Gamelismic clan

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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.

To the gamelisma itself we need to add the comma which appears next on the modified normal comma list for the full 7-limit. 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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.

Full 7-limit temperaments discussed elsewhere are:

The rest are considered below.

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.

Slendric

Main article: Slendric
See also: No-fives subgroup temperaments #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

Vals36, 77, 113, 190

Scales: slendric5, slendric6, slendric11, slendric16

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.

Subgroup: 2.3.7.13.17

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

Sval mapping: [2 2 6 7 7], 0 3 -1 1 3]]

Mapping generators: ~17/12, ~8/7

POTE generator: ~8/7 = 233.6155

Vals10, 26, 36, 154f, 190ffg

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:

[[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 (unchanged intervals): 2, 7/5

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

Vals41, 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: [1 1 -1 3 6], 0 3 17 -1 -13]]

POTE generator: ~8/7 = 234.459

Minimax tuning:

[[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 (unchanged intervals): 2, 11/9

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

Vals: 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: [1 1 -1 3 6 8], 0 3 17 -1 -13 -22]]

POTE generator: ~8/7 = 234.482

Minimax tuning:

  • 13- and 15-odd-limit: ~8/7 = [3/14 1/14 0 0 0 -1/28
Eigenmonzos (unchanged intervals): 2, 13/9

Algebraic generator: Gatetone, positive root of 4x6 - 7x - 1. Recurrence converges slowly.

Vals: 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: [1 1 -1 3 6 8 8], 0 3 17 -1 -13 -22 -20]]

POTE generator: ~8/7 = 234.524

Minimax tuning:

  • 17-odd-limit: ~8/7 = [3/13 1/13 0 0 0 0 -1/26
Eigenmonzos (unchanged intervals): 2, 18/17

Vals: 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: [1 1 -1 3 6 -1], 0 3 17 -1 -13 24]]

POTE generator: ~8/7 = 234.639

Vals: 5, 41f, 46, 133ff

Badness: 0.033986

Aerodino

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243, 1029/1024

Mapping: [1 1 -1 3 -3], 0 3 17 -1 33]]

POTE generator: ~8/7 = 234.728

Vals: 41e, 46

Badness: 0.054294

13-limit

Comma list: 91/90, 176/175, 245/243, 847/845

Mapping: [1 1 -1 3 -3 -1], 0 3 17 -1 33 24]]

POTE generator: ~8/7 = 234.782

Vals: 41ef, 46

Badness: 0.035836

Varan

Comma list: 100/99, 245/243, 1029/1024

Mapping: [1 1 -1 3 -2], 0 3 17 -1 28]]

POTE generator: ~8/7 = 234.145

Vals: 36ce, 41

Badness: 0.044937

13-limit

Comma list: 100/99, 105/104, 245/243, 352/351

Mapping: [1 1 -1 3 -2 0], 0 3 17 -1 28 19]]

POTE generator: ~8/7 = 234.089

Vals: 36ce, 41

Badness: 0.032284

Guiron

See also: Schismatic family

Subgroup: 2.3.5.7

Comma list: 1029/1024, 10976/10935

Mapping: [1 1 7 3], 0 3 -24 -1]]

Mapping generators: ~2, ~8/7

Wedgie⟨⟨3 -24 -1 -45 -10 65]]

POTE generator: ~8/7 = 233.930

Minimax tuning:

[[1 0 0 0, [15/8 0 -1/8 0, [0 0 1 0, [65/24 0 1/24 0]
Eigenmonzos (unchanged intervals): 2, 5

Vals36, 41, 77, 118, 277d

Badness: 0.047544

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 10976/10935

Mapping: [1 1 7 3 -2], 0 3 -24 -1 28]]

Mapping generators: ~2, ~8/7

POTE generator: ~8/7 = 233.931

Minimax tuning:

[[1 0 0 0 0, [15/8 0 -1/8 0 0, [0 0 1 0 0, [65/24 0 1/24 0 0, [37/6 0 -7/6 0 0]
Eigenmonzos (unchanged intervals): 2, 5

