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Porwell temperaments: Difference between revisions

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= Hendecatonic =
= Hendecatonic =
The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represents [[9/7]].
The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represents [[9/7]].
Subgroup: 2.3.5.7


[[Comma list]]: 6144/6125, 10976/10935
[[Comma list]]: 6144/6125, 10976/10935


[[Mapping]]: [<11 0 43 -4], <0 1 -1 2|]
[[Mapping]]: [{{val| 11 0 43 -4 }}, {{val| 0 1 -1 2 }}]


{{Multival|legend=1| 11 -11 22 -43 4 82 }}
{{Multival|legend=1| 11 -11 22 -43 4 82 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 10976/10935
Comma list: 121/120, 176/175, 10976/10935


Mapping: [<11 0 43 -4 38], <0 1 -1 2 0|]
Mapping: [{{val| 11 0 43 -4 38 }}, {{val| 0 1 -1 2 0 }}]


POTE generator: ~3/2 = 702.636
POTE generator: ~3/2 = 702.636
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== Icosidillic ==
== Icosidillic ==
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 6144/6125, 9801/9800
Comma list: 3388/3375, 6144/6125, 9801/9800


Mapping: [<22 0 86 -8 111|, <0 1 -1 2 -1|]
Mapping: [{{val| 22 0 86 -8 111 }}, {{val| 0 1 -1 2 -1 }}]


POTE generator: ~3/2 = 702.914
POTE generator: ~3/2 = 702.914
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= Hemischis =
= Hemischis =
{{see also| Schismatic family }}
{{see also| Schismatic family }}
Subgroup: 2.3.5.7


[[Comma list]]: 6144/6125, 19683/19600
[[Comma list]]: 6144/6125, 19683/19600


[[Mapping]]: [<1 0 15 -17|, <0 2 -16 25|]
[[Mapping]]: [{{val| 1 0 15 -17 }}, {{val| 0 2 -16 25 }}]


{{Multival|legend=1| 2 -16 25 -30 34 103 }}
{{Multival|legend=1| 2 -16 25 -30 34 103 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 8019/8000, 5632/5625
Comma list: 540/539, 8019/8000, 5632/5625


Mapping: [<1 0 15 -17 51|, <0 2 -16 25 -60|]
Mapping: [{{val| 1 0 15 -17 51 }}, {{val| 0 2 -16 25 -60 }}]


POTE generator: ~81/70 = 249.199
POTE generator: ~81/70 = 249.199
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 4096/4095
Comma list: 351/350, 540/539, 676/675, 4096/4095


Mapping: [<1 0 15 -17 51 14|, <0 2 -16 25 -60 -13|]
Mapping: [{{val| 1 0 15 -17 51 14 }}, {{val| 0 2 -16 25 -60 -13 }}]


POTE generator: ~15/13 = 249.199
POTE generator: ~15/13 = 249.199
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== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095
Comma list: 351/350, 442/441, 561/560, 676/675, 4096/4095


Map: [<1 0 15 -17 51 14 -49|, <0 2 -16 25 -60 -13 67|]
Map: [{{val| 1 0 15 -17 51 14 -49 }}, {{val| 0 2 -16 25 -60 -13 67 }}]


POTE generator: ~15/13 = 249.190
POTE generator: ~15/13 = 249.190
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= Twothirdtonic =
= Twothirdtonic =
Subgroup: 2.3.5.7
[[Comma list]]: 686/675, 6144/6125
[[Comma list]]: 686/675, 6144/6125


[[Mapping]]: [<1 3 2 4|, <0 -13 3 -11|]
[[Mapping]]: [{{val| 1 3 2 4 }}, {{val| 0 -13 3 -11 }}]


{{Multival|legend=1| 13 -3 11 -35 -19 34 }}
{{Multival|legend=1| 13 -3 11 -35 -19 34 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 686/675
Comma list: 121/120, 176/175, 686/675


Mapping: [<1 3 2 4 4|, <0 -13 3 -11 -5|]
Mapping: [{{val| 1 3 2 4 4 }}, {{val| 0 -13 3 -11 -5 }}]


