Ragismic family: Difference between revisions

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Temperaments discussed elsewhere include:

* ''[[Sensigh]]'' → [[~~Sensamagic~~ family #Sensigh|~~Sensamagic~~ family]]

* ''[[Sensigh]]'' → [[Sengic family #Sensigh|Sengic family]]

* ''[[Catakleismoid]]'' → [[~~Marvel~~ family #Catakleismoid|~~Marvel~~ family]]

* ''[[Catakleismoid]]'' → [[Kleismic rank-3 family #Catakleismoid|Kleismic rank-3 family]]

* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]]

Line 15:

: mapping generators: ~2, ~3, ~5

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: 10/9 length = 0.789, 6/5 length = 0.921

: Angle (10/9, 6/5) = 105.299°

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0018{{c}}, ~3/2 = 701.9851{{c}}, ~5/4 = 386.2710{{c}}

: [[error map]]: {{val| +0.002 +0.032 -0.039 -0.014 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9855{{c}}, ~5/4 = 386.2724{{c}}

: error map: {{val| 0.000 +0.031 -0.041 -0.017 }}

[[Minimax tuning]]:

* [[7-odd-limit]] [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

* [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7

* [[9-odd-limit]] [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

* [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

{{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}

[[Projection pair]]: ~7 = ~4374/625

[[Badness]] (Sintel): 0.0515

[[Projection pair]]: <code>7 ~4374/625</code>

Scales: [[Ragismic19]], [[Ragismic chromatic]]

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{{~~Optimal ET sequence~~|~~legend~~=~~1| 7~~, 19, ~~26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee~~ }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.4709{{c}}, ~3/2 = 701.3876{{c}}, ~5/4 = 385.3287{{c}}

: [[error map]]: {{val| +0.471 -0.097 -0.043 -0.427 -0.833 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2311{{c}}, ~5/4 = 385.3753{{c}}

: error map: {{val| 0.000 -0.724 -0.938 -1.709 -2.579 }}

[[Badness]]: 0.~~721 × 10-3~~

{{Optimal ET sequence|legend=1| 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 938bcddeee, 1056bcdddeeee }}

[[Badness]] (Sintel): 0.866

=== 13-limit ===

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Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }}

{{~~Optimal ET sequence|legend~~=~~1| 7~~, 19, 26, ~~46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff~~ }}

Optimal tunings:

* WE: ~2 = 1200.6829{{c}}, ~3/2 = 701.4188{{c}}, ~5/4 = 385.0695{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.1881{{c}}, ~5/4 = 385.1147{{c}}

Badness: 0.~~840 × 10-3~~

{{Optimal ET sequence|legend=0| 19, 26, 45f, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}

Badness (Sintel): 0.785

== Ulmo ==

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{{~~Optimal ET sequence~~|~~legend~~=~~1| 7~~, 39, ~~46, 53, 80, 126, 179, 259cd, 385bcd~~ }}

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.1423{{c}}, ~3/2 = 703.8558{{c}}, ~5/4 = 389.2089{{c}}

: [[error map]]: {{val| -0.858 +1.043 +1.180 +1.329 -2.745 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9658{{c}}, ~5/4 = 388.9716{{c}}

: error map: {{val| 0.000 +2.011 +2.658 +3.048 -1.501 }}

[[Badness]]: 1.~~23 × 10-3~~

{{Optimal ET sequence|legend=1| 19e, 27e, 34d, 46, 53, 80, 126, 179, 259cd }}

[[Badness]] (Sintel): 1.48

=== 13-limit ===

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Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }}

{{~~Optimal ET sequence|legend~~=~~1| 7~~, 39, 46, ~~53, 80, 133d, 179, 312cdf~~ }}

Optimal tunings:

* WE: ~2 = 1199.5491{{c}}, ~3/2 = 703.6725{{c}}, ~5/4 = 388.5875{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7489{{c}}, ~5/4 = 388.5028{{c}}

Badness: 0.~~932 × 10-3~~

{{Optimal ET sequence|legend=0| 19e, 27e, 34d, 46, 53, 80, 133d, 179 }}

Badness (Sintel): 0.871

== Thor ==

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: mapping generators: ~99/70, ~3, ~5

: ~~mapping generators~~: ~99/70, ~3, ~5

[[Optimal tuning]]s:

