Sensamagic clan: Difference between revisions

m Cleanup (1/2)
m Cleanup (2/2)
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= Bohpier =
= Bohpier =
== 5-limit ==
== 5-limit ==
Subgroup: 2.3.5
[[Comma list]]: 1220703125/1162261467
[[Comma list]]: 1220703125/1162261467


[[Mapping]]: [<1 0 0|, <0 13 19|]
[[Mapping]]: [{{val| 1 0 0 }}, {{val| 0 13 19 }}]


[[POTE generator]]: ~27/25 = 146.476
[[POTE generator]]: ~27/25 = 146.476
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== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 3125/3087
[[Comma list]]: 245/243, 3125/3087


[[Mapping]]: [<1 0 0 0|, <0 13 19 23|]
[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 13 19 23 }}]


{{Multival|legend=1| 13 19 23 0 0 0 }}
{{Multival|legend=1| 13 19 23 0 0 0 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 1344/1331
Comma list: 100/99, 245/243, 1344/1331


POTE generator: ~12/11 = 146.545
POTE generator: ~12/11 = 146.545


Mapping: [<1 0 0 0 2|, <0 13 19 23 12|]
Mapping: [{{val| 1 0 0 0 2 }}, {{val| 0 13 19 23 12 }}]


{{Val list|legend=1| 41, 90e, 131e }}
{{Val list|legend=1| 41, 90e, 131e }}
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 275/273
Comma list: 100/99, 144/143, 196/195, 275/273


POTE generator: ~12/11 = 146.603
POTE generator: ~12/11 = 146.603


Mapping: [<1 0 0 0 2 2|, <0 13 19 23 12 14|]
Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 13 19 23 12 14 }}]


{{Val list|legend=1| 41, 90ef, 131ef, 221bdeff }}
{{Val list|legend=1| 41, 90ef, 131ef, 221bdeff }}
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= Sensa aka escaped =
= Sensa aka escaped =
{{see also| Escapade family #Escaped }}
{{see also| Escapade family #Escaped }}
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 65625/65536
[[Comma list]]: 245/243, 65625/65536


[[Mapping]]: [<1 2 2 4|, <0 -9 7 -26|]
[[Mapping]]: [{{val| 1 2 2 4 }}, {{val| 0 -9 7 -26 }}]


{{Multival|legend=1| 9 -7 26 -32 16 80 }}
{{Multival|legend=1| 9 -7 26 -32 16 80 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 4000/3993
Comma list: 245/243, 385/384, 4000/3993


Mapping: [<1 2 2 4 3|, <0 -9 7 -26 10|]
Mapping: [{{val| 1 2 2 4 3 }}, {{val| 0 -9 7 -26 10 }}]


POTE generator: ~28/27 = 55.126
POTE generator: ~28/27 = 55.126
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 245/243, 352/351, 385/384, 625/624
Comma list: 245/243, 352/351, 385/384, 625/624


Mapping: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]
Mapping: [{{val| 1 2 2 4 3 2 }}, {{val| 0 -9 7 -26 10 37 }}]


POTE generator: ~28/27 = 55.138
POTE generator: ~28/27 = 55.138
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= Salsa =
= Salsa =
{{see also| Schismatic family }}
{{see also| Schismatic family }}
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 32805/32768
[[Comma list]]: 245/243, 32805/32768


[[Mapping]]: [<1 1 7 -1|, <0 2 -16 13|]
[[Mapping]]: [{{val| 1 1 7 -1 }}, {{val| 0 2 -16 13 }}]


{{Multival|legend=1| 2 -16 13 -30 15 75 }}
{{Multival|legend=1| 2 -16 13 -30 15 75 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 243/242, 245/242, 385/384
Comma list: 243/242, 245/242, 385/384


Mapping: [<1 1 7 -1 2|, <0 2 -16 13 5|]
Mapping: [{{val| 1 1 7 -1 2 }}, {{val| 0 2 -16 13 5 }}]


POTE generator: ~11/9 = 351.014
POTE generator: ~11/9 = 351.014
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 243/242, 245/242
Comma list: 105/104, 144/143, 243/242, 245/242


Mapping: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]
Mapping: [{{val| 1 1 7 -1 2 4 }}, {{val| 0 2 -16 13 5 -1 }}]


POTE generator: ~11/9 = 351.025
POTE generator: ~11/9 = 351.025
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= Pycnic =
= Pycnic =
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 525/512
[[Comma list]]: 245/243, 525/512


[[Mapping]]: [<1 3 -1 8|, <0 -3 7 -11|]
[[Mapping]]: [{{val| 1 3 -1 8 }}, {{val| 0 -3 7 -11 }}]


{{Multival|legend=1| 3 -7 11 -18 9 45 }}
{{Multival|legend=1| 3 -7 11 -18 9 45 }}
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= Cohemiripple =
= Cohemiripple =
{{see also| Ripple family }}
{{see also| Ripple family }}
Subgroup: 2.3.5.7


[[Comma list]]: 245/243, 1323/1250
[[Comma list]]: 245/243, 1323/1250


[[Mapping]]: [<1 7 11 12|, <0 -10 -16 -17|]
[[Mapping]]: [{{val| 1 7 11 12 }}, {{val| 0 -10 -16 -17 }}]


