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Gamelismic clan: Difference between revisions

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{{main|Miracle}}
{{main|Miracle}}


[[Comma|Commas]]: 225/224, 1029/1024
[[Comma list]]: 225/224, 1029/1024


[[Minimax_tuning|Minimax tuning]]:
[[POTE generator]]: ~15/14 = 116.675


7-limit: [|1 0 0 0>, |25/13 6/13 -6/13 0>,
Mapping: [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2 }}]
|25/13 -7/13 7/13 0&gt;, |35/13 -2/13 2/13 0&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 6/5
Wedgie: {{wedgie| 6 -7 -2 -25 -20 15 }}


9-limit: [|1 0 0 0&gt;, |25/19 12/19 -6/19 0&gt;,
[[Minimax tuning]]:
|50/19 -14/19 7/19 0&gt;, |55/19 -4/19 2/19 0&gt;<nowiki>]</nowiki>
* [[7-odd-limit]]:
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/13 6/13 -6/13 0 }}, {{monzo| 25/13 -7/13 7/13 0 }}, {{monzo| 35/13 -2/13 2/13 0 }}]
: [[Eigenmonzo]]s: 2, 6/5
* [[9-odd-limit]]:
: [{{monzo| 1 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 }}, {{monzo| 50/19 -14/19 7/19 0 }}, {{monzo| 55/19 -4/19 2/19 0 }}]
: [[Eigenmonzo]]s: 2, 10/9


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12


[[POTE_tuning|POTE generator]]: ~15/14 = 116.675
{{Val list|legend=1| 10, 21, 31, 41, 72, 175 }}


Algebraic generator: Secor59, [[Algebraic_number|positive root]] of 15x^6-8x^4-12
[[Badness]]: 0.0167
 
Map: [&lt;1 1 3 3|, &lt;0 6 -7 -2|]
 
Wedgie: &lt;&lt;6 -7 -2 -25 -20 15||
 
EDOs: {{EDOs|10, 21, 31, 41, 72, 175}}
 
Badness: 0.0167


== 11-limit ==
== 11-limit ==
[[Comma|Commas]]: 225/224, 243/242, 385/384
[[Comma list]]: 225/224, 243/242, 385/384


[[Minimax_tuning|Minimax tuning]]:
[[POTE generator]]: ~15/14 = 116.633


[|1 0 0 0 0&gt;, |25/19 12/19 -6/19 0 0&gt;,
[[Mapping]]: [{{val| 1 1 3 3 2 }}, {{val| 0 6 -7 -2 15 }}]
|50/19 -14/19 7/19 0 0&gt;, |55/19 -4/19 2/19 0 0&gt;,
|53/19 30/19 -15/19 0 0&gt;<nowiki>]</nowiki>


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9
[[Minimax tuning]]:
 
* [[11-odd-limit]]:  
[[POTE_tuning|POTE generator]]: ~15/14 = 116.633
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: [[Eigenmonzo]]s: 2, 10/9


Algebraic generator: Secor59
Algebraic generator: Secor59


Map: [&lt;1 1 3 3 2|, &lt;0 6 -7 -2 15|]
{{Val list|legend=1| 10, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}
 
[[EDO|EDOs]]: {{EDOs|10, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde}}


Badness: 0.0107
[[Badness]]: 0.0107


{{see also|Chords of miracle}}
{{see also| Chords of miracle }}


=== Miraculous ===
=== Miraculous ===
Commas: 105/104, 144/143, 196/195, 243/242
Comma list: 105/104, 144/143, 196/195, 243/242


POTE generator: ~15/14 = 116.747
POTE generator: ~15/14 = 116.747


Map: [&lt;1 1 3 3 2 4|, &lt;0 6 -7 -2 15 -3|]
Mapping: [{{val| 1 1 3 3 2 4 }}, {{val| 0 6 -7 -2 15 -3 }}]


EDOs: {{EDOs|10, 31, 41, 72f, 113f, 185cff}}
{{Val list|legend=1| 10, 31, 41, 72f, 113f, 185cff }}


Badness: 0.0187
Badness: 0.0187


=== Benediction ===
=== Benediction ===
Commas: 225/224, 243/242, 351/350, 385/384
Comma list: 225/224, 243/242, 351/350, 385/384


POTE generator: ~15/14 = 116.574
POTE generator: ~15/14 = 116.574


Map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]
Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 6 -7 -2 15 -34 }}]


