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Gamelismic clan: Difference between revisions

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= Slendric =
= Slendric =
{{main| Slendric }}
{{main| Slendric }}
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 233.688
EDO generator: [[36edo|7\36]], [[41edo|8\41]], [[77edo|15\77]]
Scales (Scala files): [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]
<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: 2.3.7
Subgroup: 2.3.7
Line 27: Line 15:


[[Gencom]]: [2 8/7; 1029/1024]  
[[Gencom]]: [2 8/7; 1029/1024]  
[[POTE generator]]: ~8/7 = 233.688


{{Val list|legend=1| 36, 77, 113, 190 }}
{{Val list|legend=1| 36, 77, 113, 190 }}


</div></div>
Scales: [[slendric5]], [[slendric6]], [[slendric11]], [[slendric16]]


== Full seven limit extensions ==
== Full seven limit extensions ==
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal_lists|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]], which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.


Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Mothra|mothra]], [[Schismatic family #Guiron|guiron]] and [[Sensipent family #Heinz|heinz]]. The rest are considered below.
Discussed elsewhere are [[Archytas clan #Blacksmith|blacksmith]], [[Meantone family #Mothra|mothra]], [[Schismatic family #Guiron|guiron]] and [[Sensipent family #Heinz|heinz]]. The rest are considered below.
Line 42: Line 32:
= 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
Subgroup: 2.3.5.7
Line 60: Line 38:


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


{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}
{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]:
* [[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 }}]
: [{{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
: [[Eigenmonzo]]s: 2, 6/5
* [[9-odd-limit]]:
* [[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 }}]
: [{{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]]s: 2, 10/9
Line 77: Line 57:
[[Badness]]: 0.0167
[[Badness]]: 0.0167


</div></div>
Scales: [[Miracle 10]], [[Blackjack]]


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 116.633
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
Subgroup: 2.3.5.7.11
Line 98: Line 66:


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


Minimax tuning:
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 }}]
: [[Eigenmonzo]]s: 2, 10/9
: Eigenmonzos: 2, 10/9


Algebraic generator: Secor59
Algebraic generator: Secor59
Line 110: Line 80:
Badness: 0.0107
Badness: 0.0107


</div></div>
Scales: [[Miracle 10]], [[Blackjack]]


=== 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
Subgroup: 2.3.5.7.11.13
Line 131: Line 89:


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


{{Val list|legend=1| 10, 21e, 31, 41, 72f, 113f, 185cff }}
{{Val list|legend=1| 10, 21e, 31, 41, 72f, 113f, 185cff }}
Line 136: Line 96:
Badness: 0.0187
Badness: 0.0187


</div></div>
Scales: [[Miracle 10]], [[Blackjack]]


=== 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
Subgroup: 2.3.5.7.11.13
Line 157: Line 105:


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


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


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
Subgroup: 2.3.5.7.11.13.17
Line 183: Line 119:


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


{{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
Subgroup: 2.3.5.7.11.13
Line 207: Line 131:


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


{{Val list|legend=1| 31f, 41, 72, 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
Subgroup: 2.3.5.7.11.13
Line 233: Line 145:


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


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11.13.17
Line 259: Line 159:


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


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11.13
Line 285: Line 173:


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


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


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
Subgroup: 2.3.5.7.11.13.17
Line 311: Line 187:


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


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


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
Subgroup: 2.3.5.7.11.13
Line 337: Line 201:


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


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11.13.17
Line 363: Line 215:


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


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11
Line 389: Line 229:


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


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


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
Subgroup: 2.3.5.7.11.13
Line 415: Line 243:


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


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


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
Subgroup: 2.3.5.7.11
Line 441: Line 257:


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


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


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
Subgroup: 2.3.5.7.11.13
Line 467: Line 271:


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


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


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
Subgroup: 2.3.5.7.11
Line 493: Line 285:


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


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


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


= 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
Subgroup: 2.3.5.7
Line 520: Line 300:


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


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and 9-odd-limit:
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5


