Orwellismic temperaments: Difference between revisions

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These temper out |6 3 -1 -3> = 1728/1715, the orwellisma.
These temper out |6 3 -1 -3> = 1728/1715, the orwellisma.


Temperaments not discussed here include [[Meantone family|cynder]], [[Archytas clan|superpyth]], [[Starling temperaments|myna]], [[Jubilismic clan|doublewide]], [[Bug family|beep]], and [[Semicomma family|orwell]].
Temperaments not discussed here include [[Meantone family|cynder]], [[Archytas clan|superpyth]], [[Starling temperaments|myna]], [[Hemifamity temperaments|buzzard]], [[Jubilismic clan|doublewide]], [[Bug family|beep]], and [[Semicomma family|orwell]].


=Secant=
=Secant=
Line 13: Line 13:
Wedgie: <<14 30 4 15 -33 -75|
Wedgie: <<14 30 4 15 -33 -75|


EDOs: 26, 58, 84, 142, 368cd
EDOs: {{EDOs|26, 58, 84, 142, 368cd}}


Badness: 0.0953
Badness: 0.0953
Line 24: Line 24:
Map: [<2 1 0 5 6|, <0 7 15 2 3|]
Map: [<2 1 0 5 6|, <0 7 15 2 3|]


EDOs: 26, 58, 142e, 200cde
EDOs: {{EDOs|26, 58, 142e, 200cde}}


Badness: 0.0464
Badness: 0.0464
Line 35: Line 35:
Map: [<2 1 0 5 6 4|, <0 7 15 2 3 11|]
Map: [<2 1 0 5 6 4|, <0 7 15 2 3 11|]


EDOs: 26, 58, 84, 142ef
EDOs: {{EDOs|26, 58, 84, 142ef}}


Badness: 0.0250
Badness: 0.0250
Line 48: Line 48:
Wedgie: <<16 -3 17 -42 -18 48||
Wedgie: <<16 -3 17 -42 -18 48||


EDOs: 9, 49, 58, 165cd, 223bcd
EDOs: {{EDOs|9, 49, 58, 165cd, 223bcd}}


Badness: 0.1171
Badness: 0.1171
Line 59: Line 59:
Map: [<1 14 0 16 12|, <0 -16 3 -17 -11|]
Map: [<1 14 0 16 12|, <0 -16 3 -17 -11|]


EDOs: 9, 49, 58, 165cde
EDOs: {{EDOs|9, 49, 58, 165cde}}


Badness: 0.0407
Badness: 0.0407
Line 70: Line 70:
Map: [<1 14 0 16 12 20|, <0 -16 3 -17 -11 -21|]
Map: [<1 14 0 16 12 20|, <0 -16 3 -17 -11 -21|]


EDOs: 9, 49f, 58
EDOs: {{EDOs|9, 49f, 58}}


Badness: 0.0237
Badness: 0.0237
Line 81: Line 81:
Map: [<1 2 3|, <0 -11 -18|]
Map: [<1 2 3|, <0 -11 -18|]


EDOs: 26, 27, 53, 239, 292, 345, 398, 451
EDOs: {{EDOs|26, 27, 53, 239, 292, 345, 398, 451}}


Badness: 0.1172
Badness: 0.1172
Line 94: Line 94:
Wedgie: <<11 18 5 3 -23 -39||
Wedgie: <<11 18 5 3 -23 -39||


EDOs: 26, 27, 53, 80, 133d, 186d, 319d
EDOs: {{EDOs|26, 27, 53, 80, 133d, 186d, 319d}}


Badness: 0.0426
Badness: 0.0426
Line 105: Line 105:
Map: [<1 2 3 3 5|, <0 -11 -18 -5 -41|]
Map: [<1 2 3 3 5|, <0 -11 -18 -5 -41|]


EDOs: 53, 80, 213d, 293bcd
EDOs: {{EDOs|53, 80, 213d, 293bcd}}


Badness: 0.034
Badness: 0.034
Line 116: Line 116:
Map: [<1 2 3 3 5 4|, <0 -11 -18 -5 -41 -8|]
Map: [<1 2 3 3 5 4|, <0 -11 -18 -5 -41 -8|]


EDOs: 53, 80, 133d, 213d
EDOs: {{EDOs|53, 80, 133d, 213d}}


Badness: 0.0239
Badness: 0.0239
Line 127: Line 127:
Map: [<1 2 3 3 4|, <0 -11 -18 -5 -14|]
Map: [<1 2 3 3 4|, <0 -11 -18 -5 -14|]


EDOs: 26, 27e, 53e, 80e
EDOs: {{EDOs|26, 27e, 53e, 80e}}


Badness: 0.0418
Badness: 0.0418
Line 138: Line 138:
Map: [<1 2 3 3 4 4|, <0 -11 -18 -5 -14 -8|]
Map: [<1 2 3 3 4 4|, <0 -11 -18 -5 -14 -8|]


