User:Xenllium

Xenllium joined Xenharmonic Wiki on 15 November 2018. The name "Xenllium" is a portmanteau of "Xenharmonic" and "Trillium".

Rank two temperaments which this user proposed names

This user proposed new names for following temperaments.

Proposed on 14 March 2019

Icositritonic (46 & 161)
7-limit
Commas: 6144/6125, 9920232/9765625

POTE generator: ~64/63 = 29.3586

Map: [<23 37 54 64|, <0 -1 -1 1|]

EDOs: 23, 46, 69, 115, 161, 207

Badness: 0.1966

11-limit
Commas: 441/440, 6144/6125, 35937/35840

POTE generator: ~64/63 = 29.3980

Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]

EDOs: 23, 46, 69, 115, 161, 207

Badness: 0.06461

13-limit
Commas: 351/350, 441/440, 847/845, 3584/3575

POTE generator: ~64/63 = 29.2830

Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]

EDOs: 46, 115, 161, 207

Badness: 0.04048

17-limit
Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088

POTE generator: ~64/63 = 29.2800

Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]

EDOs: 46, 115, 161, 207

Badness: 0.02468

19-limit
Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845

POTE generator: ~64/63 = 29.3760

Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]

EDOs: 46, 115, 161, 207

Badness: 0.02158

23-limit
Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845

POTE generator: ~64/63 = 29.3471

Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]

EDOs: 46, 115, 161, 207

Badness: 0.01774

Tetracontahenatonic (41 & 410)
7-limit
Commas: 2401/2400, 52613349376/52301766015

POTE generator: ~8/7 = 231.0446

Map: [<41 65 95 115|, <0 0 2 1|]

EDOs: 41, 328, 369, 410, 451, 492

Badness: 0.1346

11-limit
Commas: 2401/2400, 59290/59049, 131072/130977

POTE generator: ~8/7 = 231.3847

Map: [<41 65 95 115 142|, <0 0 2 1 -2|]

EDOs: 41, 328e, 369e, 410, 451, 492

Badness: 0.1002

13-limit
Commas: 2080/2079, 2401/2400, 4096/4095, 59290/59049

POTE generator: ~8/7 = 231.3787

Map: [<41 65 95 115 142 152|, <0 0 2 1 -2 -3|]

EDOs: 41, 410, 451, 492

Badness: 0.06051

Tetracontahenic (41 & 328)
Commas: 2401/2400, 16384/16335, 19712/19683

POTE generator: ~8/7 = 230.8276

Map: [<41 65 95 115 142|, <0 0 2 1 -1|]

EDOs: 41, 328, 369, 410e

Badness: 0.0644

Hectaheptacontahenatonic (171 & 17442)
7-limit
Commas: |2 -9 21 -13>, |10 -54 12 17>

POTE generator: ~7/5 = 582.5244

Map: [<171 271 397 480|, <0 3 5 6|]

EDOs: 171, 342, 513, 684, 855, 1026, 1197, 1368, 16416, 16587, 16758, 16929, 17100, 17271, 17442, 17613, 17784, 17955, 18126, 18297, 18468, 18639, 18810

Badness: 0.2863

Proposed on 15 March 2019

Tetracontatroid (258 & 301)
5-limit
Comma: |168 -43 -43>

POTE generator: ~|-68 18 17> = 4.3194

Map: [<43 68 100|, <0 1 -1|]

EDOs: 43, 258, 301, 559, 817, 860, 1376, 1935

7-limit
Commas: 5250987/5242880, 2202927104/2197265625

POTE generator: ~703125/702464 = 4.1632

Map: [<43 68 100 121|, <0 1 -1 -2|]

EDOs: 43, 258, 301, 344, 559, 860, 1161

Badness: 0.2300

11-limit
Commas: 41503/41472, 172032/171875, 1240029/1239040

POTE generator: ~540/539 = 4.1828

Map: [<43 68 100 121 148|, <0 1 -1 -2 5|]

EDOs: 43e, 258, 301, 559, 860, 1161

Badness: 0.1111

13-limit
Commas: 2200/2197, 4096/4095, 21168/21125, 39366/39325

POTE generator: ~540/539 = 4.1765

Map: [<43 68 100 121 148 159|, <0 1 -1 -2 5 1|]

EDOs: 43e, 258, 301, 559, 860f

Badness: 0.0714

Tetracontaheptatonic (94 & 705)
7-limit
Commas: 242137805625/240518168576, 247669456896/247165842875

POTE generator: ~3/2 = 701.394

Map: [<47 75 107 133|, <0 -1 4 -2|]

EDOs: 94, 611, 705, 799, 893

11-limit
Commas: 24057/24010, 1366875/1362944, 16808715/16777216

POTE generator: ~3/2 = 701.406

Map: [<47 75 107 133 161|, <0 -1 4 -2 3|]

EDOs: 94, 611, 705, 799, 893

Badness: 0.2808

13-limit
Commas: 1575/1573, 24057/24010, 41472/41405, 916839/913952

POTE generator: ~3/2 = 701.368

Map: [<47 75 107 133 161 175|, <0 -1 4 -2 3 -2|]

EDOs: 94, 611, 705, 799, 893f

Badness: 0.1443

Proposed on 24 March 2019

Tetracontahexoid (46 & 414)
7-limit
Commas: 4375/4374, |-51 8 2 12>

POTE generator: ~3/2 = 701.6074

Map: [<46 73 107 129|, <0 -1 -2 1|]