EDOs: {{EDOs|31, 72, 103, 175f}}
{{Val list|legend=1| 31, 72, 103, 175f }}


Badness: 0.0157
Badness: 0.0157


==== 17-limit ====
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 351/350, 375/374
Comma list: 225/224, 243/242, 273/272, 351/350, 375/374


POTE generator: ~15/14 = 116.585
POTE generator: ~15/14 = 116.585


Map: [&lt;1 1 3 3 2 7 7|, &lt;0 6 -7 -2 15 -34 -30|]
Mapping: [{{val| 1 1 3 3 2 7 7 }}, {{val| 0 6 -7 -2 15 -34 -30 }}]


EDOs: {{EDOs|31, 72, 103, 175f}}
{{Val list|legend=1| 31, 72, 103, 175f }}


=== Manna ===
=== Manna ===
Commas: 225/224, 243/242, 325/324, 385/384
Comma list: 225/224, 243/242, 325/324, 385/384


POTE generator: ~15/14 = 116.739
POTE generator: ~15/14 = 116.739


Map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]
Mapping: [{{val| 1 1 3 3 2 0 }}, {{val| 0 6 -7 -2 15 38 }}]


EDOs: {{EDOs|10f, 31f, 41, 72, 113, 185cf, 257cff}}
{{Val list|legend=1| 10f, 31f, 41, 72, 113, 185cf, 257cff }}


Badness: 0.0170
Badness: 0.0170


=== Semimiracle ===
=== Semimiracle ===
Commas: 169/168, 225/224, 243/242, 385/384
Comma list: 169/168, 225/224, 243/242, 385/384


POTE generator: ~15/14 = 116.624
POTE generator: ~15/14 = 116.624


Map: [&lt;2 2 6 6 4 7|, &lt;0 6 -7 -2 15 2|]
Mapping: [{{val| 2 2 6 6 4 7 }}, {{val| 0 6 -7 -2 15 2 }}]


EDOs: {{EDOs|10, 62, 72}}
{{Val list|legend=1| 10, 62, 72 }}


Badness: 0.0246
Badness: 0.0246


==== 17-limit ====
==== 17-limit ====
Commas: 169/168, 221/220, 225/224, 243/242, 273/272
Comma list: 169/168, 221/220, 225/224, 243/242, 273/272


POTE generator: ~15/14 = 116.628
POTE generator: ~15/14 = 116.628


Map: [&lt;2 2 6 6 4 7 7|, &lt;0 6 -7 -2 15 2 6|]
Mapping: [{{val| 2 2 6 6 4 7 7 }}, {{val| 0 6 -7 -2 15 2 6 }}]


EDOs: {{EDOs|10, 62, 72}}
{{Val list|legend=1| 10, 62, 72 }}


Badness: 0.0161
Badness: 0.0161


=== Hemisecordite ===
=== Hemisecordite ===
Commas: 225/224, 243/242, 385/384, 847/845
Comma list: 225/224, 243/242, 385/384, 847/845


POTE generator: ~27/26 = 58.288
POTE generator: ~27/26 = 58.288


Map: [&lt;1 1 3 3 2 2|, &lt;0 12 -14 -4 30 35|]
Mapping: [{{val| 1 1 3 3 2 2 }}, {{val| 0 12 -14 -4 30 35 }}]


EDOs: {{EDOs|41, 62, 103, 247c, 350bcde}}
{{Val list|legend=1| 41, 62, 103, 247c, 350bcde }}


Badness: 0.0256
Badness: 0.0256


==== 17-limit ====
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 385/384, 847/845
Comma list: 225/224, 243/242, 273/272, 385/384, 847/845


POTE generator: ~27/26 = 58.261
POTE generator: ~27/26 = 58.261


Map: [&lt;1 1 3 3 2 2 2|, &lt;0 12 -14 -4 30 35 43|]
Mapping: [{{val| 1 1 3 3 2 2 2 }}, {{val| 0 12 -14 -4 30 35 43 }}]


EDOs: {{EDOs|41, 62, 103}}
{{Val list|legend=1| 41, 62, 103 }}


Badness: 0.0225
Badness: 0.0225


=== Phicordial ===
=== Phicordial ===
Commas: 225/224, 243/242, 385/384, 2200/2197
Comma list: 225/224, 243/242, 385/384, 2200/2197


