Jubilismic clan: Difference between revisions

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= No-3 jubilismic =
= No-3 jubilismic =


Period: 1\2
Subgroup: 2.5.7
 
Optimal ([[POTE]]) generator: ~5/4 = 380.840
 
EDO generators: [[6edo|2\6]], [[10edo|3\10]], [[16edo|5\16]], [[22edo|7\22]]
 
<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


[[Sval]] [[mapping]]: [{{val| 2 1 1 }}, {{val| 0 1 1 }}]
[[Sval]] [[mapping]]: [{{val| 2 1 1 }}, {{val| 0 1 1 }}]


[[Gencom]] [[mapping]]: [{{val| 2 0 1 1 }}, {{val| 0 0 1 1 }}]
[[Gencom]] [[mapping]]: [{{val| 2 0 1 1 }}, {{val| 0 0 1 1 }}]
[[POTE generator]]: ~5/4 = 380.840


{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
</div></div>


= Diminished =
= Diminished =
<span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:Verminderte_Temperaturen|Deutsch]]</span>
{{see also|Dimipent family}}
{{see also| Dimipent family }}
 
Period: 1\4
 
Optimal ([[POTE]]) generator: ~3/2 = 699.523
 
EDO generators: [[8edo|5\8]], [[12edo|7\12]], [[16edo|9\16]]
 
Scales (Scala files): [[diminished12]]
 
<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


Comma list: 36/35, 50/49
[[Comma list]]: 36/35, 50/49


Mapping: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]
[[Mapping]]: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]


Mapping generators: ~6/5, ~3
Mapping generators: ~6/5, ~3
[[POTE generator]]: ~3/2 = 699.523


{{Val list|legend=1| 4, 8d, 12 }}
{{Val list|legend=1| 4, 8d, 12 }}


Badness: 0.0224
[[Badness]]: 0.0224


</div></div>
Scales: [[diminished12]]


== 11-limit ==
== 11-limit ==
Period: 1\4
Optimal ([[POTE]]) generator: ~3/2 = 709.109
EDO generators: [[12edo|7\12]], [[20edo|12\20]]
Scales (Scala files): [[diminished12]]
<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 74: Line 42:


Mapping generators: ~6/5, ~3
Mapping generators: ~6/5, ~3
POTE generator: ~3/2 = 709.109


{{Val list|legend=1| 4, 8d, 12, 32cddee, 44cddeee }}
{{Val list|legend=1| 4, 8d, 12, 32cddee, 44cddeee }}
Line 79: Line 49:
Badness: 0.0221
Badness: 0.0221


</div></div>
Scales: [[diminished12]]


=== 13-limit ===
=== 13-limit ===
Period: 1\4
Optimal ([[POTE]]) generator: ~3/2 = 713.773
EDO generators: [[12edo|7\12]], [[20edo|12\20]]
Scales (Scala files): [[diminished12]]
<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 102: Line 60:


Mapping generators: ~6/5, ~3
Mapping generators: ~6/5, ~3
POTE generator: ~3/2 = 713.773


{{Val list|legend=1| 4, 8d, 12f, 20cdef }}
{{Val list|legend=1| 4, 8d, 12f, 20cdef }}
Line 107: Line 67:
Badness: 0.0195
Badness: 0.0195


</div></div>
Scales: [[diminished12]]


== Demolished ==
== Demolished ==
Period: 1\4
Optimal ([[POTE]]) generator: ~3/2 = 689.881
EDO generators: [[12edo|7\12]], [[16edo|9\16]], [[28edo|14\28]]
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 130: Line 78:


Mapping generators: ~6/5, ~3
Mapping generators: ~6/5, ~3
POTE generator: ~3/2 = 689.881


{{Val list|legend=1| 12, 28, 40de }}
{{Val list|legend=1| 12, 28, 40de }}


Badness: 0.0266
Badness: 0.0266
</div></div>


== Hemidim ==
== Hemidim ==
Period: 1\4
Optimal ([[POTE]]) generator: ~12/11 = 101.679
EDO generators: [[12edo|7\12]]
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 158: Line 94:


Mapping generators: ~6/5, ~11/7
Mapping generators: ~6/5, ~11/7
POTE generator: ~12/11 = 101.679


{{Val list|legend=1| 12 }}
{{Val list|legend=1| 12 }}


Badness: 0.0550
Badness: 0.0550
</div></div>


= Doublewide =
= Doublewide =


Period: 1\2
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~6/5 = 325.719
 
EDO generators: [[22edo|6\22]], [[26edo|7\26]], [[48edo|13\48]]
 
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]]: 50/49, 875/864


Comma list: 50/49, 875/864
[[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]


Mapping: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]
[[POTE generator]]: ~6/5 = 325.719


{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}
{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}


Badness: 0.0435
[[Badness]]: 0.0435
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~6/5 = 325.548
EDO generators: [[22edo|6\22]], [[26edo|7\26]], [[48edo|13\48]]
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 210: Line 122:


Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
POTE generator: ~6/5 = 325.548


{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}
{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c, 118cd }}


Badness: 0.0321
Badness: 0.0321
</div></div>


== Fleetwood ==
== Fleetwood ==
Period: 1\2
Optimal ([[POTE]]) generator: ~6/5 = 327.038
EDO generators: [[22edo|6\22]]
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 236: Line 136:


Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]
Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]
POTE generator: ~6/5 = 327.038


{{Val list|legend=1| 22 }}
{{Val list|legend=1| 22 }}


Badness: 0.0352
Badness: 0.0352
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\2
Optimal ([[POTE]]) generator: ~6/5 = 327.841
EDO generators: [[22edo|6\22]]
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 262: Line 150:


Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
POTE generator: ~6/5 = 327.841


{{Val list|legend=1| 18e, 22, 84bddf }}
{{Val list|legend=1| 18e, 22, 84bddf }}


Badness: 0.0318
Badness: 0.0318
</div></div>


== Cavalier ==
== Cavalier ==
Period: 1\2
Optimal ([[POTE]]) generator: ~6/5 = 323.427
EDO generators: [[26edo|7\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 288: Line 164:


Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]
Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]
POTE generator: ~6/5 = 323.427


{{Val list|legend=1| 22e, 26 }}
{{Val list|legend=1| 22e, 26 }}


Badness: 0.0529
Badness: 0.0529
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\2
Optimal ([[POTE]]) generator: ~6/5 = 323.396
EDO generators: [[26edo|7\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 314: Line 178:


Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
POTE generator: ~6/5 = 323.396


{{Val list|legend=1| 22ef, 26 }}
{{Val list|legend=1| 22ef, 26 }}


Badness: 0.0350
Badness: 0.0350
</div></div>


= Lemba =
= Lemba =
Line 325: Line 189:
{{see also| Gamelismic clan #Lemba }}
{{see also| Gamelismic clan #Lemba }}


Period: 1\2
Subgroup: 2.3.5.7
 
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
[[Comma list]]: 50/49, 525/512


Comma list: 50/49, 525/512
[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]


Mapping: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
[[POTE generator]]: ~8/7 = 232.089


{{Val list|legend=1| 10, 16, 26, 62 }}
{{Val list|legend=1| 10, 16, 26, 62 }}


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 368: Line 208:


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 394: Line 222:


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>


= Crepuscular =
= Crepuscular =
{{see also| Fifive family #Crepuscular }}
{{see also| Fifive family #Crepuscular }}
Period: 1\2
Optimal ([[POTE]]) generator: ~27/25 = 140.349
EDO generators: [[26edo|3\26]], [[34edo|4\34]]
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


Comma list: 50/49, 4375/4374
[[Comma list]]: 50/49, 4375/4374


Mapping: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]
[[Mapping]]: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]


{{Multival|legend=1| 10 14 14 -1 -6 -7 }}
{{Multival|legend=1| 10 14 14 -1 -6 -7 }}
[[POTE generator]]: ~27/25 = 140.349


{{Val list|legend=1| 26, 34d, 60d, 94d }}
{{Val list|legend=1| 26, 34d, 60d, 94d }}