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


{{Val list|legend=1| 41, 87, 128, 215d }}
{{Val list|legend=1| 41, 87, 128, 215d }}
Line 532: Line 314:
[[Badness]]: 0.0371
[[Badness]]: 0.0371


</div></div>
Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]


== 11-limit ==
== 11-limit ==
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
Subgroup: 2.3.5.7.11
Line 553: Line 323:


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 }}]
POTE generator: ~8/7 = 234.459


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 }}]
: [[Eigenmonzo]]s: 2, 11/9
: Eigenmonzos: 2, 11/9


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.
Line 565: Line 337:
Badness: 0.0231
Badness: 0.0231


</div></div>
Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]


=== 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
Subgroup: 2.3.5.7.11.13
Line 586: Line 346:


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 }}]
POTE generator: ~8/7 = 234.482


Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit:
* 13- and 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: Eigenmonzos: 2, 13/9
: Eigenmonzos: 2, 13/9
Line 598: Line 360:
Badness: 0.0184
Badness: 0.0184


</div></div>
Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]


==== 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
Subgroup: 2.3.5.7.11.13.17
Line 619: Line 369:


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 }}]
POTE generator: ~8/7 = 234.524


Minimax tuning:  
Minimax tuning:  
Line 627: Line 379:
Badness: 0.0167
Badness: 0.0167


</div></div>
Scales: [[rodan26opt]], [[rodan31opt]], [[rodan41opt]]


=== 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
Subgroup: 2.3.5.7.11.13
Line 648: Line 388:


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 }}]
POTE generator: ~8/7 = 234.639


{{Val list|legend=1| 41f, 46, 133ff }}
{{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
Subgroup: 2.3.5.7.11
Line 674: Line 402:


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 }}]
POTE generator: ~8/7 = 234.728


{{Val list|legend=1| 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


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 }}]
POTE generator: ~8/7 = 234.782


{{Val list|legend=1| 41ef, 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


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 }}]
POTE generator: ~8/7 = 234.145


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


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 }}]
POTE generator: ~8/7 = 234.089


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


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


= Valentine =
= Valentine =
Line 759: Line 451:
== 5-limit ==
== 5-limit ==


Period: 1\1
Subgroup: 2.3.5
 
Optimal ([[POTE]]) generator: ~25/24 = 78.039
 
EDO generators: [[15edo|1\15]], [[16edo|1\16]], [[31edo|2\31]], [[46edo|3\46]], [[77edo|5\77]]
 
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]]: 1990656/1953125


Comma list: 1990656/1953125
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]


Mapping: [{{val| 1 1 2 }}, {{val| 0 9 5 }}]
[[POTE generator]]: ~25/24 = 78.039


{{Val list|legend=1| 15, 31, 46, 77, 123 }}
{{Val list|legend=1| 15, 31, 46, 77, 123 }}


Badness: 0.1228
[[Badness]]: 0.1228
 
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~21/20 = 77.864
EDO generators: [[15edo|1\15]], [[16edo|1\16]], [[31edo|2\31]], [[46edo|3\46]], [[77edo|5\77]]
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
Subgroup: 2.3.5.7
Line 804: Line 472:


Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20
[[POTE generator]]: ~21/20 = 77.864


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7-odd-limit:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s: 2, 7/6
: [[Eigenmonzo]]s: 2, 7/6
* 9-odd-limit:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7


Algebraic generator: [[Algebraic number|smaller root]] of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.  
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.  


{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}
{{Val list|legend=1| 15, 31, 46, 77, 185, 262cd }}


Badness: 0.0311
[[Badness]]: 0.0311
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~21/20 = 77.881
EDO generators: [[15edo|1\15]], [[16edo|1\16]], [[31edo|2\31]], [[46edo|3\46]], [[77edo|5\77]]
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
Subgroup: 2.3.5.7.11
Line 842: Line 498:


Mapping generators: ~2, ~21/20
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.881


Minimax tuning:
Minimax tuning:
* 11-odd-limit:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]
: Eigenmonzos: 2, 11/7
: Eigenmonzos: 2, 11/7


Algebraic generator: [[Algebraic number|positive root]] of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.