EDOs: 26, 27e, 53e
EDOs: {{EDOs|26, 27e, 53e}}


Badness: 0.0277
Badness: 0.0277
Line 149: Line 149:
Map: [<1 2 3 3 3|, <0 -11 -18 -5 12|]
Map: [<1 2 3 3 3|, <0 -11 -18 -5 12|]


EDOs: 26, 53
EDOs: {{EDOs|26, 53}}


Badness: 0.0533
Badness: 0.0533
Line 160: Line 160:
Map: [<1 2 3 3 3 4|, <0 -11 -18 -5 12 -8|]
Map: [<1 2 3 3 3 4|, <0 -11 -18 -5 12 -8|]


EDOs: 26, 53, 132e, 185cdef, 238cdef
EDOs: {{EDOs|26, 53, 132e, 185cdef, 238cdef}}


Badness: 0.0288
Badness: 0.0288
Line 171: Line 171:
Map: [<1 3 -3|, <0 -4 15|]
Map: [<1 3 -3|, <0 -4 15|]


EDOs: 14, 17, 31, 79, 110, 361bc
EDOs: {{EDOs|14, 17, 31, 79, 110, 361bc}}


Badness: 0.7234
Badness: 0.7234
Line 184: Line 184:
Wedgie: <<4 -15 9 -33 3 63||
Wedgie: <<4 -15 9 -33 3 63||


EDOs: 14, 17, 31, 110, 141, 172b, 375bc
EDOs: {{EDOs|14, 17, 31, 110, 141, 172b, 375bc}}


Badness: 0.0938
Badness: 0.0938
Line 195: Line 195:
Map: [<1 3 -3 6 7|, <0 -4 15 -9 -10|]
Map: [<1 3 -3 6 7|, <0 -4 15 -9 -10|]


EDOs: 14, 17, 31, 79, 110e, 141e
EDOs: {{EDOs|14, 17, 31, 79, 110e, 141e}}


Badness: 0.0396
Badness: 0.0396
Line 206: Line 206:
Map: [<1 3 -3 6 7 3|, <0 -4 15 -9 -10 2|]
Map: [<1 3 -3 6 7 3|, <0 -4 15 -9 -10 2|]


EDOs: 14, 17, 31, 79f, 110ef, 141ef
EDOs: {{EDOs|14, 17, 31, 79f, 110ef, 141ef}}


Badness: 0.0374
Badness: 0.0374
Line 217: Line 217:
Map: [<1 2 3|, <0 -13 -21|]
Map: [<1 2 3|, <0 -13 -21|]


EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc
EDOs: {{EDOs|31, 156c, 187c, 218bc, 249bc, 280bc}}


Badness: 1.3447
Badness: 1.3447
Line 230: Line 230:
Wedgie: <<13 21 6 3 -27 -45||
Wedgie: <<13 21 6 3 -27 -45||


EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc
EDOs: {{EDOs|31, 156c, 187c, 218bc, 249bc, 280bc}}


Badness: 0.1073
Badness: 0.1073
Line 241: Line 241:
Map: [<1 2 3 3 4|, <0 -13 -21 -6 -17|]
Map: [<1 2 3 3 4|, <0 -13 -21 -6 -17|]


EDOs: 31, 156ce, 187ce, 218bce, 249bce
EDOs: {{EDOs|31, 156ce, 187ce, 218bce, 249bce}}


Badness: 0.0442
Badness: 0.0442
Line 252: Line 252:
Map: [<1 2 3 3 4 4|, <0 -13 -21 -6 -17 -9|]
Map: [<1 2 3 3 4 4|, <0 -13 -21 -6 -17 -9|]


EDOs: 31, 94cf, 125cf
EDOs: {{EDOs|31, 94cf, 125cf}}


Badness: 0.0381
Badness: 0.0381
[[Category:Temperament]]

Revision as of 10:26, 14 March 2021

These temper out |6 3 -1 -3> = 1728/1715, the orwellisma.

Temperaments not discussed here include cynder, superpyth, myna, buzzard, doublewide, beep, and orwell.

Secant

Commas: 1728/1715, 177147/175000

POTE generator: ~10/9 = 185.885

Map: [<2 1 0 5|, <0 7 15 2|]

Wedgie: <<14 30 4 15 -33 -75|

EDOs: 26, 58, 84, 142, 368cd

Badness: 0.0953

11-limit

Commas: 441/440, 1344/1331, 1728/1715

POTE genertor: ~10/9 = 185.962

Map: [<2 1 0 5 6|, <0 7 15 2 3|]

EDOs: 26, 58, 142e, 200cde

Badness: 0.0464

13-limit

Commas: 144/143, 351/350, 364/363, 441/440

POTE generator: ~10/9 = 185.955

Map: [<2 1 0 5 6 4|, <0 7 15 2 3 11|]

EDOs: 26, 58, 84, 142ef

Badness: 0.0250

Infraorwell

Commas: 1728/1715, 28672/28125

POTE generator: ~7/6 = 269.032

Map: [<1 14 0 16|, <0 -16 3 -17|]

