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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 the both 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.

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

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

Lattice basis: 8/7 0.5192 5/4 2.3219
Angle(8/7, 5/4) = 90 degrees
Map to lattice: [<0 3 0 -1|, <0 0 1 0|]

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

No-fives POTE generator: 233.688
EDOs: 5, 36, 77, 190

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.

Miracle

Commas: 1029/1024, 225/224

Minimax tuning:
7-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-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

POTE generator: 116.675
Algebraic generator: Secor59, positive root of 15x^6-8x^4-12

Map: [<1 1 3 3|, <0 6 -7 -2|]
Wedgie: <<6 -7 -2 -25 -20 15||
EDOs: 10, 21, 31, 41, 72, 175
Badness: 0.0167

11-limit

Commas: 1029/1024, 225/224, 243/242

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: 2, 10/9

POTE generator: 116.633
Algebraic generator: Secor59

Map: [<1 1 3 3 2|, <0 6 -7 -2 15|]
EDOs: 10, 31, 41, 72, 247c, 319bcde, 391bcde, 463bcde
Badness: 0.0107

Chords of miracle

Revelation

Commas: 99/98, 176/175, 1029/1024

POTE generator: ~15/14 = 116.277

Map: [<1 1 3 3 5|, <0 6 -7 -2 -16|]
EDOs: 10, 21, 31
Badness: 0.0329

13-limit

Commas: 66/65, 99/98, 105/104, 1001/1000

POTE generator: ~15/14 = 116.268

Map: [<1 1 3 3 5 4|, <0 6 -7 -2 -16 -3|]
EDOs: 10, 21, 31
Badness: 0.0295

Miraculous

Commas: 105/104, 144/143, 196/195, 275/273

POTE generator: ~15/14 = 116.747

Map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|]
EDOs: 10, 31, 41, 72f, 113f, 185cf
Badness: 0.0187

Benediction

Commas: 225/224, 243/242, 351/350, 441/440

POTE generator: ~15/14 = 116.574

Map: [<1 1 3 3 2 7|, <0 6 -7 -2 15 -34|]
EDOs: 31, 72, 103, 175f
Badness: 0.0157

17-limit

Commas: 225/224, 243/242, 273/272, 351/350, 385/384

POTE generator: ~15/14 = 116.585

Map: [<1 1 3 3 2 7 7|, <0 6 -7 -2 15 -34 -30|]
EDOs: 31, 72, 103, 175f

Manna

Commas: 225/224, 243/242, 325/324, 385/384

POTE generator: ~15/14 = 116.739

Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 38|]
EDOs: 10f, 31f, 41, 72, 113, 185cf, 257cf
Badness: 0.0170

Semimiracle

Commas: 169/168, 225/224, 243/242, 385/384

POTE generator: ~15/14 = 116.624

Map: [<2 2 6 6 4 7|, <0 6 -7 -2 15 2|]
EDOs: 10, 62, 72
Badness: 0.0246

17-limit

Commas: 169/168, 221/220, 225/224, 243/242, 385/384

POTE generator: ~15/14 = 116.628

Map: [<2 2 6 6 4 7 7|, <0 6 -7 -2 15 2 6|]
EDOs: 10, 62, 72
Badness: 0.0161

Hemimiracle

Commas: 225/224, 245/242, 1029/1024

POTE generator: ~33/32 = 58.408

Map: [<1 1 3 3 4|, <0 12 -14 -4 -11|]
EDOs: 20, 21, 41, 123c, 144e, 185ce, 226ce
Badness: 0.0592

13-limit

Commas: 105/104, 196/195, 245/242, 512/507

POTE generator: ~33/32 = 58.430

Map: [<1 1 3 3 4 4|, <0 12 -14 -4 -11 -6|]
EDOs: 20, 21, 41, 123cf, 144ef, 185cef
Badness: 0.0432