Vals: 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: [1 1 7 3 -2 0], 0 3 -24 -1 28 19]]

Mapping generators: ~2, ~8/7

POTE generator: ~8/7 = 233.890

Vals: 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 and 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: [1 1 1], 0 3 7]]

Wedgie⟨⟨3 7 4]]

POTE generator: ~10/9 = 227.426

Vals5, 16, 21, 37b

Badness: 0.161799

7-limit

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1024

Mapping: [1 1 1 3], 0 3 7 -1]]

Wedgie⟨⟨3 7 -1 4 -10 -22]]

POTE generator: ~8/7 = 228.334

Vals5, 11c, 16, 21

Badness: 0.060663

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 1029/1024

Mapping: [1 1 1 3 1], 0 3 7 -1 13]]

POTE generator: ~8/7 = 227.373

Vals: 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: [1 1 1 3 1 2], 0 3 7 -1 13 9]]

POTE generator: ~8/7 = 227.230

Vals: 16, 21, 37b

Badness: 0.032664

Spartan

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1024

Mapping: [1 1 1 3 5], 0 3 7 -1 -8]]

POTE generator: ~8/7 = 229.535

Vals: 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: [1 1 1 3 5 2], 0 3 7 -1 -8 9]]

POTE generator: ~8/7 = 229.059

Vals5, 16e, 21, 68bccef

Badness: 0.047071

Music

Gidorah

Main article: University temperament

5-limit (university)

Subgroup: 2.3.5

Comma list: 144/125

Mapping: [1 1 2], 0 3 2]]

POTE generator: ~6/5 = 235.4416

Vals5, 31cccc, 36…, 41…, 46…, 51

Badness: 0.101806

7-limit

Subgroup: 2.3.5.7

Comma list: 21/20, 144/125

Mapping: [1 1 2 3], 0 3 2 -1]]

Wedgie⟨⟨3 2 -1 -4 -10 -8]]

POTE generator: ~8/7 = 230.762

Vals5, 16c, 21cc, 26ccc

Badness: 0.062262

Oncle

For the 5-limit version of this temperament, see High badness temperaments #Oncle.

Subgroup: 2.3.5.7

Comma list: 1029/1024, 2430/2401

Mapping: [1 1 6 3], 0 3 -19 -1]]

POTE generator: ~8/7 = 232.498

Vals31, 98c, 129c, 160bc

Badness: 0.088384

Archaeotherium

For the 5-limit version of this temperament, see High badness temperaments #Archaeotherium.

Subgroup: 2.3.5.7

Comma list: 405/392, 1029/1024

Mapping: [1 1 5 3], 0 3 -14 -1]]

POTE generator: ~8/7 = 230.258

Vals21, 26, 47, 73bc, 99bc

Badness: 0.146306

Clyndro

See also: Pelogic family

Subgroup: 2.3.5.7

Comma list: 135/128, 360/343

Mapping: [1 1 4 3], 0 3 -9 -1]]

Wedgie⟨⟨3 -9 -1 -21 -10 23]]

POTE generator: ~8/7 = 226.469

Vals5c, 11, 16

Badness: 0.159179

11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 352/343

Mapping: [1 1 4 3 4], 0 3 -9 -1 -3]]

POTE generator: ~8/7 = 226.428

Vals: 5c, 11, 16

Badness: 0.069703

Miracle

Main article: Miracle

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1024

Mapping: [1 1 3 3], 0 6 -7 -2]]

Mapping generator: 2, ~15/14

Wedgie⟨⟨6 -7 -2 -25 -20 15]]

POTE generator: ~15/14 = 116.675

Minimax tuning:

[[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]
Eigenmonzos (unchanged intervals): 2, 6/5
[[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]
Eigenmonzos (unchanged intervals): 2, 10/9

Tuning ranges:

  • 7-odd-limit diamond monotone: ~15/14 = [114.286, 120.000] (2\21 to 1\10)
  • 9-odd-limit diamond monotone: ~15/14 = [116.129, 120.000] (3\31 to 1\10)
  • 7- and 9-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]
  • 7-odd-limit diamond monotone and tradeoff: ~15/14 = [115.587, 116.993]
  • 9-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]

