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.

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

Vals36, 77, 113, 190

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 15625/15552 and has a generator of 6/5 with a 1/3 octave period.

Discussed elsewhere are blacksmith, lemba, mothra, echidnic, tritikleismic, valentine, 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:

[[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

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

Subgroup: 2.3.5

Comma list: [2 -32 11

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

POTE generator: ~27/25 = 137.962

Vals26, 61, 87, 287, 374, 461

Badness: 1.381216

7-limit

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

Vals118, 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

Vals103, 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: 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

Baladic

See also: Subgroup temperaments #No-fives subgroup

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.


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