Wedgie: <<16 -3 17 -42 -18 48||

EDOs: 9, 49, 58, 165cd, 223bcd

Badness: 0.1171

11-limit

Commas: 176/175, 540/539, 1344/1331

POTE generator: ~7/6 = 269.036

Map: [<1 14 0 16 12|, <0 -16 3 -17 -11|]

EDOs: 9, 49, 58, 165cde

Badness: 0.0407

13-limit

Commas: 144/143, 176/175, 196/195, 364/363

POTE generator: ~7/6 = 269.021

Map: [<1 14 0 16 12 20|, <0 -16 3 -17 -11 -21|]

EDOs: 9, 49f, 58

Badness: 0.0237

Quartonic

Comma: 390625000/387420489

POTE generator: ~250/243 = 45.233

Map: [<1 2 3|, <0 -11 -18|]

EDOs: 26, 27, 53, 239, 292, 345, 398, 451

Badness: 0.1172

7-limit

Commas: 1728/1715, 4000/3969

POTE generator: ~36/35 = 45.139

Map: [<1 2 3 3|, <0 -11 -18 -5|]

Wedgie: <<11 18 5 3 -23 -39||

EDOs: 26, 27, 53, 80, 133d, 186d, 319d

Badness: 0.0426

11-limit

Commas: 176/175, 540/539, 2200/2187

POTE generator: ~36/35 = 45.041

Map: [<1 2 3 3 5|, <0 -11 -18 -5 -41|]

EDOs: 53, 80, 213d, 293bcd

Badness: 0.034

13-limit

Commas: 169/168, 176/175, 325/324, 540/539

POTE generator: ~36/35 = 45.080

Map: [<1 2 3 3 5 4|, <0 -11 -18 -5 -41 -8|]

EDOs: 53, 80, 133d, 213d

Badness: 0.0239

Quarto

Commmas: 100/99, 245/242, 864/847

POTE generator: ~36/35 = 45.132

Map: [<1 2 3 3 4|, <0 -11 -18 -5 -14|]

EDOs: 26, 27e, 53e, 80e

Badness: 0.0418

13-limit

Commas: 78/77, 100/99, 144/143, 245/242

POTE generator: ~36/35 = 45.205

Map: [<1 2 3 3 4 4|, <0 -11 -18 -5 -14 -8|]

EDOs: 26, 27e, 53e

Badness: 0.0277

Quartz

Commas: 99/98, 385/384, 4000/3969

POTE generator: ~36/35 = 45.385

Map: [<1 2 3 3 3|, <0 -11 -18 -5 12|]

EDOs: 26, 53

Badness: 0.0533

13-limit

Commas: 99/98, 169/168, 275/273, 385/384

POTE generator: ~36/35 = 45.387

Map: [<1 2 3 3 3 4|, <0 -11 -18 -5 12 -8|]

EDOs: 26, 53, 132e, 185cdef, 238cdef

Badness: 0.0288

Sentinel

Comma: 8968066875/8589934592

POTE generator: ~512/405 = 425.474

Map: [<1 3 -3|, <0 -4 15|]

EDOs: 14, 17, 31, 79, 110, 361bc

Badness: 0.7234

7-limit

Commas: 1728/1715, 3645/3584

POTE generator: ~9/7 = 425.596

Map: [<1 3 -3 6|, <0 -4 15 -9|]

Wedgie: <<4 -15 9 -33 3 63||

EDOs: 14, 17, 31, 110, 141, 172b, 375bc

Badness: 0.0938

11-limit

Commas: 99/98, 243/242, 385/384

POTE generator: ~9/7 = 425.550

Map: [<1 3 -3 6 7|, <0 -4 15 -9 -10|]

EDOs: 14, 17, 31, 79, 110e, 141e

Badness: 0.0396

13-limit

Commas: 99/98, 105/104, 144/143, 243/242

POTE generator: ~9/7 = 425.501

Map: [<1 3 -3 6 7 3|, <0 -4 15 -9 -10 2|]

EDOs: 14, 17, 31, 79f, 110ef, 141ef

Badness: 0.0374

Diesic

Comma: 10460353203/9765625000

POTE generator: ~6561/6250 = 38.571

Map: [<1 2 3|, <0 -13 -21|]

EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 1.3447

7-limit

Commas: 1728/1715, 5103/5000

POTE generator: ~36/35 = 38.567

Map: [<1 2 3 3|, <0 -13 -21 -6|]

Wedgie: <<13 21 6 3 -27 -45||

EDOs: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 0.1073

11-limit

Commas: 121/120, 441/440, 891/875

POTE generator: ~36/35 = 38.565

Map: [<1 2 3 3 4|, <0 -13 -21 -6 -17|]

EDOs: 31, 156ce, 187ce, 218bce, 249bce

Badness: 0.0442

13-limit

Commas: 66/65, 121/120, 343/338, 441/440

POTE generator: ~36/35 = 38.444

Map: [<1 2 3 3 4 4|, <0 -13 -21 -6 -17 -9|]

EDOs: 31, 94cf, 125cf

Badness: 0.0381

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