* [[WE]]: ~99/70 = 600.0103{{c}}, ~3/2 = 701.9669{{c}}, ~5/4 = 386.2245{{c}}

: [[error map]]: {{val| +0.021 +0.033 -0.048 +0.045 -0.126 }}

* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9706{{c}}, ~5/4 = 386.2375{{c}}

: error map: {{val| 0.000 +0.016 -0.076 +0.018 -0.177 }}

[[Minimax tuning]]:

* [[11-odd-limit]] [[~~Eigenmonzo~~ basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5

* [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5

{{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}

[[Badness]]: 0.~~0888 × 10-3~~

[[Badness]] (Sintel): 0.107

[[Projection pair]]s: 2 ~~= ~~~9801/4900, ~7 ~~= ~~~21434787/3062500, ~11 ~~= ~~~2310905821257/210087500000 to 3.5.14/11

[[Projection pair]]s: <code>2 9801/4900, 7 21434787/3062500, 11 2310905821257/210087500000</code> to 3.5.14/11

=== Thunor ===

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: 10/9 length = 0.4234, 6/5 length = 0.8426

: Angle (10/9, 6/5) = 84.126°

Optimal tunings:

* WE: ~99/70 = 599.9809{{c}}, ~3/2 = 702.0647{{c}}, ~5/4 = 386.3428{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0675{{c}}, ~5/4 = 386.3276{{c}}

Minimax tuning:

* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13

{{Optimal ET sequence|legend=1| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}

{{Optimal ET sequence|legend=0| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}

Badness (Sintel): 0.319

~~Badness~~: ~~0.341 × 10-3~~

Scales: [[Thunor46]]

=== Rym ===

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Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }}

{{~~Optimal ET sequence|legend~~=~~1| 46~~, ~~72f~~, ~~106~~, ~~118, 152, 224, 270, 494, 764, 1106, 1376, 1870~~ }}

Optimal tunings:

* WE: ~99/70 = 599.9913{{c}}, ~3/2 = 702.0254{{c}}, ~5/4 = 386.3155{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0354{{c}}, ~5/4 = 386.3214{{c}}

Badness: 0.~~549 × 10-3~~

{{Optimal ET sequence|legend=0| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}

Badness (Sintel): 0.514

=== Donar ===

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Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}

: mapping generators: ~99/70, ~3, ~220/117

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: 44/39 length = 0.3480, 6/5 length = 0.7828

: Angle (44/39, 6/5) = 85.3977°

Optimal tunings:

* WE: ~99/70 = 600.0175{{c}}, ~3/2 = 701.9460{{c}}, ~220/117 = 1093.1197{{c}}

* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9416{{c}}, ~220/117 = 1093.0962{{c}}

Minimax tuning:

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* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11

{{Optimal ET sequence|legend=1| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}

{{Optimal ET sequence|legend=0| 34d, 46, 80, 144, 178, 190, 224, 270, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}

Badness: 0.~~322 × 10-3~~

Badness (Sintel): 0.301

Scales: [[Donar46]]

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: mapping generators: ~2, ~343/198, ~5

: ~~mapping generators~~: ~2, ~343/198, ~5

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.0031{{c}}, ~343/198 = 950.9942{{c}}, ~5/4 = 386.2812{{c}}

: [[error map]]: {{val| +0.021 +0.033 -0.048 +0.045 -0.126 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/198 = 950.9930{{c}}, ~5/4 = 386.2838{{c}}

: error map: {{val| 0.000 +0.016 -0.076 +0.018 -0.177 }}

{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}

[[Badness]] (Sintel): 0.362

== Bragi ==

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: mapping generators: ~2, ~3, ~320/297

: ~~mapping generators~~: ~2, ~3, ~320/297

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9750{{c}}, ~3/2 = 702.0222{{c}}, ~320/297 = 128.7779{{c}}

: [[error map]]: {{val| -0.025 +0.042 -0.030 -0.006 +0.046 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0330{{c}}, ~320/297 = 128.7791{{c}}

: error map: {{val| 0.000 +0.078 +0.024 +0.056 +0.141 }}

{{Optimal ET sequence|legend=1| 19, 27, 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}

~~{{Optimal ET sequence|legend=~~1~~| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}~~

[[Badness]] (Sintel): 1.03

=== 13-limit ===

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Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }}

{{Optimal ET sequence|legend=1| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}

Optimal tunings:

* WE: ~2 = 1199.9874{{c}}, ~3/2 = 702.0172{{c}}, ~14/13 = 128.7600{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0228{{c}}, ~14/13 = 128.7608{{c}}

{{Optimal ET sequence|legend=0| 19, 27, 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}

Badness (Sintel): 0.865

== Vidar ==

Vidar tempers out the [[luxma]] and shares the same generators with [[lux]], from which it only differs in the mapping of [[prime interval|prime]] [[7/1|7]].

