: error map: ⟨0.000 +0.001374 -0.004512 -0.004808]

			{{Optimal ET sequence\|legend=1\|11, 12e, 26, 41, 94, 135, 566, 701, 836, 877, 1012, 1713, 1848, 4573, 4708, 6556, 11264, 17820}} …

			[[Badness]] (Sintel): 0.032

			Notable temperaments not appearing in the optimal ET sequence are {{Edos\|15, 217, 311}}.

			=== Linnaeus ===
			A weak extension of microorganic adding the [[chalmersia]] and the [[insanisma]], which surfaces as a detemperament of [[vulture]].

			[[Subgroup]]: 2.3.5.7.11.13

			[[Comma list]]: [[67110351/67108864]], [[123201/123200]], [[5767168/5767125]]

			{{Mapping\|legend=1\|1 0 4 -11 27 15\|0 2 3 -1 1 -3\| 0 0 5 18 -30 11}}
			[[Optimal tuning\|Optimal tunings]]:

			* [[WE]]: ~2 = 1200.000535{{c}}, ~359424/207515 = 950.976364{{c}}, ~2695/1536 = 973.322574{{c}}

			: [[error map]]: ⟨+0.000535 −0.002272 +0.004652 −0.001831 −0.004338 +0.002963]

			* [[CWE]]: ~2 = 1200.000000 ¢, ~3/2 = 950.975971 ¢, ~539/512 = 973.322136 ¢

			: error map: ⟨0.000000 −0.003059 +0.003520 −0.003432 −0.006047 +0.000931]

			{{Optimal ET sequence\|legend=1\|53, 217, 270, 1551f, 1604, 1821, 1874, 2091, 2144, 2361, 2414, 2631, 2684, 5315, 5585, 8269, 8539, 14124, 16808}} …

			Badness (Sintel): 0.349

	== Satwethezo-atritribigu (171 & 1547 & 4973) ==		== Satwethezo-atritribigu (171 & 1547 & 4973) ==

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:23Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
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	Comma list: {{monzo\| 47 4 -19 }}		Comma list: {{monzo\| 47 4 -19 }}

	{{Mapping\|legend=2\| 1 -7 1 \| 0 19 4 }}		{{Mapping\|legend=3\| 1 -7 1 \| 0 19 4 }}
	: mapping generators: ~2, ~16807/12288		: mapping generators: ~2, ~16807/12288

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	[[Comma list]]: {{monzo\| 109 -67 -1 }}		[[Comma list]]: {{monzo\| 109 -67 -1 }}

	{{Mapping\|legend=2\| 1 0 109 \| 0 1 -67 }}		{{Mapping\|legend=3\| 1 0 109 \| 0 1 -67 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	[[Comma list]]: {{monzo\| -32 -64 71 }}		[[Comma list]]: {{monzo\| -32 -64 71 }}

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

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:28Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 78125000/78121827, {{monzo\| -48 0 11 8 }}		Comma list: 78125000/78121827, {{monzo\| -48 0 11 8 }}

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

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	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 -36 -36 -98 \| 0 51 52 138 }}		{{Mapping\|legend=0\| 1 -36 -36 -98 \| 0 51 52 138 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 78125000/78121827, {{monzo\| -52 17 12 -1 }}		Comma list: 78125000/78121827, {{monzo\| -52 17 12 -1 }}

	~~Mapping:~~ {{~~mapping~~\| 1 -1 11 63 \| 0 14 -47 -326 }}		{{Mapping\|legend=0\| 1 -1 11 63 \| 0 14 -47 -326 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 151263/151250, 21437500/21434787, 369140625/369098752		Comma list: 151263/151250, 21437500/21434787, 369140625/369098752

	~~Mapping:~~ {{~~mapping~~\| 1 -1 11 63 134 \| 0 14 -47 -326 -707 }}		{{Mapping\|legend=0\| 1 -1 11 63 134 \| 0 14 -47 -326 -707 }}

	Optimal tunings:		Optimal tunings:
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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 -7 132 1 \| 0 19 -287 4 }}		{{Mapping\|legend=0\| 1 -7 132 1 \| 0 19 -287 4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 184549376/184528125, 199297406/199290375		Comma list: 184549376/184528125, 199297406/199290375

