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=== 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.
== Rodan ==
{{main| Rodan }}
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 1029/1024
[[Mapping]]: [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1 }}]
{{Multival|legend=1| 3 17 -1 20 -10 -50 }}
[[POTE generator]]: ~8/7 = 234.417
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [[Eigenmonzo]]s: 2, 7/5
[[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.
{{Val list|legend=1| 41, 87, 128, 215d }}
[[Badness]]: 0.037112
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 441/440
Mapping: [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13 }}]
POTE generator: ~8/7 = 234.459
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: Eigenmonzos: 2, 11/9
Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
Vals: {{Val list| 41, 46, 87 }}
Badness: 0.023093
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 352/351, 364/363
Mapping: [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22 }}]
POTE generator: ~8/7 = 234.482
Minimax tuning:
* 13- and 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: Eigenmonzos: 2, 13/9
Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.
Vals: {{Val list| 41, 46, 87 }}
Badness: 0.018448
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 154/153, 196/195, 245/243, 256/255, 273/272
Mapping: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}]
POTE generator: ~8/7 = 234.524
Minimax tuning:
* 17-odd-limit eigenmonzos: 2, 18/17
Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }}
Badness: 0.016743
Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
==== Aerodactyl ====
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 245/243, 385/384, 441/440
Mapping: [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24 }}]
POTE generator: ~8/7 = 234.639
Vals: {{Val list| 5, 41f, 46, 133ff }}
Badness: 0.033986
=== Aerodino ===
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243, 1029/1024
Mapping: [{{val| 1 1 -1 3 -3 }}, {{val| 0 3 17 -1 33 }}]
POTE generator: ~8/7 = 234.728
Vals: {{Val list| 41e, 46 }}
Badness: 0.054294
==== 13-limit ====
Comma list: 91/90, 176/175, 245/243, 847/845
Mapping: [{{val| 1 1 -1 3 -3 -1 }}, {{val| 0 3 17 -1 33 24 }}]
POTE generator: ~8/7 = 234.782
Vals: {{Val list| 41ef, 46 }}
Badness: 0.035836
=== Varan ===
Comma list: 100/99, 245/243, 1029/1024
Mapping: [{{val| 1 1 -1 3 -2 }}, {{val| 0 3 17 -1 28 }}]
POTE generator: ~8/7 = 234.145
Vals: {{Val list| 36ce, 41 }}
Badness: 0.044937
==== 13-limit ====
Comma list: 100/99, 105/104, 245/243, 352/351
Mapping: [{{val| 1 1 -1 3 -2 0 }}, {{val| 0 3 17 -1 28 19 }}]
POTE generator: ~8/7 = 234.089
Vals: {{Val list| 36ce, 41 }}
Badness: 0.032284
== Guiron ==
{{see also| Schismatic family }}
Subgroup: 2.3.5.7
[[Comma list]]: 1029/1024, 10976/10935
[[Mapping]]: [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1 }}]
Mapping generators: ~2, ~8/7
{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}
[[POTE generator]]: ~8/7 = 233.930
[[Minimax tuning]]:
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [[Eigenmonzo]]s: 2, 5/4
{{Val list|legend=1| 36, 41, 77, 118, 277d }}
[[Badness]]: 0.047544
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 10976/10935
Mapping: [{{val| 1 1 7 3 -2 }}, {{val| 0 3 -24 -1 28 }}]
Mapping generators: ~2, ~8/7
POTE generator: ~8/7 = 233.931
Minimax tuning:
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]
: Eigenmonzos: 2, 5/4
Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }}
Badness: 0.026648
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 729/728
Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]
Mapping generators: ~2, ~8/7
POTE generator: ~8/7 = 233.890
Vals: {{Val list| 36e, 41, 77, 118 }}
Badness: 0.028444
== Gorgo ==
In the 5-limit, gorgo tempers out the '''laconic comma''', [[2187/2000]], which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in [[16edo|16EDO]] and [[21edo|21EDO]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.
=== 5-limit (laconic) ===
Subgroup: 2.3.5
[[Comma list]]: 2187/2000
[[Mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 7 }}]
{{Multival|legend=1| 3 7 4 }}
[[POTE generator]]: ~10/9 = 227.426
{{Val list|legend=1| 5, 16, 21, 37b }}
[[Badness]]: 0.161799
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 36/35, 1029/1024
[[Mapping]]: [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1 }}]
{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
[[POTE generator]]: ~8/7 = 228.334
{{Val list|legend=1| 5, 11c, 16, 21 }}
[[Badness]]: 0.060663
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44, 1029/1024
Mapping: [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13 }}]
POTE generator: ~8/7 = 227.373
Vals: {{Val list| 16, 21, 37b }}
Badness: 0.049500
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44, 507/500
Mapping: [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9 }}]
POTE generator: ~8/7 = 227.230
Vals: {{Val list| 16, 21, 37b }}
Badness: 0.032664
=== Spartan ===
Subgroup: 2.3.5.7.11
Comma list: 36/35, 56/55, 1029/1024
Mapping: [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8 }}]
POTE generator: ~8/7 = 229.535
Vals: {{Val list| 5, 16e, 21, 47c, 68bcce }}
Badness: 0.062683
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 56/55, 507/500
Mapping: [{{val| 1 1 1 3 5 2 }}, {{val| 0 3 7 -1 -8 9 }}]
POTE generator: ~8/7 = 229.059
{{Val list|legend=1| 5, 16e, 21, 68bccef }}
Badness: 0.047071
=== Music ===
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]
== Gidorah ==
{{main| University temperament }}
=== 5-limit (university) ===
Subgroup: 2.3.5
[[Comma list]]: 144/125
[[Mapping]]: [{{val| 1 1 2 }}, {{val| 0 3 2 }}]
[[POTE generator]]: ~6/5 = 235.4416
{{Val list|legend=1| 5, 31cccc, 36…, 41…, 46…, 51… }}
[[Badness]]: 0.101806
=== 7-limit ===
Subgroup: 2.3.5.7
[[Comma list]]: 21/20, 144/125
[[Mapping]]: [{{val| 1 1 2 3 }}, {{val| 0 3 2 -1 }}]
{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}
[[POTE generator]]: ~8/7 = 230.762
{{Val list|legend=1| 5, 16c, 21cc, 26ccc }}
[[Badness]]: 0.062262
== Clyndro ==
{{see also| Pelogic family }}
Subgroup: 2.3.5.7
[[Comma list]]: 135/128, 360/343
[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]
{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}
[[POTE generator]]: ~8/7 = 226.469
{{Val list|legend=1| 5c, 11, 16 }}
[[Badness]]: 0.159179
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 33/32, 45/44, 352/343
Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]
POTE generator: ~8/7 = 226.428
Vals: {{Val list| 5c, 11, 16 }}
Badness: 0.069703