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 4375/4374, 100663296/100656875

: mapping generators: ~2, ~3, ~55/48

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9928{{c}}, ~3/2 = 701.9969{{c}}, ~55/48 = 235.6566{{c}}

: [[error map]]: {{val| -0.007 +0.035 -0.036 -0.016 +0.022 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9988{{c}}, ~55/48 = 235.6593{{c}}

: error map: {{val| 0.000 +0.044 -0.022 -0.002 +0.048 }}

~~: mapping generators: ~2~~, ~3, ~~~96/55~~

{{Optimal ET sequence|legend=1| 45, 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}

~~{{Optimal ET sequence|legend=~~1~~| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}~~

[[Badness]] (Sintel): 1.32

=== 13-limit ===

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Comma list: 4225/4224, 4375/4374, 6656/6655

Mapping: {{mapping| 1 0 ~~0 1~~ 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }}

Mapping: {{mapping| 1 0 -5 21 9 13 | 0 1 4 -9 -3 -5 | 0 0 5 -20 -4 -7 }}

Optimal tunings:

* WE: ~2 = 1200.0042{{c}}, ~3/2 = 701.9794{{c}}, ~55/48 = 235.6710{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9775{{c}}, ~55/48 = 235.6698{{c}}

{{Optimal ET sequence|legend=0| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}

~~{{Optimal ET sequence|legend=1| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}~~

Badness (Sintel): 0.593

[[Category:Temperament families]]

[[Category:Ragismic family| ]]

~~[[Category:Ragismic| ]] ~~

[[Category:Rank 3]]

