Sensamagic clan: Difference between revisions

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+lambda (3.5.7 sensamagic)
m Edo lists
Line 49: Line 49:
[[POTE generator]]: ~27/25 = 146.474
[[POTE generator]]: ~27/25 = 146.474


{{Val list|legend=1| 41, 49, 90, 131 }}
{{Val list|legend=1| 41, 131 }}


[[Badness]]: 0.0682
[[Badness]]: 0.0682
Line 100: Line 100:
[[POTE generator]]: ~28/27 = 55.122
[[POTE generator]]: ~28/27 = 55.122


{{Val list|legend=1| 22, 43d, 65, 87, 109, 196, 283 }}
{{Val list|legend=1| 22, 65, 87, 196, 283 }}


[[Badness]]: 0.0887
[[Badness]]: 0.0887
Line 114: Line 114:
POTE generator: ~28/27 = 55.126
POTE generator: ~28/27 = 55.126


{{Val list|legend=1| 22, 43d, 65, 87, 109, 196, 283 }}
{{Val list|legend=1| 22, 65, 87, 196, 283 }}


Badness: 0.0358
Badness: 0.0358
Line 128: Line 128:
POTE generator: ~28/27 = 55.138
POTE generator: ~28/27 = 55.138


{{Val list|legend=1| 22, 65, 87, 109, 196, 283 }}
{{Val list|legend=1| 22, 65, 87, 283 }}


Badness: 0.0317
Badness: 0.0317
Line 190: Line 190:
[[POTE generator]]: ~45/32 = 567.720
[[POTE generator]]: ~45/32 = 567.720


{{Val list|legend=1| 17, 19, 36c, 55c, 74cd, 93cdd }}
{{Val list|legend=1| 17, 19, 55c, 74cd, 93cdd }}


[[Badness]]: 0.0737
[[Badness]]: 0.0737
Line 251: Line 251:
[[POTE generator]]: ~9/7 = 439.076
[[POTE generator]]: ~9/7 = 439.076


{{Val list|legend=1| 41, 317bc, 358bc, 399bc }}
{{Val list|legend=1| 11cd, 30d, 41, 317bcc, 358bcc, 399bcc }}


[[Badness]]: 0.1394
[[Badness]]: 0.1394
Line 265: Line 265:
POTE generator: ~9/7 = 439.152
POTE generator: ~9/7 = 439.152


{{Val list|legend=1| 41, 153be, 194be, 235bce }}
{{Val list|legend=1| 11cd, 30d, 41, 153be, 194be, 235bcee }}


Badness: 0.0709
Badness: 0.0709
Line 279: Line 279:
POTE generator: ~9/7 = 439.119
POTE generator: ~9/7 = 439.119


{{Val list|legend=1| 41 }}
{{Val list|legend=1| 11cdf, 30df, 41 }}


Badness: 0.0528
Badness: 0.0528
Line 294: Line 294:
[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~5/4 = 391.225


{{Val list|legend=1| 40, 43, 46, 181c, 227c, 273c, 319c }}
{{Val list|legend=1| 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.3602
[[Badness]]: 0.3602
Line 310: Line 310:
[[POTE generator]]: ~5/4 = 391.465
[[POTE generator]]: ~5/4 = 391.465


{{Val list|legend=1| 46, 95, 141bc, 187bc, 328bc }}
{{Val list|legend=1| 46, 95, 141bc, 187bc, 328bbcc }}


[[Badness]]: 0.1084
[[Badness]]: 0.1084
Line 338: Line 338:
POTE generator: ~5/4 = 391.366
POTE generator: ~5/4 = 391.366


{{Val list|legend=1| 46, 233bcf, 279bcf }}
{{Val list|legend=1| 46, 233bcff, 279bccff }}


Badness: 0.0430
Badness: 0.0430
Line 352: Line 352:
[[POTE generator]]: ~3/2 = 704.536
[[POTE generator]]: ~3/2 = 704.536


{{Val list|legend=1| 17, 46, 109, 155, 264b, 419b }}
{{Val list|legend=1| 17, 29c, 46, 109, 155, 264b, 419b }}


[[Badness]]: 0.14058
[[Badness]]: 0.14058
Line 366: Line 366:
POTE generator: ~3/2 = 704.554
POTE generator: ~3/2 = 704.554


{{Val list|legend=1| 17, 46, 109, 264b, 373b, 637be }}
{{Val list|legend=1| 17, 29c, 46, 109, 264b, 373b, 637be }}


Badness: 0.0507
Badness: 0.0507
Line 380: Line 380:
POTE generator: ~3/2 = 704.571
POTE generator: ~3/2 = 704.571


{{Val list|legend=1| 17, 46, 63, 109, 218f, 373bf }}
{{Val list|legend=1| 17, 29c, 46, 63, 109, 218f, 373bf }}


Badness: 0.0327
Badness: 0.0327

Revision as of 16:03, 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.

Lambda

Subgroup: 3.5.7

Comma list: 245/243

Sval mapping: [⟨1 1 2], ⟨0 -2 1]]

Sval mapping generators: ~3, ~9/7

Gencom mapping: [⟨0 1 1 2], ⟨0 0 -2 1]]

POTE generator: ~9/7 = 440.4881

Vals: b4, b9, b13, b56, b69, b82, b95

Extensions

For full 7-limit extensions, we have bohpier, sensa/escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as father, sidi, godzilla, hedgehog, superpyth, sensi, magic, rodan, octacot, clyde, shrutar discussed elsewhere.

Tempering out 245/243 alone in the full 7-limit leads to a rank-3 temperament, sensamagic, 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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