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[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }}
: {{monzo list| 1 0 0 0 | 5/3 0 1/6 -1/6 | 25/9 0 17/18 -17/18 | 25/9 0 -1/18 1/18 }}
: {{Monzo list| 1 0 0 0 | 5/3 0 1/6 -1/6 | 25/9 0 17/18 -17/18 | 25/9 0 -1/18 1/18 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5


Line 217: Line 217:
[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: {{monzo list| 1 0 0 0 | 15/8 0 -1/8 0 | 0 0 1 0 | 65/24 0 1/24 0 }}
: {{Monzo list| 1 0 0 0 | 15/8 0 -1/8 0 | 0 0 1 0 | 65/24 0 1/24 0 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5


Line 455: Line 455:
[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
: {{monzo list| 1 0 0 0 | 25/13 6/13 -6/13 0 | 25/13 -7/13 7/13 0 | 35/13 -2/13 2/13 0 }}
: {{Monzo list| 1 0 0 0 | 25/13 6/13 -6/13 0 | 25/13 -7/13 7/13 0 | 35/13 -2/13 2/13 0 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.5/3
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: {{monzo list| 1 0 0 0 | 25/19 12/19 -6/19 0 | 50/19 -14/19 7/19 0 | 55/19 -4/19 2/19 0 }}
: {{Monzo list| 1 0 0 0 | 25/19 12/19 -6/19 0 | 50/19 -14/19 7/19 0 | 55/19 -4/19 2/19 0 }}
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/5


Line 760: Line 760:


== Hemiseven ==
== Hemiseven ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 19683/19600
[[Comma list]]: 1029/1024, 19683/19600


[[Mapping]]: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
{{Mapping|legend=1| 1 4 14 2 | 0 -6 -29 2 }}


{{Multival|legend=1| 6 29 -2 32 -20 -86 }}
{{Multival|legend=1| 6 29 -2 32 -20 -86 }}


[[POTE generator]]: ~320/243 = 483.267
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~320/243 = 483.267


{{Optimal ET sequence|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}
{{Optimal ET sequence|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}
Line 779: Line 779:
Comma list: 385/384, 441/440, 19683/19600
Comma list: 385/384, 441/440, 19683/19600


Mapping: [{{val| 1 4 14 2 -5 }}, {{val| 0 -6 -29 2 21 }}]
Mapping: {{mapping| 1 4 14 2 -5 | 0 -6 -29 2 21 }}


POTE generator: ~320/243 = 483.276
Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 483.276


{{Optimal ET sequence|legend=1| 72, 77, 149, 221e, 293de }}
{{Optimal ET sequence|legend=1| 72, 77, 149, 221e, 293de }}
Line 792: Line 792:
Comma list: 351/350, 385/384, 441/440, 676/675
Comma list: 351/350, 385/384, 441/440, 676/675


Mapping: [{{val| 1 4 14 2 -5 19 }}, {{val| 0 -6 -29 2 21 -38 }}]
Mapping: {{mapping| 1 4 14 2 -5 19 | 0 -6 -29 2 21 -38 }}


POTE generator: ~120/91 = 483.256
Optimal tuning (POTE): ~2 = 1\1, ~120/91 = 483.256


{{Optimal ET sequence|legend=1| 72, 77, 149, 221ef }}
{{Optimal ET sequence|legend=1| 72, 77, 149, 221ef }}
Line 805: Line 805:
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675


Mapping: [{{val| 1 4 14 2 -5 19 21 }}, {{val| 0 -6 -29 2 21 -38 -42 }}]
Mapping: {{mapping| 1 4 14 2 -5 19 21 | 0 -6 -29 2 21 -38 -42 }}


POTE generator: ~45/34 = 483.261
Optimal tuning (POTE): ~2 = 1\1, ~45/34 = 483.261


{{Optimal ET sequence|legend=1| 72, 77, 149, 221ef }}
{{Optimal ET sequence|legend=1| 72, 77, 149, 221ef }}
Line 814: Line 814:


== Unidec ==
== Unidec ==
{{main| Unidec }}
{{Main| Unidec }}


Subgroup: 2.3.5
=== 5-limit (unidecmic) ===
[[Subgroup]]: 2.3.5


[[Comma list]]: 31381059609/31250000000
[[Comma list]]: 31381059609/31250000000


[[Mapping]]: [{{val| 2 5 8 }}, {{val| 0 -6 -11 }}]
{{Mapping|legend=1| 2 5 8 | 0 -6 -11 }}


