Sensipent family: Difference between revisions

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= Sensipent =
= Sensipent =
[[Comma list]]: 78732/78125
[[Comma list]]: 78732/78125
Line 45: Line 44:
[[Badness]]: 0.0256
[[Badness]]: 0.0256


==Sensor==
== Sensor ==
[[Comma|Comma]]s: 126/125, 245/243, 385/384
Comma list: 126/125, 245/243, 385/384


[[POTE_tuning|POTE generator]]: ~9/7 = 443.294
Mapping: [{{val| 1 6 8 11 -6 }}, {{val| 0 -7 -9 -13 15 }}]


[[Map|Map]]: [<1 6 8 11 -6|, <0 -7 -9 -13 15|]
POTE generator: ~9/7 = 443.294


[[EDO|EDO]]s: 19, 27, 46, 111d, 157d, 268cdd
{{Val list|legend=1| 19, 27, 46, 111d, 157d, 268cdd }}


[[Badness|Badness]]: 0.0379
Badness: 0.0379


===13-limit===
=== 13-limit ===
[[Comma|Comma]]s: 91/90, 126/125, 169/168, 385/384
Comma list: 91/90, 126/125, 169/168, 385/384


[[POTE_tuning|POTE generator]]: ~9/7 = 443.321
Mapping: [{{val| 1 6 8 11 -6 10 }}, {{val| 0 -7 -9 -13 15 -10 }}]


[[Map|Map]]: [<1 6 8 11 -6 10|, <0 -7 -9 -13 15 -10|]
POTE generator: ~9/7 = 443.321


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27]], [[46edo|46]], [[111edo|111df]], [[157edo|157df]]
{{Val list|legend=1| 19, 27, 46, 111df, 157df }}


[[Badness|Badness]]: 0.0256
Badness: 0.0256


==Sensis==
== Sensis ==
[[Comma|Comma]]s: 56/55, 100/99, 245/243
Comma list: 56/55, 100/99, 245/243


[[POTE_tuning|POTE generator]]: 443.962
Mapping: [{{val| 1 6 8 11 6 }}, {{val| 0 -7 -9 -13 -4 }}]


[[Map|Map]]: [<1 6 8 11 6|, <0 -7 -9 -13 -4|]
POTE generator: ~9/7 = 443.962


[[EDO|EDO]]s: [[19edo|19]], [[27edo|27e]], [[73edo|73ee]]
{{Val list|legend=1| 19, 27e, 73ee


[[Badness|Badness]]: 0.0287
Badness: 0.0287


===13-limit===
=== 13-limit ===
[[Comma|Comma]]s: 56/55, 78/77, 91/90, 100/99
Comma list: 56/55, 78/77, 91/90, 100/99


[[POTE_tuning|POTE generator]]: 443.945
Mapping: [{{val| 1 6 8 11 6 10 }}, {{val| 0 -7 -9 -13 -4 -10 }}]


[[Map|Map]]: [<1 6 8 11 6 10|, <0 -7 -9 -13 -4 -10|]
POTE generator: ~9/7 = 443.945


[[EDO|EDO]]s: 19, 27e, 46e, 73ee
{{Val list|legend=1| 19, 27e, 46e, 73ee }}


[[Badness|Badness]]: 0.0200
Badness: 0.0200


==Sensus==
== Sensus ==
[[Comma|Comma]]s: 126/125, 176/175, 245/243
Comma list: 126/125, 176/175, 245/243


[[POTE_generator|POTE generator]]: ~9/7 = 443.626
Mapping: [{{val| 1 6 8 11 23 }}, {{val| 0 -7 -9 -13 -31 }}]


[[Map|Map]]: [<1 6 8 11 23|, <0 -7 -9 -13 -31|]
POTE generator: ~9/7 = 443.626


[[EDO|EDO]]s: 19e, 27e, 46, 119c, 165c
{{Val list|legend=1| 19e, 27e, 46, 119c, 165c }}


[[Badness|Badness]]: 0.0295
Badness: 0.0295


===13-limit===
=== 13-limit ===
[[Comma|Comma]]s: 91/90, 126/125, 169/168, 352/351
Comma list: 91/90, 126/125, 169/168, 352/351


[[POTE_generator|POTE generator]]: ~9/7 = 443.559
Mapping: [{{val| 1 6 8 11 23 10 }}, {{val| 0 -7 -9 -13 -31 -10 }}]


[[Map|Map]]: [<1 6 8 11 23 10|, <0 -7 -9 -13 -31 -10|]
POTE generator: ~9/7 = 443.559


[[EDO|EDO]]s: 19e, 27e, 46, 165cf, 211bccf, 257bccff, [[303edo|303bccdff]]
{{Val list|legend=1| 19e, 27e, 46, 165cf, 211bccf, 257bccff, 303bccdff }}


[[Badness|Badness]]: 0.0208
Badness: 0.0208


See [[Chords_of_sensus|Chords of sensus]] for a listing of chords.
== Sensa ==
Comma list: 55/54, 77/75, 99/98