Algebraic generator: Secor59, positive root of 15x6 - 8x4 - 12

Vals10, 21, 31, 41, 72

Badness: 0.016742

Scales: Miracle 10, Blackjack

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 385/384

Mapping: [1 1 3 3 2], 0 6 -7 -2 15]]

POTE generator: ~15/14 = 116.633

Minimax tuning:

[[1 0 0 0 0, [25/19 12/19 -6/19 0 0, [50/19 -14/19 7/19 0 0, [55/19 -4/19 2/19 0 0, [53/19 30/19 -15/19 0 0]
Eigenmonzos (unchanged intervals): 2, 10/9

Tuning ranges:

  • 11-odd-limit diamond monotone: ~15/14 = [116.129, 117.073] (3\31 to 4\41)
  • 11-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]
  • 11-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]

Algebraic generator: Secor59

Vals: 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde

Badness: 0.010684

Scales: Miracle 10, Blackjack

Miraculous

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 243/242

Mapping: [1 1 3 3 2 4], 0 6 -7 -2 15 -3]]

POTE generator: ~15/14 = 116.747

Vals: 10, 21e, 31, 41, 72f, 113f, 185cff

Badness: 0.018669

Scales: Miracle 10, Blackjack

Benediction

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 385/384

Mapping: [1 1 3 3 2 7], 0 6 -7 -2 15 -34]]

POTE generator: ~15/14 = 116.574

Vals: 31, 72, 103, 175f

Badness: 0.015715

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 351/350, 375/374

Mapping: [1 1 3 3 2 7 7], 0 6 -7 -2 15 -34 -30]]

POTE generator: ~15/14 = 116.585

Vals: 31, 72, 103, 175f

Badness: 0.012537

Manna

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 325/324, 385/384

Mapping: [1 1 3 3 2 0], 0 6 -7 -2 15 38]]

POTE generator: ~15/14 = 116.739

Vals: 31f, 41, 72, 185cf, 257cff

Badness: 0.017012

Semimiracle

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 243/242, 385/384

Mapping: [2 2 6 6 4 7], 0 6 -7 -2 15 2]]

POTE generator: ~15/14 = 116.624

Vals: 10, 62, 72

Badness: 0.024622

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 225/224, 243/242, 273/272

Mapping: [2 2 6 6 4 7 7], 0 6 -7 -2 15 2 6]]

POTE generator: ~15/14 = 116.628

Vals: 10, 62, 72

Badness: 0.016130

Hemisecordite

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 847/845

Mapping: [1 1 3 3 2 2], 0 12 -14 -4 30 35]]

POTE generator: ~27/26 = 58.288

Vals: 41, 62, 103, 247c, 350bcde

Badness: 0.025589

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 385/384, 847/845

Mapping: [1 1 3 3 2 2 2], 0 12 -14 -4 30 35 43]]

POTE generator: ~27/26 = 58.261

Vals: 41, 62, 103

Badness: 0.022535

Phicordial

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 2200/2197

Mapping: [1 7 -4 1 17 4], 0 -18 21 6 -45 -1]]

POTE generator: ~16/13 = 361.121

Vals: 103, 113, 216c

Badness: 0.033198

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197

Mapping: [1 7 -4 1 17 4 8], 0 -18 21 6 -45 -1 -13]]

POTE generator: ~16/13 = 361.123

Vals: 103, 113, 216c

Badness: 0.024705

Revelation

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1029/1024

Mapping: [1 1 3 3 5], 0 6 -7 -2 -16]]

POTE generator: ~15/14 = 116.277

Vals: 10e, 21, 31

Badness: 0.032946

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 105/104, 512/507

Mapping: [1 1 3 3 5 4], 0 6 -7 -2 -16 -3]]

POTE generator: ~15/14 = 116.268

Vals: 10e, 21, 31

Badness: 0.029452

Hemimiracle

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 1029/1024

Mapping: [1 1 3 3 4], 0 12 -14 -4 -11]]