== Miracle ==
== Miracle ==
Line 280: Line 635:
Badness: 0.042687
Badness: 0.042687


== Rodan ==
== Hemiseven ==
{{main| Rodan }}
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 19683/19600
 
[[Mapping]]: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
 
{{Multival|legend=1| 6 29 -2 32 -20 -86 }}


Subgroup: 2.3.5.7
[[POTE generator]]: ~320/243 = 483.267


[[Comma list]]: 245/243, 1029/1024
{{Val list|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}


[[Mapping]]: [{{val| 1 1 -1 3 }}, {{val| 0 3 17 -1 }}]
[[Badness]]: 0.056557


{{Multival|legend=1| 3 17 -1 20 -10 -50 }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[POTE generator]]: ~8/7 = 234.417
Comma list: 385/384, 441/440, 19683/19600


[[Minimax tuning]]:
Mapping: [{{val| 1 4 14 2 -5 }}, {{val| 0 -6 -29 2 21 }}]
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/3 0 1/6 -1/6 }}, {{monzo| 25/9 0 17/18 -17/18 }}, {{monzo| 25/9 0 -1/18 1/18 }}]
: [[Eigenmonzo]]s: 2, 7/5


[[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.
POTE generator: ~320/243 = 483.276


{{Val list|legend=1| 41, 87, 128, 215d }}
Vals: {{Val list| 72, 77, 149, 221e, 293de }}


[[Badness]]: 0.037112
Badness: 0.028467


Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=== 11-limit ===
Comma list: 351/350, 385/384, 441/440, 676/675
Subgroup: 2.3.5.7.11


Comma list: 245/243, 385/384, 441/440
Mapping: [{{val| 1 4 14 2 -5 19 }}, {{val| 0 -6 -29 2 21 -38 }}]


Mapping: [{{val| 1 1 -1 3 6 }}, {{val| 0 3 17 -1 -13 }}]
POTE generator: ~120/91 = 483.256


POTE generator: ~8/7 = 234.459
Vals: {{Val list| 72, 77, 149, 221ef }}


Minimax tuning:  
Badness: 0.021900
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: Eigenmonzos: 2, 11/9


Algebraic generator: [[Algebraic number|positive root]] of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Vals: {{Val list| 41, 46, 87 }}
Comma list: 273/272, 351/350, 385/384, 441/440, 676/675


