Gamelismic clan

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

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:

• 7- and 9-odd-limit: ~8/7 = [2/9 0 1/18 -1/18⟩

[[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.

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: ~8/7 = [4/19 2/19 0 0 -1/19⟩

[[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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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:

• 7- and 9-odd-limit: ~8/7 = [7/24 0 -1/24⟩

[[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

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:

• 11-odd-limit: ~8/7 = [7/24 0 -1/24⟩

[[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: Template:Val list

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: Template:Val list

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

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

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: Template:Val list

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: Template:Val list

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: Template:Val list

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

Badness: 0.047071

Music

• Gorgo Example by Herman Miller

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

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

Badness: 0.062262

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

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: Template:Val list

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:

• 7-odd-limit: ~15/14 = [2/13 1/13 -1/13⟩

[[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

• 9-odd-limit: ~15/14 = [1/19 2/19 -1/19⟩

[[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

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:

• 11-odd-limit: ~15/14 = [1/19 2/19 -1/19⟩

[[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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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

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: Template:Val list

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: Template:Val list

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: Template:Val list

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

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:

• 7-odd-limit: ~10/9 = [3/26 0 -1/13 1/13⟩

[[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

• 9-odd-limit: ~10/9 = [5/28 -1/7 0 1/14⟩

[[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

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:

• 11-odd-limit: ~10/9 = [5/28 -1/7 0 1/14⟩

[[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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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

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: Template:Val list

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: Template:Val list

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

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: Template:Val list

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: Template:Val list

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

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: Template:Val list

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: Template:Val list

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

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

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: Template:Val list

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: Template:Val list

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

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

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: Template:Val list

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

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: Template:Val list

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: Template:Val list

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