Porwell temperaments
This family of temperaments tempers out the porwell comma, [11 1 -3 -2⟩ = 6144/6125, and includes hendecatonic, hemischis, twothirdtonic, nessafof, septisuperfourth, whoops, and polypyth.
Discussed elsewhere are:
- Hexadecimal (+36/35) → Pelogic family
- Porcupine (+64/63), also in: Porcupine family
- Mohajira (+81/80), also in: Meantone family
- Valentine (+126/125), also in: Starling temperaments
- Orwell (+225/224), also in: Semicomma family
- Shrutar (+245/243), also in: Diaschismic family
- Quinkee (+1029/1000) → Cloudy clan
- Hemiwürschmidt (+2401/2400 or 3136/3125) → Hemimean clan
- Hemikleismic (+4000/3969) → Kleismic family
- Amity (+4375/4374 or 5120/5103), also in: Amity family and Ragismic microtemperaments
- Freivald (+6272/6075) → Passion family
- Grendel (+16875/16807) → Mirkwai clan
- Hemischis (+19683/19600) → Schismatic family
- Bison (+78732/78125) → Sensipent family
- Hemimabila (+117649/116640) → Mabila family
- Septisuperfourth (+118098/117649) → Escapade family
- Trident (+14348907/14336000) → Tricot family
- Hemimaquila (+[-5 10 5 -8⟩) → Maquila family
- Decimaleap (+[15 -18 1 4⟩) → Quintaleap family
- Twilight (+[19 -22 2 4⟩) → Undim family
Hendecatonic
The hendecatonic temperament has a period of 1/11 octave, which represents 16/15 and four times of which represent 9/7.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 10976/10935
Mapping: [⟨11 0 43 -4], ⟨0 1 -1 2]]
- mapping generators: ~16/15, ~3
Wedgie: ⟨⟨ 11 -11 22 -43 4 82 ]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.054
Optimal ET sequence: 22, 55, 77, 99
Badness: 0.041081
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 10976/10935
Mapping: [⟨11 0 43 -4 38], ⟨0 1 -1 2 0]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.636
Optimal ET sequence: 22, 55, 77, 99, 176e, 275e
Badness: 0.046088
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350, 4459/4455
Mapping: [⟨11 0 43 -4 38 93], ⟨0 1 -1 2 0 -3]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.291
Optimal ET sequence: 22, 55, 77, 99, 176e
Badness: 0.040099
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023
Mapping: [⟨11 0 43 -4 38 93 45], ⟨0 1 -1 2 0 -3 0]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 702.301
Optimal ET sequence: 22, 55, 77, 99, 176eg
Badness: 0.029054
Cohendecatonic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 896/891, 4375/4356
Mapping: [⟨11 0 43 -4 73], ⟨0 1 -1 2 -2]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.686
Optimal ET sequence: 22, 77e, 99e, 121, 220e
Badness: 0.038042
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 540/539, 625/624
Mapping: [⟨11 0 43 -4 73 128], ⟨0 1 -1 2 -2 -5]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.888
Optimal ET sequence: 22, 77eff, 99ef, 121, 341bdeeff
Badness: 0.036112
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
Mapping: [⟨11 0 43 -4 73 128 45], ⟨0 1 -1 2 -2 -5 0]]
Optimal tuning (POTE): ~16/15 = 1\11, ~3/2 = 703.877
Optimal ET sequence: 22, 77eff, 99ef, 121, 220efg, 341bdeeffgg
Badness: 0.022590
Icosidillic
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 6144/6125, 9801/9800
Mapping: [⟨22 0 86 -8 111], ⟨0 1 -1 2 -1]]
- mapping generators: ~33/32, ~3
Optimal tuning (POTE): ~33/32 = 1\22, ~3/2 = 702.914
Optimal ET sequence: 22, 154, 176, 198
Badness: 0.057725
Twothirdtonic
Subgroup: 2.3.5.7
Comma list: 686/675, 6144/6125
Mapping: [⟨1 3 2 4], ⟨0 -13 3 -11]]
- mapping generators: ~2, ~15/14
Wedgie: ⟨⟨ 13 -3 11 -35 -19 34 ]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 130.401
Optimal ET sequence: 9, 28b, 37, 46
Badness: 0.099601
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 686/675
Mapping: [⟨1 3 2 4 4], ⟨0 -13 3 -11 -5]]
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 130.430
Optimal ET sequence: 9, 28b, 37, 46
Badness: 0.040768
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 176/175
Mapping: [⟨1 3 2 4 4 5], ⟨0 -13 3 -11 -5 -12]]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 130.409
Optimal ET sequence: 9, 28b, 37, 46
Badness: 0.025941
Semaja
Cryptically named by Petr Pařízek in 2011, semaja adds the gariboh comma to the comma list. The name actually refers to the fact that two of its ~8/7 generator steps reach a 13/10[1].