Badness: 0.023093
Mapping: [{{val| 1 4 14 2 -5 19 21 }}, {{val| 0 -6 -29 2 21 -38 -42 }}]


Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
POTE generator: ~45/34 = 483.261


==== 13-limit ====
Vals: {{Val list| 72, 77, 149, 221ef }}
Subgroup: 2.3.5.7.11.13


Comma list: 196/195, 245/243, 352/351, 364/363
Badness: 0.015701


Mapping: [{{val| 1 1 -1 3 6 8 }}, {{val| 0 3 17 -1 -13 -22 }}]
== Lemba ==
{{main| Lemba }}
{{see also| Jubilismic clan #Lemba }}


POTE generator: ~8/7 = 234.482
Subgroup: 2.3.5.7


Minimax tuning:
[[Comma list]]: 50/49, 525/512
* 13- and 15-odd-limit
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 23/14 3/14 0 0 0 -3/28 }}, {{monzo| 37/14 17/14 0 0 0 -17/28 }}, {{monzo| 39/14 -1/14 0 0 0 1/28 }}, {{monzo| 45/14 -13/14 0 0 0 13/28 }}, {{monzo| 23/7 -11/7 0 0 0 11/14 }}]
: Eigenmonzos: 2, 13/9


Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.
[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]


Vals: {{Val list| 41, 46, 87 }}
Mapping generators: ~7/5, ~8/7


Badness: 0.018448
{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}


Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
[[POTE generator]]: ~8/7 = 232.089


===== 17-limit =====
{{Val list|legend=1| 10, 16, 26 }}
Subgroup: 2.3.5.7.11.13.17


Comma list: 154/153, 196/195, 245/243, 256/255, 273/272
[[Badness]]: 0.062208


Mapping: [{{val| 1 1 -1 3 6 8 8 }}, {{val| 0 3 17 -1 -13 -22 -20 }}]
=== 11-limit ===
Subgroup: 2.3.5.7.11


POTE generator: ~8/7 = 234.524
Comma list: 45/44, 50/49, 385/384


Minimax tuning:  
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
* 17-odd-limit eigenmonzos: 2, 18/17


Vals: {{Val list| 41, 46, 87, 220dg, 307dgg }}
POTE generator: ~8/7 = 230.974


Badness: 0.016743
Vals: {{Val list| 10, 16, 26 }}


Scales: [[Rodan26opt]], [[Rodan31opt]], [[Rodan41opt]]
Badness: 0.041563


==== Aerodactyl ====
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 91/90, 245/243, 385/384, 441/440
Comma list: 45/44, 50/49, 65/64, 78/77
 
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
 
POTE generator: ~8/7 = 230.966
 
Vals: {{Val list| 10, 16, 26 }}
 
Badness: 0.025477
 
== Unidec ==
{{main| Unidec }}


Mapping: [{{val| 1 1 -1 3 6 -1 }}, {{val| 0 3 17 -1 -13 24 }}]
Subgroup: 2.3.5


POTE generator: ~8/7 = 234.639
[[Comma list]]: 31381059609/31250000000


Vals: {{Val list| 5, 41f, 46, 133ff }}
[[Mapping]]: [{{val| 2 5 8 }}, {{val| 0 -6 -11 }}]


Badness: 0.033986
Mapping generators: ~177147/125000, ~10/9


=== Aerodino ===
[[POTE generator]]: ~10/9 = 183.047
Subgroup: 2.3.5.7.11


Comma list: 176/175, 245/243, 1029/1024
{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}


Mapping: [{{val| 1 1 -1 3 -3 }}, {{val| 0 3 17 -1 33 }}]
[[Badness]]: 0.082423


POTE generator: ~8/7 = 234.728
Scales: [[Unidec26]]


Vals: {{Val list| 41e, 46 }}
=== 7-limit ===
Subgroup: 2.3.5.7


Badness: 0.054294
[[Comma list]]: 1029/1024, 4375/4374


==== 13-limit ====
[[Mapping]]: [{{val| 2 5 8 5 }}, {{val| 0 -6 -11 2 }}]
Comma list: 91/90, 176/175, 245/243, 847/845


Mapping: [{{val| 1 1 -1 3 -3 -1 }}, {{val| 0 3 17 -1 33 24 }}]
Mapping generators: ~1225/864, ~10/9


POTE generator: ~8/7 = 234.782
{{Multival|legend=1| 12 22 -4 7 -40 -71 }}


Vals: {{Val list| 41ef, 46 }}
[[POTE generator]]: ~10/9 = 183.161


Badness: 0.035836
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{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 }}]
: [[Eigenmonzo]]s: 2, 7/5
* [[9-odd-limit]]
: [{{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 }}]
: [[Eigenmonzo]]s: 2, 9/7