POTE generator: ~33/32 = 58.408

Vals: 20, 21, 41, 144e, 185cee, 226cee

Badness: 0.059232

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 245/242, 512/507

Mapping: [1 1 3 3 4 4], 0 12 -14 -4 -11 -6]]

POTE generator: ~33/32 = 58.430

Vals: 20, 21, 41, 144eff, 185ceeff

Badness: 0.043151

Oracle

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 1029/1024

Mapping: [1 7 -4 1 3], 0 -12 14 4 1]]

POTE generator: ~11/8 = 541.668

Vals: 11, 20, 31, 82e, 113e, 144ee

Badness: 0.042687

Hemiseven

Subgroup: 2.3.5.7

Comma list: 1029/1024, 19683/19600

Mapping: [1 4 14 2], 0 -6 -29 2]]

Wedgie⟨⟨6 29 -2 32 -20 -86]]

POTE generator: ~320/243 = 483.267

Vals72, 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: [1 4 14 2 -5], 0 -6 -29 2 21]]

POTE generator: ~320/243 = 483.276

Vals: 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

Mapping: [1 4 14 2 -5 19], 0 -6 -29 2 21 -38]]

POTE generator: ~120/91 = 483.256

Vals: 72, 77, 149, 221ef

Badness: 0.021900

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440, 676/675

Mapping: [1 4 14 2 -5 19 21], 0 -6 -29 2 21 -38 -42]]

POTE generator: ~45/34 = 483.261

Vals: 72, 77, 149, 221ef

Badness: 0.015701

Unidec

Main article: Unidec

Subgroup: 2.3.5

Comma list: 31381059609/31250000000

Mapping: [2 5 8], 0 -6 -11]]

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

POTE generator: ~10/9 = 183.047

Vals26, 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

Mapping: [2 5 8 5], 0 -6 -11 2]]

Mapping generators: ~1225/864, ~10/9

Wedgie⟨⟨12 22 -4 7 -40 -71]]

POTE generator: ~10/9 = 183.161

Minimax tuning:

[[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]
Eigenmonzos (unchanged intervals): 2, 7/5
[[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]
Eigenmonzos (unchanged intervals): 2, 9/7

Vals26, 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

Mapping: [2 5 8 5 6], 0 -6 -11 2 3]]

Mapping generators: ~99/70, ~10/9

Minimax tuning:

[[1 0 0 0 0, [10/7 6/7 0 -3/7 0, [57/28 11/7 0 -11/14 0, [20/7 -2/7 0 1/7 0, [99/28 -3/7 0 3/14 0]
Eigenmonzos (unchanged intervals): 2, 9/7

Vals: 26, 46, 72, 118, 190

Badness: 0.015479

Scales: Unidec26

Ekadash

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 729/728

Mapping: [2 5 8 5 6 19], 0 -6 -11 2 3 -38]]

Mapping generators: ~99/70, ~10/9

POTE generator: ~10/9 = 183.187

Vals: 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: [2 5 8 5 6 8], 0 -6 -11 2 3 -2]]

Mapping generators: ~91/64, ~10/9

POTE generator: ~10/9 = 183.198

Vals: 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: [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

Vals: 26, 46, 72, 190ffg

Badness: 0.011676

Scales: Unidec26

Superkleismic

See also: Shibboleth family #Superkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 1029/1024

Mapping: [1 4 5 2], 0 -9 -10 3]]

Wedgie⟨⟨9 10 -3 -5 -30 -35]]

POTE generator: ~6/5 = 321.930

Vals11c, 15, 26, 41

Badness: 0.047932

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 385/384

Mapping: [1 4 5 2 4], 0 -9 -10 3 -2]]

POTE generator: ~6/5 = 321.847

Vals: 11c, 15, 26, 41, 261ccdee

Badness: 0.025659

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 245/243, 1188/1183

Mapping: [1 4 5 2 4 8], 0 -9 -10 3 -2 -16]]

