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Gamelismic clan: Difference between revisions

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Databoxes for superkleismic to clyndro; edo list reviewed
Finish databoxes; edo list reviewed
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= Necromanteion =
= Necromanteion =
Period: 1\1
Optimal ([[POTE]]) generator: ~48/35 = 541.779
EDO generator: [[31edo|14\31]], [[51edo|23\51]]
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
[[Comma list]]: 1029/1024, 5103/5000
[[Comma list]]: 1029/1024, 5103/5000
POTE generator: ~48/35 = 541.779


[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]
[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]


{{Val list|legend=1| 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd }}
{{Val list|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}


[[Badness]]: 0.1177
[[Badness]]: 0.1177
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/11 = 541.729
EDO generator: [[31edo|14\31]], [[51edo|23\51]]
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: 176/175, 243/242, 1029/1024
Comma list: 176/175, 243/242, 1029/1024
POTE generator: ~15/11 = 541.729


Mapping: [{{val| 1 7 10 1 17 }}, {{val| 0 -12 -17 4 -30 }}]
Mapping: [{{val| 1 7 10 1 17 }}, {{val| 0 -12 -17 4 -30 }}]


{{Val list|legend=1| 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde }}
{{Val list|legend=1| 20ce, 31, 113c, 144c, 175c, 381bccdee }}


Badness: 0.0535
Badness: 0.0535
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/11 = 541.606
EDO generator: [[31edo|14\31]], [[51edo|23\51]]
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: 144/143, 176/175, 243/242, 343/338
Comma list: 144/143, 176/175, 243/242, 343/338
POTE generator: ~15/11 = 541.606


Mapping: [{{val| 1 7 10 1 17 1 }}, {{val| 0 -12 -17 4 -30 6 }}]
Mapping: [{{val| 1 7 10 1 17 1 }}, {{val| 0 -12 -17 4 -30 6 }}]


{{Val list|legend=1| 31, 51ce, 82cf, 113cf, 144cf }}
{{Val list|legend=1| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}


Badness: 0.0470
Badness: 0.0470
</div></div>


= Widefourth =
= Widefourth =
Period: 1\1
Optimal ([[POTE]]) generator: ~3125/2304 = 524.210
EDO generator: [[87edo|38\87]], [[103edo|45\103]], [[190edo|83\190]]
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
[[Comma list]]: 1029/1024, 48828125/48771072
[[Comma list]]: 1029/1024, 48828125/48771072
POTE generator: ~3125/2304 = 524.210


[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]
Line 1,675: Line 1,733:
[[Wedgie]]: {{wedgie| 33 13 -11 -56 -110 -62 }}
[[Wedgie]]: {{wedgie| 33 13 -11 -56 -110 -62 }}


{{Val list|legend=1| 16, 71, 87, 103, 190 }}
{{Val list|legend=1| 16, 55b, 71, 87, 103, 190 }}


[[Badness]]: 0.1541
[[Badness]]: 0.1541
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3125/2304 = 524.210
EDO generator: [[87edo|38\87]], [[103edo|45\103]], [[190edo|83\190]]
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: 385/384, 441/440, 234375/234256
Comma list: 385/384, 441/440, 234375/234256
POTE generator: ~3125/2304 = 524.210


Mapping: [{{val| 1 16 8 -2 17 }}, {{val| 0 -33 -13 11 -31 }}]
Mapping: [{{val| 1 16 8 -2 17 }}, {{val| 0 -33 -13 11 -31 }}]


{{Val list|legend=1| 16, 71, 87, 103, 190 }}
{{Val list|legend=1| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.0408
Badness: 0.0408
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~65/48 = 524.209
EDO generator: [[87edo|38\87]], [[103edo|45\103]], [[190edo|83\190]]
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: 385/384, 441/440, 625/624, 847/845
Comma list: 385/384, 441/440, 625/624, 847/845
POTE generator: ~65/48 = 524.209


Mapping: [{{val| 1 16 8 -2 17 12 }}, {{val| 0 -33 -13 11 -31 -19 }}]
Mapping: [{{val| 1 16 8 -2 17 12 }}, {{val| 0 -33 -13 11 -31 -19 }}]


{{Val list|legend=1| 16, 71, 87, 103, 190 }}
{{Val list|legend=1| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.0216
Badness: 0.0216
</div></div>


= Tritriple =
= Tritriple =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~864/625 = 559.332
EDO generator: [[103edo|48\103]], [[118edo|55\118]], [[133edo|62\133]]
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
Comma list: {{monzo| 31 20 -27 }}
Comma list: {{monzo| 31 20 -27 }}
POTE generator: ~864/625 = 559.332


Mapping: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]
Mapping: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]


