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Gamelismic family: Difference between revisions

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= Gamelan =
= Gamelan =
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6875, ~5/4 = 385.1853
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]]
Scales (Scala files): [[portent26]]
<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
[[Comma list]]: 1029/1024


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[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7
</div></div>


= Portent =
= Portent =
Portent has a [[Normal lists #normal interval list|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
Portent has a [[Normal lists #normal interval list|normal comma list]] [1029/1024, 385/384] and also tempers out 441/440.
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6884, ~5/4 = 385.1618
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]]
Scales (Scala files): [[portent26]]
<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
Comma list: 385/384, 441/440
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: [[Eigenmonzo]]s: 2, 11/10, 9/7
: [[Eigenmonzo]]s: 2, 11/10, 9/7


{{Val list|legend=1| 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190 }}
{{Val list|legend=1| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}


Badness: 0.234 × 10<sup>-3</sup>
Badness: 0.234 × 10<sup>-3</sup>


Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
</div></div>


== Portending ==
== Portending ==
Comma list: 325/324, 364/363, 441/440
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.9128, ~5/4 = 384.7278
 
EDO generator: [[41edo|(8, 13)\41]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
 
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


Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 0 0 1 0 -1 -2 }}]
Mapping: [{{val| 1 1 0 3 5 6 }}, {{val| 0 3 0 -1 4 12 }}, {{val| 0 0 1 0 -1 -2 }}]
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Badness: 0.627 × 10<sup>-3</sup>
Badness: 0.627 × 10<sup>-3</sup>
</div></div>


== Portentous ==
== Portentous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.6843, ~5/4 = 384.9830
EDO generator: [[31edo|(6, 10)\31]], [[72edo|(14, 23)\72]], [[87edo|(17, 28)\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: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624
Comma list: 385/384, 441/440, 625/624


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Badness: 0.662 × 10<sup>-3</sup>
Badness: 0.662 × 10<sup>-3</sup>
</div></div>


== Ominous ==
== Ominous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.4088, ~5/4 = 385.3825
EDO generator: [[31edo|(6, 10)\31]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
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
Comma list: 351/350, 385/384, 441/440


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Badness: 0.751 × 10<sup>-3</sup>
Badness: 0.751 × 10<sup>-3</sup>
</div></div>


=== 17-limit ===
=== 17-limit ===
Comma list: 273/272, 351/350, 441/440, 561/560
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.4313, ~5/4 = 385.2890
 
EDO generator: [[31edo|(6, 10)\31]], [[46edo|(9, 15)\46]], [[72edo|(14, 23)\72]]
 
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


Mapping: [{{val| 1 1 0 3 5 1 1 }}, {{val| 0 3 0 -1 4 -10 -8 }}, {{val| 0 0 1 0 -1 2 2 }}]
Mapping: [{{val| 1 1 0 3 5 1 1 }}, {{val| 0 3 0 -1 4 -10 -8 }}, {{val| 0 0 1 0 -1 2 2 }}]
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Badness: 0.612 × 10<sup>-3</sup>
Badness: 0.612 × 10<sup>-3</sup>
</div></div>


== Momentous ==
== Momentous ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.4088, ~5/4 = 385.3825
EDO generator: [[31edo|(6, 10)\31]], [[41edo|(8, 13)\41]], [[46edo|(9, 15)\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">
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384
Comma list: 196/195, 352/351, 385/384


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Badness: 0.832 × 10<sup>-3</sup>
Badness: 0.832 × 10<sup>-3</sup>
</div></div>


== Foreboding ==
== Foreboding ==
Period: 1\1
Optimal ([[POTE]]) generators: ~8/7 = 233.3664, ~5/4 = 382.3425
EDO generator: [[10edo|(3, 6)\10]], [[15edo|(5, 9)\15]], [[31edo|(6, 10)\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
Comma list: 105/104, 144/143, 275/273
Comma list: 105/104, 144/143, 275/273


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Badness: 0.873 × 10<sup>-3</sup>
Badness: 0.873 × 10<sup>-3</sup>
</div></div>


= Gamel =
= Gamel =
Comma list: 1029/1024, 540/539
 
Period: 1\1
 
Optimal ([[POTE]]) generators: ~8/7 = 233.2909, ~5/4 = 384.2120
 
EDO generator: [[31edo|(6, 10)\31]], [[36edo|(7, 12)\36]], [[72edo|(14, 23)\72]]
 
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: 540/539, 1029/1024


Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}]
Mapping: [{{val| 1 1 0 3 -1 }}, {{val| 0 3 0 -1 11 }}, {{val| 0 0 1 0 1 }}]
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Badness: 0.853 × 10<sup>-3</sup>
Badness: 0.853 × 10<sup>-3</sup>
</div></div>


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Gamelan]]
[[Category:Gamelismic]]
[[Category:Gamelismic]]
[[Category:Rank 3]]
[[Category:Rank 3]]
[[Category:Gamelan]]
[[Category:Portent]]
Retrieved from "https://en.xen.wiki/w/Gamelismic_family"