=== Varan ===
{{Val list|legend=1| 26, 46, 72, 118, 190 }}
Comma list: 100/99, 245/243, 1029/1024


Mapping: [{{val| 1 1 -1 3 -2 }}, {{val| 0 3 17 -1 28 }}]
[[Badness]]: 0.038393


POTE generator: ~8/7 = 234.145
Scales: [[Unidec26]]


Vals: {{Val list| 36ce, 41 }}
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.044937
Comma list: 385/384, 441/440, 4375/4374


==== 13-limit ====
Mapping: [{{val| 2 5 8 5 6 }}, {{val| 0 -6 -11 2 3 }}]
Comma list: 100/99, 105/104, 245/243, 352/351


Mapping: [{{val| 1 1 -1 3 -2 0 }}, {{val| 0 3 17 -1 28 19 }}]
Mapping generators: ~99/70, ~10/9


POTE generator: ~8/7 = 234.089
Minimax tuning:
* 11-odd-limit
: [{{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: 2, 9/7


Vals: {{Val list| 36ce, 41 }}
Vals: {{Val list| 26, 46, 72, 118, 190 }}


Badness: 0.032284
Badness: 0.015479


== Guiron ==
Scales: [[Unidec26]]
{{see also| Schismatic family }}


Subgroup: 2.3.5.7
=== Ekadash ===
Subgroup: 2.3.5.7.11.13


[[Comma list]]: 1029/1024, 10976/10935
Comma list: 385/384, 441/440, 625/624, 729/728


[[Mapping]]: [{{val| 1 1 7 3 }}, {{val| 0 3 -24 -1 }}]
Mapping: [{{val| 2 5 8 5 6 19 }}, {{val| 0 -6 -11 2 3 -38 }}]


Mapping generators: ~2, ~8/7
Mapping generators: ~99/70, ~10/9


{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}
POTE generator: ~10/9 = 183.187


[[POTE generator]]: ~8/7 = 233.930
Vals: {{Val list| 26f, 46f, 72, 118, 190, 262df, 452cdef }}


[[Minimax tuning]]:
Badness: 0.020381
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 65/24 0 1/24 0 }}]
: [[Eigenmonzo]]s: 2, 5/4


{{Val list|legend=1| 36, 41, 77, 118, 277d }}
Scales: [[Unidec26]]


[[Badness]]: 0.047544
=== Hendec ===
Subgroup: 2.3.5.7.11.13


=== 11-limit ===
Comma list: 169/168, 325/324, 364/363, 385/384
Subgroup: 2.3.5.7.11


Comma list: 385/384, 441/440, 10976/10935
Mapping: [{{val| 2 5 8 5 6 8 }}, {{val| 0 -6 -11 2 3 -2 }}]


Mapping: [{{val| 1 1 7 3 -2 }}, {{val| 0 3 -24 -1 28 }}]
Mapping generators: ~91/64, ~10/9


Mapping generators: ~2, ~8/7
POTE generator: ~10/9 = 183.198


POTE generator: ~8/7 = 233.931
Vals: {{Val list| 26, 46, 72, 190ff }}


Minimax tuning:
Badness: 0.017707
* 11-odd-limit
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]
: Eigenmonzos: 2, 5/4


Vals: {{Val list| 36e, 41, 77, 118, 159, 277d }}
Scales: [[Unidec26]]


Badness: 0.026648
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


=== 13-limit ===
Comma list: 169/168, 221/220, 273/272, 325/324, 364/363
Subgroup: 2.3.5.7.11.13


Comma list: 196/195, 352/351, 385/384, 729/728
Mapping: [{{val| 2 5 8 5 6 8 10 }}, {{val| 0 -6 -11 2 3 -2 -6 }}]


Mapping: [{{val| 1 1 7 3 -2 0 }}, {{val| 0 3 -24 -1 28 19 }}]
Mapping generators: ~17/12, ~10/9


Mapping generators: ~2, ~8/7
POTE generator: ~10/9 = 183.196


POTE generator: ~8/7 = 233.890
Vals: {{Val list| 26, 46, 72, 190ffg }}


Vals: {{Val list| 36e, 41, 77, 118 }}
Badness: 0.011676


Badness: 0.028444
Scales: [[Unidec26]]


== Valentine ==
== Valentine ==
Line 603: Line 969:
Badness: 0.032749
Badness: 0.032749