Subgroup: 2.3.5.7
Comma list: 3125/3087, 6144/6125
Mapping: [⟨1 -2 1 3], ⟨0 19 7 -1]]
- mapping generators: ~2, ~8/7
Wedgie: ⟨⟨ 19 7 -1 -33 -55 -22 ]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.4834
Optimal ET sequence: 16, 37, 53, 196d
Badness: 0.107023
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 3125/3087
Mapping: [⟨1 -2 1 3 1], ⟨0 19 7 -1 13]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.4856
Optimal ET sequence: 16, 37, 53
Badness: 0.059838
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 176/175, 275/273
Mapping: [⟨1 -2 1 3 1 2], ⟨0 19 7 -1 13 9]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.4794
Optimal ET sequence: 16, 37, 53
Badness: 0.032564
Nessafof
- For the 5-limit version, see High-badness temperaments #Nessafof.
Cryptically named by Petr Pařízek in 2011[2], nessafof adds the landscape comma and has a third-octave period. The name actually refers to the fact that it has a neutral-second generator, and that a semi-augmented fourth, stacked 5 times, makes 5/1[1].
Subgroup: 2.3.5.7
Comma list: 6144/6125, 250047/250000
Mapping: [⟨3 2 5 10], ⟨0 7 5 -4]]
- mapping generators: ~63/50, ~35/32
Wedgie: ⟨⟨ 21 15 -12 -25 -78 -70 ]]
Optimal tuning (POTE): ~63/50 = 1\3, ~35/32 = 157.480
Optimal ET sequence: 15, 54b, 69, 84, 99, 282, 381
Badness: 0.045048
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 250047/250000
Mapping: [⟨3 2 5 10 8], ⟨0 7 5 -4 6]]
Optimal tuning (POTE): ~63/50 = 1\3, ~12/11 = 157.520
Optimal ET sequence: 15, 54be, 69e, 84e, 99
Badness: 0.068427
Nessa
Subgroup: 2.3.5.7.11
Comma list: 441/440, 1344/1331, 4375/4356
Mapping: [⟨3 2 5 10 10], ⟨0 7 5 -4 1]]
Optimal tuning (POTE): ~44/35 = 1\3, ~35/32 = 157.539
Optimal ET sequence: 15, 54b, 69, 84, 99e
Badness: 0.048836
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 364/363, 441/440, 625/624
Mapping: [⟨3 2 5 10 10 6], ⟨0 7 5 -4 1 13]]
Optimal tuning (POTE): ~44/35 = 1\3, ~35/32 = 157.429
Optimal ET sequence: 15, 54bf, 69, 84, 99ef, 183ef, 282eeff
Badness: 0.037409
Aufo
- For the 5-limit version, see High badness temperaments #Untriton.
Also named by Petr Pařízek in 2011, aufo refers to the augmented fourth, which is a generator of this temperament[1].
Subgroup: 2.3.5.7
Comma list: 6144/6125, 177147/175616
Mapping: [⟨1 6 -7 19], ⟨0 -9 19 -33]]
- mapping generators: ~2, ~45/32
Wedgie: ⟨⟨ 9 -19 33 -51 27 130 ]]
Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.782
Optimal ET sequence: 53, 161, 214
Badness: 0.121428
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 177147/175616
Mapping: [⟨1 6 -7 19 1], ⟨0 -9 19 -33 5]]
Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.811
Optimal ET sequence: 53, 108e, 161e
Badness: 0.088631
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 351/350, 58806/57967
Mapping: [⟨1 6 -7 19 1 -12], ⟨0 -9 19 -33 5 32]]
Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.788
Optimal ET sequence: 53, 108e, 161e, 214ee
Badness: 0.058507
Aufic
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625, 72171/71680
Mapping: [⟨1 6 -7 19 -25], ⟨0 -9 19 -33 58]]
Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.800
Optimal ET sequence: 53, 108, 161, 214, 375
Badness: 0.075149
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845, 4096/4095
Mapping: [⟨1 6 -7 19 -25 -12], ⟨0 -9 19 -33 58 32]]
Optimal tuning (POTE): ~2 = 1\1, ~45/32 = 588.796
Optimal ET sequence: 53, 108, 161, 214, 375, 589be
Badness: 0.039050
Whoops
- For the 5-limit version, see Very high accuracy temperaments #Whoosh.
Also named by Petr Pařízek in 2011, whoops is a relatively simple extension to the otherwise very accurate microtemperament known as whoosh[1].
