Sensipent family: Difference between revisions

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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, heinz, and [[Breedsmic temperaments #Catafourth|catafourth]].
= Sensipent =
= Sensipent =
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: 78732/78125
[[Comma list]]: 78732/78125


[[Mapping]]: [{{val| 1 6 8 }}, {{val| 0 -7 -9 }}]
[[Mapping]]: [{{val| 1 -1 -1 }}, {{val| 0 7 9 }}]


[[POTE generator]]: 162/125 = 443.058
[[POTE generator]]: 162/125 = 443.058


{{Val list|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}
{{Val list|legend=1| 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c }}
[[Badness]]: 0.035220


= Sensi =
= Sensi =
{{main| Sensi }}
{{main| Sensi }}
{{see also| Sensamagic clan #Sensi }}
{{see also| Sensamagic clan #Sensi }}
Line 25: Line 28:


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 126/125, 245/243
[[Comma list]]: 126/125, 245/243


[[Mapping]]: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}]
[[Mapping]]: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}]


Mapping generators: ~2, ~14/9
Mapping generators: ~2, ~9/7


{{Multival|legend=1| 7 9 13 -2 1 5 }}
{{Multival|legend=1| 7 9 13 -2 1 5 }}
Line 50: Line 52:
{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}
{{Val list|legend=1| 19, 27, 46, 157d, 203cd, 249cdd, 295ccdd }}


[[Badness]]: 0.0256
[[Badness]]: 0.025622


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


Comma list: 91/90, 126/125, 169/168
Comma list: 91/90, 126/125, 169/168


Sval mapping: [{{val| 1 6 8 11 10 }}, {{val| 0 -7 -9 -13 -10 }}]
Sval mapping: [{{val| 1 -1 -1 -2 0 }}, {{val| 0 7 9 13 10 }}]


Gencom mapping: [{{val| 1 6 8 11 0 10 }}, {{val| 0 -7 -9 -13 0 -10 }}]
Gencom mapping: [{{val| 1 -1 -1 -2 0 0 }}, {{val| 0 7 9 13 0 10 }}]


Gencom: [2 9/7; 91/90 126/125 169/168]
Gencom: [2 9/7; 91/90 126/125 169/168]
Line 66: Line 67:
POTE generator: ~9/7 = 443.322
POTE generator: ~9/7 = 443.322


{{Val list|legend=1| 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


Comma list: 126/125, 245/243, 385/384
Comma list: 126/125, 245/243, 385/384


Mapping: [{{val| 1 6 8 11 -6 }}, {{val| 0 -7 -9 -13 15 }}]
Mapping: [{{val| 1 -1 -1 -2 9 }}, {{val| 0 7 9 13 -15 }}]


POTE generator: ~9/7 = 443.294
POTE generator: ~9/7 = 443.294


{{Val list|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}
Vals: {{Val list| 19, 27, 46, 111d, 157d, 268cdd }}


Badness: 0.0379
Badness: 0.037942


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


Comma list: 91/90, 126/125, 169/168, 385/384
Comma list: 91/90, 126/125, 169/168, 385/384


Mapping: [{{val| 1 6 8 11 -6 10 }}, {{val| 0 -7 -9 -13 15 -10 }}]
Mapping: [{{val| 1 -1 -1 -2 9 0 }}, {{val| 0 7 9 13 -15 10 }}]


POTE generator: ~9/7 = 443.321
POTE generator: ~9/7 = 443.321


{{Val list|legend=1| 19, 27, 46, 111df, 157df }}
Vals: {{Val list| 19, 27, 46, 111df, 157df }}


Badness: 0.0256
Badness: 0.025575


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


Comma list: 56/55, 100/99, 245/243
Comma list: 56/55, 100/99, 245/243


Mapping: [{{val| 1 6 8 11 6 }}, {{val| 0 -7 -9 -13 -4 }}]
Mapping: [{{val| 1 -1 -1 -2 2 }}, {{val| 0 7 9 13 4 }}]


POTE generator: ~9/7 = 443.962
POTE generator: ~9/7 = 443.962


{{Val list|legend=1| 19, 27e, 73ee }}
Vals: {{Val list| 8d, 19, 27e, 73ee }}


Badness: 0.0287
Badness: 0.028680


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


Comma list: 56/55, 78/77, 91/90, 100/99
Comma list: 56/55, 78/77, 91/90, 100/99


Mapping: [{{val| 1 6 8 11 6 10 }}, {{val| 0 -7 -9 -13 -4 -10 }}]
Mapping: [{{val| 1 -1 -1 -2 2 0 }}, {{val| 0 7 9 13 4 10 }}]


