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

POTE generator: ~8/7 = 233.688

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]

Full seven limit children

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, guiron and heinz. The rest are considered below.

Miracle

Main article: Miracle

Comma list: 225/224, 1029/1024

POTE generator: ~15/14 = 116.675

Mapping: [⟨1 1 3 3], ⟨0 6 -7 -2]]

Wedgie: ⟨⟨6 -7 -2 -25 -20 15]]

Minimax tuning:

• 7-odd-limit:

[[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: 2, 6/5

• 9-odd-limit:

[[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: 2, 10/9

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

Badness: 0.0167

11-limit

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

POTE generator: ~15/14 = 116.633

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

Minimax tuning:

• 11-odd-limit:

[[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: 2, 10/9

Algebraic generator: Secor59

Badness: 0.0107

See also: Chords of miracle

Miraculous

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

POTE generator: ~15/14 = 116.747

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

Badness: 0.0187

Benediction

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

POTE generator: ~15/14 = 116.574

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

Badness: 0.0157

17-limit

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

POTE generator: ~15/14 = 116.585

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

Manna

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

POTE generator: ~15/14 = 116.739

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

Badness: 0.0170

Semimiracle

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

POTE generator: ~15/14 = 116.624

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

Badness: 0.0246

17-limit

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

POTE generator: ~15/14 = 116.628

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

Badness: 0.0161

Hemisecordite

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

POTE generator: ~27/26 = 58.288

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

Badness: 0.0256

17-limit

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

POTE generator: ~27/26 = 58.261

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

Badness: 0.0225

Phicordial

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

POTE generator: ~16/13 = 361.121

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

Badness: 0.0332

17-limit

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

POTE generator: ~16/13 = 361.123

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

Badness: 0.0247

Revelation

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

POTE generator: ~15/14 = 116.277

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

Badness: 0.0329

13-limit

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

POTE generator: ~15/14 = 116.268

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

Badness: 0.0295

Hemimiracle

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

POTE generator: ~33/32 = 58.408

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

Badness: 0.0592

13-limit

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

POTE generator: ~33/32 = 58.430

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

Badness: 0.0432

Oracle

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

POTE generator: ~11/8 = 541.668

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

Badness: 0.0427

Music

By Gene Ward Smith

• Rachmaninoff Plays Blackjack play

By Joseph Pehrson

• Black and Jill
• Blacklight
• Blackjack

Rodan

Main article: Rodan

Commas: 245/243, 1029/1024

7+9 limit 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: 2, 7/5

POTE generator: ~8/7 = 234.417

Algebraic generator: larger root of 20x^2-36x+15, or (9+√6)/10.

Map: [<1 1 -1 3|, <0 3 17 -1|]

EDOs: 5, 41, 87, 128, 215d

Badness: 0.0371

11-limit

Commas: 245/243, 385/384, 441/440

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: 2, 11/9

POTE generator: ~8/7 = 234.459

Algebraic generator: positive root of x^2+16x-31, or √95-8.

Map: [<1 1 -1 3 6|, <0 3 17 -1 -13|]

EDOs: 5, 41, 46, 87

Badness: 0.0231

See also: Chords of rodan

13-limit

Commas: 196/195, 245/243, 352/351, 364/363

13 and 15 limit minimax

[|1 0 0 0 0 0>, |23/14 3/14 0 0 0 -3/28>, |37/14 17/14 0 0 0 -17/28>, |39/14 -1/14 0 0 0 1/28>, |45/14 -13/14 0 0 0 13/28>, |23/7 -11/7 0 0 0 11/14>]

Eigenmonzos: 2, 13/9

POTE generator: ~8/7 = 234.482

Algebraic generator: Gatetone, positive root of 4x^6-7x-1. Recurrence converges slowly.