{{Val list|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}
{{Val list|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}


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


= Unidec =
= Unidec =
Line 860: Line 516:


== 5-limit ==
== 5-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.047
EDO generator: [[26edo|4\26]], [[46edo|7\46]], [[72edo|11\72]], [[118edo|18\118]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5
Line 880: Line 524:


Mapping generators: ~177147/125000, ~10/9
Mapping generators: ~177147/125000, ~10/9
[[POTE generator]]: ~10/9 = 183.047


{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}
{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}
Line 885: Line 531:
Badness: 0.0824
Badness: 0.0824


</div></div>
Scales: [[unidec26]]


== 7-limit ==
== 7-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.161
EDO generator: [[26edo|4\26]], [[46edo|7\46]], [[72edo|11\72]], [[118edo|18\118]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5.7
Line 909: Line 543:
Mapping generators: ~1225/864, ~10/9
Mapping generators: ~1225/864, ~10/9


[[Wedgie]]: {{wedgie| 12 22 -4 7 -40 -71 }}
{{Multival|legend=1| 12 22 -4 7 -40 -71 }}
 
[[POTE generator]]: ~10/9 = 183.161


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7-odd-limit:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 47/26 0 6/13 -6/13 }}, {{monzo| 71/26 0 11/13 -11/13 }}, {{monzo| 71/26 0 -2/13 2/13 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5
* 9-odd-limit:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 57/28 11/7 0 -11/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7
Line 923: Line 559:
[[Badness]]: 0.0384
[[Badness]]: 0.0384


</div></div>
Scales: [[unidec26]]


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.165
EDO generator: [[26edo|4\26]], [[46edo|7\46]], [[72edo|11\72]], [[118edo|18\118]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5.7.11
Line 948: Line 572:


Minimax tuning:
Minimax tuning:
* 11-odd-limit:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: [[Eigenmonzo]]s: 2, 9/7
: Eigenmonzos: 2, 9/7


{{Val list|legend=1| 26, 46, 72, 118, 190 }}
{{Val list|legend=1| 26, 46, 72, 118, 190 }}
Line 956: Line 580:
Badness: 0.0155
Badness: 0.0155


</div></div>
Scales: [[unidec26]]


=== Ekadash ===
=== Ekadash ===
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.187
EDO generator: [[72edo|11\72]], [[118edo|18\118]], [[190edo|29\190]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5.7.11.13
Line 979: Line 591:


Mapping generators: ~99/70, ~10/9
Mapping generators: ~99/70, ~10/9
POTE generator: ~10/9 = 183.187


{{Val list|legend=1| 26f, 46f, 72, 118, 190, 262df, 452cdef }}
{{Val list|legend=1| 26f, 46f, 72, 118, 190, 262df, 452cdef }}
Line 984: Line 598:
Badness: 0.0204
Badness: 0.0204


</div></div>
Scales: [[unidec26]]


=== Hendec ===
=== Hendec ===
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.198
EDO generator: [[26edo|4\26]], [[46edo|7\46]], [[72edo|11\72]], [[118edo|18\118]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5.7.11.13
Line 1,007: Line 609:


Mapping generators: ~91/64, ~10/9
Mapping generators: ~91/64, ~10/9
POTE generator: ~10/9 = 183.198


{{Val list|legend=1| 26, 46, 72, 190ff }}
{{Val list|legend=1| 26, 46, 72, 190ff }}
Line 1,012: Line 616:
Badness: 0.0177
Badness: 0.0177


</div></div>
Scales: [[unidec26]]


==== 17-limit ====
==== 17-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~10/9 = 183.196
EDO generator: [[26edo|4\26]], [[46edo|7\46]], [[72edo|11\72]], [[118edo|18\118]]
Scales (Scala files): [[unidec26]]
<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
Subgroup: 2.3.5.7.11.13.17
Line 1,035: Line 627:


Mapping generators: ~17/12, ~10/9
Mapping generators: ~17/12, ~10/9
POTE generator: ~10/9 = 183.196


{{Val list|legend=1| 26, 46, 72, 190ffg }}
{{Val list|legend=1| 26, 46, 72, 190ffg }}


