Sensipent family: Difference between revisions

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* ''[[catafourth]]'', {2401/2400, 78732/78125} → [[Breedsmic temperaments #Catafourth]]
* ''[[catafourth]]'', {2401/2400, 78732/78125} → [[Breedsmic temperaments #Catafourth]]


= Sensipent =
== Sensipent ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 25: Line 25:
[[Badness]]: 0.035220
[[Badness]]: 0.035220


= Sensi =
== Sensi ==
{{main| Sensi }}
{{main| Sensi }}
{{see also| Sensamagic clan #Sensi }}
{{see also| Sensamagic clan #Sensi }}
Line 31: Line 31:
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."
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 ==
=== Septimal sensi ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 58: Line 58:
[[Badness]]: 0.025622
[[Badness]]: 0.025622


=== Sensation ===
==== Sensation ====
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


Line 73: Line 73:
Vals: {{Val list| 19, 27, 46, 111de, 157de }}
Vals: {{Val list| 19, 27, 46, 111de, 157de }}


== Sensor ==
=== Sensor ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 86: Line 86:
Badness: 0.037942
Badness: 0.037942


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 99: Line 99:
Badness: 0.025575
Badness: 0.025575


== Sensis ==
=== Sensis ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 112: Line 112:
Badness: 0.028680
Badness: 0.028680


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 125: Line 125:
Badness: 0.020017
Badness: 0.020017


== Sensus ==
=== Sensus ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 138: Line 138:
Badness: 0.029486
Badness: 0.029486


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 151: Line 151:
Badness: 0.020789
Badness: 0.020789


== Sensa ==
=== Sensa ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 164: Line 164:
Badness: 0.036835
Badness: 0.036835


=== 13-limit ===
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 177: Line 177:
Badness: 0.023258
Badness: 0.023258


== Hemisensi ==
=== Hemisensi ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 190: Line 190:
Badness: 0.048714
Badness: 0.048714


= Sensei =
== Sensei ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 205: Line 205:
[[Badness]]: 0.059218
[[Badness]]: 0.059218


= Bison =
== Bison ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 220: Line 220:
[[Badness]]: 0.070375
[[Badness]]: 0.070375


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 233: Line 233:
Badness: 0.037132
Badness: 0.037132


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 246: Line 246:
Badness: 0.023504
Badness: 0.023504


= Heinz =
== Heinz ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 259: Line 259:
[[Badness]]: 0.115385
[[Badness]]: 0.115385


== 11-limit ==
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 272: Line 272:
Badness: 0.042412
Badness: 0.042412


== 13-limit ==
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 285: Line 285:
Badness: 0.025779
Badness: 0.025779


== 17-limit ==
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 298: Line 298:
Badness: 0.018479
Badness: 0.018479


== 19-limit ==
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Revision as of 21:52, 1 June 2021


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

Template:Val list

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:

[[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.

Template:Val list

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

Template:Val list

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

Template:Val list

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

Template:Val list

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

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