Map: [<1 1 -1 3 6 8|, <0 3 17 -1 -13 -22|]

Generators: 2, 8/7

EDOs: 41, 46, 87

Badness: 0.0184

17-limit

Commas: 154/153, 196/195, 245/243, 256/255, 273/272

Eigenmonzos: 2, 18/17

POTE generator: ~8/7 = 234.524

Map: [<1 1 -1 3 6 8 8|, <0 3 17 -1 -13 -22 -20|]

Edos: 41, 46, 87, 220dg, 307dgg

Badness: 0.0167

Aerodactyl

Commas: 91/90, 245/243, 385/384, 441/440

POTE generator: ~8/7 = 234.639

Map: [<1 1 -1 3 6 -1|, <0 3 17 -1 -13 24|

EDOs: 5, 41f, 46, 51c

Badness: 0.0340

Aerodino

Commas: 176/175, 245/243, 1029/1024

POTE generator: ~8/7 = 234.728

Map: [<1 1 -1 3 -3|, <0 3 17 -1 33|

EDOS: 5e, 41e, 46

Badness: 0.0543

13-limit

Commas: 91/90, 176/175, 245/243, 847/845

POTE generator: ~8/7 = 234.782

Map: [<1 1 -1 3 -3 -1|, <0 3 17 -1 33 24|

EDOs: 5e, 46

Badness: 0.0358

Varan

Commas: 100/99, 245/243, 1029/1024

POTE generator: ~8/7 = 234.145

Map: [<1 1 -1 3 -2|, <0 3 17 -1 28|

EDOs: 5e, 41, 46e

Badness: 0.0449

13-limit

Commas: 100/99, 105/104, 245/243, 352/351

POTE generator: ~8/7 = 234.089

Map: [<1 1 -1 3 -2 0|, <0 3 17 -1 28 19|

EDOs: 5e, 41

Badness: 0.0323

Music

By Gene Ward Smith

• Pianodactyl play

Valentine

Main article: Valentine

See also: Starling temperaments § Valentine

5-limit

Comma: 1990656/1953125

POTE generator: ~25/24 = 78.039

Map: [<1 1 2|, <0 9 5|]

EDOs: 15, 31, 46, 77, 123

Badness: 0.1228

7-limit

Commas: 126/125, 1029/1024

Minimax tuning:

7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |17/6 5/12 0 -5/12>, [5/2 -1/4 0 1/4>]

Eigenmonzos: 2, 7/6

9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |47/21 10/21 0 -5/21>, |20/7 -2/7 0 1/7>]

Eigenmonzos: 2, 9/7

POTE generator: ~21/20 = 77.864

Algebraic generator: smaller root of x^2-89x+92, or (89-sqrt(7553))/2, at 77.8616 cents.

Map: [<1 1 2 3|, <0 9 5 -3|]

Mapping generators: 2, 21/20

EDOs: 15, 31, 46, 77, 185, 262cd

Badness: 0.0311

11-limit

Commas: 121/120, 126/125, 176/175

Minimax tuning:

[|1 0 0 0 0>, |1 0 0 -9/10 9/10>, |2 0 0 -1/2 1/2>, |3 0 0 3/10 -3/10>, |3 0 0 -7/10 7/10>]

Eigenmonzos: 2, 11/7

POTE generator: ~21/20 = 77.881

Algebraic generator: positive root of 4x^3+15x^2-21, or else Gontrand2, the smallest positive root of 4x^7-8x^6+5.

Map: [<1 1 2 3 3|, <0 9 5 -3 7|]

Mapping generators: 2, 21/20

EDOs: 15, 31, 46, 77, 262cdee, 339cdeee

Badness: 0.0167

See also: Chords of valentine

Unidec

5-limit

Comma: 31381059609/31250000000

POTE generator: ~10/9 = 183.047

Map: [<2 5 8|, <0 -6 -11|]

EDOs: 26, 46, 72, 118, 2524, 2642, 2760, 5002bc

Badness: 0.0824

7-limit

Commas: 1029/1024, 4375/4374

Minimax tuning:

7-limit: [|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: 2, 7/5

9-limit: [|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: 2, 9/7

POTE generator: ~10/9 = 183.161

Map: [<2 5 8 5|, <0 -6 -11 2|]

Wedgie: <<12 22 -4 7 -40 -71||

EDOs: 26, 46, 72, 118, 190

Badness: 0.0384

11-limit

Commas: 385/384, 441/440, 4375/4374

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: 2, 9/7

POTE generator: ~10/9 = 183.165

Map: [<2 5 8 5 6|, <0 -6 -11 2 3|]

EDOs: 26, 46, 72, 118, 190

Badness: 0.0155

Chords of unidec

Ekadash

Commas: 385/384, 441/440, 625/624, 729/728

POTE generator: ~10/9 = 183.187

Map: [<2 5 8 5 6 19|, <0 -6 -11 2 3 -38|]

EDOs: 20cf, 26f, 46f, 72, 118, 190, 262df, 452cdef

Badness: 0.0204

Hendec

Commas: 169/168, 325/324, 364/363, 1716/1715

POTE generator: ~10/9 = 183.187

Map: [<2 5 8 5 6 8|, <0 -6 -11 2 3 -2|]

EDOs: 26, 46, 72

Badness: 0.0177

17-limit

Commas: 169/168, 221/220, 273/272, 325/324, 364/363

POTE generator: ~10/9 = 183.196

Map: [<2 5 8 5 6 8 10|, <0 -6 -11 2 3 -2 -6|]

EDOs: 26, 46, 72

Music

Hypnocloudsmack 2 by Andrew Heathwaite

Hemithirds

Main article: Hemithirds

See also: Luna family § Hemithirds

7-limit

Commas: 1029/1024, 3136/3125

Minimax tuning:

7-limit: [|1 0 0 0>, |5/2 3/4 0 -3/4>, |11/5 -1/10 0 1/10>, |5/2 -1/4 0 1/4>]

Eigenmonzos: 2, 7/6

9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |82/35 -4/35 0 2/35>, |20/7 -2/7 0 1/7>]

Eigenmonzos: 2, 7/6

POTE generator: ~28/25 = 193.244

Map: [<1 4 2 2|, <0 -15 2 5|]

EDOs: 31, 87, 118

Badness: 0.0443

11-limit

Commas: 385/384, 441/440, 3136/3125

Minimax tuning:

[|1 0 0 0 0>, |11/9 0 0 -5/9 5/9>, |64/27 0 0 2/27 -2/27>, |79/27 0 0 5/27 -5/27>, |79/27 0 0 -22/27 22/27>]

Eigenmonzos: 2, 11/7

POTE generator: ~28/25 = 193.227

Map: [<1 4 2 2 7|, <0 -15 2 5 -22|]

EDOs: 31, 87, 118

Badness: 0.0190

See also: Chords of hemithirds

13-limit

Commas: 196/195, 352/351, 1001/1000, 1029/1024

POTE generator: ~28/25 = 193.166

Map: [<1 4 2 2 7 0|, <0 -15 2 5 -22 23|]

EDOs: 31, 56, 87, 118, 205d

Badness: 0.0217

Hemiseven

Commas: 1029/1024, 19683/19600

POTE generator: ~320/243 = 483.267

Map: [<1 4 14 2|, <0 -6 -29 2|]

Wedgie: <<6 29 -2 32 -20 -86||

EDOs: 5, 72, 77, 149, 221, 514bd, 735bcd

Badness: 0.0566

11-limit

Commas: 385/384, 441/440, 19683/19600

POTE generator: ~320/243 = 483.276

Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|]

EDOs: 72, 77, 149, 221e, 293de

Badness: 0.0285

13-limit

Commas: 351/350, 385/384, 441/440, 676/675

POTE generator: ~320/243 = 483.256

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

EDOs: 72, 77, 149, 221ef

17-limit

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

POTE generator: ~320/243 = 483.261

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

EDOs: 72, 77, 149, 221ef

Tritikleismic

See also: Kleismic family § Tritikleismic

7-limit

Commas: 1029/1024, 15625/15552

Minimax tunings:

7-limit: [|1 0 0 0>, |2 0 6/7 -6/7>, |8/3 0 5/7 -5/7>, |8/3 0 -2/7 2/7>]

Eigenmonzos: 2, 7/5

9-limit: [|1 0 0 0>, |10/7 6/7 0 -3/7>, |46/21 5/7 0 -5/14>, |20/7 -2/7 0 1/7>]

Eigenmonzos: 2, 9/7

POTE generator: ~6/5 = 316.872

Map: [<3 0 3 10|, <0 6 5 -2|]

EDOs: 15, 72, 87, 159, 231

Badness: 0.0563

11-limit

Commas: 385/384, 441/440, 4000/3993

Minimax tuning:

[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |46/21 5/7 0 -5/14 0>, |20/7 -2/7 0 1/7 0>, |71/21 3/7 0 -3/14 0>]

Eigenmonzos: 2, 9/7

POTE generator: ~6/5 = 316.881

Map: [<3 0 3 10 8|, <0 6 5 -2 3|]

EDOs: 72, 159, 231

Badness: 0.0193

13-limit

Commas: 325/324, 364/363, 441/440, 625/624

Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|]

EDOs: 15, 72, 87, 159

17-limit

Commas: 273/272, 325/324, 364/363, 375/374, 385/384

Map: [<3 0 3 10 8 0 -2|, <0 6 5 -2 3 14 18|]

EDOs: 15g, 72, 87, 159

Superkleismic

See also: Shibboleth family § Superkleismic

Commas: 875/864, 1029/1024

POTE generator: ~6/5 = 321.930

Map: [<1 4 5 2|, <0 -9 -10 3|]

EDOs: 11c, 15, 26, 41

Badness: 0.0479

11-limit

Commas: 100/99, 245/242, 385/384

POTE generator: ~6/5 = 321.847

Map: [<1 4 5 2 4|, <0 -9 -10 3 -2|]

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

Badness: 0.0257

13-limit

Commas: 100/99, 105/104, 245/243, 1188/1183

POTE generator: ~6/5 = 321.994

Map: [<1 4 5 2 4 8|, <0 -9 -10 3 -2 -16|]

EDOs: 11cf, 15, 26, 41

Badness: 0.0215

Gorgo

See also: Laconic family § Gorgo

Commas: 36/35, 1029/1024

POTE generator: ~8/7 = 228.334

Map: [<1 1 1 3|, <0 3 7 -1|]

Wedgie: <<3 7 -1 4 -10 -22||

EDOs: 5, 16, 21

Badness: 0.0607

11-limit

Commas: 36/35, 56/55, 1029/1024

POTE generator: ~8/7 = 229.535

Map: [<1 1 1 3 5|, <0 3 7 -1 -8|]

EDOs: 5, 16e, 21, 47c, 68bce

Badness: 0.0627

13-limit

Commas: 27/26, 36/35, 56/55, 507/500

POTE generator: ~8/7 = 229.059

Map: [<1 1 1 3 5 2|, <0 3 7 -1 -8 9|]

EDOs 5, 21, 68bcef

Badness: 0.0471

Music

Gorgo Example by Herman Miller

Lemba

See also: Jubilismic clan § Lemba

See also: Lemba

Commas: 50/49, 525/512

POTE generator: ~8/7 = 232.089

Map: [<2 2 5 6|, <0 3 -1 -1|]

Wedgie: <<6 -2 -2 -17 -20 1||

EDOs: 10, 16, 26

Badness: 0.0622

Music

By Herman Miller

• Lemba Galatsia
• GPO Lemba

Gidorah

See also: University temperament

Commas: 21/20, 144/125

POTE generator: ~8/7 = 230.762

Map: [<1 1 2 3|, <0 3 2 -1|]

