Sensamagic clan: Difference between revisions

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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
Line 274: Line 336:


== 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
Line 285: Line 350:


== 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
Line 295: Line 363:
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]]

Revision as of 14:54, 16 April 2021

The sensamagic clan tempers out the sensamagic comma, 245/243, a triprime comma with no factors of 2, ⟨0 -5 1 2] to be exact. There are a number of linear temperaments in the clan (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a rank three temperament for which 283edo is the optimal patent val.

Bohpier

5-limit

Subgroup: 2.3.5

Comma list: 1220703125/1162261467

Mapping: [⟨1 0 0], ⟨0 13 19]]

POTE generator: ~27/25 = 146.476

Template:Val list

Badness: 0.8605

7-limit

Subgroup: 2.3.5.7

Comma list: 245/243, 3125/3087

Mapping: [⟨1 0 0 0], ⟨0 13 19 23]]

Wedgie: ⟨⟨ 13 19 23 0 0 0 ]]

POTE generator: ~27/25 = 146.474

Template:Val list

Badness: 0.0682

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243, 1344/1331

POTE generator: ~12/11 = 146.545

Mapping: [⟨1 0 0 0 2], ⟨0 13 19 23 12]]

Template:Val list

Badness: 0.0339

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 144/143, 196/195, 275/273

POTE generator: ~12/11 = 146.603

Mapping: [⟨1 0 0 0 2 2], ⟨0 13 19 23 12 14]]

Template:Val list

Badness: 0.0249

Music

by Chris Vaisvil:

Sensa aka escaped

See also: Escapade family § Escaped

Subgroup: 2.3.5.7

Comma list: 245/243, 65625/65536

Mapping: [⟨1 2 2 4], ⟨0 -9 7 -26]]

Wedgie: ⟨⟨ 9 -7 26 -32 16 80 ]]

POTE generator: ~28/27 = 55.122

Template:Val list

Badness: 0.0887

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 4000/3993

Mapping: [⟨1 2 2 4 3], ⟨0 -9 7 -26 10]]

POTE generator: ~28/27 = 55.126

Template:Val list

Badness: 0.0358

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 245/243, 352/351, 385/384, 625/624

Mapping: [⟨1 2 2 4 3 2], ⟨0 -9 7 -26 10 37]]

POTE generator: ~28/27 = 55.138

Template:Val list

Badness: 0.0317

Salsa

See also: Schismatic family

Subgroup: 2.3.5.7

Comma list: 245/243, 32805/32768

Mapping: [⟨1 1 7 -1], ⟨0 2 -16 13]]

Wedgie: ⟨⟨ 2 -16 13 -30 15 75 ]]

POTE generator: ~128/105 = 351.049

Template:Val list

Badness: 0.08015

11-limit

Subgroup: 2.3.5.7.11

Comma list: 243/242, 245/242, 385/384

Mapping: [⟨1 1 7 -1 2], ⟨0 2 -16 13 5]]

POTE generator: ~11/9 = 351.014

Template:Val list

Badness: 0.0394

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 243/242, 245/242

Mapping: [⟨1 1 7 -1 2 4], ⟨0 2 -16 13 5 -1]]

POTE generator: ~11/9 = 351.025

Template:Val list

Badness: 0.0310

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.

Subgroup: 2.3.5.7

Comma list: 245/243, 525/512

Mapping: [⟨1 3 -1 8], ⟨0 -3 7 -11]]

Wedgie: ⟨⟨ 3 -7 11 -18 9 45 ]]

POTE generator: ~45/32 = 567.720

Template:Val list

Badness: 0.0737

Cohemiripple

See also: Ripple family

Subgroup: 2.3.5.7

Comma list: 245/243, 1323/1250

Mapping: [⟨1 7 11 12], ⟨0 -10 -16 -17]]

Wedgie: ⟨⟨ 10 16 17 2 -1 -5 ]]

POTE generator: ~7/5 = 549.944

Template:Val list

Badness: 0.1902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 77/75, 243/242, 245/242

Mapping: [⟨1 7 11 12 17], ⟨0 -10 -16 -17 -25]]

POTE generator: ~7/5 = 549.945

Template:Val list

Badness: 0.0827

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 77/75, 147/143, 243/242

Mapping: [⟨1 7 11 12 17 14], ⟨0 -10 -16 -17 -25 -19]]

POTE generator: ~7/5 = 549.958

Template:Val list

Badness: 0.0499

Superthird

Subgroup: 2.3.5.7

Comma list: 245/243, 78125/76832

Mapping: [⟨1 13 15 25], ⟨0 -18 -20 -35]]

Wedgie: ⟨⟨ 18 20 35 -10 5 25 ]]

POTE generator: ~9/7 = 439.076

Template:Val list

Badness: 0.1394

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243, 78125/76832

Mapping: [⟨1 13 15 25 6], ⟨0 -18 -20 -35 -4]]

POTE generator: ~9/7 = 439.152

Template:Val list

Badness: 0.0709

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 144/143, 196/195, 1375/1352

Mapping: [⟨1 13 15 25 6 24], ⟨0 -18 -20 -35 -4 -32]]

POTE generator: ~9/7 = 439.119

Template:Val list

Badness: 0.0528

Magus

5-limit

Subgroup: 2.3.5

Comma list: 50331648/48828125

Mapping: [⟨1 9 3], ⟨0 -11 -1]]

POTE generator: ~5/4 = 391.225

Template:Val list

Badness: 0.3602

7-limit

Subgroup: 2.3.5.7

Comma list: 245/243, 28672/28125

Mapping: [⟨1 9 3 21], ⟨0 -11 -1 -27]]

Wedgie: ⟨⟨ 11 1 27 -24 12 60 ]]

POTE generator: ~5/4 = 391.465

Template:Val list

Badness: 0.1084

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243, 1331/1323

Mapping: [⟨1 9 3 21 23], ⟨0 -11 -1 -27 -29]]

POTE generator: ~5/4 = 391.503

Template:Val list

Badness: 0.0451

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 176/175, 245/243, 1331/1323

Mapping: [⟨1 9 3 21 23 1], ⟨0 -11 -1 -27 -29 4]]

POTE generator: ~5/4 = 391.366

Template:Val list

Badness: 0.0430

Leapweek

Subgroup: 2.3.5.7

Comma list: 245/243, 2097152/2066715

Mapping: [⟨1 1 17 -6], ⟨0 1 -25 15]]

POTE generator: ~3/2 = 704.536

Template:Val list

Badness: 0.14058

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 1331/1323

Mapping: [⟨1 1 17 -6 -3], ⟨0 1 -25 15 11]]

POTE generator: ~3/2 = 704.554

Template:Val list

Badness: 0.0507

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 245/243, 352/351, 364/363

Mapping: [⟨1 1 17 -6 -3 -1], ⟨0 1 -25 15 11 8]]

POTE generator: ~3/2 = 704.571

Template:Val list

Badness: 0.0327

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