Mapping generators: ~177147/125000, ~10/9
: mapping generators: ~177147/125000, ~10/9


[[POTE generator]]: ~10/9 = 183.047
[[Optimal tuning]] ([[POTE]]): ~177147/125000 = 1\2, ~10/9 = 183.047


{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}


[[Badness]]: 0.082423
[[Badness]]: 0.082423
Scales: [[Unidec26]]


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 4375/4374
[[Comma list]]: 1029/1024, 4375/4374


[[Mapping]]: [{{val| 2 5 8 5 }}, {{val| 0 -6 -11 2 }}]
{{Mapping|legend=1| 2 5 8 5 | 0 -6 -11 2 }}
 
Mapping generators: ~1225/864, ~10/9


{{Multival|legend=1| 12 22 -4 7 -40 -71 }}
{{Multival|legend=1| 12 22 -4 7 -40 -71 }}


[[POTE generator]]: ~10/9 = 183.161
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~10/9 = 183.161


[[Minimax tuning]]:
[[Minimax tuning]]:
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }}
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }}
: [{{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 }}]
: {{Monzo list| 1 0 0 0 | 47/26 0 6/13 -6/13 | 71/26 0 11/13 -11/13 | 71/26 0 -2/13 2/13 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.7/5
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{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 list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 57/28 11/7 0 -11/14 | 20/7 -2/7 0 1/7 }}
: [[Eigenmonzo]]s (unchanged-intervals): 2, 9/7
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.9/7


{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}


[[Badness]]: 0.038393
[[Badness]]: 0.038393
Scales: [[Unidec26]]


=== 11-limit ===
=== 11-limit ===
Line 864: Line 859:
Comma list: 385/384, 441/440, 4375/4374
Comma list: 385/384, 441/440, 4375/4374


Mapping: [{{val| 2 5 8 5 6 }}, {{val| 0 -6 -11 2 3 }}]
Mapping: {{mapping| 2 5 8 5 6 | 0 -6 -11 2 3 }}
 
Mapping generators: ~99/70, ~10/9


Minimax tuning:
Minimax tuning:
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{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 }}]
: Eigenmonzos (unchanged-intervals): 2, 9/7
: Eigenmonzo (unchanged-interval) basis: 2.9/7


{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}


Badness: 0.015479
Badness: 0.015479
Scales: [[Unidec26]]


==== Ekadash ====
==== Ekadash ====
Line 884: Line 875:
Comma list: 385/384, 441/440, 625/624, 729/728
Comma list: 385/384, 441/440, 625/624, 729/728


Mapping: [{{val| 2 5 8 5 6 19 }}, {{val| 0 -6 -11 2 3 -38 }}]
Mapping: {{mapping| 2 5 8 5 6 19 | 0 -6 -11 2 3 -38 }}


Mapping generators: ~99/70, ~10/9
Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 183.187
 
POTE generator: ~10/9 = 183.187


{{Optimal ET sequence|legend=1| 26f, 46f, 72, 118, 190, 262df, 452cdef }}
{{Optimal ET sequence|legend=1| 26f, 46f, 72, 118, 190, 262df, 452cdef }}


Badness: 0.020381
Badness: 0.020381
Scales: [[Unidec26]]


==== Hendec ====
==== Hendec ====
Line 901: Line 888:
Comma list: 169/168, 325/324, 364/363, 385/384
Comma list: 169/168, 325/324, 364/363, 385/384


Mapping: [{{val| 2 5 8 5 6 8 }}, {{val| 0 -6 -11 2 3 -2 }}]
Mapping: {{mapping| 2 5 8 5 6 8 | 0 -6 -11 2 3 -2 }}
 
Mapping generators: ~91/64, ~10/9


POTE generator: ~10/9 = 183.198
Optimal tuning (POTE): ~91/64 = 1\2, ~10/9 = 183.198


{{Optimal ET sequence|legend=1| 26, 46, 72, 190ff }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 190ff }}


Badness: 0.017707
Badness: 0.017707
Scales: [[Unidec26]]


===== 17-limit =====
===== 17-limit =====
Line 918: Line 901:
Comma list: 169/168, 221/220, 273/272, 325/324, 364/363
Comma list: 169/168, 221/220, 273/272, 325/324, 364/363


