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
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 15625/15536 and has a generator of 6/5 with a 1/3 octave period.
Discussed elsewhere are blacksmith, mothra, echidnic, trismegistus, hemithirds, gamity, triwell 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.
Miracle
Subgroup: 2.3.5.7
Comma list: 225/224, 1029/1024
Mapping: [⟨1 1 3 3], ⟨0 6 -7 -2]]
POTE generator: ~15/14 = 116.675
Wedgie: ⟨⟨ 6 -7 -2 -25 -20 15 ]]
- [[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
- [[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
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
- [[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
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
Badness: 0.0187
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
Badness: 0.0157
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
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
Badness: 0.0170
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
Badness: 0.0246
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
Badness: 0.0161
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
Badness: 0.0256
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
Badness: 0.0225
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
Badness: 0.0332
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
Badness: 0.0247
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
Badness: 0.0329
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
Badness: 0.0295
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
Badness: 0.0592
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
Badness: 0.0432
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
Badness: 0.0427
Rodan
Subgroup: 2.3.5.7
Comma list: 245/243, 1029/1024
Mapping: [⟨1 1 -1 3], ⟨0 3 17 -1]]
POTE generator: ~8/7 = 234.417
- 7- and 9-odd-limit
- [[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
Algebraic generator: larger root of 20x2 - 36x + 15, or (9 + √6)/10.
Badness: 0.0371
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
- [[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
Algebraic generator: positive root of x2 + 16x - 31, or √95 - 8.
Badness: 0.0231
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
- [[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
Algebraic generator: Gatetone, positive root of 4x6 - 7x - 1. Recurrence converges slowly.
Badness: 0.0184
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 eigenmonzos: 2, 18/17
Badness: 0.0167
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
Badness: 0.0340
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
Badness: 0.0543
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
Badness: 0.0358
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
Badness: 0.0449
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
Badness: 0.0323
Guiron
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
POTE generator: ~8/7 = 233.930
Wedgie: ⟨⟨ 3 -24 -1 -45 -10 65 ]]
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [15/8 0 -1/8 0⟩, [0 0 1 0⟩, [65/24 0 1/24 0⟩]
- Eigenmonzos: 2, 5/4
Badness: 0.0475
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
- [[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: 2, 5/4
Badness: 0.0266
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 729/728
Mapping generators: ~2, ~8/7
Mapping: [⟨1 1 7 3 -2 0], ⟨0 3 -24 -1 28 19]]
POTE generator: ~8/7 = 233.890
Badness: 0.0284
Valentine
5-limit
Subgroup: 2.3.5
Comma list: 1990656/1953125
Mapping: [⟨1 1 2], ⟨0 9 5]]
POTE generator: ~25/24 = 78.039
Badness: 0.1228
7-limit
Subgroup: 2.3.5.7
Comma list: 126/125, 1029/1024
Mapping: [⟨1 1 2 3], ⟨0 9 5 -3]]
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.864
- [[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
- [[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
Algebraic generator: smaller root of x2 - 89x + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
Badness: 0.0311
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 176/175
Mapping: [⟨1 1 2 3 3], ⟨0 9 5 -3 7]]
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.881
Minimax tuning:
- 11-odd-limit
- [[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
Algebraic generator: positive root of 4x3 + 15x2 - 21, or else Gontrand2, the smallest positive root of 4x7 - 8x6 + 5.
