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Gamelismic clan: Difference between revisions

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→Slendric: databoxified
→Miracle: databoxified; edo list reviewed
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== Subgroup extensions ==
== Subgroup extensions ==
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.


= Miracle =
= Miracle =
{{main|Miracle}}
{{main| Miracle }}
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~15/14 = 116.675
 
EDO generators: [[31edo|3\31]], [[41edo|4\41]], [[72edo|7\72]]
 
Scales (Scala files): [[Miracle 10]], [[Blackjack]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7


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


[[POTE generator]]: ~15/14 = 116.675
[[Mapping]]: [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2 }}]


Mapping: [{{val| 1 1 3 3 }}, {{val| 0 6 -7 -2 }}]
{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}
 
Wedgie: {{wedgie| 6 -7 -2 -25 -20 15 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 61: Line 74:
Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12
Algebraic generator: Secor59, [[Algebraic number|positive root]] of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12


{{Val list|legend=1| 10, 21, 31, 41, 72, 175 }}
{{Val list|legend=1| 10, 21, 31, 41, 72 }}


[[Badness]]: 0.0167
[[Badness]]: 0.0167
</div></div>


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


[[POTE generator]]: ~15/14 = 116.633
Period: 1\1


[[Mapping]]: [{{val| 1 1 3 3 2 }}, {{val| 0 6 -7 -2 15 }}]
Optimal ([[POTE]]) generator: ~15/14 = 116.633


[[Minimax tuning]]:
EDO generators: [[31edo|3\31]], [[41edo|4\41]], [[72edo|7\72]]
 
Scales (Scala files): [[Miracle 10]], [[Blackjack]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 243/242, 385/384
 
Mapping: [{{val| 1 1 3 3 2 }}, {{val| 0 6 -7 -2 15 }}]
 
Minimax tuning:
* [[11-odd-limit]]:  
* [[11-odd-limit]]:  
: [{{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 }}]
: [{{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 }}]
Line 79: Line 107:
Algebraic generator: Secor59
Algebraic generator: Secor59


{{Val list|legend=1| 10, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}
{{Val list|legend=1| 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}


[[Badness]]: 0.0107
Badness: 0.0107


{{see also| Chords of miracle }}
</div></div>


=== Miraculous ===
=== Miraculous ===
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.747
EDO generators: [[31edo|3\31]], [[41edo|4\41]]
Scales (Scala files): [[Miracle 10]], [[Blackjack]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 243/242
Comma list: 105/104, 144/143, 196/195, 243/242
POTE generator: ~15/14 = 116.747


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


{{Val list|legend=1| 10, 31, 41, 72f, 113f, 185cff }}
{{Val list|legend=1| 10, 21e, 31, 41, 72f, 113f, 185cff }}


Badness: 0.0187
Badness: 0.0187
</div></div>


=== Benediction ===
=== Benediction ===
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.574
EDO generators: [[31edo|3\31]], [[72edo|7\72]], [[103edo|10\103]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 385/384
Comma list: 225/224, 243/242, 351/350, 385/384
POTE generator: ~15/14 = 116.574


Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 6 -7 -2 15 -34 }}]
Mapping: [{{val| 1 1 3 3 2 7 }}, {{val| 0 6 -7 -2 15 -34 }}]
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Badness: 0.0157
Badness: 0.0157
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.585
EDO generators: [[31edo|3\31]], [[72edo|7\72]], [[103edo|10\103]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13.17
Comma list: 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


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


{{Val list|legend=1| 31, 72, 103, 175f }}
{{Val list|legend=1| 31, 72, 103, 175f }}
</div></div>


=== Manna ===
=== Manna ===
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.739
EDO generators: [[41edo|4\41]], [[72edo|7\72]], [[113edo|11\113]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 325/324, 385/384
Comma list: 225/224, 243/242, 325/324, 385/384
POTE generator: ~15/14 = 116.739


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


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


Badness: 0.0170
Badness: 0.0170
</div></div>


=== Semimiracle ===
=== Semimiracle ===
Period: 1\2
Optimal ([[POTE]]) generator: ~15/14 = 116.624
EDO generators: [[62edo|6\62]], [[72edo|7\72]], [[82edo|8\82]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 243/242, 385/384
Comma list: 169/168, 225/224, 243/242, 385/384
POTE generator: ~15/14 = 116.624


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


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


Badness: 0.0246
Badness: 0.0246
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~15/14 = 116.628
EDO generators: [[62edo|6\62]], [[72edo|7\72]], [[82edo|8\82]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13.17
Comma list: 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