{{Val list|legend=1| 15, 103, 118, 133, 959, 1077 }}
{{Val list|legend=1| 118, 959, 1077 }}


Badness: 0.2836
Badness: 0.2836
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~864/625 = 559.295
EDO generator: [[103edo|48\103]], [[118edo|55\118]], [[133edo|62\133]]
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
[[Comma list]]: 1029/1024, 1959552/1953125
[[Comma list]]: 1029/1024, 1959552/1953125
POTE generator: ~864/625 = 559.295


[[Mapping]]: [{{val| 1 -11 -7 7 }}, {{val| 0 27 20 -9 }}]
[[Mapping]]: [{{val| 1 -11 -7 7 }}, {{val| 0 27 20 -9 }}]


{{Val list|legend=1| 15, 103, 118, 133, 339d }}
{{Val list|legend=1| 103, 118, 339d }}


[[Badness]]: 0.1186
[[Badness]]: 0.1186
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~864/625 = 559.295
EDO generator: [[103edo|48\103]], [[118edo|55\118]], [[133edo|62\133]]
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: 385/384, 441/440, 43923/43750
Comma list: 385/384, 441/440, 43923/43750


Line 1,731: Line 1,866:
Mapping: [{{val| 1 -11 -7 7 -4 }}, {{val| 0 27 20 -9 16 }}]
Mapping: [{{val| 1 -11 -7 7 -4 }}, {{val| 0 27 20 -9 16 }}]


{{Val list|legend=1| 15, 103, 118, 133, 339de }}
{{Val list|legend=1| 103, 118, 339de }}


Badness: 0.0353
Badness: 0.0353
</div></div>


= Restles =
= Restles =
Period: 1\1
Optimal ([[POTE]]) generator: ~315/256 = 358.5485
EDO generator: [[77edo|23\77]], [[87edo|26\87]], [[164edo|49\164]]
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
[[Comma list]]: 1029/1024, 153664/151875
[[Comma list]]: 1029/1024, 153664/151875
POTE generator: ~315/256 = 358.5485


[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]
[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]


{{Val list|legend=1| 10, 67, 77, 87, 164 }}
{{Val list|legend=1| 77, 87, 164 }}


[[Badness]]: 0.1080
[[Badness]]: 0.1080
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~27/22 = 358.5713
EDO generator: [[77edo|23\77]], [[87edo|26\87]], [[164edo|49\164]]
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: 385/384, 441/440, 153664/151875
Comma list: 385/384, 441/440, 153664/151875
POTE generator: ~27/22 = 358.5713


Mapping: [{{val| 1 -2 8 4 -7 }}, {{val| 0 12 -19 -4 35 }}]
Mapping: [{{val| 1 -2 8 4 -7 }}, {{val| 0 12 -19 -4 35 }}]


{{Val list|legend=1| 10, 77, 87, 164 }}
{{Val list|legend=1| 77, 87, 164 }}


Badness: 0.0547
Badness: 0.0547
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 358.5739
EDO generator: [[77edo|23\77]], [[87edo|26\87]], [[164edo|49\164]]
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: 196/195, 352/351, 385/384, 676/675
Comma list: 196/195, 352/351, 385/384, 676/675
POTE generator: ~16/13 = 358.5739


Mapping: [{{val| 1 -2 8 4 -7 4 }}, {{val| 0 12 -19 -4 35 -1 }}]
Mapping: [{{val| 1 -2 8 4 -7 4 }}, {{val| 0 12 -19 -4 35 -1 }}]


{{Val list|legend=1| 10, 77, 87, 164 }}
{{Val list|legend=1| 77, 87, 164 }}


Badness: 0.0282
Badness: 0.0282
</div></div>


= Baladic =
= Baladic =
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.
Period: 1\2
Optimal ([[POTE]]) generator: ~8/7 = 233.6155
EDO generator: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]], [[36edo|7\36]], [[46edo|9\46]], [[62edo|12\62]], [[82edo|16\82]], [[118edo|23\118]]
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">


Comma list: 169/168, 273/272, 289/288
Comma list: 169/168, 273/272, 289/288


Period: 1\2
Sval mapping: [{{val| 2 2 6 7 7 }}, {{val| 0 3 -1 1 3 }}]


POTE generator: ~8/7 = 233.6155
Mapping generators: ~17/12, ~8/7


Sval mapping: [{{val| 2 2 6 7 7 }}, {{val| 0 3 -1 1 3 }}]
{{Val list|legend=1| 10, 26, 36, 154f, 190ffg }}


{{Val list|legend=1| 26, 36, 46, 82, 118f }}
</div></div>


[[Category:Theory]]
[[Category:Theory]]
Line 1,788: Line 1,982:
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]
{{todo| review | improve readability }}
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