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Sensipent family: Difference between revisions

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= Sensipent =
= Sensipent =
Subgroup: 2.3.5
[[Comma list]]: 78732/78125
[[Comma list]]: 78732/78125


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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."
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."
Subgroup: 2.3.5.7


[[Comma list]]: 126/125, 245/243
[[Comma list]]: 126/125, 245/243
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== Sensor ==
== Sensor ==
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Comma list: 126/125, 245/243, 385/384


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=== 13-limit ===
=== 13-limit ===
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


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== Sensis ==
== Sensis ==
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Comma list: 56/55, 100/99, 245/243


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=== 13-limit ===
=== 13-limit ===
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


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== Sensus ==
== Sensus ==
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Comma list: 126/125, 176/175, 245/243


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=== 13-limit ===
=== 13-limit ===
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


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== Sensa ==
== Sensa ==
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Comma list: 55/54, 77/75, 99/98


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=== 13-limit ===
=== 13-limit ===
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


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== Hemisensi ==
== Hemisensi ==
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Comma list: 126/125, 243/242, 245/242


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


Mapping: [<1 6 8 23|, <0 -7 -9 -32|]
Subgroup: 2.3.5.7


Wedgie: <<7 9 32 -2 31 49||
[[Comma list]]: 225/224, 78732/78125


POTE generator: ~125/81 = 757.245
[[Mapping]]: [{{val| 1 6 8 23 }}, {{val| 0 -7 -9 -32 }}]
 
{{Multival|legend=1| 7 9 32 -2 31 49 }}
 
[[POTE generator]]: ~125/81 = 757.245


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


Badness: 0.0592
[[Badness]]: 0.0592


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


Mapping: [<2 5 7 3|, <0 -7 -9 10|]
Subgroup: 2.3.5.7
 
[[Comma list]]: 6144/6125, 78732/78125
 
[[Mapping]]: [{{val| 2 5 7 3 }}, {{val| 0 -7 -9 10 }}]


Wedgie: <<14 18 -20 -4 -71 -97||
{{Multival|legend=1| 14 18 -20 -4 -71 -97 }}


POTE generator: ~35/32 = 156.925
[[POTE generator]]: ~35/32 = 156.925


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


Badness: 0.0704
[[Badness]]: 0.0704


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 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|]
Mapping: [{{val| 2 5 7 3 3 }}, {{val| 0 -7 -9 10 15 }}]


POTE generator: ~35/32 = 156.883
POTE generator: ~35/32 = 156.883
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Badness: 0.0371
Badness: 0.0371


==13-limit==
== 13-limit ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 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|]
Mapping: [{{val| 2 5 7 3 3 4 }}, {{val| 0 -7 -9 10 15 13 }}]


POTE generator: ~35/32 = 156.904
POTE generator: ~35/32 = 156.904
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= Heinz =
= Heinz =
[[Comma list]]: 78732/78125, 1029/1024


[[Mapping]]: [<1 13 17 -1|, <0 -21 -27 7|]
Subgroup: 2.3.5.7
 
[[Comma list]]: 1029/1024, 78732/78125
 
[[Mapping]]: [{{val| 1 13 17 -1 }}, {{val| 0 -21 -27 7 }}]


[[POTE generator]]: ~48/35 = 546.815
[[POTE generator]]: ~48/35 = 546.815
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== 11-limit ==
== 11-limit ==
Comma list: 385/384, 441/440, 88208/87500


Mapping: [<1 13 17 -1 4|, <0 -21 -27 7 -1|]
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 441/440, 78732/78125
 
Mapping: [{{val| 1 13 17 -1 4 }}, {{val| 0 -21 -27 7 -1 }}]


POTE generator: ~11/8 = 547.631
POTE generator: ~11/8 = 547.631
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== 13-limit ==
== 13-limit ==
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: [<1 13 17 -1 4 -5|, <0 -21 -27 7 -1 16|]
Mapping: [{{val| 1 13 17 -1 4 -5 }}, {{val| 0 -21 -27 7 -1 16 }}]


POTE generator: ~11/8 = 547.629
POTE generator: ~11/8 = 547.629
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== 17-limit ==
== 17-limit ==
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: [<1 13 17 -1 4 -5 3|, <0 -21 -27 7 -1 16 2|]
Mapping: [{{val| 1 13 17 -1 4 -5 3 }}, {{val| 0 -21 -27 7 -1 16 2 }}]


POTE generator: ~11/8 = 547.635
POTE generator: ~11/8 = 547.635
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== 19-limit ==
== 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
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|]
Mapping: [{{val| 1 13 17 -1 4 -5 3 -5 }}, {{val| 0 -21 -27 7 -1 16 2 17 }}]


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