==Sensa==
Mapping: [{{val| 1 6 8 11 11 }}, {{val| 0 -7 -9 -13 -12 }}]
Commas: 55/54, 77/75, 99/98


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


Map: [<1 6 8 11 11|, <0 -7 -9 -13 -12|]
{{Val list|legend=1| 19e, 27, 46ee }}


EDOs: 19e, 27, 46ee
Badness: 0.0368


Badness: 0.0368
=== 13-limit ===
Comma list: 55/54, 66/65, 77/75, 143/140


===13-limit===
Mapping: [{{val| 1 6 8 11 11 10 }}, {{val| 0 -7 -9 -13 -12 -11 }}]
Commas: 55/54, 66/65, 77/75, 143/140


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


Map: [<1 6 8 11 11 10|, <0 -7 -9 -13 -12 -11|]
{{Val list|legend=1| 19e, 27, 46ee }}


EDOs: 19e, 27, 46ee
Badness: 0.0233


Badness: 0.0233
== Hemisensi ==
Comma list: 126/125, 243/242, 245/242


=Hemisensi=
Mapping: [{{val| 1 13 17 24 32 }}, {{val| 0 -14 -18 -26 -35 }}]
Commas: 126/125, 243/242, 245/242


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


Map: [<1 13 17 24 32|, <0 -14 -18 -26 -35|]
{{Val list|legend=1| 27e, 65, 157de, 222cde }}
 
EDOs: 27e, 65, 157de, 222cde


Badness: 0.0487
Badness: 0.0487


=Sensei=
= Sensei =
Commas: 225/224, 78732/78125
Comma list: 225/224, 78732/78125


POTE generator: ~125/81 = 757.245
Mapping: [<1 6 8 23|, <0 -7 -9 -32|]


Map: [<1 6 8 23|, <0 -7 -9 -32|]
Wedgie: <<7 9 32 -2 31 49||


Wedgie: <<7 9 32 -2 31 49||
POTE generator: ~125/81 = 757.245


EDOs: 19, 84, 103, 187, 290b
{{Val list|legend=1| 19, 84, 103, 187, 290b }}


Badness: 0.0592
Badness: 0.0592


=Bison=
= Bison =
Commas: 6144/6125, 78732/78125
Comma list: 6144/6125, 78732/78125


POTE generator: ~35/32 = 156.925
Mapping: [<2 5 7 3|, <0 -7 -9 10|]


Map: [<2 5 7 3|, <0 -7 -9 10|]
Wedgie: <<14 18 -20 -4 -71 -97||


Wedgie: <<14 18 -20 -4 -71 -97||
POTE generator: ~35/32 = 156.925


EDOs: 8, 38, 46, 84, 130
{{Val list|legend=1| 8, 38, 46, 84, 130 }}


Badness: 0.0704
Badness: 0.0704


==11-limit==
== 11-limit ==
Commas: 441/440, 6144/6125, 8019/8000
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
POTE generator: ~35/32 = 156.883


Map: [<2 5 7 3 3|, <0 -7 -9 10 15|]
{{Val list|legend=1| 46, 84, 130, 306, 436ce }}
 
EDOs: 46, 84, 130, 306, 436ce


Badness: 0.0371
Badness: 0.0371


==13-limit==
==13-limit==
Commas: 351/350, 364/363, 441/440, 10985/10976
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
POTE generator: ~35/32 = 156.904


Map: [<2 5 7 3 3 4|, <0 -7 -9 10 15 13|]
{{Val list|legend=1| 46, 84, 130, 566ce, 596cef }}
 
EDOs: 46, 84, 130, 566ce, 596cef


Badness: 0.0235
Badness: 0.0235


=Heinz=
= Heinz =
[[Comma|Comma]]s: 78732/78125, 1029/1024
[[Comma list]]: 78732/78125, 1029/1024


[[POTE_generator|POTE generator]]: ~48/35 = 546.815
[[Mapping]]: [<1 13 17 -1|, <0 -21 -27 7|]


[[Map|Map]]: [<1 13 17 -1|, <0 -21 -27 7|]
[[POTE generator]]: ~48/35 = 546.815


[[EDO|EDO]]s: [[46edo|46]], [[103edo|103]], [[149edo|149]], [[699edo|699bd]]
{{Val list|legend=1| 46, 103, 149, 699bd }}


[[Badness|Badness]]: 0.1154
[[Badness]]: 0.1154


==11-limit==
== 11-limit ==
[[Comma|Comma]]s: 385/384, 441/440, 88208/87500
Comma list: 385/384, 441/440, 88208/87500


[[POTE_generator|POTE generator]]: ~11/8 = 547.631
Mapping: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]


[[Map|Map]]: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]
POTE generator: ~11/8 = 547.631


[[EDO|EDO]]s: 46, 103, 149
{{Val list|legend=1| 46, 103, 149 }}


[[Badness|Badness]]: 0.0424
Badness: 0.0424
 
==13-limit==
[[Comma|Comma]]s: 351/350, 385/384, 441/440, 847/845


[[POTE_generator|POTE generator]]: ~11/8 = 547.629
== 13-limit ==
Comma list: 351/350, 385/384, 441/440, 847/845