Badness: 0.0167
Dwynwen
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 176/175
Mapping: [⟨1 1 2 3 3 2], ⟨0 9 5 -3 7 26]]
POTE generator: ~21/20 = 78.219
Badness: 0.0235
Lupercalia
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 126/125
Mapping: [⟨1 1 2 3 3 3], ⟨0 9 5 -3 7 11]]
POTE generator: ~21/20 = 77.709
Badness: 0.0213
Valentino
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 176/175, 196/195
Mapping: [⟨1 1 2 3 3 5], ⟨0 9 5 -3 7 -20]]
POTE generator: ~21/20 = 77.958
Badness: 0.0207
Semivalentine
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 126/125, 169/168, 176/175
Mapping: [⟨2 2 4 6 6 7], ⟨0 9 5 -3 7 3]]
POTE generator: ~21/20 = 77.839
Badness: 0.0327
Unidec
5-limit
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: 0.0824
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
- [[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
- [[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
Badness: 0.0384
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
- [[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
Badness: 0.0155
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
Badness: 0.0204
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
Badness: 0.0177
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
Scales: unidec26
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: 0.0566
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
Badness: 0.0285
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
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
Tritikleismic
Subgroup: 2.3.5.7
Comma list: 1029/1024, 15625/15552
Mapping: [⟨3 0 3 10], ⟨0 6 5 -2]]
Mapping generators: ~63/50, ~6/5
POTE generator: ~6/5 = 316.872
- [[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
- [[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
Badness: 0.0563
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 4000/3993
Mapping: [⟨3 0 3 10 8], ⟨0 6 5 -2 3]]
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.881
Minimax tuning:
- 11-odd-limit
- [[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
Badness: 0.0193
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 625/624
Mapping: [⟨3 0 3 10 8 0], ⟨0 6 5 -2 3 14]]
Mapping generators: ~44/35, ~6/5
POTE generator: ~6/5 = 316.9585
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 375/374, 385/384
Mapping: [⟨3 0 3 10 8 0 -2], ⟨0 6 5 -2 3 14 18]]
Mapping generators: ~34/27, ~6/5
POTE generator: ~6/5 = 316.9082
Superkleismic
Subgroup: 2.3.5.7
Comma list: 875/864, 1029/1024
Mapping: [⟨1 4 5 2], ⟨0 -9 -10 3]]
POTE generator: ~6/5 = 321.930
Badness: 0.0479
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
Badness: 0.0257
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
Badness: 0.0215
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 -1 4 -10 -22 ]]
POTE generator: ~10/9 = 227.426
Badness: 0.1618
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: 0.0607
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
Badness: 0.0495
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
Badness: 0.0327
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
Badness: 0.0627
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: 0.0471
Music
Lemba
Subgroup: 2.3.5.7
Comma list: 50/49, 525/512
Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]
Mapping generators: ~7/5, ~8/7
Wedgie: ⟨⟨ 6 -2 -2 -17 -20 1 ]]
POTE generator: ~8/7 = 232.089
Badness: 0.0622
11-limit
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49, 385/384
Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]
POTE generator: ~8/7 = 230.974
Badness: 0.0416
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 45/44, 50/49, 65/64, 78/77
Mapping: [⟨2 2 5 6 5 7], ⟨0 3 -1 -1 5 1]]
POTE generator: ~8/7 = 230.966
Badness: 0.0255
Gidorah
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: 0.1018
7-limit
Subgroup: 2.3.5.7
Comma list: 21/20, 144/125
Mapping: [⟨1 1 2 3], ⟨0 3 2 -1]]
POTE generator: ~8/7 = 230.762
Badness: 0.0623
Clyndro
Subgroup: 2.3.5.7
Comma list: 135/128, 360/343
Mapping: [⟨1 1 4 3], ⟨0 3 -9 -1]]
POTE generator: ~8/7 = 226.469
Badness: 0.1592
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
Badness: 0.0697
Necromanteion
Subgroup: 2.3.5.7
Comma list: 1029/1024, 5103/5000
Mapping: [⟨1 7 10 1], ⟨0 -12 -17 4]]
POTE generator: ~48/35 = 541.779
Badness: 0.1177
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
Badness: 0.0535
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
Badness: 0.0470
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: 0.1541
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: ~3125/2304 = 524.210
Badness: 0.0408
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
Badness: 0.0216
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]]
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
Restles
Subgroup: 2.3.5.7
Comma list: 1029/1024, 153664/151875
Mapping: [⟨1 -2 8 4], ⟨0 12 -19 -4]]
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]]
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
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.
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