POTE generator: ~9/7 = 443.945
POTE generator: ~9/7 = 443.945


{{Val list|legend=1| 19, 27e, 46e, 73ee }}
Vals: {{Val list| 19, 27e, 46e, 73ee }}


Badness: 0.0200
Badness: 0.020017


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


Comma list: 126/125, 176/175, 245/243
Comma list: 126/125, 176/175, 245/243


Mapping: [{{val| 1 6 8 11 23 }}, {{val| 0 -7 -9 -13 -31 }}]
Mapping: [{{val| 1 -1 -1 -2 -8 }}, {{val| 0 7 9 13 31 }}]


POTE generator: ~9/7 = 443.626
POTE generator: ~9/7 = 443.626


{{Val list|legend=1| 19e, 27e, 46, 119c, 165c }}
Vals: {{Val list| 19e, 27e, 46, 119c, 165c }}


Badness: 0.0295
Badness: 0.029486


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


Comma list: 91/90, 126/125, 169/168, 352/351
Comma list: 91/90, 126/125, 169/168, 352/351


Mapping: [{{val| 1 6 8 11 23 10 }}, {{val| 0 -7 -9 -13 -31 -10 }}]
Mapping: [{{val| 1 -1 -1 -2 -8 0 }}, {{val| 0 7 9 13 31 10 }}]


POTE generator: ~9/7 = 443.559
POTE generator: ~9/7 = 443.559


{{Val list|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}
Vals: {{Val list| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}


Badness: 0.0208
Badness: 0.020789


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


Comma list: 55/54, 77/75, 99/98
Comma list: 55/54, 77/75, 99/98


Mapping: [{{val| 1 6 8 11 11 }}, {{val| 0 -7 -9 -13 -12 }}]
Mapping: [{{val| 1 -1 -1 -2 -1 }}, {{val| 0 7 9 13 12 }}]


POTE generator: ~9/7 = 443.518
POTE generator: ~9/7 = 443.518


{{Val list|legend=1| 19e, 27, 46ee }}
Vals: {{Val list| 19e, 27, 46ee }}


Badness: 0.0368
Badness: 0.036835


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


Comma list: 55/54, 66/65, 77/75, 143/140
Comma list: 55/54, 66/65, 77/75, 143/140


Mapping: [{{val| 1 6 8 11 11 10 }}, {{val| 0 -7 -9 -13 -12 -11 }}]
Mapping: [{{val| 1 -1 -1 -2 -1 0 }}, {{val| 0 7 9 13 12 11 }}]


POTE generator: ~9/7 = 443.506
POTE generator: ~9/7 = 443.506


{{Val list|legend=1| 19e, 27, 46ee }}
Vals: {{Val list| 19e, 27, 46ee }}


Badness: 0.0233
Badness: 0.023258


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


Comma list: 126/125, 243/242, 245/242
Comma list: 126/125, 243/242, 245/242


Mapping: [{{val| 1 13 17 24 32 }}, {{val| 0 -14 -18 -26 -35 }}]
Mapping: [{{val| 1 -1 -1 -2 -3 }}, {{val| 0 14 18 26 35 }}]


POTE generator: ~25/22 = 221.605
POTE generator: ~25/22 = 221.605


{{Val list|legend=1| 27e, 65, 157de, 222cde }}
Vals: {{Val list| 27e, 65, 157de, 222cde }}


Badness: 0.0487
Badness: 0.048714


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


[[Comma list]]: 225/224, 78732/78125
[[Comma list]]: 225/224, 78732/78125


[[Mapping]]: [{{val| 1 6 8 23 }}, {{val| 0 -7 -9 -32 }}]
[[Mapping]]: [{{val| 1 -1 -1 -9 }}, {{val| 0 7 9 32 }}]


{{Multival|legend=1| 7 9 32 -2 31 49 }}
{{Multival|legend=1| 7 9 32 -2 31 49 }}
Line 208: Line 199:
{{Val list|legend=1| 19, 84, 103, 187, 290b }}
{{Val list|legend=1| 19, 84, 103, 187, 290b }}