POTE generator: ~15/14 = 130.430
POTE generator: ~15/14 = 130.430
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 169/168, 176/175
Comma list: 91/90, 121/120, 169/168, 176/175


Mapping: [<1 3 2 4 4 5|, <0 -13 3 -11 -5 -12|]
Mapping: [{{val| 1 3 2 4 4 5 }}, {{val| 0 -13 3 -11 -5 -12 }}]


POTE generator: ~15/14 = 130.409
POTE generator: ~15/14 = 130.409
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= Nessafof =
= Nessafof =
Subgroup: 2.3.5.7
[[Comma list]]: 6144/6125, 250047/250000
[[Comma list]]: 6144/6125, 250047/250000


[[Mapping]]: [<3 2 5 10|, <0 7 5 -4|]
[[Mapping]]: [{{val| 3 2 5 10 }}, {{val| 0 7 5 -4 }}]


{{Multival|legend=1| 21 15 -12 -25 -78 -70 }}
{{Multival|legend=1| 21 15 -12 -25 -78 -70 }}
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= Septisuperfourth =
= Septisuperfourth =
Subgroup: 2.3.5.7
[[Comma list]]: 6144/6125, 118098/117649
[[Comma list]]: 6144/6125, 118098/117649


[[Mapping]]: [<2 4 4 7|, <0 -9 7 -15|]
[[Mapping]]: [{{val| 2 4 4 7 }}, {{val| 0 -9 7 -15 }}]


{{Multival|legend=1| 18 -14 30 -64 -3 109 }}
{{Multival|legend=1| 18 -14 30 -64 -3 109 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 5632/5625
Comma list: 540/539, 4000/3993, 5632/5625


Mapping: [<2 4 4 7 6|, <0 -9 7 -15 10|]
Mapping: [{{val| 2 4 4 7 6 }}, {{val| 0 -9 7 -15 10 }}]


POTE generator: ~48/35 = 544.696
POTE generator: ~48/35 = 544.696
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4000/3993, 21168/21125
Comma list: 540/539, 729/728, 4000/3993, 21168/21125


Mapping: [<2 4 4 7 6 11|, <0 -9 7 -15 10 -39|]
Mapping: [{{val| 2 4 4 7 6 11 }}, {{val| 0 -9 7 -15 10 -39 }}]


POTE generator: ~48/35 = 544.675
POTE generator: ~48/35 = 544.675
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== Septisuperquad ==
== Septisuperquad ==
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539, 5632/5625
Comma list: 351/350, 364/363, 540/539, 5632/5625


Mapping: [<2 4 4 7 6 5|, <0 -9 7 -15 10 26|]
Mapping: [{{val| 2 4 4 7 6 5 }}, {{val| 0 -9 7 -15 10 26 }}]


POTE generator: ~48/35 = 544.641
POTE generator: ~48/35 = 544.641
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= Whoops =
= Whoops =
{{see also| Very high accuracy temperaments #Whoosh }}
{{see also| Very high accuracy temperaments #Whoosh }}
Subgroup: 2.3.5.7


[[Comma list]]: 6144/6125, 244140625/243045684
[[Comma list]]: 6144/6125, 244140625/243045684


[[Mapping]]: [<1 17 14 -7|, <0 -33 -25 21|]
[[Mapping]]: [{{val| 1 17 14 -7 }}, {{val| 0 -33 -25 21 }}]


{{Multival|legend=1| 33 25 -21 -37 -126 -119 }}
{{Multival|legend=1| 33 25 -21 -37 -126 -119 }}
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== 11-limit ==
== 11-limit ==
Comma list: 6144/6125, 3025/3024, 4000/3993
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 4000/3993, 6144/6125


Mapping: [<1 17 14 -7 10|, <0 -33 -25 21 -14|]
Mapping: [{{val| 1 17 14 -7 10 }}, {{val| 0 -33 -25 21 -14 }}]


