Xenharmonic Wiki

Gamelismic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
→Hemithirds: databoxified; comma list reviewed; +wedgie copied from luna family
Databoxes for hemiseven to tritikleismic; edo list reviewed
Line 39: Line 39:
== Subgroup extensions ==
== Subgroup extensions ==
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.
No-five subgroup extensions of slendric include [[Chromatic pairs #Radon|radon]], the 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, the 2.3.7.13.17 extension, considered below.


= Miracle =
= Miracle =
Line 1,044: Line 1,043:
{{main| Hemithirds }}
{{main| Hemithirds }}
{{see also| Luna family #Hemithirds }}
{{see also| Luna family #Hemithirds }}
== 7-limit ==


Period: 1\1
Period: 1\1
Line 1,139: Line 1,136:


= Hemiseven =
= Hemiseven =
Period: 1\1
Optimal ([[POTE]]) generator: ~320/243 = 483.267
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
Comma list: 1029/1024, 19683/19600
Comma list: 1029/1024, 19683/19600
POTE generator: ~320/243 = 483.267


Mapping: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
Mapping: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
Line 1,147: Line 1,157:
Wedgie: {{wedgie| 6 29 -2 32 -20 -86 }}
Wedgie: {{wedgie| 6 29 -2 32 -20 -86 }}


{{Val list|legend=1| 5, 72, 77, 149, 221, 514bd, 735bcd }}
{{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
Comma list: 385/384, 441/440, 19683/19600
Comma list: 385/384, 441/440, 19683/19600
POTE generator: ~320/243 = 483.276


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 }}]
Line 1,161: Line 1,186:


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
Comma list: 351/350, 385/384, 441/440, 676/675
Comma list: 351/350, 385/384, 441/440, 676/675
POTE generator: ~120/91 = 483.256


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 }}]


{{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
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675
POTE generator: ~45/34 = 483.261


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 }}]


{{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 }}


== 7-limit ==
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
 
[[Comma list]]: 1029/1024, 15625/15552
[[Comma list]]: 1029/1024, 15625/15552


POTE generator: ~6/5 = 316.872
[[Mapping]]: [{{val| 3 0 3 10 }}, {{val| 0 6 5 -2 }}]


[[Mapping]]: [{{val| 3 0 3 10 }}, {{val| 0 6 5 -2 }}]
Mapping generators: ~63/50, ~6/5


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 1,198: Line 1,268:
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7


{{Val list|legend=1| 15, 72, 87, 159, 231 }}
{{Val list|legend=1| 15, 42bc, 57, 72, 87, 159, 231 }}


[[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
Comma list: 385/384, 441/440, 4000/3993
Comma list: 385/384, 441/440, 4000/3993


POTE generator: ~6/5 = 316.881
Mapping: [{{val| 3 0 3 10 8 }}, {{val| 0 6 5 -2 3 }}]


Mapping: [{{val| 3 0 3 10 8 }}, {{val| 0 6 5 -2 3 }}]
Mapping generators: ~44/35, ~6/5


Minimax tuning:
Minimax tuning:
Line 1,214: Line 1,301:
: [[Eigenmonzo]]s: 2, 9/7
: [[Eigenmonzo]]s: 2, 9/7


{{Val list|legend=1| 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 ==
Comma list: 325/324, 364/363, 441/440, 625/624
 
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
 
Comma list: 325/324, 364/363, 385/384, 625/624


Mapping: [{{val| 3 0 3 10 8 0 }}, {{val| 0 6 5 -2 3 14 }}]
Mapping: [{{val| 3 0 3 10 8 0 }}, {{val| 0 6 5 -2 3 14 }}]


{{Val list|legend=1| 15, 72, 87, 159 }}
Mapping generators: ~44/35, ~6/5
 
{{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
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384


Mapping: [{{val| 3 0 3 10 8 0 -2 }}, {{val| 0 6 5 -2 3 14 18 }}]
Mapping: [{{val| 3 0 3 10 8 0 -2 }}, {{val| 0 6 5 -2 3 14 18 }}]


{{Val list|legend=1| 15g, 72, 87, 159 }}
Mapping generators: ~34/27, ~6/5
 
{{Val list|legend=1| 72, 159, 231f }}
 
</div></div>


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