Badness: 0.0867
[[Badness]]: 0.0867
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~12/11 = 140.587
EDO generators: [[26edo|3\26]], [[34edo|4\34]]
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 449: Line 253:


Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]
Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]
POTE generator: ~12/11 = 140.587


{{Val list|legend=1| 26, 34d, 60d, 94de }}
{{Val list|legend=1| 26, 34d, 60d, 94de }}


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


== 13-limit ==
== 13-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~12/11 = 140.554
EDO generators: [[26edo|3\26]], [[34edo|4\34]]
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 475: Line 267:


Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]
Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]
POTE generator: ~12/11 = 140.554


{{Val list|legend=1| 26, 34d, 60d, 94de }}
{{Val list|legend=1| 26, 34d, 60d, 94de }}


Badness: 0.0244
Badness: 0.0244
</div></div>


= Bipyth =
= Bipyth =
Period: 1\2
Optimal ([[POTE]]) generator: ~3/2 = 709.437
EDO generators: [[22edo|13\22]]
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


Comma list: 50/49, 20480/19683
[[Comma list]]: 50/49, 20480/19683


Mapping: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]
[[Mapping]]: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]


{{Multival|legend=1| 2 18 18 24 23 -9 }}
{{Multival|legend=1| 2 18 18 24 23 -9 }}
[[POTE generator]]: ~3/2 = 709.437


{{Val list|legend=1| 10cd, 12cd, 22 }}
{{Val list|legend=1| 10cd, 12cd, 22 }}


Badness: 0.1650
[[Badness]]: 0.1650
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~3/2 = 709.310
EDO generators: [[22edo|13\22]]
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 529: Line 297:


Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
POTE generator: ~3/2 = 709.310


{{Val list|legend=1| 10cd, 12cde, 22 }}
{{Val list|legend=1| 10cd, 12cde, 22 }}


Badness: 0.0709
Badness: 0.0709
</div></div>


= Elvis =
= Elvis =
== 5-limit ==
== 5-limit ==


Period: 1\2
Subgroup: 2.3.5
 
Optimal ([[POTE]]) generator: ~45/32 = 554.546
 
EDO generators: [[26edo|12\26]]
 
Scales (Scala files):


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Comma list]]: 36905625/33554432
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5
[[Mapping]]: [{{val| 2 1 10 }}, {{val| 0 2 -5 }}]


Comma list: 36905625/33554432
[[POTE generator]]: ~45/32 = 554.546
 
Mapping: [{{val| 2 1 10 }}, {{val| 0 2 -5 }}]


{{Val list|legend=1| 26, 80bc, 106bc, 132bc }}
{{Val list|legend=1| 26, 80bc, 106bc, 132bc }}


Badness: 0.8840
[[Badness]]: 0.8840
 
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~45/32 = 553.721
EDO generators: [[26edo|12\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


Comma list: 50/49, 8505/8192
[[Comma list]]: 50/49, 8505/8192


Mapping: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]
[[Mapping]]: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]


{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
[[POTE generator]]: ~45/32 = 553.721


{{Val list|legend=1| 24c, 26 }}
{{Val list|legend=1| 24c, 26 }}


Badness: 0.1415
[[Badness]]: 0.1415
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~11/8 = 553.882
EDO generators: [[26edo|12\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 610: Line 342:


Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
POTE generator: ~11/8 = 553.882


{{Val list|legend=1| 26 }}
{{Val list|legend=1| 26 }}


Badness: 0.0632
Badness: 0.0632
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~11/8 = 553.892
EDO generators: [[26edo|12\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 636: Line 356:


Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
POTE generator: ~11/8 = 553.892


{{Val list|legend=1| 26 }}
{{Val list|legend=1| 26 }}


Badness: 0.0440
Badness: 0.0440
</div></div>


= Comic =
= Comic =
== 5-limit ==
== 5-limit ==


Period: 1\2
Subgroup: 2.3.5
 
Optimal ([[POTE]]) generator: ~81/80 = 55.382
 
EDO generators: [[22edo|1\22]]
 
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]]: 5120000/4782969


Comma list: 5120000/4782969
[[Mapping]]: [{{val| 2 1 -3 }}, {{val| 0 2 7 }}]


