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Gamelismic clan: Difference between revisions

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{{see also|University temperament}}
{{see also|University temperament}}


Commas: 21/20, 144/125
[[Comma list]]: 21/20, 144/125


POTE generator: ~8/7 = 230.762
POTE generator: ~8/7 = 230.762


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


EDOs: {{EDOs|5, 11, 16c, 21cc, 26ccc}}
{{Val list|legend=1| 5, 11, 16c, 21cc, 26ccc }}


Badness: 0.0623
[[Badness]]: 0.0623


= Clyndro =
= Clyndro =
Commas: 135/128, 360/343
[[Comma list]]: 135/128, 360/343


POTE generator: ~8/7 = 226.469
POTE generator: ~8/7 = 226.469


Map: [<1 1 4 3|, <0 3 -9 -1|]
[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]


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


Badness: 0.1592
[[Badness]]: 0.1592


== 11-limit ==
== 11-limit ==
Commas: 33/32, 45/44, 352/343
Comma list: 33/32, 45/44, 352/343


POTE generator: ~8/7 = 226.428
POTE generator: ~8/7 = 226.428


Map: [<1 1 4 3 4|, <0 3 -9 -1 -3|]
Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]


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


Badness: 0.0697
Badness: 0.0697


= Necromanteion =
= Necromanteion =
Commas: 1029/1024, 5103/5000
[[Comma list]]: 1029/1024, 5103/5000


POTE generator: ~48/35 = 541.779
POTE generator: ~48/35 = 541.779


Map: [<1 7 10 1|, <0 -12 -17 4|]
[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]


EDOs: {{EDOs|11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd}}
{{Val list|legend=1| 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd }}


Badness: 0.1177
[[Badness]]: 0.1177


== 11-limit ==
== 11-limit ==
Commas: 176/175, 243/242, 1029/1024
Comma list: 176/175, 243/242, 1029/1024


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


Map: [<1 7 10 1 17|, <0 -12 -17 4 -30|]
Mapping: [{{val| 1 7 10 1 17 }}, {{val| 0 -12 -17 4 -30 }}]


EDOs: {{EDOs|31, 82c, 113c, 144c, 175c, 350bcde, 381bcde}}
{{Val list|legend=1| 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde }}


Badness: 0.0535
Badness: 0.0535


== 13-limit ==
== 13-limit ==
Commas: 144/143, 176/175, 243/242, 343/338
Comma list: 144/143, 176/175, 243/242, 343/338


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


Map: [<1 7 10 1 17 1|, <0 -12 -17 4 -30 6|]
Mapping: [{{val| 1 7 10 1 17 1 }}, {{val| 0 -12 -17 4 -30 6 }}]


EDOs: {{EDOs|31, 51ce, 82cf, 113cf, 144cf}}
{{Val list|legend=1| 31, 51ce, 82cf, 113cf, 144cf }}


Badness: 0.0470
Badness: 0.0470


= Widefourth =
= Widefourth =
Commas: 1029/1024, 48828125/48771072
[[Comma list]]: 1029/1024, 48828125/48771072


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


Map: [<1 16 8 -2|, <0 -33 -13 11|]
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]


Wedgie: <<33 13 -11 -56 -110 -62||
[[Wedgie]]: {{wedgie| 33 13 -11 -56 -110 -62 }}


EDOs: {{EDOs|16, 71, 87, 103, 190}}
{{Val list|legend=1| 16, 71, 87, 103, 190 }}


Badness: 0.1541
[[Badness]]: 0.1541


== 11-limit ==
== 11-limit ==
Commas: 385/384, 441/440, 234375/234256
Comma list: 385/384, 441/440, 234375/234256


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


Map: [<1 16 8 -2 17|, <0 -33 -13 11 -31|]
Mapping: [{{val| 1 16 8 -2 17 }}, {{val| 0 -33 -13 11 -31 }}]


EDOs: {{EDOs|16, 71, 87, 103, 190}}
{{Val list|legend=1| 16, 71, 87, 103, 190 }}


Badness: 0.0408
Badness: 0.0408


== 13-limit ==
== 13-limit ==
Commas: 385/384, 441/440, 625/624, 847/845
Comma list: 385/384, 441/440, 625/624, 847/845


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


Map: [<1 16 8 -2 17 12|, <0 -33 -13 11 -31 -19|]
Mapping: [{{val| 1 16 8 -2 17 12 }}, {{val| 0 -33 -13 11 -31 -19 }}]