Mapping: [{{val| 2 5 8 5 6 8 10 }}, {{val| 0 -6 -11 2 3 -2 -6 }}]
Mapping: {{mapping| 2 5 8 5 6 8 10 | 0 -6 -11 2 3 -2 -6 }}
 
Mapping generators: ~17/12, ~10/9


POTE generator: ~10/9 = 183.196
Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 183.196


{{Optimal ET sequence|legend=1| 26, 46, 72, 190ffg }}
{{Optimal ET sequence|legend=1| 26, 46, 72, 190ffg }}


Badness: 0.011676
Badness: 0.011676
Scales: [[Unidec26]]


== Superkleismic ==
== Superkleismic ==
{{main| Superkleismic }}
{{Main| Superkleismic }}
{{see also| Shibboleth family #Superkleismic }}
{{See also| Shibboleth family #Superkleismic }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 875/864, 1029/1024
[[Comma list]]: 875/864, 1029/1024


[[Mapping]]: [{{val| 1 4 5 2 }}, {{val| 0 -9 -10 3 }}]
{{Mapping|legend=1| 1 4 5 2 | 0 -9 -10 3 }}


{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}
{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}


[[POTE generator]]: ~6/5 = 321.930
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 321.930


{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
Line 953: Line 932:
Comma list: 100/99, 245/242, 385/384
Comma list: 100/99, 245/242, 385/384


Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]
Mapping: {{mapping| 1 4 5 2 4 | 0 -9 -10 3 -2 }}


POTE generator: ~6/5 = 321.847
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.847


{{Optimal ET sequence|legend=1| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
Line 966: Line 945:
Comma list: 100/99, 105/104, 144/143, 245/243
Comma list: 100/99, 105/104, 144/143, 245/243


Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -16 }}


POTE generator: ~6/5 = 321.994
Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994


{{Optimal ET sequence|legend=1| 11cf, 15, 26, 41 }}
{{Optimal ET sequence|legend=1| 11cf, 15, 26, 41 }}
Line 975: Line 954:


== Lagaca ==
== Lagaca ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 11529602/11390625
[[Comma list]]: 1029/1024, 11529602/11390625


[[Mapping]]: [{{val| 2 5 2 5 }}, {{val| 0 -9 13 3 }}]
{{Mapping|legend=1| 2 5 2 5 | 0 -9 13 3 }}


{{Multival|legend=1| 18 -26 -6 -83 -60 59 }}
{{Multival|legend=1| 18 -26 -6 -83 -60 59 }}


[[POTE generator]]: ~15/14 = 122.027
[[Optimal tuning]] ([[POTE]]): ~3375/2401 = 1\2, ~15/14 = 122.027


{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}
{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}
Line 990: Line 969:


== Necromanteion ==
== Necromanteion ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 5103/5000
[[Comma list]]: 1029/1024, 5103/5000


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


{{Multival|legend=1| 12 17 -4 -1 -40 -57 }}
{{Multival|legend=1| 12 17 -4 -1 -40 -57 }}


[[POTE generator]]: ~48/35 = 541.779
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 541.779


{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}
Line 1,009: Line 988:
Comma list: 176/175, 243/242, 1029/1024
Comma list: 176/175, 243/242, 1029/1024


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


POTE generator: ~15/11 = 541.729
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.729


{{Optimal ET sequence|legend=1| 20ce, 31, 113c, 144c, 175c, 381bccdee }}
{{Optimal ET sequence|legend=1| 20ce, 31, 113c, 144c, 175c, 381bccdee }}
Line 1,022: Line 1,001:
Comma list: 144/143, 176/175, 243/242, 343/338
Comma list: 144/143, 176/175, 243/242, 343/338


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


POTE generator: ~15/11 = 541.606
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.606


{{Optimal ET sequence|legend=1| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}
{{Optimal ET sequence|legend=1| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}
Line 1,031: Line 1,010:


== Restles ==
== Restles ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 153664/151875
[[Comma list]]: 1029/1024, 153664/151875


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


{{Multival|legend=1| 12 -19 -4 -58 -40 44 }}
{{Multival|legend=1| 12 -19 -4 -58 -40 44 }}


[[POTE generator]]: ~315/256 = 358.5485
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~315/256 = 358.5485