{{Multival|legend=1| 10 16 17 2 -1 -5 }}
{{Multival|legend=1| 10 16 17 2 -1 -5 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 77/75, 243/242, 245/242
Comma list: 77/75, 243/242, 245/242


Mapping: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]
Mapping: [{{val| 1 7 11 12 17 }}, {{val| 0 -10 -16 -17 -25 }}]


POTE generator: ~7/5 = 549.945
POTE generator: ~7/5 = 549.945
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 77/75, 147/143, 243/242
Comma list: 66/65, 77/75, 147/143, 243/242


Mapping: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]
Mapping: [{{val| 1 7 11 12 17 14 }}, {{val| 0 -10 -16 -17 -25 -19 }}]


POTE generator: ~7/5 = 549.958
POTE generator: ~7/5 = 549.958
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= Superthird =
= Superthird =
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 78125/76832
[[Comma list]]: 245/243, 78125/76832


[[Mapping]]: [<1 13 15 25|, <0 -18 -20 -35|]
[[Mapping]]: [{{val| 1 13 15 25 }}, {{val| 0 -18 -20 -35 }}]


{{Multival|legend=1| 18 20 35 -10 5 25 }}
{{Multival|legend=1| 18 20 35 -10 5 25 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 78125/76832
Comma list: 100/99, 245/243, 78125/76832


Mapping: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]
Mapping: [{{val| 1 13 15 25 6 }}, {{val| 0 -18 -20 -35 -4 }}]


POTE generator: ~9/7 = 439.152
POTE generator: ~9/7 = 439.152
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 1375/1352
Comma list: 100/99, 144/143, 196/195, 1375/1352


Mapping: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]
Mapping: [{{val| 1 13 15 25 6 24 }}, {{val| 0 -18 -20 -35 -4 -32 }}]


POTE generator: ~9/7 = 439.119
POTE generator: ~9/7 = 439.119
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= Magus =
= Magus =
== 5-limit ==
== 5-limit ==
Subgroup: 2.3.5
[[Comma list]]: 50331648/48828125
[[Comma list]]: 50331648/48828125


[[Mapping]]: [<1 9 3|, <0 -11 -1|]
[[Mapping]]: [{{val| 1 9 3 }}, {{val| 0 -11 -1 }}]


[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~5/4 = 391.225
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== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 28672/28125
[[Comma list]]: 245/243, 28672/28125


[[Mapping]]: [<1 9 3 21|, <0 -11 -1 -27|]
[[Mapping]]: [{{val| 1 9 3 21 }}, {{val| 0 -11 -1 -27 }}]


{{Multival|legend=1| 11 1 27 -24 12 60 }}
{{Multival|legend=1| 11 1 27 -24 12 60 }}
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243, 1331/1323
Comma list: 176/175, 245/243, 1331/1323


Mapping: [<1 9 3 21 23|, <0 -11 -1 -27 -29|]
Mapping: [{{val| 1 9 3 21 23 }}, {{val| 0 -11 -1 -27 -29 }}]


POTE generator: ~5/4 = 391.503
POTE generator: ~5/4 = 391.503
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 176/175, 245/243, 1331/1323
Comma list: 91/90, 176/175, 245/243, 1331/1323


Mapping: [<1 9 3 21 23 1|, <0 -11 -1 -27 -29 4|]
Mapping: [{{val| 1 9 3 21 23 1 }}, {{val| 0 -11 -1 -27 -29 4 }}]


POTE generator: ~5/4 = 391.366
POTE generator: ~5/4 = 391.366
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= Leapweek =
= Leapweek =
Subgroup: 2.3.5.7
[[Comma list]]: 245/243, 2097152/2066715
[[Comma list]]: 245/243, 2097152/2066715


[[Mapping]]: [<1 1 17 -6|, <0 1 -25 15|]
[[Mapping]]: [{{val| 1 1 17 -6 }}, {{val| 0 1 -25 15 }}]


[[POTE generator]]: ~3/2 = 704.536
[[POTE generator]]: ~3/2 = 704.536
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 1331/1323
Comma list: 245/243, 385/384, 1331/1323


Mapping: [<1 1 17 -6 -3|, <0 1 -25 15 11|]
Mapping: [{{val| 1 1 17 -6 -3 }}, {{val| 0 1 -25 15 11 }}]


POTE generator: ~3/2 = 704.554
POTE generator: ~3/2 = 704.554
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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 245/243, 352/351, 364/363
Comma list: 169/168, 245/243, 352/351, 364/363


Mapping: [<1 1 17 -6 -3 -1|, <0 1 -25 15 11 8|]
Mapping: [{{val| 1 1 17 -6 -3 -1 }}, {{val| 0 1 -25 15 11 8 }}]


POTE generator: ~3/2 = 704.571
POTE generator: ~3/2 = 704.571
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Badness: 0.0327
Badness: 0.0327


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament clan]]
[[Category:Temperament clan]]
[[Category:Sensamagic]]
[[Category:Sensamagic]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]