@@ Line 3: / Line 3: @@
 Temperaments discussed elsewhere include:
-* ''[[Sensigh]]'' → [[Sensamagic family #Sensigh|Sensamagic family]]
+* ''[[Sensigh]]'' → [[Sengic family #Sensigh|Sengic family]]
-* ''[[Catakleismoid]]'' → [[Marvel family #Catakleismoid|Marvel family]]
+* ''[[Catakleismoid]]'' → [[Kleismic rank-3 family #Catakleismoid|Kleismic rank-3 family]]
 * ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]]
@@ Line 15: / Line 15: @@
 {{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }}
 : mapping generators: ~2, ~3, ~5
@@ Line 23: / Line 22: @@
 : 10/9 length = 0.789, 6/5 length = 0.921
 : Angle (10/9, 6/5) = 105.299°
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0018{{c}}, ~3/2 = 701.9851{{c}}, ~5/4 = 386.2710{{c}}
+: [[error map]]: {{val| +0.002 +0.032 -0.039 -0.014 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9855{{c}}, ~5/4 = 386.2724{{c}}
+: error map: {{val| 0.000 +0.031 -0.041 -0.017 }}
 [[Minimax tuning]]:
-* [[7-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
+* [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
-* [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
+* [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
 {{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}
-[[Projection pair]]: ~7 = ~4374/625
+[[Badness]] (Sintel): 0.0515
+[[Projection pair]]: <code>7 ~4374/625</code>
 Scales: [[Ragismic19]], [[Ragismic chromatic]]
@@ Line 41: / Line 48: @@
 {{Mapping|legend=1| 1 0 0 1 6 | 0 1 0 7 -6 | 0 0 1 -4 3 }}
-{{Optimal ET sequence|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4709{{c}}, ~3/2 = 701.3876{{c}}, ~5/4 = 385.3287{{c}}
+: [[error map]]: {{val| +0.471 -0.097 -0.043 -0.427 -0.833 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2311{{c}}, ~5/4 = 385.3753{{c}}
+: error map: {{val| 0.000 -0.724 -0.938 -1.709 -2.579 }}
-[[Badness]]: 0.721 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=1| 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 938bcddeee, 1056bcdddeeee }}
+[[Badness]] (Sintel): 0.866
 === 13-limit ===
@@ Line 52: / Line 65: @@
 Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }}
-{{Optimal ET sequence|legend=1| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
+Optimal tunings:
+* WE: ~2 = 1200.6829{{c}}, ~3/2 = 701.4188{{c}}, ~5/4 = 385.0695{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.1881{{c}}, ~5/4 = 385.1147{{c}}
-Badness: 0.840 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 19, 26, 45f, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
+Badness (Sintel): 0.785
 == Ulmo ==
@@ Line 63: / Line 80: @@
 {{Mapping|legend=1| 1 0 0 1 -3 | 0 1 0 7 7 | 0 0 1 -4 -2 }}
-{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.1423{{c}}, ~3/2 = 703.8558{{c}}, ~5/4 = 389.2089{{c}}
+: [[error map]]: {{val| -0.858 +1.043 +1.180 +1.329 -2.745 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.9658{{c}}, ~5/4 = 388.9716{{c}}
+: error map: {{val| 0.000 +2.011 +2.658 +3.048 -1.501 }}
-[[Badness]]: 1.23 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=1| 19e, 27e, 34d, 46, 53, 80, 126, 179, 259cd }}
+[[Badness]] (Sintel): 1.48
 === 13-limit ===
@@ Line 74: / Line 97: @@
 Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }}
-{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}
+Optimal tunings:
+* WE: ~2 = 1199.5491{{c}}, ~3/2 = 703.6725{{c}}, ~5/4 = 388.5875{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7489{{c}}, ~5/4 = 388.5028{{c}}
-Badness: 0.932 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 19e, 27e, 34d, 46, 53, 80, 133d, 179 }}
+Badness (Sintel): 0.871
 == Thor ==
@@ Line 84: / Line 111: @@
 {{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }}
+: mapping generators: ~99/70, ~3, ~5
-: mapping generators: ~99/70, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~99/70 = 600.0103{{c}}, ~3/2 = 701.9669{{c}}, ~5/4 = 386.2245{{c}}
+: [[error map]]: {{val| +0.021 +0.033 -0.048 +0.045 -0.126 }}
+* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9706{{c}}, ~5/4 = 386.2375{{c}}
+: error map: {{val| 0.000 +0.016 -0.076 +0.018 -0.177 }}
 [[Minimax tuning]]:
-* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5
+* [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5
 {{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
-[[Badness]]: 0.0888 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.107
-[[Projection pair]]s: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
+[[Projection pair]]s: <code>2 9801/4900, 7 21434787/3062500, 11 2310905821257/210087500000</code> to 3.5.14/11
 === Thunor ===
@@ Line 108: / Line 140: @@
 : 10/9 length = 0.4234, 6/5 length = 0.8426
 : Angle (10/9, 6/5) = 84.126°
+Optimal tunings:
+* WE: ~99/70 = 599.9809{{c}}, ~3/2 = 702.0647{{c}}, ~5/4 = 386.3428{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0675{{c}}, ~5/4 = 386.3276{{c}}
 Minimax tuning:
 * 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13
-{{Optimal ET sequence|legend=1| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
