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
Proposed on 21 March 2021
Decic (10 & 50)
7-limit
Commas: 225/224, 16807/16384
POTE generator: ~3/2 = 698.696
Map: [<10 0 39 28|, <0 1 -1 0|]
EDOs: 10, 50, 60, 110d, 170cdd
Badness: 0.089135
11-limit
Commas: 225/224, 385/384, 3087/3025
POTE generator: ~3/2 = 696.791
Map: [<10 0 39 28 3|, <0 1 -1 0 2|]
EDOs: 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde
Badness: 0.063900
13-limit
Commas: 105/104, 144/143, 196/195, 2200/2197
POTE generator: ~3/2 = 696.993
Map: [<10 0 39 28 3 37|, <0 1 -1 0 2 0|]
EDOs: 10, 50, 160bcdd, 210bcddde, 260bbcddde
Badness: 0.036880
17-limit
Commas: 105/104, 144/143, 170/169, 196/195, 221/220
POTE generator: ~3/2 = 697.085
Map: [<10 0 39 28 3 37 25|, <0 1 -1 0 2 0 1|]
EDOs: 10, 50, 160bcddg, 210bcdddegg
Badness: 0.025064
Proposed on 22 March 2021
Cloudtone (5 & 50)
7-limit
Commas: 81/80, 16807/16384
POTE generator: ~3/2 = 695.720
Map: [<5 0 -20 14|, <0 1 4 0|]
EDOs: 5, 45, 50, 55
Badness: 0.102256
11-limit
Commas: 81/80, 385/384, 2401/2376
POTE generator: ~3/2 = 696.536
Map: [<5 0 -20 14 41|, <0 1 4 0 -3|]
EDOs: 5, 50, 55, 105d, 155bdd, 205bddd
Badness: 0.070378
13-limit
Commas: 81/80, 105/104, 144/143, 2401/2376
POTE generator: ~3/2 = 696.162
Map: [<5 0 -20 14 41 -21|, <0 1 4 0 -3 5|]
EDOs: 5, 50, 55
Badness: 0.048829
Proposed on 3 April 2021
Pentacloud (5 & 60)
7-limit
Commas: 245/243, 16807/16384
POTE generator: ~3/2 = 700.548
Map: [<5 0 -28 14|, <0 1 5 0|]
EDOs: 5, 60, 65, 125d, 185cdd
Badness: 0.120942
11-limit
Commas: 245/243, 385/384, 3087/3025
POTE generator: ~3/2 = 701.377
Map: [<5 0 -28 14 49|, <0 1 5 0 -4|]
EDOs: 5, 60, 65
Badness: 0.093248
13-limit
Commas: 105/104, 144/143, 245/243, 3087/3025
POTE generator: ~3/2 = 700.996
Map: [<5 0 -28 14 49 -29|, <0 1 5 0 -4 6|]
EDOs: 5, 60, 65, 125de, 190ddef
Badness: 0.067549
Hemipental (125 & 130)
7-limit
Commas: 19683/19600, 589824/588245
POTE generator: ~8/7 = 230.654
Map: [<5 8 12 14|, <0 -2 -10 1|]
EDOs: 5, 125, 130, 255, 385
Badness: 0.104163
11-limit
Commas: 540/539, 8019/8000, 180224/180075
POTE generator: ~8/7 = 230.634
Map: [<5 8 12 14 18|, <0 -2 -10 1 -18|]
EDOs: 5e, 125, 130, 255, 385, 640, 1025b
Badness: 0.047624
13-limit
Commas: 540/539, 1575/1573, 4096/4095, 8019/8000
POTE generator: ~8/7 = 230.668
Map: [<5 8 12 14 18 18|, <0 -2 -10 1 -18 13|]
EDOs: 5ef, 125, 130, 255, 385, 515, 900ef
Badness: 0.041043
Sengasec (10 & 55)
7-limit
Commas: 686/675, 16807/16384
POTE generator: ~16/15 = 111.113
Map: [<5 7 13 14|, <0 2 -3 0|]
EDOs: 10, 55, 65, 140dd, 205ddd, 270ddd
Badness: 0.156259
11-limit
Commas: 243/242, 385/384, 686/675
POTE generator: ~16/15 = 110.659
Map: [<5 7 13 14 15|, <0 2 -3 0 5|]
EDOs: 10, 55, 65