[[Badness]]: 0.0592
[[Badness]]: 0.059218


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


Line 224: Line 214:
{{Val list|legend=1| 8, 38, 46, 84, 130 }}
{{Val list|legend=1| 8, 38, 46, 84, 130 }}


[[Badness]]: 0.0704
[[Badness]]: 0.070375


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


Line 236: Line 225:
POTE generator: ~35/32 = 156.883
POTE generator: ~35/32 = 156.883


{{Val list|legend=1| 46, 84, 130, 306, 436ce }}
Vals: {{Val list| 46, 84, 130, 306, 436ce }}


Badness: 0.0371
Badness: 0.037132


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


Line 250: Line 238:
POTE generator: ~35/32 = 156.904
POTE generator: ~35/32 = 156.904


{{Val list|legend=1| 46, 84, 130, 566ce, 596cef }}
Vals: {{Val list| 46, 84, 130, 566ce, 596cef }}


Badness: 0.0235
Badness: 0.023504


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


[[Comma list]]: 1029/1024, 78732/78125
[[Comma list]]: 1029/1024, 78732/78125


[[Mapping]]: [{{val| 1 13 17 -1 }}, {{val| 0 -21 -27 7 }}]
[[Mapping]]: [{{val| 1 -8 -10 6 }}, {{val| 0 21 27 -7 }}]


[[POTE generator]]: ~48/35 = 546.815
[[POTE generator]]: ~48/35 = 546.815


{{Val list|legend=1| 46, 103, 149, 699bd }}
{{Val list|legend=1| 46, 103, 149, 699bdd }}


[[Badness]]: 0.1154
[[Badness]]: 0.115385


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


Comma list: 385/384, 441/440, 78732/78125
Comma list: 385/384, 441/440, 78732/78125


Mapping: [{{val| 1 13 17 -1 4 }}, {{val| 0 -21 -27 7 -1 }}]
Mapping: [{{val| 1 -8 -10 6 3 }}, {{val| 0 21 27 -7 1 }}]


POTE generator: ~11/8 = 547.631
POTE generator: ~11/8 = 547.631


{{Val list|legend=1| 46, 103, 149 }}
Vals: {{Val list| 46, 103, 149, 252e, 401bdee }}


Badness: 0.0424
Badness: 0.042412


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


Comma list: 351/350, 385/384, 441/440, 847/845
Comma list: 351/350, 385/384, 441/440, 847/845


Mapping: [{{val| 1 13 17 -1 4 -5 }}, {{val| 0 -21 -27 7 -1 16 }}]
Mapping: [{{val| 1 -8 -10 6 3 11 }}, {{val| 0 21 27 -7 1 -16 }}]


POTE generator: ~11/8 = 547.629
POTE generator: ~11/8 = 547.629


{{Val list|legend=1| 46, 57, 103, 149, 252e, 401bde }}
Vals: {{Val list| 46, 103, 149, 252ef, 401bdeef }}


Badness: 0.0258
Badness: 0.025779


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


Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845


Mapping: [{{val| 1 13 17 -1 4 -5 3 }}, {{val| 0 -21 -27 7 -1 16 2 }}]
Mapping: [{{val| 1 -8 -10 6 3 11 5 }}, {{val| 0 21 27 -7 1 -16 -2 }}]


POTE generator: ~11/8 = 547.635
POTE generator: ~11/8 = 547.635


{{Val list|legend=1| 46, 103, 149, 252ef, 401bdef }}
Vals: {{Val list| 46, 103, 149, 252ef, 401bdeef }}


Badness: 0.0185
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


Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968


Mapping: [{{val| 1 13 17 -1 4 -5 3 -5 }}, {{val| 0 -21 -27 7 -1 16 2 17 }}]
Mapping: [{{val| 1 -8 -10 6 3 11 5 12 }}, {{val| 0 21 27 -7 1 -16 -2 -17 }}]


POTE generator: ~11/8 = 547.614
POTE generator: ~11/8 = 547.614


{{Val list|legend=1| 46, 103h, 149h, 252efh }}
Vals: {{Val list| 46, 103h, 149h, 252efhh }}


Badness: 0.0190
Badness: 0.019005


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 03:08, 19 May 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, heinz, and catafourth.

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."

7-limit

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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