== Unidec ==
== Superkleismic ==
{{main| Unidec }}
{{see also| Shibboleth family #Superkleismic }}
 
Subgroup: 2.3.5
 
[[Comma list]]: 31381059609/31250000000
 
[[Mapping]]: [{{val| 2 5 8 }}, {{val| 0 -6 -11 }}]
 
Mapping generators: ~177147/125000, ~10/9
 
[[POTE generator]]: ~10/9 = 183.047
 
{{Val list|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}
 
[[Badness]]: 0.082423
 
Scales: [[Unidec26]]


=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 1029/1024, 4375/4374
[[Comma list]]: 875/864, 1029/1024


[[Mapping]]: [{{val| 2 5 8 5 }}, {{val| 0 -6 -11 2 }}]
[[Mapping]]: [{{val| 1 4 5 2 }}, {{val| 0 -9 -10 3 }}]


Mapping generators: ~1225/864, ~10/9
{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}


{{Multival|legend=1| 12 22 -4 7 -40 -71 }}
[[POTE generator]]: ~6/5 = 321.930


[[POTE generator]]: ~10/9 = 183.161
{{Val list|legend=1| 11c, 15, 26, 41 }}


[[Minimax tuning]]:
[[Badness]]: 0.047932
* [[7-odd-limit]]
: [{{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 }}]
: [[Eigenmonzo]]s: 2, 7/5
* [[9-odd-limit]]
: [{{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 }}]
: [[Eigenmonzo]]s: 2, 9/7
 
{{Val list|legend=1| 26, 46, 72, 118, 190 }}
 
[[Badness]]: 0.038393
 
Scales: [[Unidec26]]


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 385/384, 441/440, 4375/4374
Comma list: 100/99, 245/242, 385/384


Mapping: [{{val| 2 5 8 5 6 }}, {{val| 0 -6 -11 2 3 }}]
Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]


Mapping generators: ~99/70, ~10/9
POTE generator: ~6/5 = 321.847


Minimax tuning:
Vals: {{Val list| 11c, 15, 26, 41, 261ccdee }}
* 11-odd-limit
: [{{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: 2, 9/7


Vals: {{Val list| 26, 46, 72, 118, 190 }}
Badness: 0.025659
 
Badness: 0.015479
 
Scales: [[Unidec26]]
 
=== Ekadash ===
Subgroup: 2.3.5.7.11.13
 
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 generators: ~99/70, ~10/9
 
POTE generator: ~10/9 = 183.187
 
Vals: {{Val list| 26f, 46f, 72, 118, 190, 262df, 452cdef }}
 
Badness: 0.020381
 
Scales: [[Unidec26]]
 
=== Hendec ===
Subgroup: 2.3.5.7.11.13
 
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 generators: ~91/64, ~10/9
 
POTE generator: ~10/9 = 183.198
 
Vals: {{Val list| 26, 46, 72, 190ff }}
 
Badness: 0.017707
 
Scales: [[Unidec26]]
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
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 generators: ~17/12, ~10/9
 
POTE generator: ~10/9 = 183.196
 
Vals: {{Val list| 26, 46, 72, 190ffg }}
 
Badness: 0.011676
 
Scales: [[Unidec26]]
 
== Hemiseven ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 19683/19600
 
[[Mapping]]: [{{val| 1 4 14 2 }}, {{val| 0 -6 -29 2 }}]
 
{{Multival|legend=1| 6 29 -2 32 -20 -86 }}
 
[[POTE generator]]: ~320/243 = 483.267
 
{{Val list|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}
 
[[Badness]]: 0.056557
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 19683/19600
 
Mapping: [{{val| 1 4 14 2 -5 }}, {{val| 0 -6 -29 2 21 }}]
 
POTE generator: ~320/243 = 483.276
 
Vals: {{Val list| 72, 77, 149, 221e, 293de }}
 
Badness: 0.028467


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 351/350, 385/384, 441/440, 676/675
Comma list: 100/99, 105/104, 245/243, 1188/1183


Mapping: [{{val| 1 4 14 2 -5 19 }}, {{val| 0 -6 -29 2 21 -38 }}]
Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]


POTE generator: ~120/91 = 483.256
POTE generator: ~6/5 = 321.994


Vals: {{Val list| 72, 77, 149, 221ef }}
Vals: {{Val list| 11cf, 15, 26, 41 }}


Badness: 0.021900
Badness: 0.021478
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
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 }}]
 
POTE generator: ~45/34 = 483.261
 
Vals: {{Val list| 72, 77, 149, 221ef }}
 
Badness: 0.015701


== Tritikleismic ==
== Tritikleismic ==
Line 851: Line 1,089:
Badness: 0.013551
Badness: 0.013551


