Sensipent family

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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:

Sensipent

Subgroup: 2.3.5

Comma list: 78732/78125

Mapping: [1 -1 -1], 0 7 9]]

POTE generator: 162/125 = 443.058

Optimal GPV sequence8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c

Badness: 0.035220

Sensi

Main article: Sensi
See also: Sensamagic clan #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

Minimax tuning:

Eigenmonzos (unchanged intervals): 2, 7
Eigenmonzos (unchanged intervals): 2, 9/5

Tuning ranges:

  • 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.

Optimal GPV sequence19, 27, 46, 157d, 203cd, 249cdd, 295ccdd

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: 19, 27, 46, 111de, 157de

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: 19, 27, 46, 111d, 157d, 268cdd

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: 19, 27, 46, 111df, 157df

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: 19, 27, 46, 157df, 203cdff, 249cddff

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: 8d, 19, 27e, 73ee

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: 19, 27e, 46e, 73ee

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: 19e, 27e, 46, 119c, 165c

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: 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff

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: 19eg, 27eg, 46

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: 19e, 27, 46ee

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: 19e, 27, 46ee

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: 27e, 38d, 65, 157de, 222cde

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: 27e, 38df, 65f

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: 8d, …, 38d, 46, 176dde, 222cdde, 268cddee

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: 8d, …, 38df, 46

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

Optimal GPV sequence19, 84, 103, 187, 290b

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

Optimal GPV sequence46, 111, 157, 268cd

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: 46, 65d, 111, 268cd, 379cdd

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: 46, 65d, 111, 268cd, 379cddf

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: 46, 65d, 111, 268cdg, 379cddfg

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

Optimal GPV sequence8, 38, 46, 84, 130

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: 46, 84, 130, 306, 436ce

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: 46, 84, 130, 566ce, 596cef

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

Optimal GPV sequence46, 103, 149, 699bdd

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: 46, 103, 149, 252e, 401bdee

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: 46, 103, 149, 252ef, 401bdeef

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: 46, 103, 149, 252ef, 401bdeef

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: 46, 103h, 149h, 252efhh

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

Optimal GPV sequence27, 57, 84, 111, 195d, 306d

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: 27e, 84e, 111

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: 27e, 84e, 111

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: 27eg, 84e, 111

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: 27eg, 84e, 111

Badness: 0.018466