POTE generator: ~16/13 = 361.121
POTE generator: ~16/13 = 361.121


Map: [&lt;1 7 -4 1 17 4|, &lt;0 -18 21 6 -45 -1|]
Mapping: [{{val| 1 7 -4 1 17 4 }}, {{val| 0 -18 21 6 -45 -1 }}]


EDOs: {{EDOs|10, 103, 113, 216c}}
{{Val list|legend=1| 10, 103, 113, 216c }}


Badness: 0.0332
Badness: 0.0332


==== 17-limit ====
==== 17-limit ====
Commas: 225/224, 243/242, 273/272, 441/440, 2200/2197
Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197


POTE generator: ~16/13 = 361.123
POTE generator: ~16/13 = 361.123


Map: [&lt;1 7 -4 1 17 4 8|, &lt;0 -18 21 6 -45 -1 -13|]
Mapping: [{{val| 1 7 -4 1 17 4 8 }}, {{val| 0 -18 21 6 -45 -1 -13 }}]


EDOs: {{EDOs|10, 103, 113, 216c}}
{{Val list|legend=1| 10, 103, 113, 216c }}


Badness: 0.0247
Badness: 0.0247


== Revelation ==
== Revelation ==
Commas: 99/98, 176/175, 1029/1024
Comma list: 99/98, 176/175, 1029/1024


POTE generator: ~15/14 = 116.277
POTE generator: ~15/14 = 116.277


Map: [&lt;1 1 3 3 5|, &lt;0 6 -7 -2 -16|]
Mapping: [{{val| 1 1 3 3 5 }}, {{val| 0 6 -7 -2 -16 }}]


EDOs: {{EDOs|10e, 21, 31}}
{{Val list|legend=1| 10e, 21, 31 }}


Badness: 0.0329
Badness: 0.0329


=== 13-limit ===
=== 13-limit ===
Commas: 66/65, 99/98, 105/104, 512/507
Comma list: 66/65, 99/98, 105/104, 512/507


POTE generator: ~15/14 = 116.268
POTE generator: ~15/14 = 116.268


Map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
Mapping: [{{val| 1 1 3 3 5 4 }}, {{val| 0 6 -7 -2 -16 -3 }}]


EDOs: {{EDOs|10e, 21, 31}}
{{Val list|legend=1| 10e, 21, 31 }}


Badness: 0.0295
Badness: 0.0295


== Hemimiracle ==
== Hemimiracle ==
Commas: 225/224, 245/242, 1029/1024
Comma list: 225/224, 245/242, 1029/1024


POTE generator: ~33/32 = 58.408
POTE generator: ~33/32 = 58.408


Map: [&lt;1 1 3 3 4|, &lt;0 12 -14 -4 -11|]
Mapping: [{{val| 1 1 3 3 4 }}, {{val| 0 12 -14 -4 -11 }}]


EDOs: {{EDOs|20, 21, 41, 144e, 185cee, 226cee}}
{{Val list|legend=1| 20, 21, 41, 144e, 185cee, 226cee }}


Badness: 0.0592
Badness: 0.0592


=== 13-limit ===
=== 13-limit ===
Commas: 105/104, 196/195, 245/242, 512/507
Comma list: 105/104, 196/195, 245/242, 512/507


POTE generator: ~33/32 = 58.430
POTE generator: ~33/32 = 58.430


Map: [&lt;1 1 3 3 4 4|, &lt;0 12 -14 -4 -11 -6|]
Mapping: [{{val| 1 1 3 3 4 4 }}, {{val| 0 12 -14 -4 -11 -6 }}]


EDOs: {{EDOs|20, 21, 41, 144eff, 185ceeff}}
{{Val list|legend=1| 20, 21, 41, 144eff, 185ceeff }}


Badness: 0.0432
Badness: 0.0432


== Oracle ==
== Oracle ==
Commas: 121/120, 225/224, 1029/1024
Comma list: 121/120, 225/224, 1029/1024


POTE generator: ~11/8 = 541.668
POTE generator: ~11/8 = 541.668


Map: [&lt;1 7 -4 1 3|, &lt;0 -12 14 4 1|]
Mapping: [{{val| 1 7 -4 1 3 }}, {{val| 0 -12 14 4 1 }}]


EDOs: {{EDOs|11, 20, 31, 51, 82e, 113e, 144ee}}
{{Val list|legend=1| 11, 20, 31, 51, 82e, 113e, 144ee }}


Badness: 0.0427
Badness: 0.0427
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