== Superkleismic ==
== Necromanteion ==
{{see also| Shibboleth family #Superkleismic }}
 
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 875/864, 1029/1024
[[Comma list]]: 1029/1024, 5103/5000


[[Mapping]]: [{{val| 1 4 5 2 }}, {{val| 0 -9 -10 3 }}]
[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]


{{Multival|legend=1| 9 10 -3 -5 -30 -35 }}
{{Multival|legend=1| 12 17 -4 -1 -40 -57 }}


[[POTE generator]]: ~6/5 = 321.930
[[POTE generator]]: ~48/35 = 541.779


{{Val list|legend=1| 11c, 15, 26, 41 }}
{{Val list|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}


[[Badness]]: 0.047932
[[Badness]]: 0.117680


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 100/99, 245/242, 385/384
Comma list: 176/175, 243/242, 1029/1024


Mapping: [{{val| 1 4 5 2 4 }}, {{val| 0 -9 -10 3 -2 }}]
Mapping: [{{val| 1 7 10 1 17 }}, {{val| 0 -12 -17 4 -30 }}]


POTE generator: ~6/5 = 321.847
POTE generator: ~15/11 = 541.729


Vals: {{Val list| 11c, 15, 26, 41, 261ccdee }}
Vals: {{Val list| 20ce, 31, 113c, 144c, 175c, 381bccdee }}


Badness: 0.025659
Badness: 0.053459


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 100/99, 105/104, 245/243, 1188/1183
Comma list: 144/143, 176/175, 243/242, 343/338


Mapping: [{{val| 1 4 5 2 4 8 }}, {{val| 0 -9 -10 3 -2 -16 }}]
Mapping: [{{val| 1 7 10 1 17 1 }}, {{val| 0 -12 -17 4 -30 6 }}]


POTE generator: ~6/5 = 321.994
POTE generator: ~15/11 = 541.606


Vals: {{Val list| 11cf, 15, 26, 41 }}
Vals: {{Val list| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}


Badness: 0.021478
Badness: 0.047015


== Gorgo ==
== Restles ==
In the 5-limit, gorgo tempers out the '''laconic comma''', [[2187/2000]], which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in [[16edo|16EDO]] and [[21edo|21EDO]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.
 
=== 5-limit (laconic) ===
Subgroup: 2.3.5
 
[[Comma list]]: 2187/2000
 
[[Mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 7 }}]
 
{{Multival|legend=1| 3 7 4 }}
 
[[POTE generator]]: ~10/9 = 227.426
 
{{Val list|legend=1| 5, 16, 21, 37b }}
 
[[Badness]]: 0.161799
 
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 36/35, 1029/1024
[[Comma list]]: 1029/1024, 153664/151875


[[Mapping]]: [{{val| 1 1 1 3 }}, {{val| 0 3 7 -1 }}]
[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]


{{Multival|legend=1| 3 7 -1 4 -10 -22 }}
{{Multival|legend=1| 12 -19 -4 -58 -40 44 }}


[[POTE generator]]: ~8/7 = 228.334
[[POTE generator]]: ~315/256 = 358.5485


{{Val list|legend=1| 5, 11c, 16, 21 }}
{{Val list|legend=1| 10, 77, 87, 164 }}


[[Badness]]: 0.060663
[[Badness]]: 0.108011


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 36/35, 45/44, 1029/1024
Comma list: 385/384, 441/440, 153664/151875


Mapping: [{{val| 1 1 1 3 1 }}, {{val| 0 3 7 -1 13 }}]
Mapping: [{{val| 1 -2 8 4 -7 }}, {{val| 0 12 -19 -4 35 }}]


POTE generator: ~8/7 = 227.373
POTE generator: ~27/22 = 358.5713


Vals: {{Val list| 16, 21, 37b }}
Vals: {{Val list| 10, 77, 87, 164 }}


Badness: 0.049500
Badness: 0.054655
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 36/35, 45/44, 507/500
 
Mapping: [{{val| 1 1 1 3 1 2 }}, {{val| 0 3 7 -1 13 9 }}]
 
POTE generator: ~8/7 = 227.230
 
Vals: {{Val list| 16, 21, 37b }}
 
Badness: 0.032664
 
=== Spartan ===
Subgroup: 2.3.5.7.11
 
Comma list: 36/35, 56/55, 1029/1024
 
Mapping: [{{val| 1 1 1 3 5 }}, {{val| 0 3 7 -1 -8 }}]
 