{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
Line 1,050: Line 1,029:
Comma list: 385/384, 441/440, 153664/151875
Comma list: 385/384, 441/440, 153664/151875


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


POTE generator: ~27/22 = 358.5713
Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 358.5713


{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
Line 1,063: Line 1,042:
Comma list: 196/195, 352/351, 385/384, 676/675
Comma list: 196/195, 352/351, 385/384, 676/675


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


POTE generator: ~16/13 = 358.5739
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 358.5739


{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}
Line 1,074: Line 1,053:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Quartemka]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Quartemka]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 1250000/1240029
[[Comma list]]: 1029/1024, 1250000/1240029


[[Mapping]]: [{{val| 1 4 6 2 }}, {{val| 0 -21 -32 7 }}]
{{Mapping|legend=1| 1 4 6 2 | 0 -21 -32 7 }}


{{Multival|legend=1| 21 32 -7 2 -70 -106 }}
{{Multival|legend=1| 21 32 -7 2 -70 -106 }}


[[POTE generator]]: ~27/25 = 138.006
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 138.006


{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}
Line 1,093: Line 1,072:
Comma list: 385/384, 441/440, 800000/793881
Comma list: 385/384, 441/440, 800000/793881


Mapping: [{{val| 1 4 6 2 3 }}, {{val| 0 -21 -32 7 4 }}]
Mapping: {{mapping| 1 4 6 2 3 | 0 -21 -32 7 4 }}


POTE generator: ~27/25 = 137.990
Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 137.990


{{Optimal ET sequence|legend=1| 26, 61, 87, 200, 287d, 487cdd }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 200, 287d, 487cdd }}
Line 1,106: Line 1,085:
Comma list: 325/324, 364/363, 385/384, 2200/2197
Comma list: 325/324, 364/363, 385/384, 2200/2197


Mapping: [{{val| 1 4 6 2 3 6 }}, {{val| 0 -21 -32 7 4 -20 }}]
Mapping: {{mapping| 1 4 6 2 3 6 | 0 -21 -32 7 4 -20 }}


POTE generator: ~13/12 = 137.990
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 137.990


{{Optimal ET sequence|legend=1| 26, 61, 87, 200, 487cdd }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 200, 487cdd }}
Line 1,117: Line 1,096:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritriple]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritriple]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 1959552/1953125
[[Comma list]]: 1029/1024, 1959552/1953125


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


{{Multival|legend=1| 27 20 -9 -31 -90 -77 }}
{{Multival|legend=1| 27 20 -9 -31 -90 -77 }}


[[POTE generator]]: ~864/625 = 559.295
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~864/625 = 559.295


{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 339d }}
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 339d }}
Line 1,136: Line 1,115:
Comma list: 385/384, 441/440, 43923/43750
Comma list: 385/384, 441/440, 43923/43750


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


POTE generator: ~242/175 = 559.293
Optimal tuning (POTE): ~2 = 1\1, ~242/175 = 559.293


{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 339de }}
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 339de }}
Line 1,145: Line 1,124:


== Widefourth ==
== Widefourth ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1029/1024, 48828125/48771072
[[Comma list]]: 1029/1024, 48828125/48771072


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


{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}
{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}


[[POTE generator]]: ~3125/2304 = 524.210
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3125/2304 = 524.210


{{Optimal ET sequence|legend=1| 16, 55b, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=1| 16, 55b, 71, 87, 103, 190 }}
Line 1,164: Line 1,143:
Comma list: 385/384, 441/440, 234375/234256
Comma list: 385/384, 441/440, 234375/234256


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


POTE generator: ~847/625 = 524.210
Optimal tuning (POTE): ~2 = 1\1, ~847/625 = 524.210


{{Optimal ET sequence|legend=1| 16, 55be, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=1| 16, 55be, 71, 87, 103, 190 }}
Line 1,177: Line 1,156:
Comma list: 385/384, 441/440, 625/624, 847/845
Comma list: 385/384, 441/440, 625/624, 847/845


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


POTE generator: ~65/48 = 524.209
Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 524.209


{{Optimal ET sequence|legend=1| 16, 55be, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=1| 16, 55be, 71, 87, 103, 190 }}
Line 1,187: Line 1,166:
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Gamelismic clan| ]] <!-- main article -->
[[Category:Gamelismic clan| ]] <!-- main article -->
[[Category:Miracle]]
[[Category:Rodan]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"