+{{Optimal ET sequence|legend=0| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
+Badness (Sintel): 0.319
-Badness: 0.341 × 10<sup>-3</sup>
+Scales: [[Thunor46]]
 === Rym ===
@@ Line 123: / Line 161: @@
 Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }}
-{{Optimal ET sequence|legend=1| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}
+Optimal tunings:
+* WE: ~99/70 = 599.9913{{c}}, ~3/2 = 702.0254{{c}}, ~5/4 = 386.3155{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0354{{c}}, ~5/4 = 386.3214{{c}}
-Badness: 0.549 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}
+Badness (Sintel): 0.514
 === Donar ===
@@ Line 133: / Line 175: @@
 Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}
 : mapping generators: ~99/70, ~3, ~220/117
@@ Line 141: / Line 182: @@
 : 44/39 length = 0.3480, 6/5 length = 0.7828
 : Angle (44/39, 6/5) = 85.3977°
+Optimal tunings:
+* WE: ~99/70 = 600.0175{{c}}, ~3/2 = 701.9460{{c}}, ~220/117 = 1093.1197{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9416{{c}}, ~220/117 = 1093.0962{{c}}
 Minimax tuning:
@@ Line 146: / Line 191: @@
 * 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11
-{{Optimal ET sequence|legend=1| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
+{{Optimal ET sequence|legend=0| 34d, 46, 80, 144, 178, 190, 224, 270, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
-Badness: 0.322 × 10<sup>-3</sup>
+Badness (Sintel): 0.301
 Scales: [[Donar46]]
@@ Line 158: / Line 203: @@
 {{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }}
+: mapping generators: ~2, ~343/198, ~5
-: mapping generators: ~2, ~343/198, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0031{{c}}, ~343/198 = 950.9942{{c}}, ~5/4 = 386.2812{{c}}
+: [[error map]]: {{val| +0.021 +0.033 -0.048 +0.045 -0.126 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/198 = 950.9930{{c}}, ~5/4 = 386.2838{{c}}
+: error map: {{val| 0.000 +0.016 -0.076 +0.018 -0.177 }}
 {{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}
+[[Badness]] (Sintel): 0.362
 == Bragi ==
@@ Line 169: / Line 221: @@
 {{Mapping|legend=1| 1 0 2 -7 8 | 0 1 0 7 -3 | 0 0 3 -12 2 }}
+: mapping generators: ~2, ~3, ~320/297
-: mapping generators: ~2, ~3, ~320/297
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9750{{c}}, ~3/2 = 702.0222{{c}}, ~320/297 = 128.7779{{c}}
+: [[error map]]: {{val| -0.025 +0.042 -0.030 -0.006 +0.046 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0330{{c}}, ~320/297 = 128.7791{{c}}
+: error map: {{val| 0.000 +0.078 +0.024 +0.056 +0.141 }}
+{{Optimal ET sequence|legend=1| 19, 27, 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}
-{{Optimal ET sequence|legend=1| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}
+[[Badness]] (Sintel): 1.03
 === 13-limit ===
@@ Line 181: / Line 240: @@
 Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }}
-{{Optimal ET sequence|legend=1| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}
+Optimal tunings:
+* WE: ~2 = 1199.9874{{c}}, ~3/2 = 702.0172{{c}}, ~14/13 = 128.7600{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0228{{c}}, ~14/13 = 128.7608{{c}}
+{{Optimal ET sequence|legend=0| 19, 27, 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}
+Badness (Sintel): 0.865
 == Vidar ==
+Vidar tempers out the [[luxma]] and shares the same generators with [[lux]], from which it only differs in the mapping of [[prime interval|prime]] [[7/1|7]].
 [[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 4375/4374, 100663296/100656875
-{{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }}
+{{Mapping|legend=1| 1 0 -5 21 9 | 0 1 4 -9 -3 | 0 0 5 -20 -4 }}
+: mapping generators: ~2, ~3, ~55/48
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9928{{c}}, ~3/2 = 701.9969{{c}}, ~55/48 = 235.6566{{c}}
+: [[error map]]: {{val| -0.007 +0.035 -0.036 -0.016 +0.022 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9988{{c}}, ~55/48 = 235.6593{{c}}
+: error map: {{val| 0.000 +0.044 -0.022 -0.002 +0.048 }}
-: mapping generators: ~2, ~3, ~96/55
+{{Optimal ET sequence|legend=1| 45, 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}
-{{Optimal ET sequence|legend=1| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}
+[[Badness]] (Sintel): 1.32
 === 13-limit ===
@@ Line 199: / Line 273: @@
 Comma list: 4225/4224, 4375/4374, 6656/6655
-Mapping: {{mapping| 1 0 0 1 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }}
+Mapping: {{mapping| 1 0 -5 21 9 13 | 0 1 4 -9 -3 -5 | 0 0 5 -20 -4 -7 }}
+Optimal tunings:
+* WE: ~2 = 1200.0042{{c}}, ~3/2 = 701.9794{{c}}, ~55/48 = 235.6710{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9775{{c}}, ~55/48 = 235.6698{{c}}
+{{Optimal ET sequence|legend=0| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}
-{{Optimal ET sequence|legend=1| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}
+Badness (Sintel): 0.593
 [[Category:Temperament families]]
 [[Category:Ragismic family| ]] <!-- main article -->
-[[Category:Ragismic| ]] <!-- key article -->
 [[Category:Rank 3]]