Oracle

Commas: 121/120, 225/224, 1029/1024

POTE generator: ~11/8 = 541.668

Map: [<1 7 -4 1 3|, <0 -12 14 4 1|]
EDOs: 11, 20, 31, 51, 82e, 113e, 144e

Hemisecordite

Commas: 225/224, 243/242, 441/440, 847/845

POTE generator: ~27/26 = 58.288

Map: [<1 1 3 3 2 2|, <0 12 -14 -4 30 35|]
EDOs: 41, 62, 103, 247c, 350bcde
Badness: 0.0256

17-limit

Commas: 225/224, 243/242, 273/272, 441/440, 847/845

POTE generator: ~27/26 = 58.261

Map: [<1 1 3 3 2 2 2|, <0 12 -14 -4 30 35 43|]
EDOs: 41, 62, 103
Badness: 0.0225

Phicordial

Commas: 225/224, 243/242, 441/440, 2200/2197

POTE generator: ~16/13 = 361.121

Map: [<1 7 -4 1 17 4|, <0 -18 21 6 -45 -1|]
EDOs: 10, 103, 113, 216c
Badness: 0.0332

17-limit

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

POTE generator: ~16/13 = 361.123

Map: [<1 7 -4 1 17 4 8|, <0 -18 21 6 -45 -1 -13|]
EDOs: 10, 103, 113, 216c
Badness: 0.0247

Music

By Gene Ward Smith
Rachmaninoff Plays Blackjack play
By Joseph Pehrson
Black and Jill
Blacklight
Blackjack

Rodan

Commas: 1029/1024, 245/243

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: 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: 41, 87, 128
Badness: 0.0371

11-limit

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

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: 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: 41, 87, 389d
Badness: 0.0231

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: 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, 273/272, 364/363

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, 307dg
Badness: 0.0167

Music

By Gene Ward Smith
Pianodactyl play

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: 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: 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: 46
Badness: 0.0358

Varan

Commas: 100/99, 245/243, 2835/2816

POTE generator: ~8/7 = 234.145

Map: [<1 1 -1 3 -2|, <0 3 17 -1 28|
EDOs: 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: 41
Badness: 0.0323

Valentine

7-limit

Commas: 1029/1024, 126/125

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: 77.864
Algebraic generator: smaller root of x^2-89x+92, or (89-√7553)/2, at 77.8616 cents.

Map: [<1 1 2 3|, <0 9 5 -3|]
Wedgie: <<9 5 -3 -13 -30 -21||
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: 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|]
Generators: 2, 21/20
Edos: 15, 31, 46, 77, 262cde, 339cde
Badness: 0.0167

Chords of valentine

Unidec

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

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: 183.165

Map: [<2 5 8 5 6|, <0 -6 -11 2 3|]
EDOs: 26, 46, 72, 118, 190


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
Bad: 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
Bad: 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


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

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

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

7-limit

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

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

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

Map: [<3 0 3 10 8|, <0 6 5 -2 3|]
EDOs: 72, 159, 231

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

Commas: 1029/1024, 875/864

POTE generator: ~6/5 = 321.930

Map: [<1 4 5 2|, <0 -9 -10 3|]
EDOs: 11, 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: 15, 26, 41, 261
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: 11, 15, 26, 41
Badness: 0.0215

Gorgo

Commas: 36/35, 1029/1024

POTE generator: 228.334

Map: [<1 1 1 3|, <0 3 7 -1|]
Wedgie: <<3 7 -1 4 -10 -22||
EDOs: 5, 16, 21

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

Commas: 50/49, 525/512

POTE generator: 232.089

Map: [<2 2 5 6|, <3 -1 -1|]
Wedgie: <<6 -2 -2 -17 -20 1||
EDOs: 10, 16, 26

Music

By Herman Miller
Lemba Galatsia
GPO Lemba

Gidorah

Commas: 21/20, 144/125

POTE generator: ~8/7 = 230.762

Map: [<1 1 2 3|, <0 3 2 -1|]
EDOs: 5, 11, 21, 26
Badness: 0.0623

Clyndro

Commas: 1029/1024, 135/128

POTE generator: ~8/7 = 226.469

Map: [<1 1 4 3|, <0 3 -9 -1|]
EDOs: 16

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