POTE generator: ~6/5 = 321.994

Vals: 11cf, 15, 26, 41

Badness: 0.021478

Lagaca

Subgroup: 2.3.5.7

Comma list: 1029/1024, 11529602/11390625

Mapping: [2 5 2 5], 0 -9 13 3]]

Wedgie⟨⟨18 -26 -6 -83 -60 59]]

POTE generator: ~15/14 = 122.027

Vals10, 98, 108, 118

Badness: 0.144345

Necromanteion

Subgroup: 2.3.5.7

Comma list: 1029/1024, 5103/5000

Mapping: [1 7 10 1], 0 -12 -17 4]]

Wedgie⟨⟨12 17 -4 -1 -40 -57]]

POTE generator: ~48/35 = 541.779

Vals11c, 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: [1 7 10 1 17], 0 -12 -17 4 -30]]

POTE generator: ~15/11 = 541.729

Vals: 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

Mapping: [1 7 10 1 17 1], 0 -12 -17 4 -30 6]]

POTE generator: ~15/11 = 541.606

Vals: 20ce, 31, 51ce, 82cf, 113cf, 144cf

Badness: 0.047015

Restles

Subgroup: 2.3.5.7

Comma list: 1029/1024, 153664/151875

Mapping: [1 -2 8 4], 0 12 -19 -4]]

Wedgie⟨⟨12 -19 -4 -58 -40 44]]

POTE generator: ~315/256 = 358.5485

Vals10, 77, 87, 164

Badness: 0.108011

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [1 -2 8 4 -7], 0 12 -19 -4 35]]

POTE generator: ~27/22 = 358.5713

Vals: 10, 77, 87, 164

Badness: 0.054655

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 676/675

Mapping: [1 -2 8 4 -7 4], 0 12 -19 -4 35 -1]]

POTE generator: ~16/13 = 358.5739

Vals: 10, 77, 87, 164

Badness: 0.028187

Quartemka

For the 5-limit version of this temperament, see High badness temperaments #Quartemka.

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1250000/1240029

Mapping: [1 4 6 2], 0 -21 -32 7]]

Wedgie⟨⟨21 32 -7 2 -70 -106]]

POTE generator: ~27/25 = 138.006

Vals26, 61, 87, 113, 200

Badness: 0.152287

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 800000/793881

Mapping: [1 4 6 2 3], 0 -21 -32 7 4]]

POTE generator: ~27/25 = 137.990

Vals: 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: [1 4 6 2 3 6], 0 -21 -32 7 4 -20]]

POTE generator: ~13/12 = 137.990

Vals: 26, 61, 87, 200, 487cdd

Badness: 0.028393

Tritriple

Subgroup: 2.3.5

Comma list: [31 20 -27

Mapping: [1 -11 -7], 0 27 20]]

POTE generator: ~864/625 = 559.332

Vals15, 88, 103, 118, 959, 1077

Badness: 0.283570

7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1959552/1953125

Mapping: [1 -11 -7 7], 0 27 20 -9]]

Wedgie⟨⟨27 20 -9 -31 -90 -77]]

POTE generator: ~864/625 = 559.295

Vals15, 88, 103, 118, 339d

Badness: 0.118640

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 43923/43750

Mapping: [1 -11 -7 7 -4], 0 27 20 -9 16]]

POTE generator: ~242/175 = 559.293

Vals: 15, 88, 103, 118, 339de

Badness: 0.035350

Widefourth

Subgroup: 2.3.5.7

Comma list: 1029/1024, 48828125/48771072

Mapping: [1 16 8 -2], 0 -33 -13 11]]

Wedgie⟨⟨33 13 -11 -56 -110 -62]]

POTE generator: ~3125/2304 = 524.210

Vals16, 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: [1 16 8 -2 17], 0 -33 -13 11 -31]]

POTE generator: ~847/625 = 524.210

Vals: 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: [1 16 8 -2 17 12], 0 -33 -13 11 -31 -19]]

POTE generator: ~65/48 = 524.209

Vals: 16, 55be, 71, 87, 103, 190

Badness: 0.021636