</div></div>
Scales: [[unidec26]]


= Hemithirds =
= Hemithirds =
{{main| Hemithirds }}
{{main| Hemithirds }}
{{see also| Luna family #Hemithirds }}
{{see also| Luna family #Hemithirds }}
Period: 1\1
Optimal ([[POTE]]) generator: ~28/25 = 193.244
EDO generator: [[31edo|5\31]], [[56edo|9\56]], [[87edo|14\87]], [[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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 1,063: Line 645:


{{Multival|legend=1| 15 -2 -5 -38 -50 -6 }}
{{Multival|legend=1| 15 -2 -5 -38 -50 -6 }}
[[POTE generator]]: ~28/25 = 193.244


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7-odd-limit:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}]
: [[Eigenmonzo]]s: 2, 7/6
: [[Eigenmonzo]]s: 2, 7/6
* 9-odd-limit:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 7/6
: [[Eigenmonzo]]s: 2, 7/6
Line 1,075: Line 659:


Badness: 0.0443
Badness: 0.0443
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~28/25 = 193.227
EDO generator: [[31edo|5\31]], [[56edo|9\56]], [[87edo|14\87]], [[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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 1,098: Line 668:
Mapping: [{{val| 1 4 2 2 7 }}, {{val| 0 -15 2 5 -22 }}]
Mapping: [{{val| 1 4 2 2 7 }}, {{val| 0 -15 2 5 -22 }}]


[[Minimax tuning]]:
POTE generator: ~28/25 = 193.227
* 11-odd-limit:
 
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}]
: [[Eigenmonzo]]s: 2, 11/7
: Eigenmonzos: 2, 11/7


{{Val list|legend=1| 31, 87, 118 }}
{{Val list|legend=1| 31, 87, 118 }}


Badness: 0.0190
Badness: 0.0190
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~28/25 = 193.166
EDO generator: [[31edo|5\31]], [[56edo|9\56]], [[87edo|14\87]], [[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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 1,128: Line 686:


Mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]
Mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]
POTE generator: ~28/25 = 193.166


{{Val list|legend=1| 31, 56, 87, 118, 205d }}
{{Val list|legend=1| 31, 56, 87, 118, 205d }}


Badness: 0.0217
Badness: 0.0217
</div></div>


= Hemiseven =
= Hemiseven =


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generator: ~320/243 = 483.267
[[Comma list]]: 1029/1024, 19683/19600


EDO generator: [[72edo|29\72]], [[77edo|31\77]], [[149edo|60\149]]
[[Mapping]]: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]


Scales (Scala files):
{{Multival|legend=1| 6 29 -2 32 -20 -86 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[POTE generator]]: ~320/243 = 483.267
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 1029/1024, 19683/19600
 
Mapping: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
 
Wedgie: {{wedgie| 6 29 -2 32 -20 -86 }}


{{Val list|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}
{{Val list|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}


Badness: 0.0566
[[Badness]]: 0.0566
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~320/243 = 483.276
EDO generator: [[72edo|29\72]], [[77edo|31\77]], [[149edo|60\149]]
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
Subgroup: 2.3.5.7.11
Line 1,182: Line 716:


Mapping: [{{val| 1 4 14 2 -5 }}, {{val| 0 -6 -29 2 21 }}]
Mapping: [{{val| 1 4 14 2 -5 }}, {{val| 0 -6 -29 2 21 }}]
POTE generator: ~320/243 = 483.276


{{Val list|legend=1| 72, 77, 149, 221e, 293de }}
{{Val list|legend=1| 72, 77, 149, 221e, 293de }}


Badness: 0.0285
Badness: 0.0285
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~120/91 = 483.256
EDO generator: [[72edo|29\72]], [[77edo|31\77]], [[149edo|60\149]]
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
Subgroup: 2.3.5.7.11.13
Line 1,208: Line 730:


Mapping: [{{val| 1 4 14 2 -5 19 }}, {{val| 0 -6 -29 2 21 -38 }}]
Mapping: [{{val| 1 4 14 2 -5 19 }}, {{val| 0 -6 -29 2 21 -38 }}]
POTE generator: ~120/91 = 483.256