EDOs: 5, 11, 16c, 21cc, 26ccc

Badness: 0.0623

Clyndro

Commas: 135/128, 360/343

POTE generator: ~8/7 = 226.469

Map: [<1 1 4 3|, <0 3 -9 -1|]

EDOs: 5c, 11, 16

Badness: 0.1592

11-limit

Commas: 33/32, 45/44, 352/343

POTE generator: ~8/7 = 226.428

Map: [<1 1 4 3 4|, <0 3 -9 -1 -3|]

EDOs: 5c, 11, 16

Badness: 0.0697

Necromanteion

Commas: 1029/1024, 5103/5000

POTE generator: ~48/35 = 541.779

Map: [<1 7 10 1|, <0 -12 -17 4|]

EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c, 175c, 206bc, 237bc, 505bcd

Badness: 0.1177

11-limit

Commas: 176/175, 243/242, 1029/1024

POTE generator: ~15/11 = 541.729

Map: [<1 7 10 1 17|, <0 -12 -17 4 -30|]

EDOs: 31, 82c, 113c, 144c, 175c, 350bcde, 381bcde

Badness: 0.0535

13-limit

Commas: 144/143, 176/175, 243/242, 343/338

POTE generator: ~15/11 = 541.606

Map: [<1 7 10 1 17 1|, <0 -12 -17 4 -30 6|]

EDOs: 31, 51ce, 82cf, 113cf, 144cf

Badness: 0.0470

Widefourth

Commas: 1029/1024, 48828125/48771072

POTE generator: ~3125/2304 = 524.210

Map: [<1 16 8 -2|, <0 -33 -13 11|]

Wedgie: <<33 13 -11 -56 -110 -62||

EDOs: 16, 71, 87, 103, 190

Badness: 0.1541

11-limit

Commas: 385/384, 441/440, 234375/234256

POTE generator: ~3125/2304 = 524.210

Map: [<1 16 8 -2 17|, <0 -33 -13 11 -31|]

EDOs: 16, 71, 87, 103, 190

Badness: 0.0408

13-limit

Commas: 385/384, 441/440, 625/624, 847/845

POTE generator: ~65/48 = 524.209

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

EDOs: 16, 71, 87, 103, 190

Badness: 0.0216

Tritriple

5-limit

Comma: |31 20 -27>

POTE generator: ~864/625 = 559.332

Map: [<1 -11 -7|, <0 27 20|]

EDOs: 15, 103, 118, 133, 959, 1077

Badness: 0.2836

7-limit

Commas: 1029/1024, 1959552/1953125

POTE generator: ~864/625 = 559.295

Map: [<1 -11 -7 7|, <0 27 20 -9|]

EDOs: 15, 103, 118, 133, 339d

Badness: 0.1186

11-limit

Commas: 385/384, 441/440, 43923/43750

POTE generator: ~242/175 = 559.293

Map: [<1 -11 -7 7 -4|, <0 27 20 -9 16|]

EDOs: 15, 103, 118, 133, 339de

Badness: 0.0353

Restles

Commas: 1029/1024, 153664/151875

POTE generator: ~315/256 = 358.5485

Map: [<1 -2 8 4|, <0 12 -19 -4|]

EDOs: 10, 67, 77, 87, 164

Badness: 0.1080

11-limit

Commas: 385/384, 441/440, 153664/151875

POTE generator: ~27/22 = 358.5713

Map: [<1 -2 8 4 -7|, <0 12 -19 -4 35|]

EDOs: 10, 77, 87, 164

Badness: 0.0547

13-limit

Commas: 196/195, 352/351, 385/384, 676/675

POTE generator: ~16/13 = 358.5739

Map: [<1 -2 8 4 -7 4|, <0 12 -19 -4 35 -1|]

EDOs: 10, 77, 87, 164

Badness: 0.0282

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.

Commas: 169/168, 273/272, 289/288

Period: 1\2

POTE generator: ~8/7 = 233.6155

Map: [<2 2 6 7 7|, <0 3 -1 1 3|]

EDOs: 26, 36, 46, 82, 118f