Subgroup: 2.3.5.7
Comma list: 6144/6125, 244140625/243045684
Mapping: [⟨1 17 14 -7], ⟨0 -33 -25 21]]
- mapping generators: ~2, ~441/320
Wedgie: ⟨⟨ 33 25 -21 -37 -126 -119 ]]
Optimal tuning (POTE): ~2 = 1\1, ~441/320 = 560.519
Optimal ET sequence: 15, 122d, 137, 152, 608d, 623bd, 775bcd
Badness: 0.175840
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 6144/6125
Mapping: [⟨1 17 14 -7 10], ⟨0 -33 -25 21 -14]]
Optimal tuning (POTE): ~2 = 1\1, ~242/175 = 560.519
Optimal ET sequence: 15, 122d, 137, 152, 608de, 623bde, 775bcde
Badness: 0.043743
Polypyth
- For the 5-limit version, see High badness temperaments #Leapday.
Polypyth (46 & 121) tempers out the same 5-limit comma as the leapday temperament (29 & 46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 179200/177147
Mapping: [⟨1 0 -31 52], ⟨0 1 21 -31]]
- mapping generators: ~2, ~3
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.174
Optimal ET sequence: 46, 121, 167, 288b, 455bcd, 743bcd
Badness: 0.137995
11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 2200/2187, 6144/6125
Mapping: [⟨1 0 -31 52 59], ⟨0 1 21 -31 -35]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.177
Optimal ET sequence: 46, 121, 167, 288be, 455bcde
Badness: 0.051131
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1716/1715
Mapping: [⟨1 0 -31 52 59 64], ⟨0 1 21 -31 -35 -38]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.168
Optimal ET sequence: 46, 121, 167, 288be
Badness: 0.030292
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
Mapping: [⟨1 0 -31 52 59 64 39], ⟨0 1 21 -31 -35 -38 -22]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.168
Optimal ET sequence: 46, 121, 167, 288beg
Badness: 0.019051
Icositritonic
The icositritonic temperament (46 & 161) has a period of 1/23 octave, so six period represents 6/5 and nine period represents 21/16.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 9920232/9765625
Mapping: [⟨23 0 17 101], ⟨0 1 1 -1]]
- mapping generators: ~1323/1280, ~3
Wedgie: ⟨⟨ 23 23 -23 -17 -101 -118 ]]
Optimal tuning (POTE): ~1323/1280 = 1\23, ~64/63 = 29.3586
Optimal ET sequence: 46, 115, 161, 207, 368c
Badness: 0.196622
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 35937/35840
Mapping: [⟨23 0 17 101 116], ⟨0 1 1 -1 -1]]
Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3980
Optimal ET sequence: 46, 115, 161, 207, 368c
Badness: 0.064613
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 847/845, 3584/3575
Mapping: [⟨23 0 17 101 116 158], ⟨0 1 1 -1 -1 -2]]
Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.2830
Optimal ET sequence: 46, 115, 161, 207, 368c
Badness: 0.040484
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
Mapping: [⟨23 0 17 101 116 158 94], ⟨0 1 1 -1 -1 -2 0]]
Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.2800
Optimal ET sequence: 46, 115, 161, 207, 368c
Badness: 0.024676
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
Mapping: [⟨23 0 17 101 116 158 94 207], ⟨0 1 1 -1 -1 -2 0 -3]]
Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3760
Optimal ET sequence: 46, 115, 161, 207, 368c
Badness: 0.021579
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
Mapping: [⟨23 0 17 101 116 158 94 207 104], ⟨0 1 1 -1 -1 -2 0 -3 0]]
Optimal tuning (POTE): ~33/32 = 1\23, ~64/63 = 29.3471
Optimal ET sequence: 46, 115, 161, 207, 368ci
Badness: 0.017745
Countermiracle
The countermiracle temperament (31 & 145) tempers out the trimyna, 50421/50000 and the quince comma, 823543/819200.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 50421/50000
Mapping: [⟨1 4 3 3], ⟨0 -25 -7 -2]]
- mapping generators: ~2, ~343/320
Wedgie: ⟨⟨ 25 7 2 -47 -67 -15 ]]
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9169
Optimal ET sequence: 31, 114, 145, 176, 559cc, 735cc
Badness: 0.102326
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 6144/6125
Mapping: [⟨1 4 3 3 8], ⟨0 -25 -7 -2 -47]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9158
Optimal ET sequence: 31, 114e, 145, 176
Badness: 0.039162
Countermiraculous
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 1001/1000, 6144/6125
Mapping: [⟨1 4 3 3 8 1], ⟨0 -25 -7 -2 -47 28]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8803
Optimal ET sequence: 31, 83e, 114e, 145, 321ceff