{{Val list|legend=1| 72, 77, 149, 221ef }}
{{Val list|legend=1| 72, 77, 149, 221ef }}
</div></div>


== 17-limit ==
== 17-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~45/34 = 483.261
EDO generator: [[72edo|29\72]], [[77edo|31\77]], [[149edo|60\149]]
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
Subgroup: 2.3.5.7.11.13.17
Line 1,232: Line 742:


Mapping: [{{val| 1 4 14 2 -5 19 21 }}, {{val| 0 -6 -29 2 21 -38 -42 }}]
Mapping: [{{val| 1 4 14 2 -5 19 21 }}, {{val| 0 -6 -29 2 21 -38 -42 }}]
POTE generator: ~45/34 = 483.261


{{Val list|legend=1| 72, 77, 149, 221ef }}
{{Val list|legend=1| 72, 77, 149, 221ef }}
</div></div>


= Tritikleismic =
= Tritikleismic =
{{see also| Kleismic family #Tritikleismic }}
{{see also| Kleismic family #Tritikleismic }}
Period: 1\3
Optimal ([[POTE]]) generator: ~6/5 = 316.872
EDO generator: [[57edo|15\57]], [[72edo|19\72]], [[87edo|23\87]]
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
Subgroup: 2.3.5.7
Line 1,259: Line 757:


Mapping generators: ~63/50, ~6/5
Mapping generators: ~63/50, ~6/5
[[POTE generator]]: ~6/5 = 316.872


[[Minimax tuning]]:
[[Minimax tuning]]:
* 7-odd-limit:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 0 6/7 -6/7 }}, {{monzo| 8/3 0 5/7 -5/7 }}, {{monzo| 8/3 0 -2/7 2/7 }}]
: [[Eigenmonzo]]s: 2, 7/5
: [[Eigenmonzo]]s: 2, 7/5
* 9-odd-limit:
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 46/21 5/7 0 -5/14 }}, {{monzo| 20/7 -2/7 0 1/7 }}]
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7
Line 1,271: Line 771:


[[Badness]]: 0.0563
[[Badness]]: 0.0563
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\3
Optimal ([[POTE]]) generator: ~6/5 = 316.881
EDO generator: [[57edo|15\57]], [[72edo|19\72]], [[87edo|23\87]]
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
Subgroup: 2.3.5.7.11
Line 1,295: Line 781:


Mapping generators: ~44/35, ~6/5
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.881


Minimax tuning:
Minimax tuning:
* 11-odd-limit:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 46/21 5/7 0 -5/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 71/21 3/7 0 -3/14 0 }}]
: [[Eigenmonzo]]s: 2, 9/7
: Eigenmonzos: 2, 9/7


{{Val list|legend=1| 15, 42bc, 57, 72, 159, 231 }}
{{Val list|legend=1| 15, 42bc, 57, 72, 159, 231 }}


Badness: 0.0193
Badness: 0.0193
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\3
Optimal ([[POTE]]) generator: ~6/5 = 316.9585
EDO generator: [[72edo|19\72]], [[87edo|23\87]], [[159edo|42\159]]
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
Subgroup: 2.3.5.7.11.13
Line 1,328: Line 802:


Mapping generators: ~44/35, ~6/5
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.9585


{{Val list|legend=1| 72, 87, 159 }}
{{Val list|legend=1| 72, 87, 159 }}
</div></div>


== 17-limit ==
== 17-limit ==
Period: 1\3
Optimal ([[POTE]]) generator: ~6/5 = 316.9082
EDO generator: [[72edo|19\72]], [[87edo|23\87]], [[159edo|42\159]]
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
Subgroup: 2.3.5.7.11.13.17
Line 1,354: Line 816:


Mapping generators: ~34/27, ~6/5
Mapping generators: ~34/27, ~6/5
POTE generator: ~6/5 = 316.9082


{{Val list|legend=1| 72, 159, 231f }}
{{Val list|legend=1| 72, 159, 231f }}
</div></div>