	~~Mapping:~~ {{~~mapping~~\| 7 0 0 47 -168 \| 0 1 0 -1 10 \| 0 0 1 -1 5 }}		{{Mapping\|legend=0\| 7 0 0 47 -168 \| 0 1 0 -1 10 \| 0 0 1 -1 5 }}
	: mapping generators: ~29160/26411, ~3, ~5		: mapping generators: ~29160/26411, ~3, ~5

Hkm at 05:23, 20 June 2026

2026-06-20T05:23:54Z

← Older revision		Revision as of 05:23, 20 June 2026
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	[[Badness]] (Sintel): 0.133		[[Badness]] (Sintel): 0.133

	~~== Counterquectismic ==~~
	~~{{See also\| Counterquectisma }}~~

	~~[[Subgroup]]: 2.3.5~~

	~~[[Comma list]]: {{monzo\| -500 314 1 }}~~

	~~{{Mapping\|legend=1\| 1 0 500 \| 0 1 -314 }}~~
	~~: mapping generators: ~2, ~3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1200.000184840{{c}}, ~3/2 = 701.954524421{{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 }}~~

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

	~~[[Badness]] (Sintel): 11.971~~

	~~== Quectismic ==~~
	~~{{See also\| Quectisma }}~~

	~~[[Subgroup]]: 2.3.5~~

	~~[[Comma list]]: {{monzo\| 554 -351 1 }}~~

	~~{{Mapping\|legend=1\| 1 0 -554 \| 0 1 351 }}~~
	~~: mapping generators: ~2, ~3~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1199.999902567{{c}}, ~3/2 = 701.955253373{{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 }}~~

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

	~~[[Badness]] (Sintel): 8.736~~

	~~=== Nanoquectismic ===~~
	~~Subgroup: 2.3.5.7~~

	~~Comma list: 43046721/43025920, {{monzo\| 82 -19 -3 -16 }}~~

	~~Mapping: {{mapping\| 1 0 -554 109 \| 0 1 351 -67 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1199.979407{{c}}, ~3/2 = 701.943437{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.955457{{c}}

	~~{{Optimal ET sequence\|legend=1\| 306, 665, 1636, 2301, 2966 }}~~

	~~Badness (Sintel): 15.285~~

	~~=== Conanoquectismic ===~~
	~~Subgroup: 2.3.5.7~~

	~~Comma list: {{monzo\| 33 -26 12 -7 }}, {{monzo\| -32 13 17 -10 }}~~

	~~Mapping: {{mapping\| 1 0 -554 -945 \| 0 1 351 598 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.010750{{c}}, ~3/2 = 701.961041{{c}}
	* CWE: ~2 = 1200.000000{{c}}, ~3/2 = 701.954771{{c}}

	~~{{Optimal ET sequence\|legend=1\| 306d, 359cd, 665 }}~~

	~~Badness (Sintel): 54.974~~

	== Atomic ==		== Atomic ==

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
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	[[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
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	== 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

← Older revision		Revision as of 17:38, 30 September 2026
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	Comma list: {{monzo\| 47 4 -19 }}		Comma list: {{monzo\| 47 4 -19 }}

	{{Mapping\|legend=2\| 1 -7 1 \| 0 19 4 }}		{{Mapping\|legend=3\| 1 -7 1 \| 0 19 4 }}
	: mapping generators: ~2, ~16807/12288		: mapping generators: ~2, ~16807/12288

Line 385:		Line 385:
	[[Comma list]]: {{monzo\| 109 -67 -1 }}		[[Comma list]]: {{monzo\| 109 -67 -1 }}

	{{Mapping\|legend=2\| 1 0 109 \| 0 1 -67 }}		{{Mapping\|legend=3\| 1 0 109 \| 0 1 -67 }}
	: mapping generators: ~2, ~3		: mapping generators: ~2, ~3

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	[[Comma list]]: {{monzo\| -32 -64 71 }}		[[Comma list]]: {{monzo\| -32 -64 71 }}

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