Badness: 0.039271
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224
Mapping: [⟨1 4 3 3 8 1 1], ⟨0 -25 -7 -2 -47 28 32]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8756
Optimal ET sequence: 31, 83e, 114e, 145
Badness: 0.029496
Counterbenediction
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 3146/3125, 3584/3575
Mapping: [⟨1 4 3 3 8 -2], ⟨0 -25 -7 -2 -47 59]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9335
Optimal ET sequence: 31, 114ef, 145f, 176, 207, 383c, 590cc
Badness: 0.045569
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125
Mapping: [⟨1 4 3 3 8 -2 -2], ⟨0 -25 -7 -2 -47 59 63]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9391
Optimal ET sequence: 31, 114efg, 145fg, 176, 207
Badness: 0.036289
Countermanna
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3388/3375, 6144/6125
Mapping: [⟨1 4 3 3 8 15 0 -25 -7 -2 -47 -117]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8898
Optimal ET sequence: 145, 176, 321ce
Badness: 0.053409
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375
Mapping: [⟨1 4 3 3 8 15 15], ⟨0 -25 -7 -2 -47 -117 -113]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8832
Optimal ET sequence: 145, 321ce
Badness: 0.040898
Counterrevelation
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 50421/50000
Mapping: [⟨1 4 3 3 5], ⟨0 -25 -7 -2 -16]]
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9192
Optimal ET sequence: 31, 114, 145e, 176e
Badness: 0.064070
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 13750/13689
Mapping: [⟨1 4 3 3 5 1], ⟨0 -25 -7 -2 -16 28]]
Optimal tuning (POTE): ~2 = 1\1, ~273/256 = 115.8624
Optimal ET sequence: 31, 83, 114, 145e
Badness: 0.057497
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 196/195, 10647/10625
Mapping: [⟨1 4 3 3 5 1 1], ⟨0 -25 -7 -2 -16 28 32]]
Optimal tuning (POTE): ~2 = 1\1, ~91/85 = 115.8527
Optimal ET sequence: 31, 83, 114, 145e
Badness: 0.044043
Absurdity
- For the 5-limit version, see Syntonic–chromatic equivalence continuum #Absurdity.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 177147/175000
Mapping: [⟨7 0 -17 64], ⟨0 1 3 -4]]
- mapping generators: ~972/875, ~3
Optimal tuning (POTE): ~972/875 = 1\7, ~3/2 = 700.5854 (or ~10/9 = 186.2997)
Optimal ET sequence: 77, 84, 161
Badness: 0.133520
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 72171/71680
Mapping: [⟨7 0 -17 64 124], ⟨0 1 3 -4 -9]]
Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 700.6354 (or ~10/9 = 186.3497)
Optimal ET sequence: 77, 84, 161
Badness: 0.081564
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 1188/1183, 3584/3575
Mapping: [⟨7 0 -17 64 124 37], ⟨0 1 3 -4 -9 -1]]
Optimal tuning (POTE): ~72/65 = 1\7, ~3/2 = 700.6291 (or ~10/9 = 186.3434)
Optimal ET sequence: 77, 84, 161
Badness: 0.041600
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625
Mapping: [⟨7 0 -17 64 124 37 -49], ⟨0 1 3 -4 -9 -1 7]]
Optimal tuning (POTE): ~72/65 = 1\7, ~3/2 = 700.6524 (or ~10/9 = 186.3667)
Badness: 0.031783
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
Mapping: [⟨7 0 -17 64 124 37 -49 63], ⟨0 1 3 -4 -9 -1 7 -3]]
Optimal tuning (POTE): ~21/19 = 1\7, ~3/2 = 700.6565 (or ~10/9 = 186.3708)
Badness: 0.022291
Dodifo
- For the 5-limit version, see High badness temperaments #Dodifo.
Also named by Petr Pařízek in 2011, dodifo refers to the (tetraptolemaic) double-diminished fourth, which is a generator of this temperament[1]. The extension here is a less accurate 7-limit intepretation.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 2500000/2470629
Mapping: [⟨1 12 5 4], ⟨0 -35 -9 -4]]
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 357.070
Optimal ET sequence: 37, 84, 121, 205
Badness: 0.179692
11-limit
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 2560/2541, 4375/4356
Mapping: [⟨1 12 5 4 -1], ⟨0 -35 -9 -4 15]]
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 357.048
Optimal ET sequence: 37, 84, 121, 326dee
Badness: 0.081923
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 625/624, 640/637, 1375/1372
Mapping: [⟨1 12 5 4 -1 4], ⟨0 -35 -9 -4 15 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 357.049
Optimal ET sequence: 37, 84, 121, 326deef
Badness: 0.039533