Mapping: [{{val| 2 1 -3 }}, {{val| 0 2 7 }}]
[[POTE generator]]: ~81/80 = 55.382


{{Val list|legend=1| 20c, 22, 86b, 108b, 130b }}
{{Val list|legend=1| 20c, 22, 86b, 108b, 130b }}


Badness: 0.4912
Badness: 0.4912
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~81/80 = 54.699
EDO generators: [[22edo|1\22]]
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


Comma list: 50/49, 2240/2187
[[Comma list]]: 50/49, 2240/2187


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


{{Multival|legend=1| 4 14 14 13 11 -7 }}
{{Multival|legend=1| 4 14 14 13 11 -7 }}
[[POTE generator]]: ~81/80 = 54.699


{{Val list|legend=1| 20cd, 22 }}
{{Val list|legend=1| 20cd, 22 }}


Badness: 0.0844
[[Badness]]: 0.0844
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~81/80 = 55.184
EDO generators: [[22edo|1\22]]
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 717: Line 401:


Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
POTE generator: ~81/80 = 55.184


{{Val list|legend=1| 20cde, 22 }}
{{Val list|legend=1| 20cde, 22 }}


Badness: 0.0451
Badness: 0.0451
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~81/80 = 54.435
EDO generators: [[22edo|1\22]]
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 743: Line 415:


Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
POTE generator: ~81/80 = 54.435


{{Val list|legend=1| 22 }}
{{Val list|legend=1| 22 }}
Line 751: Line 425:


= Duodecim =
= Duodecim =
Period: 1\12
Optimal ([[POTE]]) generator: ~11/8 = 565.023
EDO generators: [[24edo|11\24]], [[36edo|17\36]]
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 771: Line 433:


Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
Mapping: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
POTE generator: ~11/8 = 565.023


{{Val list|legend=1| 12, 24d, 36d }}
{{Val list|legend=1| 12, 24d, 36d }}


Badness: 0.030536
Badness: 0.030536
</div></div>


= Vigintiduo =
= Vigintiduo =
Period: 1\22
Optimal ([[POTE]]) generator: ~11/8 = 557.563
EDO generators: [[44edo|21\44]], [[66edo|31\66]]
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 799: Line 449:


Mapping: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
Mapping: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
POTE generator: ~11/8 = 557.563


{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}
{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}


Badness: 0.0484
Badness: 0.0484
</div></div>


= Vigin =
= Vigin =
Period: 1\22
Optimal ([[POTE]]) generator: ~13/8 = 844.624
EDO generators: [[44edo|31\44]]
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 825: Line 463:


Mapping: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
Mapping: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
POTE generator: ~13/8 = 844.624


{{Val list|legend=1| 22, 44 }}
{{Val list|legend=1| 22, 44 }}


Badness: 0.0298
Badness: 0.0298
</div></div>


[[Category:Theory]]
[[Category:Theory]]

Revision as of 10:36, 28 March 2021

The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are identified and the octave is divided in two. Doublewide, lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.

No-3 jubilismic

Subgroup: 2.5.7

Sval mapping: [⟨2 1 1], ⟨0 1 1]]

Gencom mapping: [⟨2 0 1 1], ⟨0 0 1 1]]

POTE generator: ~5/4 = 380.840

Template:Val list

Diminished

Deutsch

See also: Dimipent family

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 699.523

Template:Val list

Badness: 0.0224

Scales: diminished12

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 56/55

Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 709.109

Template:Val list

Badness: 0.0221

Scales: diminished12

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 50/49, 66/65

Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 713.773

Template:Val list

Badness: 0.0195

Scales: diminished12

Demolished

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 50/49

Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]

Mapping generators: ~6/5, ~3

POTE generator: ~3/2 = 689.881

Template:Val list

Badness: 0.0266

Hemidim

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 125/121

Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]