POTE generator: ~8/7 = 229.535
 
Vals: {{Val list| 5, 16e, 21, 47c, 68bcce }}
 
Badness: 0.062683
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 36/35, 56/55, 507/500
 
Mapping: [{{val| 1 1 1 3 5 2 }}, {{val| 0 3 7 -1 -8 9 }}]
 
POTE generator: ~8/7 = 229.059
 
{{Val list|legend=1| 5, 16e, 21, 68bccef }}
 
Badness: 0.047071
 
=== Music ===
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 Gorgo Example] by [[Herman Miller]]
 
== Lemba ==
{{main| Lemba }}
{{see also| Jubilismic clan #Lemba }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 50/49, 525/512
 
[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
 
Mapping generators: ~7/5, ~8/7
 
{{Multival|legend=1| 6 -2 -2 -17 -20 1 }}
 
[[POTE generator]]: ~8/7 = 232.089
 
{{Val list|legend=1| 10, 16, 26 }}
 
[[Badness]]: 0.062208
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 50/49, 385/384
 
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
 
POTE generator: ~8/7 = 230.974
 
Vals: {{Val list| 10, 16, 26 }}
 
Badness: 0.041563


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 45/44, 50/49, 65/64, 78/77
Comma list: 196/195, 352/351, 385/384, 676/675


Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
Mapping: [{{val| 1 -2 8 4 -7 4 }}, {{val| 0 12 -19 -4 35 -1 }}]


POTE generator: ~8/7 = 230.966
POTE generator: ~16/13 = 358.5739


Vals: {{Val list| 10, 16, 26 }}
Vals: {{Val list| 10, 77, 87, 164 }}


Badness: 0.025477
Badness: 0.028187


== Gidorah ==
== Quartemka ==
{{main| University temperament }}
 
=== 5-limit (university) ===
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 144/125
[[Comma list]]: {{monzo| 2 -32 11 }}


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


[[POTE generator]]: ~6/5 = 235.4416
[[POTE generator]]: ~27/25 = 137.962


{{Val list|legend=1| 5, 31cccc, 36…, 41…, 46…, 51… }}
{{Val list|legend=1| 26, 61, 87, 287, 374, 461 }}


[[Badness]]: 0.101806
[[Badness]]: 1.381216


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 21/20, 144/125
[[Comma list]]: 1029/1024, 1250000/1240029


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


{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}
{{Multival|legend=1| 21 32 -7 2 -70 -106 }}


[[POTE generator]]: ~8/7 = 230.762
[[POTE tuning|POTE generator]]: ~27/25 = 138.006


{{Val list|legend=1| 5, 16c, 21cc, 26ccc }}
{{Val list|legend=1| 26, 61, 87, 113, 200 }}


[[Badness]]: 0.062262
[[Badness]]: 0.152287
 
== Clyndro ==
{{see also| Pelogic family }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 135/128, 360/343
 
[[Mapping]]: [{{val| 1 1 4 3 }}, {{val| 0 3 -9 -1 }}]
 
{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}
 
[[POTE generator]]: ~8/7 = 226.469
 
{{Val list|legend=1| 5c, 11, 16 }}
 
[[Badness]]: 0.159179


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 33/32, 45/44, 352/343
Comma list: 385/384, 441/440, 800000/793881


Mapping: [{{val| 1 1 4 3 4 }}, {{val| 0 3 -9 -1 -3 }}]
Mapping: [{{val| 1 4 6 2 3 }}, {{val| 0 -21 -32 7 4 }}]


POTE generator: ~8/7 = 226.428
POTE generator: ~27/25 = 137.990


Vals: {{Val list| 5c, 11, 16 }}
Vals: {{Val list| 26, 61, 87, 200, 287d, 487cdd }}


Badness: 0.069703
Badness: 0.057307
 
== Necromanteion ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 5103/5000
 
[[Mapping]]: [{{val| 1 7 10 1 }}, {{val| 0 -12 -17 4 }}]
 
{{Multival|legend=1| 12 17 -4 -1 -40 -57 }}
 
[[POTE generator]]: ~48/35 = 541.779
 
{{Val list|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}
 
[[Badness]]: 0.117680
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 176/175, 243/242, 1029/1024
 
Mapping: [{{val| 1 7 10 1 17 }}, {{val| 0 -12 -17 4 -30 }}]
 
POTE generator: ~15/11 = 541.729
 
Vals: {{Val list| 20ce, 31, 113c, 144c, 175c, 381bccdee }}
 
Badness: 0.053459


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 144/143, 176/175, 243/242, 343/338
Comma list: 325/324, 364/363, 385/384, 2200/2197


