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Gamelismic clan: Difference between revisions

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= Rodan =
= Rodan =
{{main|Rodan}}
{{main|Rodan}}
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.417
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[87edo|17\87]]
Scales (Scala files): [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]
<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]]: 245/243, 1029/1024
[[Comma list]]: 245/243, 1029/1024


[[POTE generator]]: ~8/7 = 234.417
[[Mapping]]: [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1 }}]
 
Mapping: [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1 }}]


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 516: Line 529:
Algebraic generator: [[Algebraic number|larger root]] of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.
Algebraic generator: [[Algebraic number|larger root]] of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.


{{Val list|legend=1| 5, 41, 87, 128, 215d }}
{{Val list|legend=1| 41, 87, 128, 215d }}


Badness: 0.0371
[[Badness]]: 0.0371
 
</div></div>


== 11-limit ==
== 11-limit ==
[[Comma list]]: 245/243, 385/384, 441/440


[[POTE generator]]: ~8/7 = 234.459
Period: 1\1
 
Optimal ([[POTE]]) generator: ~8/7 = 234.459
 
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[87edo|17\87]]
 
Scales (Scala files): [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]
 
<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: 245/243, 385/384, 441/440


Mapping: [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13 }}]
Mapping: [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13 }}]


[[Minimax tuning]]:  
Minimax tuning:  
* 11-odd-limit:  
* 11-odd-limit:  
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
Line 534: Line 562:
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.


{{Val list|legend=1| 5, 41, 46, 87 }}
{{Val list|legend=1| 41, 46, 87 }}


Badness: 0.0231
Badness: 0.0231


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


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.482
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[87edo|17\87]]
Scales (Scala files): [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]
<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, 245/243, 352/351, 364/363
Comma list: 196/195, 245/243, 352/351, 364/363
[[POTE generator]]: ~8/7 = 234.482


Mapping: [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22 }}]
Mapping: [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22 }}]
Line 557: Line 598:


Badness: 0.0184
Badness: 0.0184
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.524
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[87edo|17\87]]
Scales (Scala files): [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]
<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: 154/153, 196/195, 245/243, 256/255, 273/272
Comma list: 154/153, 196/195, 245/243, 256/255, 273/272
[[POTE generator]]: ~8/7 = 234.524


Mapping: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}]
Mapping: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}]
Line 571: Line 627:


Badness: 0.0167
Badness: 0.0167
</div></div>


=== Aerodactyl ===
=== Aerodactyl ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.639
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[51edo|10\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: 91/90, 245/243, 385/384, 441/440
Comma list: 91/90, 245/243, 385/384, 441/440
[[POTE generator]]: ~8/7 = 234.639


Mapping: [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24 }}]
Mapping: [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24 }}]


{{Val list|legend=1| 5, 41f, 46, 51c }}
{{Val list|legend=1| 41f, 46, 133ff }}


Badness: 0.0340
Badness: 0.0340
</div></div>


== Aerodino ==
== Aerodino ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.728
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[51edo|10\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, 245/243, 1029/1024
Comma list: 176/175, 245/243, 1029/1024
POTE generator: ~8/7 = 234.728


Mapping: [{{val| 1 1 -1 3 -3 }}, {{val| 0 3 17 -1 33 }}]
Mapping: [{{val| 1 1 -1 3 -3 }}, {{val| 0 3 17 -1 33 }}]


{{Val list|legend=1| 5e, 41e, 46 }}
{{Val list|legend=1| 41e, 46 }}


Badness: 0.0543
Badness: 0.0543
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.782
EDO generators: [[41edo|8\41]], [[46edo|9\46]], [[51edo|10\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">
Comma list: 91/90, 176/175, 245/243, 847/845
Comma list: 91/90, 176/175, 245/243, 847/845
POTE generator: ~8/7 = 234.782


Mapping: [{{val| 1 1 -1 3 -3 -1 }}, {{val| 0 3 17 -1 33 24 }}]
Mapping: [{{val| 1 1 -1 3 -3 -1 }}, {{val| 0 3 17 -1 33 24 }}]


{{Val list|legend=1| 5e, 46 }}
{{Val list|legend=1| 41ef, 46 }}


Badness: 0.0358
Badness: 0.0358
</div></div>


== Varan ==
== Varan ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.145
EDO generators: [[36edo|7\36]], [[41edo|8\41]], [[46edo|9\46]]
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: 100/99, 245/243, 1029/1024
Comma list: 100/99, 245/243, 1029/1024
POTE generator: ~8/7 = 234.145


Mapping: [{{val| 1 1 -1 3 -2 }}, {{val| 0 3 17 -1 28 }}]
Mapping: [{{val| 1 1 -1 3 -2 }}, {{val| 0 3 17 -1 28 }}]


{{Val list|legend=1| 5e, 41, 46e }}
{{Val list|legend=1| 36ce, 41 }}


Badness: 0.0449
Badness: 0.0449
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 234.089
EDO generators: [[36edo|7\36]], [[41edo|8\41]], [[46edo|9\46]]
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: 100/99, 105/104, 245/243, 352/351
Comma list: 100/99, 105/104, 245/243, 352/351
POTE generator: ~8/7 = 234.089


Mapping: [{{val| 1 1 -1 3 -2 0 }}, {{val| 0 3 17 -1 28 19 }}]
Mapping: [{{val| 1 1 -1 3 -2 0 }}, {{val| 0 3 17 -1 28 19 }}]


{{Val list|legend=1| 5e, 41 }}
{{Val list|legend=1| 36ce, 41 }}


Badness: 0.0323
Badness: 0.0323
</div></div>


= Valentine =
= Valentine =
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