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

Pentacontatritonic (53 & 265)
11-limit
Commas: 540/539, 15625/15552, 32805/32768

POTE generator: ~8/7 = 230.5645

Map: [<53 84 123 149 183|, <0 0 0 -1 2|]

EDOs: 53, 265, 318, 371

Badness: 0.1151

13-limit
Commas: 540/539, 729/728, 4096/4095, 13750/13689

POTE generator: ~8/7 = 230.4000

Map: [<53 84 123 149 183 196|, <0 0 0 -1 2 1|]

EDOs: 53, 265, 318, 371

Badness: 0.06116

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

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

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

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

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

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