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