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
- 7-odd-limit: ~9/7 = [2/13 0 0 1/13⟩
- Eigenmonzos (unchanged intervals): 2, 7
- 9-odd-limit: ~9/7 = [1/5 2/5 -1/5 0⟩
- Eigenmonzos (unchanged intervals): 2, 9/5
- 7-odd-limit diamond monotone: ~9/7 = [442.105, 450.000] (7\19 to 3\8)
- 9-odd-limit diamond monotone: ~9/7 = [442.105, 444.444] (7\19 to 10\27)
- 7-odd-limit diamond tradeoff: ~9/7 = [442.179, 445.628]
- 9-odd-limit diamond tradeoff: ~9/7 = [435.084, 445.628]
- 7-odd-limit diamond monotone and tradeoff: ~9/7 = [442.179, 445.628]
- 9-odd-limit diamond monotone and tradeoff: ~9/7 = [442.105, 444.444]
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.025575
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Mapping: [⟨1 -1 -1 -2 9 0 10], ⟨0 7 9 13 -15 10 -16]]
POTE generator: ~9/7 = 443.365
Optimal GPV sequence: Template:Val list
Badness: 0.022908
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.020789
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
Mapping: [⟨1 -1 -1 -2 -8 0 -7], ⟨0 7 9 13 31 10 30]]
POTE generator: ~9/7 = 443.551
Optimal GPV sequence: Template:Val list
Badness: 0.016238
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.048714
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 243/242
Mapping: [⟨1 -1 -1 -2 -3 0], ⟨0 14 18 26 35 30]]
POTE generator: ~25/22 = 221.556
Optimal GPV sequence: Template:Val list
Badness: 0.033016
Bisensi
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 245/243
Mapping: [⟨2 5 7 9 9], ⟨0 -7 -9 -13 -8]]
POTE generator: ~11/10 = 156.692
Optimal GPV sequence: Template:Val list
Badness: 0.041723
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 169/168
Mapping: [⟨2 5 7 9 9 10], ⟨0 -7 -9 -13 -8 -10]]
POTE generator: ~11/10 = 156.725
Optimal GPV sequence: Template:Val list
Badness: 0.026339
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
Warrior
Subgroup: 2.3.5.7
Comma list: 5120/5103, 78732/78125
Mapping: [⟨1 -1 -1 15], ⟨0 7 9 -33]]
Wedgie: ⟨⟨ 7 9 -33 -2 -72 -102 ]]
POTE generator: ~162/125 = 443.289
Badness: 0.118239
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 5120/5103
Mapping: [⟨1 -1 -1 15 9], ⟨0 7 9 -33 -15]]
POTE generator: ~128/99 = 443.274
Optimal GPV sequence: Template:Val list
Badness: 0.046383
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 1331/1323
Mapping: [⟨1 -1 -1 15 9 17], ⟨0 7 9 -33 -15 -36]]
POTE generator: ~84/65 = 443.270
Optimal GPV sequence: Template:Val list
Badness: 0.028735
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
Mapping: [⟨1 -1 -1 15 9 17 10], ⟨0 7 9 -33 -15 -36 -16]]
POTE generator: ~22/17 = 443.270
Optimal GPV sequence: Template:Val list
Badness: 0.018105
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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]]
Wedgie: ⟨⟨ 21 27 -7 -6 -70 -92 ]]
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.019005
Trisensory
Subgroup: 2.3.5.7
Comma list: 1728/1715, 78732/78125
Mapping: [⟨3 4 6 8], ⟨0 7 9 4]]
Wedgie: ⟨⟨ 21 27 12 -6 -40 -48 ]]
POTE generator: ~36/35 = 43.147
Badness: 0.089740
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 78732/78125
Mapping: [⟨3 4 6 8 8], ⟨0 7 9 4 22]]
POTE generator: ~36/35 = 43.292
Optimal GPV sequence: Template:Val list
Badness: 0.058413
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 9295/9261
Mapping: [⟨3 4 6 8 8 11], ⟨0 7 9 4 22 1]]
POTE generator: ~36/35 = 43.288
Optimal GPV sequence: Template:Val list
Badness: 0.034829
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
Mapping: [⟨3 4 6 8 8 11 10], ⟨0 7 9 4 22 1 21]]
POTE generator: ~36/35 = 43.276
Optimal GPV sequence: Template:Val list
Badness: 0.024120
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
Mapping: [⟨3 4 6 8 8 11 10 12], ⟨0 7 9 4 22 1 21 7]]
POTE generator: ~36/35 = 43.292
Optimal GPV sequence: Template:Val list
Badness: 0.018466