Mapping generators: ~6/5, ~11/7

POTE generator: ~12/11 = 101.679

Template:Val list

Badness: 0.0550

Doublewide

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

POTE generator: ~6/5 = 325.719

Template:Val list

Badness: 0.0435

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 875/864

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

POTE generator: ~6/5 = 325.548

Template:Val list

Badness: 0.0321

Fleetwood

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 176/175

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

POTE generator: ~6/5 = 327.038

Template:Val list

Badness: 0.0352

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 176/175

Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]

POTE generator: ~6/5 = 327.841

Template:Val list

Badness: 0.0318

Cavalier

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 875/864

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

POTE generator: ~6/5 = 323.427

Template:Val list

Badness: 0.0529

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 325/324

Mapping: [⟨2 1 3 4 1 2], ⟨0 4 3 3 11 10]]

POTE generator: ~6/5 = 323.396

Template:Val list

Badness: 0.0350

Lemba

Main article: Lemba
See also: Gamelismic clan § Lemba

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

POTE generator: ~8/7 = 232.089

Template:Val list

Badness: 0.0622

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 385/384

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

POTE generator: ~8/7 = 230.974

Template:Val list

Badness: 0.0416

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 65/64, 78/77

Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]

POTE generator: ~8/7 = 230.966

Template:Val list

Badness: 0.0255

Crepuscular

See also: Fifive family § Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]

POTE generator: ~27/25 = 140.349

Template:Val list

Badness: 0.0867

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 1944/1925

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

POTE generator: ~12/11 = 140.587

Template:Val list

Badness: 0.0408

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 78/77, 99/98, 144/143

Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]

POTE generator: ~12/11 = 140.554

Template:Val list

Badness: 0.0244

Bipyth

Subgroup: 2.3.5.7

Comma list: 50/49, 20480/19683

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]

POTE generator: ~3/2 = 709.437

Template:Val list

Badness: 0.1650

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 896/891

Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]

POTE generator: ~3/2 = 709.310

Template:Val list

Badness: 0.0709

Elvis

5-limit

Subgroup: 2.3.5

Comma list: 36905625/33554432

Mapping: [⟨2 1 10], ⟨0 2 -5]]

POTE generator: ~45/32 = 554.546

Template:Val list

Badness: 0.8840

7-limit

Subgroup: 2.3.5.7

Comma list: 50/49, 8505/8192

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]

POTE generator: ~45/32 = 553.721

Template:Val list

Badness: 0.1415

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 1344/1331

Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]

POTE generator: ~11/8 = 553.882

Template:Val list

Badness: 0.0632

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 1053/1024

Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]

POTE generator: ~11/8 = 553.892

Template:Val list

Badness: 0.0440

Comic

5-limit

Subgroup: 2.3.5

Comma list: 5120000/4782969

Mapping: [⟨2 1 -3], ⟨0 2 7]]

POTE generator: ~81/80 = 55.382

Template:Val list

Badness: 0.4912

7-limit

Subgroup: 2.3.5.7

Comma list: 50/49, 2240/2187

Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]

Wedgie: ⟨⟨ 4 14 14 13 11 -7 ]]

POTE generator: ~81/80 = 54.699

Template:Val list

Badness: 0.0844

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 2662/2625

Mapping: [⟨2 1 -3 -2 -4], ⟨0 2 7 7 10]]

POTE generator: ~81/80 = 55.184

Template:Val list

Badness: 0.0451

13-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 65/63, 99/98, 968/945

Mapping: [⟨2 1 -3 -2 -4 3], ⟨0 2 7 7 10 4]]

POTE generator: ~81/80 = 54.435

Template:Val list

Badness: 0.0415

Duodecim

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 64/63

POTE generator: ~11/8 = 565.023

Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]

POTE generator: ~11/8 = 565.023

Template:Val list

Badness: 0.030536

Vigintiduo

Subgroup: 2.3.5.7.11

Comma list: 50/49, 64/63, 245/243

POTE generator: ~11/8 = 557.563

Mapping: [⟨22 35 51 62 0], ⟨0 0 0 0 1]]

POTE generator: ~11/8 = 557.563

Template:Val list

Badness: 0.0484

Vigin

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 64/63, 99/98

Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]

POTE generator: ~13/8 = 844.624

Template:Val list

Badness: 0.0298

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