[[Map|Map]]: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]
Mapping: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]


[[EDO|EDO]]s: 46, 57, 103, 149, 252e, 401bde
POTE generator: ~11/8 = 547.629


[[Badness|Badness]]: 0.0258
{{Val list|legend=1| 46, 57, 103, 149, 252e, 401bde }}


==17-limit==
Badness: 0.0258
[[Comma|Comma]]s: 273/272, 351/350, 385/384, 441/440, 847/845


[[POTE_generator|POTE generator]]: ~11/8 = 547.635
== 17-limit ==
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845


[[Map|Map]]: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]
Mapping: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]


[[EDO|EDO]]s: 46, 103, 149, [[252edo|252ef]], [[401edo|401bdef]]
POTE generator: ~11/8 = 547.635


[[Badness|Badness]]: 0.0185
{{Val list|legend=1| 46, 103, 149, 252ef, 401bdef }}


==19-limit==
Badness: 0.0185
[[Comma|Comma]]s: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968


[[POTE_generator|POTE generator]]: ~11/8 = 547.614
== 19-limit ==
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968


[[Map|Map]]: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|]
Mapping: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|]


[[EDO|EDO]]s: 46, 103h, 149h, 252efh
POTE generator: ~11/8 = 547.614


[[Badness|Badness]]: 0.0190
{{Val list|legend=1| 46, 103h, 149h, 252efh }}


Badness: 0.0190


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

Revision as of 06:43, 6 April 2021

Sensipent

Comma list: 78732/78125

Mapping: [⟨1 6 8], ⟨0 -7 -9]]

POTE generator: 162/125 = 443.058

Template:Val list

Sensi

Main article: 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 13-limit sensi 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."

Comma list: 126/125, 245/243

Mapping: [⟨1 6 8 11], ⟨0 -7 -9 -13]]

Mapping generators: ~2, ~14/9

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: 0.0256

Sensor

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

Mapping: [⟨1 6 8 11 -6], ⟨0 -7 -9 -13 15]]

POTE generator: ~9/7 = 443.294

Template:Val list

Badness: 0.0379

13-limit

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

Mapping: [⟨1 6 8 11 -6 10], ⟨0 -7 -9 -13 15 -10]]

POTE generator: ~9/7 = 443.321

Template:Val list

Badness: 0.0256

Sensis

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

Mapping: [⟨1 6 8 11 6], ⟨0 -7 -9 -13 -4]]

POTE generator: ~9/7 = 443.962

{{Val list|legend=1| 19, 27e, 73ee

Badness: 0.0287

13-limit

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

Mapping: [⟨1 6 8 11 6 10], ⟨0 -7 -9 -13 -4 -10]]

POTE generator: ~9/7 = 443.945

Template:Val list

Badness: 0.0200

Sensus

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

Mapping: [⟨1 6 8 11 23], ⟨0 -7 -9 -13 -31]]

POTE generator: ~9/7 = 443.626

Template:Val list

Badness: 0.0295

13-limit

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

Mapping: [⟨1 6 8 11 23 10], ⟨0 -7 -9 -13 -31 -10]]

POTE generator: ~9/7 = 443.559

Template:Val list

Badness: 0.0208

Sensa

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

Mapping: [⟨1 6 8 11 11], ⟨0 -7 -9 -13 -12]]

POTE generator: ~9/7 = 443.518

Template:Val list

Badness: 0.0368

13-limit

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

Mapping: [⟨1 6 8 11 11 10], ⟨0 -7 -9 -13 -12 -11]]

POTE generator: ~9/7 = 443.506

Template:Val list

Badness: 0.0233

Hemisensi

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

Mapping: [⟨1 13 17 24 32], ⟨0 -14 -18 -26 -35]]

POTE generator: ~25/22 = 221.605

Template:Val list

Badness: 0.0487

Sensei

Comma list: 225/224, 78732/78125

Mapping: [<1 6 8 23|, <0 -7 -9 -32|]

Wedgie: <<7 9 32 -2 31 49||

POTE generator: ~125/81 = 757.245

Template:Val list

Badness: 0.0592

Bison

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: 0.0704

11-limit

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

Template:Val list

Badness: 0.0371

13-limit

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

Template:Val list

Badness: 0.0235

Heinz

Comma list: 78732/78125, 1029/1024

Mapping: [<1 13 17 -1|, <0 -21 -27 7|]

POTE generator: ~48/35 = 546.815

Template:Val list

Badness: 0.1154

11-limit

Comma list: 385/384, 441/440, 88208/87500

Mapping: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]

POTE generator: ~11/8 = 547.631

Template:Val list

Badness: 0.0424

13-limit

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

Mapping: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]

POTE generator: ~11/8 = 547.629

Template:Val list

Badness: 0.0258

17-limit

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

Mapping: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]

POTE generator: ~11/8 = 547.635

Template:Val list

Badness: 0.0185

19-limit

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

Mapping: [<1 13 17 -1 4 -5 3 -5|, <0 -21 -27 7 -1 16 2 17|]

POTE generator: ~11/8 = 547.614

Template:Val list

Badness: 0.0190

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