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
- Porcupine
- Mohajira
- Valentine
- Orwell
- Shrutar
- Hemiwürschmidt
- Hemikleismic
- Amity
- Grendel
- Trident
Hendecatonic
The hendecatonic temperament has a period of 1/11 octave, which represents 16/15 and four times of which represents 9/7.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 10976/10935
Mapping: [⟨11 0 43 -4], ⟨0 1 -1 2]]
Wedgie: ⟨⟨ 11 -11 22 -43 4 82 ]]
POTE generator: ~3/2 = 703.054
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]]
POTE generator: ~3/2 = 702.636
Vals: Template:Val list
Badness: 0.046088
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]]
POTE generator: ~3/2 = 702.914
Vals: Template:Val list
Badness: 0.057725
Hemischis
Subgroup: 2.3.5.7
Comma list: 6144/6125, 19683/19600
Mapping: [⟨1 0 15 -17], ⟨0 2 -16 25]]
Wedgie: ⟨⟨ 2 -16 25 -30 34 103 ]]
POTE generator: ~81/70 = 249.203
Badness: 0.045817
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 8019/8000, 5632/5625
Mapping: [⟨1 0 15 -17 51], ⟨0 2 -16 25 -60]]
POTE generator: ~81/70 = 249.199
Vals: Template:Val list
Badness: 0.036289
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 4096/4095
Mapping: [⟨1 0 15 -17 51 14], ⟨0 2 -16 25 -60 -13]]
POTE generator: ~15/13 = 249.199
Vals: Template:Val list
Badness: 0.020816
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095
Map: [⟨1 0 15 -17 51 14 -49], ⟨0 2 -16 25 -60 -13 67]]
POTE generator: ~15/13 = 249.190
Vals: Template:Val list
Badness: 0.021073
Twothirdtonic
Subgroup: 2.3.5.7
Comma list: 686/675, 6144/6125
Mapping: [⟨1 3 2 4], ⟨0 -13 3 -11]]
Wedgie: ⟨⟨ 13 -3 11 -35 -19 34 ]]
POTE generator: ~15/14 = 130.401
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]]
POTE generator: ~15/14 = 130.430
Vals: Template:Val list
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]]
POTE generator: ~15/14 = 130.409
Vals: Template:Val list
Badness: 0.025941
Nessafof
Subgroup: 2.3.5.7
Comma list: 6144/6125, 250047/250000
Mapping: [⟨3 2 5 10], ⟨0 7 5 -4]]
Wedgie: ⟨⟨ 21 15 -12 -25 -78 -70 ]]
POTE generator: ~35/32 = 157.480
Badness: 0.045048
Septisuperfourth
Subgroup: 2.3.5.7
Comma list: 6144/6125, 118098/117649
Mapping: [⟨2 4 4 7], ⟨0 -9 7 -15]]
Wedgie: ⟨⟨ 18 -14 30 -64 -3 109 ]]
POTE generator: ~48/35 = 544.680
Badness: 0.059241
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 5632/5625
Mapping: [⟨2 4 4 7 6], ⟨0 -9 7 -15 10]]
POTE generator: ~48/35 = 544.696
Vals: Template:Val list
Badness: 0.024619
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4000/3993, 21168/21125
Mapping: [⟨2 4 4 7 6 11], ⟨0 -9 7 -15 10 -39]]
POTE generator: ~48/35 = 544.675
Vals: Template:Val list
Badness: 0.022887
Septisuperquad
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539, 5632/5625
Mapping: [⟨2 4 4 7 6 5], ⟨0 -9 7 -15 10 26]]
POTE generator: ~48/35 = 544.641
Vals: Template:Val list
Badness: 0.033038
Whoops
Subgroup: 2.3.5.7
Comma list: 6144/6125, 244140625/243045684
Mapping: [⟨1 17 14 -7], ⟨0 -33 -25 21]]
Wedgie: ⟨⟨ 33 25 -21 -37 -126 -119 ]]
POTE generator: ~441/320 = 560.519
Badness: 0.1758
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]]
POTE generator: ~242/175 = 560.519
Vals: Template:Val list
Badness: 0.0437
Polypyth
Subgroup: 2.3.5.7
Comma list: 6144/6125, 179200/177147
Mapping: [⟨1 0 -31 52], ⟨0 1 21 -31]]
POTE generator: ~3/2 = 704.174
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]]
POTE generator: ~3/2 = 704.177
Vals: Template:Val list
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]]
POTE generator: ~3/2 = 704.168
Vals: Template:Val list
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]]
POTE generator: ~3/2 = 704.168
Vals: Template:Val list
Badness: 0.019051
Icositritonic
The icositritonic temperament (46&161, named by Xenllium) 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 37 54 64], ⟨0 -1 -1 1]]
Wedgie: ⟨⟨ 23 23 -23 -17 -101 -118 ]]
POTE generator: ~64/63 = 29.3586
Badness: 0.196622
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 35937/35840
Mapping: [⟨23 37 54 64 79], ⟨0 -1 -1 1 1]]
POTE generator: ~64/63 = 29.3980
Vals: Template:Val list
Badness: 0.064613
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 847/845, 3584/3575
Mapping: [⟨23 37 54 64 79 84], ⟨0 -1 -1 1 1 2]]
POTE generator: ~64/63 = 29.2830
Vals: Template:Val list
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 37 54 64 79 84 94], ⟨0 -1 -1 1 1 2 0]]
POTE generator: ~64/63 = 29.2800
Vals: Template:Val list
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 37 54 64 79 84 94 96], ⟨0 -1 -1 1 1 2 0 3]]
POTE generator: ~64/63 = 29.3760
Vals: Template:Val list
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 37 54 64 79 84 94 96 104], ⟨0 -1 -1 1 1 2 0 3 0]]
POTE generator: ~64/63 = 29.3471
Vals: Template:Val list
Badness: 0.017745
Countermiracle
The countermiracle temperament (31&145, named by Xenllium) 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]]
Wedgie: ⟨⟨ 25 7 2 -47 -67 -15 ]]
POTE generator: ~343/320 = 115.917
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]]
POTE generator: ~77/72 = 115.916
Vals: Template:Val list
Badness: 0.039162