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


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


Badness: 0.0161
Badness: 0.0161
</div></div>


=== Hemisecordite ===
=== Hemisecordite ===
Period: 1\1
Optimal ([[POTE]]) generator: ~27/26 = 58.288
EDO generators: [[41edo|2\41]], [[62edo|3\62]], [[103edo|5\103]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384, 847/845
Comma list: 225/224, 243/242, 385/384, 847/845
POTE generator: ~27/26 = 58.288


Mapping: [{{val| 1 1 3 3 2 2 }}, {{val| 0 12 -14 -4 30 35 }}]
Mapping: [{{val| 1 1 3 3 2 2 }}, {{val| 0 12 -14 -4 30 35 }}]
Line 159: Line 290:


Badness: 0.0256
Badness: 0.0256
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\1
Optimal ([[POTE]]) generator: ~27/26 = 58.261
EDO generators: [[41edo|2\41]], [[62edo|3\62]], [[103edo|5\103]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13.17
Comma list: 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


Mapping: [{{val| 1 1 3 3 2 2 2 }}, {{val| 0 12 -14 -4 30 35 43 }}]
Mapping: [{{val| 1 1 3 3 2 2 2 }}, {{val| 0 12 -14 -4 30 35 43 }}]
Line 170: Line 316:


Badness: 0.0225
Badness: 0.0225
</div></div>


=== Phicordial ===
=== Phicordial ===
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 361.121
EDO generators: [[103edo|31\103]], [[113edo|34\113]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 385/384, 2200/2197
Comma list: 225/224, 243/242, 385/384, 2200/2197
POTE generator: ~16/13 = 361.121


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


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


Badness: 0.0332
Badness: 0.0332
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 361.123
EDO generators: [[103edo|31\103]], [[113edo|34\113]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13.17
Comma list: 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


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


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


Badness: 0.0247
Badness: 0.0247
</div></div>


== Revelation ==
== Revelation ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.277
EDO generators: [[21edo|2\21]], [[31edo|3\31]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1029/1024
Comma list: 99/98, 176/175, 1029/1024
POTE generator: ~15/14 = 116.277


Mapping: [{{val| 1 1 3 3 5 }}, {{val| 0 6 -7 -2 -16 }}]
Mapping: [{{val| 1 1 3 3 5 }}, {{val| 0 6 -7 -2 -16 }}]
Line 203: Line 394:


Badness: 0.0329
Badness: 0.0329
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.268
EDO generators: [[21edo|2\21]], [[31edo|3\31]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 99/98, 105/104, 512/507
Comma list: 66/65, 99/98, 105/104, 512/507
POTE generator: ~15/14 = 116.268


Mapping: [{{val| 1 1 3 3 5 4 }}, {{val| 0 6 -7 -2 -16 -3 }}]
Mapping: [{{val| 1 1 3 3 5 4 }}, {{val| 0 6 -7 -2 -16 -3 }}]
Line 214: Line 420:


Badness: 0.0295
Badness: 0.0295
</div></div>


== Hemimiracle ==
== Hemimiracle ==
Period: 1\1
Optimal ([[POTE]]) generator: ~33/32 = 58.408
EDO generators: [[20edo|1\20]], [[21edo|1\21]], [[41edo|2\41]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
Comma list: 225/224, 245/242, 1029/1024
Comma list: 225/224, 245/242, 1029/1024
POTE generator: ~33/32 = 58.408


Mapping: [{{val| 1 1 3 3 4 }}, {{val| 0 12 -14 -4 -11 }}]
Mapping: [{{val| 1 1 3 3 4 }}, {{val| 0 12 -14 -4 -11 }}]
Line 225: Line 446:


Badness: 0.0592
Badness: 0.0592
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~33/32 = 58.430
EDO generators: [[20edo|1\20]], [[21edo|1\21]], [[41edo|2\41]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 245/242, 512/507
Comma list: 105/104, 196/195, 245/242, 512/507
POTE generator: ~33/32 = 58.430


Mapping: [{{val| 1 1 3 3 4 4 }}, {{val| 0 12 -14 -4 -11 -6 }}]
Mapping: [{{val| 1 1 3 3 4 4 }}, {{val| 0 12 -14 -4 -11 -6 }}]
Line 236: Line 472:


Badness: 0.0432
Badness: 0.0432
</div></div>


== Oracle ==
== Oracle ==
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 541.668
EDO generators: [[11edo|5\11]], [[20edo|9\20]], [[31edo|14\31]]
Scales (Scala files):
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 1029/1024
Comma list: 121/120, 225/224, 1029/1024
POTE generator: ~11/8 = 541.668


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


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


Badness: 0.0427
Badness: 0.0427
</div></div>


= Rodan =
= Rodan =
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"