Mapping: [{{val| 1 7 10 1 17 1 }}, {{val| 0 -12 -17 4 -30 6 }}]
Mapping: [{{val| 1 4 6 2 3 6 }}, {{val| 0 -21 -32 7 4 -20 }}]


POTE generator: ~15/11 = 541.606
POTE generator: ~13/12 = 137.990


Vals: {{Val list| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}
Vals: {{Val list| 26, 61, 87, 200, 487cdd }}


Badness: 0.047015
Badness: 0.028393
 
== Widefourth ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 48828125/48771072
 
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]
 
{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}
 
[[POTE generator]]: ~3125/2304 = 524.210
 
{{Val list|legend=1| 16, 55b, 71, 87, 103, 190 }}
 
[[Badness]]: 0.154117
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 234375/234256
 
Mapping: [{{val| 1 16 8 -2 17 }}, {{val| 0 -33 -13 11 -31 }}]
 
POTE generator: ~847/625 = 524.210
 
Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}
 
Badness: 0.040785
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
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 }}]
 
POTE generator: ~65/48 = 524.209
 
Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}
 
Badness: 0.021636


== Tritriple ==
== Tritriple ==
Line 1,212: Line 1,266:
Badness: 0.035350
Badness: 0.035350


== Restles ==
== Widefourth ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 1029/1024, 153664/151875
[[Comma list]]: 1029/1024, 48828125/48771072


[[Mapping]]: [{{val| 1 -2 8 4 }}, {{val| 0 12 -19 -4 }}]
[[Mapping]]: [{{val| 1 16 8 -2 }}, {{val| 0 -33 -13 11 }}]


{{Multival|legend=1| 12 -19 -4 -58 -40 44 }}
{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}


[[POTE generator]]: ~315/256 = 358.5485
[[POTE generator]]: ~3125/2304 = 524.210


{{Val list|legend=1| 10, 77, 87, 164 }}
{{Val list|legend=1| 16, 55b, 71, 87, 103, 190 }}


[[Badness]]: 0.108011
[[Badness]]: 0.154117


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 385/384, 441/440, 153664/151875
Comma list: 385/384, 441/440, 234375/234256


Mapping: [{{val| 1 -2 8 4 -7 }}, {{val| 0 12 -19 -4 35 }}]
Mapping: [{{val| 1 16 8 -2 17 }}, {{val| 0 -33 -13 11 -31 }}]


POTE generator: ~27/22 = 358.5713
POTE generator: ~847/625 = 524.210


Vals: {{Val list| 10, 77, 87, 164 }}
Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.054655
Badness: 0.040785


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 196/195, 352/351, 385/384, 676/675
Comma list: 385/384, 441/440, 625/624, 847/845


Mapping: [{{val| 1 -2 8 4 -7 4 }}, {{val| 0 12 -19 -4 35 -1 }}]
Mapping: [{{val| 1 16 8 -2 17 12 }}, {{val| 0 -33 -13 11 -31 -19 }}]


POTE generator: ~16/13 = 358.5739
POTE generator: ~65/48 = 524.209


Vals: {{Val list| 10, 77, 87, 164 }}
Vals: {{Val list| 16, 55be, 71, 87, 103, 190 }}


Badness: 0.028187
Badness: 0.021636
 
== Quartemka ==
Subgroup: 2.3.5
 
[[Comma list]]: {{monzo| 2 -32 11 }}
 
[[Mapping]]: [{{val| 1 4 6 }}, {{val| 0 -21 -32 }}]
 
[[POTE generator]]: ~27/25 = 137.962
 
{{Val list|legend=1| 26, 61, 87, 287, 374, 461 }}
 
[[Badness]]: 1.381216
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 1250000/1240029
 
[[Mapping]]: [{{val| 1 4 6 2 }}, {{val| 0 -21 -32 7 }}]
 
{{Multival|legend=1| 21 32 -7 2 -70 -106 }}
 
[[POTE tuning|POTE generator]]: ~27/25 = 138.006
 
{{Val list|legend=1| 26, 61, 87, 113, 200 }}
 
[[Badness]]: 0.152287
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 800000/793881
 
Mapping: [{{val| 1 4 6 2 3 }}, {{val| 0 -21 -32 7 4 }}]
 
POTE generator: ~27/25 = 137.990
 
Vals: {{Val list| 26, 61, 87, 200, 287d, 487cdd }}
 
Badness: 0.057307
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
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 }}]
 
POTE generator: ~13/12 = 137.990
 
Vals: {{Val list| 26, 61, 87, 200, 487cdd }}
 
Badness: 0.028393


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