POTE generator: ~242/175 = 560.519
POTE generator: ~242/175 = 560.519
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= Polypyth =
= Polypyth =
Subgroup: 2.3.5.7
[[Comma list]]: 6144/6125, 179200/177147
[[Comma list]]: 6144/6125, 179200/177147


[[Mapping]]: [<1 0 -31 52|, <0 1 21 -31|]
[[Mapping]]: [{{val| 1 0 -31 52 }}, {{val| 0 1 21 -31 }}]


[[POTE generator]]: ~3/2 = 704.174
[[POTE generator]]: ~3/2 = 704.174
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 896/891, 2200/2187, 6144/6125
Comma list: 896/891, 2200/2187, 6144/6125


Mapping: [<1 0 -31 52 59|, <0 1 21 -31 -35|]
Mapping: [{{val| 1 0 -31 52 59 }}, {{val| 0 1 21 -31 -35 }}]


POTE generator: ~3/2 = 704.177
POTE generator: ~3/2 = 704.177
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 364/363, 1716/1715
Comma list: 325/324, 352/351, 364/363, 1716/1715


Mapping: [<1 0 -31 52 59 64|, <0 1 21 -31 -35 -38|]
Mapping: [{{val| 1 0 -31 52 59 64 }}, {{val| 0 1 21 -31 -35 -38 }}]


POTE generator: ~3/2 = 704.168
POTE generator: ~3/2 = 704.168
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== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715


Mapping: [<1 0 -31 52 59 64 39|, <0 1 21 -31 -35 -38 -22|]
Mapping: [{{val| 1 0 -31 52 59 64 39 }}, {{val| 0 1 21 -31 -35 -38 -22 }}]


POTE generator: ~3/2 = 704.168
POTE generator: ~3/2 = 704.168
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= Icositritonic =
= Icositritonic =
The ''icositritonic'' temperament (46&161, named by [[User:Xenllium|Xenllium]]) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].
The ''icositritonic'' temperament (46&161, named by [[User:Xenllium|Xenllium]]) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].
Subgroup: 2.3.5.7


[[Comma list]]: 6144/6125, 9920232/9765625
[[Comma list]]: 6144/6125, 9920232/9765625


[[Mapping]]: [<23 37 54 64|, <0 -1 -1 1|]
[[Mapping]]: [{{val| 23 37 54 64 }}, {{val| 0 -1 -1 1 }}]


{{Multival|legend=1| 23 23 -23 -17 -101 -118 }}
{{Multival|legend=1| 23 23 -23 -17 -101 -118 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 35937/35840
Comma list: 441/440, 6144/6125, 35937/35840


Mapping: [<23 37 54 64 79|, <0 -1 -1 1 1|]
Mapping: [{{val| 23 37 54 64 79 }}, {{val| 0 -1 -1 1 1 }}]


POTE generator: ~64/63 = 29.3980
POTE generator: ~64/63 = 29.3980
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 847/845, 3584/3575
Comma list: 351/350, 441/440, 847/845, 3584/3575


Mapping: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]
Mapping: [{{val| 23 37 54 64 79 84 }}, {{val| 0 -1 -1 1 1 2 }}]


POTE generator: ~64/63 = 29.2830
POTE generator: ~64/63 = 29.2830
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== 17-limit ==
== 17-limit ==
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088


Mapping: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]
Mapping: [{{val| 23 37 54 64 79 84 94 }}, {{val| 0 -1 -1 1 1 2 0 }}]


POTE generator: ~64/63 = 29.2800
POTE generator: ~64/63 = 29.2800
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== 19-limit ==
== 19-limit ==
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845


Mapping: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]
Mapping: [{{val| 23 37 54 64 79 84 94 96 }}, {{val| 0 -1 -1 1 1 2 0 3 }}]


POTE generator: ~64/63 = 29.3760
POTE generator: ~64/63 = 29.3760
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== 23-limit ==
== 23-limit ==
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845


Mapping: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]
Mapping: [{{val| 23 37 54 64 79 84 94 96 104 }}, {{val| 0 -1 -1 1 1 2 0 3 0 }}]


POTE generator: ~64/63 = 29.3471
POTE generator: ~64/63 = 29.3471
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