EDOs: {{EDOs|16, 71, 87, 103, 190}}
{{Val list|legend=1| 16, 71, 87, 103, 190 }}


Badness: 0.0216
Badness: 0.0216
Line 845: Line 845:
= Tritriple =
= Tritriple =
== 5-limit ==
== 5-limit ==
Comma: |31 20 -27>
Comma list: {{monzo| 31 20 -27 }}


POTE generator: ~864/625 = 559.332
POTE generator: ~864/625 = 559.332


Map: [<1 -11 -7|, <0 27 20|]
Mapping: [{{val| 1 -11 -7 }}, {{val| 0 27 20 }}]


EDOs: {{EDOs|15, 103, 118, 133, 959, 1077}}
{{Val list|legend=1| 15, 103, 118, 133, 959, 1077 }}


Badness: 0.2836
Badness: 0.2836


== 7-limit ==
== 7-limit ==
Commas: 1029/1024, 1959552/1953125
[[Comma list]]: 1029/1024, 1959552/1953125


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


Map: [<1 -11 -7 7|, <0 27 20 -9|]
[[Mapping]]: [{{val| 1 -11 -7 7 }}, {{val| 0 27 20 -9 }}]


EDOs: {{EDOs|15, 103, 118, 133, 339d}}
{{Val list|legend=1| 15, 103, 118, 133, 339d }}


Badness: 0.1186
[[Badness]]: 0.1186


== 11-limit ==
== 11-limit ==
Commas: 385/384, 441/440, 43923/43750
Comma list: 385/384, 441/440, 43923/43750


POTE generator: ~242/175 = 559.293
POTE generator: ~242/175 = 559.293


Map: [<1 -11 -7 7 -4|, <0 27 20 -9 16|]
Mapping: [{{val| 1 -11 -7 7 -4 }}, {{val| 0 27 20 -9 16 }}]


EDOs: {{EDOs|15, 103, 118, 133, 339de}}
{{Val list|legend=1| 15, 103, 118, 133, 339de }}


Badness: 0.0353
Badness: 0.0353


= Restles =
= Restles =
Commas: 1029/1024, 153664/151875
[[Comma list]]: 1029/1024, 153664/151875


POTE generator: ~315/256 = 358.5485
POTE generator: ~315/256 = 358.5485


Map: [<1 -2 8 4|, <0 12 -19 -4|]
[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]


EDOs: {{EDOs|10, 67, 77, 87, 164}}
{{Val list|legend=1| 10, 67, 77, 87, 164 }}


Badness: 0.1080
[[Badness]]: 0.1080


== 11-limit ==
== 11-limit ==
Commas: 385/384, 441/440, 153664/151875
Comma list: 385/384, 441/440, 153664/151875


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


Map: [<1 -2 8 4 -7|, <0 12 -19 -4 35|]
Mapping: [{{val| 1 -2 8 4 -7 }}, {{val| 0 12 -19 -4 35 }}]


EDOs: {{EDOs|10, 77, 87, 164}}
{{Val list|legend=1| 10, 77, 87, 164 }}


Badness: 0.0547
Badness: 0.0547


== 13-limit ==
== 13-limit ==
Commas: 196/195, 352/351, 385/384, 676/675
Comma list: 196/195, 352/351, 385/384, 676/675


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


Map: [<1 -2 8 4 -7 4|, <0 12 -19 -4 35 -1|]
Mapping: [{{val| 1 -2 8 4 -7 4 }}, {{val| 0 12 -19 -4 35 -1 }}]


EDOs: {{EDOs|10, 77, 87, 164}}
{{Val list|legend=1| 10, 77, 87, 164 }}


Badness: 0.0282
Badness: 0.0282


=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.


Commas: 169/168, 273/272, 289/288
Comma list: 169/168, 273/272, 289/288


Period: 1\2
Period: 1\2
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POTE generator: ~8/7 = 233.6155
POTE generator: ~8/7 = 233.6155


Map: [<2 2 6 7 7|, <0 3 -1 1 3|]
Sval mapping: [{{val| 2 2 6 7 7 }}, {{val| 0 3 -1 1 3 }}]


EDOs: {{EDOs|26, 36, 46, 82, 118f}}
{{Val list|legend=1| 26, 36, 46, 82, 118f }}


[[Category:Theory]]
[[Category:Theory]]
Line 931: Line 931:
[[Category:Listen]]
[[Category:Listen]]


[[Category:Todo:review]]
{{todo| review | improve readability }}
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