Gamelismic clan: Difference between revisions

Revision as of 04:11, 3 June 2021

The 2.3.7 subgroup comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo [-10 1 0 3⟩. For any member of the clan, for the rank three gamelan temperament itself, and for the rank two 2.3.7 temperament slendric, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)³ × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. 36EDO is a good tuning for gamelismic itself, though if the full 7-limit is desired, 72EDO, 77EDO or 118EDO might be preferred.

Slendric

Main article: Slendric

Subgroup: 2.3.7

Comma list: 1029/1024

Sval mapping: [⟨1 1 3], ⟨0 3 -1]]

Mapping generators: ~2, ~8/7

Gencom mapping: [⟨1 1 0 3], ⟨0 3 0 -1]]

Gencom: [2 8/7; 1029/1024]

POTE generator: ~8/7 = 233.688

Template:Val list

Scales: slendric5, slendric6, slendric11, slendric16

Full seven limit extensions

To the gamelisma itself we need to add the comma which appears next on the modified normal comma list, which is often a 5-limit comma. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use 8/7 as a generator, though in the case of gidorah that's the same as 6/5. Miracle adds 33075/32768 and uses the secor, half an 8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of 21/20 and superkleismic adds 875/864 with a generator of 6/5. Unidec adds 4375/4374, and has a generator of 10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a major third. Finally, tritikleismic adds 15625/15536 and has a generator of 6/5 with a 1/3 octave period.

Discussed elsewhere are blacksmith, mothra, echidnic, trismegistus, hemithirds, gamity, triwell, decades and heinz. The rest are considered below.

Subgroup extensions

No-five subgroup extensions of slendric include 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 article: Rodan

Subgroup: 2.3.5.7

Comma list: 245/243, 1029/1024

Mapping: [⟨1 1 -1 3], ⟨0 3 17 -1]]

Wedgie: ⟨⟨ 3 17 -1 20 -10 -50 ]]

POTE generator: ~8/7 = 234.417

Minimax tuning:

7- and 9-odd-limit

[[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⟩]

Eigenmonzos: 2, 7/5

Algebraic generator: larger root of 20x² - 36x + 15, or (9 + √6)/10.

Template:Val list

Badness: 0.037112

Scales: Rodan26opt, Rodan31opt, Rodan41opt

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 441/440

Mapping: [⟨1 1 -1 3 6], ⟨0 3 17 -1 -13]]

POTE generator: ~8/7 = 234.459

Minimax tuning:

11-odd-limit

[[1 0 0 0 0⟩, [31/19 6/19 0 0 -3/19⟩, [49/19 34/19 0 0 -17/19⟩, [53/19 -2/19 0 0 1/19⟩, [62/19 -26/19 0 0 13/19⟩]

Eigenmonzos: 2, 11/9

Algebraic generator: positive root of x² + 16x - 31, or √95 - 8.

@@ Line 29: / Line 29: @@
 === 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.
+== 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 ==
@@ Line 280: / Line 635: @@
 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
-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 ==
@@ Line 603: / Line 969: @@
 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
-[[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 ===
 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 ===
 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 ==
@@ Line 851: / Line 1,089: @@
 Badness: 0.013551
-== Superkleismic ==
+== Necromanteion ==
-{{see also| Shibboleth family #Superkleismic }}
 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 ===
 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 ===
 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
-[[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 ===
 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 ===
 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
-[[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 ===
 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 ===
 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 ===
 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 ==
@@ Line 1,212: / Line 1,266: @@
 Badness: 0.035350
-== Restles ==
+== Widefourth ==
 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 ===
 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 ===
 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 ==

Gamelismic clan: Difference between revisions

Revision as of 04:11, 3 June 2021

Slendric

Full seven limit extensions

Subgroup extensions

Rodan

11-limit

13-limit

17-limit

Aerodactyl

Aerodino

13-limit

Varan

13-limit

Guiron

11-limit

13-limit

Gorgo

5-limit (laconic)

7-limit

11-limit

13-limit

Spartan

13-limit

Music

Gidorah

5-limit (university)

7-limit

Clyndro

11-limit

Miracle

11-limit

Miraculous

Benediction

17-limit

Manna

Semimiracle

17-limit

Hemisecordite

17-limit

Phicordial

17-limit

Revelation

13-limit

Hemimiracle

13-limit

Oracle

Hemiseven

11-limit

13-limit

17-limit

Lemba

11-limit

13-limit

Unidec

7-limit

11-limit

Ekadash

Hendec

17-limit

Valentine

7-limit

11-limit

Dwynwen

Lupercalia

Valentino

Semivalentine

Superkleismic

11-limit

13-limit

Tritikleismic

11-limit

13-limit

17-limit

Necromanteion

11-limit

13-limit

Restles

11-limit

13-limit