EDOs: 46, 368, 414, 460

Badness: 0.3085

11-limit
Commas: 3025/3024, 9801/9800, 134775333/134217728

POTE generator: ~3/2 = 701.5951

Map: [<46 73 107 129 159|, <0 -1 -2 1 1|]

EDOs: 46, 368, 414, 460

Badness: 0.07378

13-limit
Commas: 3025/3024, 4225/4224, 4375/4374, 26411/26364

POTE generator: ~3/2 = 701.6419

Map: [<46 73 107 129 159 170|, <0 -1 -2 1 1 2|]

EDOs: 46, 368, 414, 460

Badness: 0.04075

17-limit
Commas: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224

POTE generator: ~3/2 = 701.6425

Map: [<46 73 107 129 159 170 188|, <0 -1 -2 1 1 2 0|]

EDOs: 46, 368, 414, 460

Badness: 0.02244

Proposed on 21 April 2019

Tertiathirds (121 & 270)
5-limit
Comma: |116 3 -52>

POTE generator: ~|-30 1 -17> = 128.886

Map: [<1 -4 2|, <0 52 3|]

EDOs: 121, 149, 270, 391, 419, 661, 689, 959

7-limit
Commas: 420175/419904, 29360128/29296875

POTE generator: ~3375/3136 = 128.888

Map: [<1 -4 2 -6|, <0 52 3 82|]

EDOs: 121, 149, 270, 391, 419, 661, 689, 959

Badness: 0.093005

11-limit
Commas: 3025/3024, 5632/5625, 117649/117612

POTE generator: ~264/245 = 128.890

Map: [<1 -4 2 -6 -9|, <0 52 3 82 116|]

EDOs: 121, 149, 270, 391, 661, 931

Badness: 0.033322

13-limit
Commas: 676/675, 1716/1715, 3025/3024, 4225/4224

POTE generator: ~14/13 = 128.890

Map: [<1 -4 2 -6 -9 -5|, <0 52 3 82 116 81|]

EDOs: 121, 149, 270, 391, 661, 931

Badness: 0.019494

17-limit
Commas: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224

POTE generator: ~14/13 = 128.891

Map: [<1 -4 2 -6 -9 -5 -3|, <0 52 3 82 116 81 66|]

EDOs: 121, 149, 270

Badness: 0.019107

Proposed on 22 April 2019

Tertiaschis (94 & 159)
7-limit
Commas: 32805/32768, 1071875/1062882

POTE generator: ~192/175 = 166.019

Map: [<1 2 -1 10|, <0 -3 24 -52|]

EDOs: 65, 94, 159, 253

Badness: 0.211859

11-limit
Commas: 385/384, 4000/3993, 19712/19683

POTE generator: ~11/10 = 166.017

Map: [<1 2 -1 10 0|, <0 -3 24 -52 25|]

EDOs: 65, 94, 159, 253

Badness: 0.061336

13-limit
Commas: 325/324, 385/384, 1575/1573, 10985/10976

POTE generator: ~11/10 = 166.016

Map: [<1 2 -1 10 0 12|, <0 -3 24 -52 25 -60|]

EDOs: 65f, 94, 159, 253

Badness: 0.036700

17-limit
Commas: 325/324, 375/374, 385/384, 595/594, 10985/10976

POTE generator: ~11/10 = 166.012

Map: [<1 2 -1 10 0 12 -2|, <0 -3 24 -52 25 -60 44|]

EDOs: 65f, 94, 159, 253

Badness: 0.026504

Proposed on 13 March 2021

Trident (53 & 229)
7-limit
Commas: 6144/6125, 14348907/14336000

POTE generator: ~4096/2835 = 634.048

Map: [<1 0 -13 25|, <0 3 29 -42|]

EDOs: 53, 176, 229, 282, 511

Badness: 0.101694

11-limit
Commas: 3388/3375, 6144/6125, 8019/8000

POTE generator: ~231/160 = 634.067

Map: [<1 0 -13 25 -33|, <0 3 29 -42 69|]

EDOs: 53, 176, 229

Badness: 0.074272

Trillium (53 & 441)
7-limit
Commas: 4375/4374, 1099511627776/1098337086315

POTE generator: ~23625/16384 = 634.012

Map: [<1 0 -13 53|, <0 3 29 -95|]

EDOs: 53, 441, 494, 935, 1376, 3193, 4569

Badness: 0.030852

11-limit
Commas: 4375/4374, 131072/130977, 759375/758912

POTE generator: ~3888/2695 = 634.009

Map: [<1 0 -13 53 -89|, <0 3 29 -95 175|]

EDOs: 53, 441, 494, 935, 1429

Badness: 0.046758

Pseudotrillium (53 & 388)
11-limit
Commas: 4375/4374, 5632/5625, 4108797/4096000

POTE generator: ~231/160 = 634.019

Map: [<1 0 -13 53 -61|, <0 3 29 -95 122|]

EDOs: 53, 335, 388

Badness: 0.111931

Tritricot (159 & 282)
7-limit
Commas: 250047/250000, 11785390260224/11767896353375

POTE generator: ~100352/91125 = 165.984

Map: [<3 6 19 30|, <0 -3 -29 -52|]

EDOs: 159, 282, 441, 2487, 2928, 3369

Badness: 0.086081

11-limit
Commas: 4000/3993, 166698/166375, 200704/200475

POTE generator: ~11/10 = 165.984

Map: [<3 6 19 30 22|, <0 -3 -29 -52 -28|]

EDOs: 159, 282, 441

Badness: 0.074002