= Superkleismic =
= Superkleismic =
{{see also| Shibboleth family #Superkleismic }}
{{see also| Shibboleth family #Superkleismic }}
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 321.930
EDO generator: [[15edo|4\15]], [[26edo|7\26]], [[41edo|11\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
Subgroup: 2.3.5.7
Line 1,379: Line 829:


[[Mapping]]: [{{val| 1 4 5 2 }}, {{val| 0 -9 -10 3 }}]
[[Mapping]]: [{{val| 1 4 5 2 }}, {{val| 0 -9 -10 3 }}]
[[POTE generator]]: ~6/5 = 321.930


{{Val list|legend=1| 11c, 15, 26, 41 }}
{{Val list|legend=1| 11c, 15, 26, 41 }}


[[Badness]]: 0.0479
[[Badness]]: 0.0479
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 321.847
EDO generator: [[15edo|4\15]], [[26edo|7\26]], [[41edo|11\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
Subgroup: 2.3.5.7.11
Line 1,405: Line 843:


Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]
Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]
POTE generator: ~6/5 = 321.847


{{Val list|legend=1| 11c, 15, 26, 41, 261ccdee }}
{{Val list|legend=1| 11c, 15, 26, 41, 261ccdee }}


Badness: 0.0257
Badness: 0.0257
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 321.994
EDO generator: [[15edo|4\15]], [[26edo|7\26]], [[41edo|11\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
Subgroup: 2.3.5.7.11.13
Line 1,431: Line 857:


Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
POTE generator: ~6/5 = 321.994


{{Val list|legend=1| 11cf, 15, 26, 41 }}
{{Val list|legend=1| 11cf, 15, 26, 41 }}


Badness: 0.0215
Badness: 0.0215
</div></div>


= Gorgo =
= Gorgo =
Line 1,442: Line 868:


== 5-limit (laconic) ==
== 5-limit (laconic) ==
Period: 1\1
Optimal ([[POTE]]) generator: ~10/9 = 227.426
EDO generator: [[16edo|3\16]], [[21edo|4\21]]
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
Subgroup: 2.3.5
Line 1,460: Line 875:
[[Mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 7 }}]
[[Mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 7 }}]


[[Wedgie]]: {{wedgie| 3 7 -1 4 -10 -22 }}
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
 
[[POTE generator]]: ~10/9 = 227.426


{{Val list|legend=1| 5, 16, 21, 37b }}
{{Val list|legend=1| 5, 16, 21, 37b }}


[[Badness]]: 0.1618
[[Badness]]: 0.1618
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 228.334
EDO generator: [[16edo|3\16]], [[21edo|4\21]]
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
Subgroup: 2.3.5.7
Line 1,487: Line 891:
[[Mapping]]: [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1 }}]
[[Mapping]]: [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1 }}]


[[Wedgie]]: {{wedgie| 3 7 -1 4 -10 -22 }}
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
 
[[POTE generator]]: ~8/7 = 228.334


{{Val list|legend=1| 5, 11c, 16, 21 }}
{{Val list|legend=1| 5, 11c, 16, 21 }}


[[Badness]]: 0.0607
[[Badness]]: 0.0607
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 227.373
EDO generator: [[16edo|3\16]], [[21edo|4\21]]
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
Subgroup: 2.3.5.7.11
Line 1,514: Line 906:


Mapping: [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13 }}]
Mapping: [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13 }}]
POTE generator: ~8/7 = 227.373


{{Val list|legend=1| 16, 21, 37b }}
{{Val list|legend=1| 16, 21, 37b }}
Line 1,522: Line 916:


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 227.230
EDO generator: [[16edo|3\16]], [[21edo|4\21]]
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
Subgroup: 2.3.5.7.11.13
Line 1,540: Line 922:


Mapping: [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9 }}]
Mapping: [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9 }}]
POTE generator: ~8/7 = 227.230


