Sensipent family
Temperaments of the sensipent family temper out the sensipent comma, 78732/78125, also known as medium semicomma. This temperament family includes sensi, sensei, bison, and heinz.
Temperaments discussed elsewhere include:
- subpental, {3136/3125, 19683/19600} → Hemimean clan #Subpental
- catafourth, {2401/2400, 78732/78125} → Breedsmic temperaments #Catafourth
Sensipent
Subgroup: 2.3.5
Comma list: 78732/78125
Mapping: [⟨1 -1 -1], ⟨0 7 9]]
POTE generator: 162/125 = 443.058
Badness: 0.035220
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 2.3.5.7.13 sensi (sensation) 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."
Septimal sensi
Subgroup: 2.3.5.7
Comma list: 126/125, 245/243
Mapping: [⟨1 -1 -1 -2], ⟨0 7 9 13]]
Mapping generators: ~2, ~9/7
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: 0.025622
Sensation
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Sval mapping: [⟨1 -1 -1 -2 0], ⟨0 7 9 13 10]]
Gencom mapping: [⟨1 -1 -1 -2 0 0], ⟨0 7 9 13 0 10]]
Gencom: [2 9/7; 91/90 126/125 169/168]
POTE generator: ~9/7 = 443.322
Vals: Template:Val list
Sensor
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Mapping: [⟨1 -1 -1 -2 9], ⟨0 7 9 13 -15]]
POTE generator: ~9/7 = 443.294
Vals: Template:Val list
Badness: 0.037942
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 385/384
Mapping: [⟨1 -1 -1 -2 9 0], ⟨0 7 9 13 -15 10]]
POTE generator: ~9/7 = 443.321
Vals: Template:Val list
Badness: 0.025575
Sensis
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: [⟨1 -1 -1 -2 2], ⟨0 7 9 13 4]]
POTE generator: ~9/7 = 443.962
Vals: Template:Val list
Badness: 0.028680
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: [⟨1 -1 -1 -2 2 0], ⟨0 7 9 13 4 10]]
POTE generator: ~9/7 = 443.945
Vals: Template:Val list
Badness: 0.020017
Sensus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Mapping: [⟨1 -1 -1 -2 -8], ⟨0 7 9 13 31]]
POTE generator: ~9/7 = 443.626
Vals: Template:Val list
Badness: 0.029486
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 352/351
Mapping: [⟨1 -1 -1 -2 -8 0], ⟨0 7 9 13 31 10]]
POTE generator: ~9/7 = 443.559
Vals: Template:Val list
Badness: 0.020789
Sensa
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Mapping: [⟨1 -1 -1 -2 -1], ⟨0 7 9 13 12]]
POTE generator: ~9/7 = 443.518
Vals: Template:Val list
Badness: 0.036835
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 77/75, 143/140
Mapping: [⟨1 -1 -1 -2 -1 0], ⟨0 7 9 13 12 11]]
POTE generator: ~9/7 = 443.506
Vals: Template:Val list
Badness: 0.023258
Hemisensi
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Mapping: [⟨1 -1 -1 -2 -3], ⟨0 14 18 26 35]]
POTE generator: ~25/22 = 221.605
Vals: Template:Val list
Badness: 0.048714
Sensei
Subgroup: 2.3.5.7
Comma list: 225/224, 78732/78125
Mapping: [⟨1 -1 -1 -9], ⟨0 7 9 32]]
Wedgie: ⟨⟨ 7 9 32 -2 31 49 ]]
POTE generator: ~125/81 = 757.245
Badness: 0.059218
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: 0.070375
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
Vals: Template:Val list
Badness: 0.037132
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
Vals: Template:Val list
Badness: 0.023504
Heinz
Subgroup: 2.3.5.7
Comma list: 1029/1024, 78732/78125
Mapping: [⟨1 -8 -10 6], ⟨0 21 27 -7]]
POTE generator: ~48/35 = 546.815
Badness: 0.115385
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 78732/78125
Mapping: [⟨1 -8 -10 6 3], ⟨0 21 27 -7 1]]
POTE generator: ~11/8 = 547.631
Vals: Template:Val list
Badness: 0.042412
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 -8 -10 6 3 11], ⟨0 21 27 -7 1 -16]]
POTE generator: ~11/8 = 547.629
Vals: Template:Val list
Badness: 0.025779
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 -8 -10 6 3 11 5], ⟨0 21 27 -7 1 -16 -2]]
POTE generator: ~11/8 = 547.635
Vals: Template:Val list
Badness: 0.018479
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 -8 -10 6 3 11 5 12], ⟨0 21 27 -7 1 -16 -2 -17]]
POTE generator: ~11/8 = 547.614
Vals: Template:Val list
Badness: 0.019005