Sensipent family
Sensipent
Subgroup: 2.3.5
Comma list: 78732/78125
Mapping: [⟨1 6 8], ⟨0 -7 -9]]
POTE generator: 162/125 = 443.058
Sensi
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 13-limit sensi tempers out 91/90. 22/17, in the middle, is even closer to the generator. 46edo is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
Subgroup: 2.3.5.7
Comma list: 126/125, 245/243
Mapping: [⟨1 6 8 11], ⟨0 -7 -9 -13]]
Mapping generators: ~2, ~14/9
Wedgie: ⟨⟨ 7 9 13 -2 1 5 ]]
POTE generator: ~9/7 = 443.383
- [[1 0 0 0⟩, [1/13 0 0 7/13⟩, [5/13 0 0 9/13⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 7
- [[1 0 0 0⟩, [2/5 14/5 -7/5 0⟩, [4/5 18/5 -9/5 0⟩, [3/5 26/5 -13/5 0⟩]
- Eigenmonzos: 2, 9/5
Algebraic generator: The real root of x5 + x4 - 4x2 + x - 1, at 443.3783 cents.
Badness: 0.0256
Sensor
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Mapping: [⟨1 6 8 11 -6], ⟨0 -7 -9 -13 15]]
POTE generator: ~9/7 = 443.294
Badness: 0.0379
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 385/384
Mapping: [⟨1 6 8 11 -6 10], ⟨0 -7 -9 -13 15 -10]]
POTE generator: ~9/7 = 443.321
Badness: 0.0256
Sensis
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: [⟨1 6 8 11 6], ⟨0 -7 -9 -13 -4]]
POTE generator: ~9/7 = 443.962
{{Val list|legend=1| 19, 27e, 73ee
Badness: 0.0287
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: [⟨1 6 8 11 6 10], ⟨0 -7 -9 -13 -4 -10]]
POTE generator: ~9/7 = 443.945
Badness: 0.0200
Sensus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Mapping: [⟨1 6 8 11 23], ⟨0 -7 -9 -13 -31]]
POTE generator: ~9/7 = 443.626
Badness: 0.0295
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 352/351
Mapping: [⟨1 6 8 11 23 10], ⟨0 -7 -9 -13 -31 -10]]
POTE generator: ~9/7 = 443.559
Badness: 0.0208
Sensa
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Mapping: [⟨1 6 8 11 11], ⟨0 -7 -9 -13 -12]]
POTE generator: ~9/7 = 443.518
Badness: 0.0368
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 77/75, 143/140
Mapping: [⟨1 6 8 11 11 10], ⟨0 -7 -9 -13 -12 -11]]
POTE generator: ~9/7 = 443.506
Badness: 0.0233
Hemisensi
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Mapping: [⟨1 13 17 24 32], ⟨0 -14 -18 -26 -35]]
POTE generator: ~25/22 = 221.605
Badness: 0.0487
Sensei
Subgroup: 2.3.5.7
Comma list: 225/224, 78732/78125
Mapping: [⟨1 6 8 23], ⟨0 -7 -9 -32]]
Wedgie: ⟨⟨ 7 9 32 -2 31 49 ]]
POTE generator: ~125/81 = 757.245
Badness: 0.0592
Bison
Subgroup: 2.3.5.7
Comma list: 6144/6125, 78732/78125
Mapping: [⟨2 5 7 3], ⟨0 -7 -9 10]]
Wedgie: ⟨⟨ 14 18 -20 -4 -71 -97 ]]
POTE generator: ~35/32 = 156.925
Badness: 0.0704
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 8019/8000
Mapping: [⟨2 5 7 3 3], ⟨0 -7 -9 10 15]]
POTE generator: ~35/32 = 156.883
Badness: 0.0371
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 10985/10976
Mapping: [⟨2 5 7 3 3 4], ⟨0 -7 -9 10 15 13]]
POTE generator: ~35/32 = 156.904
Badness: 0.0235
Heinz
Subgroup: 2.3.5.7
Comma list: 1029/1024, 78732/78125
Mapping: [⟨1 13 17 -1], ⟨0 -21 -27 7]]
POTE generator: ~48/35 = 546.815
Badness: 0.1154
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 78732/78125
Mapping: [⟨1 13 17 -1 4], ⟨0 -21 -27 7 -1]]
POTE generator: ~11/8 = 547.631
Badness: 0.0424
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 13 17 -1 4 -5], ⟨0 -21 -27 7 -1 16]]
POTE generator: ~11/8 = 547.629
Badness: 0.0258
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 13 17 -1 4 -5 3], ⟨0 -21 -27 7 -1 16 2]]
POTE generator: ~11/8 = 547.635
Badness: 0.0185
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
Mapping: [⟨1 13 17 -1 4 -5 3 -5], ⟨0 -21 -27 7 -1 16 2 17]]
POTE generator: ~11/8 = 547.614
Badness: 0.0190