{{Val list|legend=1| 16, 21, 37b }}
{{Val list|legend=1| 16, 21, 37b }}


Badness: 0.0327
Badness: 0.0327
</div></div>


== Spartan ==
== Spartan ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 229.535
EDO generator: [[21edo|4\21]], [[26edo|5\26]]
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
Subgroup: 2.3.5.7.11
Line 1,566: Line 936:


Mapping: [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8 }}]
Mapping: [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8 }}]
POTE generator: ~8/7 = 229.535


{{Val list|legend=1| 5, 16e, 21, 47c, 68bcce }}
{{Val list|legend=1| 5, 16e, 21, 47c, 68bcce }}


Badness: 0.0627
Badness: 0.0627
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 229.059
EDO generator: [[21edo|4\21]], [[26edo|5\26]]
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
Subgroup: 2.3.5.7.11.13
Line 1,592: Line 950:


Mapping: [{{val| 1 1 1 3 5 2 }}, {{val| 0 3 7 -1 -8 9 }}]
Mapping: [{{val| 1 1 1 3 5 2 }}, {{val| 0 3 7 -1 -8 9 }}]
POTE generator: ~8/7 = 229.059


{{Val list|legend=1| 5, 16e, 21, 68bccef }}
{{Val list|legend=1| 5, 16e, 21, 68bccef }}


Badness: 0.0471
Badness: 0.0471
</div></div>


== Music ==
== Music ==
Line 1,605: Line 963:
{{main| Lemba }}
{{main| Lemba }}
{{see also| Jubilismic clan #Lemba }}
{{see also| Jubilismic clan #Lemba }}
Period: 1\2
Optimal ([[POTE]]) generator: ~8/7 = 232.089
EDO generator: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]]
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
Subgroup: 2.3.5.7
Line 1,627: Line 973:


{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}
{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}
[[POTE generator]]: ~8/7 = 232.089


{{Val list|legend=1| 10, 16, 26 }}
{{Val list|legend=1| 10, 16, 26 }}


[[Badness]]: 0.0622
[[Badness]]: 0.0622
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~8/7 = 230.974
EDO generators: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]]
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
Subgroup: 2.3.5.7.11
Line 1,653: Line 987:


Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
POTE generator: ~8/7 = 230.974


{{Val list|legend=1| 10, 16, 26 }}
{{Val list|legend=1| 10, 16, 26 }}


Badness: 0.0416
Badness: 0.0416
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~8/7 = 230.966
EDO generators: [[10edo|2\10]], [[16edo|3\16]], [[26edo|5\26]]
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
Subgroup: 2.3.5.7.11.13
Line 1,679: Line 1,001:


Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
POTE generator: ~8/7 = 230.966


{{Val list|legend=1| 10, 16, 26 }}
{{Val list|legend=1| 10, 16, 26 }}


Badness: 0.0255
Badness: 0.0255
</div></div>


= Gidorah =
= Gidorah =
Line 1,690: Line 1,012:


== 5-limit (university) ==
== 5-limit (university) ==
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 235.4416
EDO generator: [[5edo|1\5]], [[11edo|2\11]], [[16edo|3\16]]
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
Subgroup: 2.3.5
Line 1,707: Line 1,018:


[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 3 2 }}]
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 3 2 }}]
[[POTE generator]]: ~6/5 = 235.4416


{{Val list|legend=1| 5, 31cccc, …, 56… }}
{{Val list|legend=1| 5, 31cccc, …, 56… }}


[[Badness]]: 0.1018
[[Badness]]: 0.1018
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 230.762
EDO generator: [[5edo|1\5]], [[11edo|2\11]], [[16edo|3\16]]
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
Subgroup: 2.3.5.7
Line 1,732: Line 1,032:


[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 3 2 -1 }}]
[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 3 2 -1 }}]
[[POTE generator]]: ~8/7 = 230.762


{{Val list|legend=1| 5, 16c, 21cc, 26ccc }}
{{Val list|legend=1| 5, 16c, 21cc, 26ccc }}


[[Badness]]: 0.0623
[[Badness]]: 0.0623
</div></div>


= Clyndro =
= Clyndro =
{{see also| Pelogic family }}
{{see also| Pelogic family }}
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 226.469
EDO generator: [[5edo|1\5]], [[11edo|2\11]], [[16edo|3\16]]
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
Subgroup: 2.3.5.7
Line 1,759: Line 1,047:


[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]
[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]
[[POTE generator]]: ~8/7 = 226.469


{{Val list|legend=1| 5c, 11, 16 }}
{{Val list|legend=1| 5c, 11, 16 }}


[[Badness]]: 0.1592
[[Badness]]: 0.1592
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~8/7 = 226.428
EDO generator: [[5edo|1\5]], [[11edo|2\11]], [[16edo|3\16]]
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
Subgroup: 2.3.5.7.11
Line 1,785: Line 1,061:


Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]
Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]
POTE generator: ~8/7 = 226.428


{{Val list|legend=1| 5c, 11, 16 }}
{{Val list|legend=1| 5c, 11, 16 }}


Badness: 0.0697
Badness: 0.0697
</div></div>


= 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
Subgroup: 2.3.5.7
Line 1,811: Line 1,075:


[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]
[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]
[[POTE generator]]: ~48/35 = 541.779


{{Val list|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}
{{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
Subgroup: 2.3.5.7.11
Line 1,837: Line 1,089:


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 }}]
POTE generator: ~15/11 = 541.729


{{Val list|legend=1| 20ce, 31, 113c, 144c, 175c, 381bccdee }}
{{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
Subgroup: 2.3.5.7.11.13
Line 1,863: Line 1,103:


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 }}]
POTE generator: ~15/11 = 541.606


{{Val list|legend=1| 20ce, 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
Subgroup: 2.3.5.7
Line 1,890: Line 1,118:
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]


[[Wedgie]]: {{wedgie| 33 13 -11 -56 -110 -62 }}
{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}
 
[[POTE generator]]: ~3125/2304 = 524.210


{{Val list|legend=1| 16, 55b, 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
Subgroup: 2.3.5.7.11
Line 1,917: Line 1,133:


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 }}]
POTE generator: ~3125/2304 = 524.210


{{Val list|legend=1| 16, 55be, 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
Subgroup: 2.3.5.7.11.13
Line 1,943: Line 1,147:


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 }}]
POTE generator: ~65/48 = 524.209


{{Val list|legend=1| 16, 55be, 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
Subgroup: 2.3.5


Optimal ([[POTE]]) generator: ~864/625 = 559.332
[[Comma list]]: {{monzo| 31 20 -27 }}


EDO generator: [[103edo|48\103]], [[118edo|55\118]], [[133edo|62\133]]
[[Mapping]]: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]


Scales (Scala files):  
[[POTE generator]]: ~864/625 = 559.332
 
<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 }}
 
Mapping: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]


{{Val list|legend=1| 118, 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
Subgroup: 2.3.5.7
Line 1,996: Line 1,176:


[[Mapping]]: [{{val| 1 -11 -7 7 }}, {{val| 0 27 20 -9 }}]
[[Mapping]]: [{{val| 1 -11 -7 7 }}, {{val| 0 27 20 -9 }}]
[[POTE generator]]: ~864/625 = 559.295


{{Val list|legend=1| 103, 118, 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
Subgroup: 2.3.5.7.11
Line 2,024: Line 1,192:


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 }}]
POTE generator: ~864/625 = 559.295


{{Val list|legend=1| 103, 118, 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
Subgroup: 2.3.5.7
Line 2,050: Line 1,206:


[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]
[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]
[[POTE generator]]: ~315/256 = 358.5485


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11
Line 2,076: Line 1,220:


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 }}]
POTE generator: ~27/22 = 358.5713


{{Val list|legend=1| 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
Subgroup: 2.3.5.7.11.13
Line 2,102: Line 1,234:


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 }}]
POTE generator: ~16/13 = 358.5739


{{Val list|legend=1| 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
Line 2,129: Line 1,249:


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


{{Val list|legend=1| 10, 26, 36, 154f, 190ffg }}
{{Val list|legend=1| 10, 26, 36, 154f, 190ffg }}
</div></div>


[[Category:Theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"