Badness: 0.081607
Proposed on 4 April 2021
Qinto (10 & 75)
11-limit
Commas: 225/224, 385/384, 332750/321489
POTE generator: ~15/14 = 112.448
Map: [<5 7 13 15 14|, <0 2 -3 -2 7|]
EDOs: 10, 75, 160cde
Badness: 0.127732
Proposed on 10 April 2021
Monzism (53 & 559)
7-limit
Commas: 4375/4374, |-55 30 2 1>
POTE generator: ~310078125/268435456 = 249.0207
Map: [<1 2 10 -25|, <0 -2 -37 134|]
EDOs: 53, 559, 612, 1277, 1889
Badness: 0.046569
11-limit
Commas: 4375/4374, 41503/41472, 184549376/184528125
POTE generator: ~231/200 = 249.0193
Map: [<1 2 10 -25 46|, <0 -2 -37 134 -205|]
EDOs: 53, 559, 612
Badness: 0.057083
Proposed on 18 April 2021
Houborizic (53 & 113)
7-limit
Commas: 225/224, 1250000/1240029
POTE generator: ~243/200 = 339.763
Map: [<1 3 6 13|, <0 -5 -13 -36|]
EDOs: 7d, 46d, 53, 113, 166
Badness: 0.066638
11-limit
Commas: 225/224, 385/384, 1250000/1240029
POTE generator: ~243/200 = 339.763
Map: [<1 3 6 13 -9|, <0 -5 -13 -36 44|]
EDOs: 53, 113, 166
Badness: 0.067891
Houbor (7d & 53)
11-limit
Commas: 121/120, 225/224, 2200/2187
POTE generator: ~11/9 = 339.814
Map: [<1 3 6 13 6|, <0 -5 -13 -36 -9|]
EDOs: 7d, 46d, 53, 60e, 113e
Badness: 0.045232
Gamity (46 & 113)
7-limit
Commas: 1029/1024, 1071875/1062882
POTE generator: ~189/160 = 286.787
Map: [<1 -2 -7 4|, <0 15 39 -5|]
EDOs: 46, 113, 159
Badness: 0.125733
11-limit
Commas: 385/384, 441/440, 1071875/1062882
POTE generator: ~33/28 = 286.797
Map: [<1 -2 -7 4 8|, <0 15 39 -5 -19|]
EDOs: 46, 113, 159
Badness: 0.051111
Proposed on 19 April 2021
Familia (113 & 152)
7-limit
Commas: 16875/16807, 1600000/1594323
POTE generator: ~11907/10000 = 307.941
Map: [<1 8 19 20|, <0 -25 -65 -67|]
EDOs: 113, 152, 265, 417, 986d
Badness: 0.144551
11-limit
Commas: 540/539, 1375/1372, 1600000/1594323
POTE generator: ~3200/2673 = 307.906
Map: [<1 8 19 20 5|, <0 -25 -65 -67 -6|]
EDOs: 113, 152, 417, 569de, 721de
Badness: 0.051740
Proposed on 25 April 2021
Sabric (53 & 190)
7-limit
Commas: 4375/4374, 2109375/2097152
POTE generator: ~75/64 = 271.607
Map: [<1 0 3 -11|, <0 7 -3 61|]
EDOs: 53, 137d, 190, 243
Badness: 0.088355
Quadrawell (31 & 212)
7-limit
Commas: 2401/2400, 2109375/2097152
POTE generator: ~8/7 = 232.094
Map: [<1 7 0 3|, <0 -28 12 -1|]
EDOs: 31, 119, 150, 181, 212, 243, 698cd, 941cd
Badness: 0.075754
11-limit
Commas: 385/384, 1375/1372, 14641/14580
POTE generator: ~8/7 = 232.083
Map: [<1 7 0 3 11|, <0 -28 12 -1 -39|]
EDOs: 31, 119, 150, 181, 212, 455ee, 667cdee
Badness: 0.036493
Proposed on 26 April 2021
Rainwell (31 & 265)
7-limit
Commas: 16875/16807, 2100875/2097152
POTE generator: ~2625/2048 = 425.673
Map: [<1 14 -3 6|, <0 -35 15 -9|]
EDOs: 31, 172, 203, 234, 265, 296
Badness: 0.143488
11-limit
Commas: 540/539, 1375/1372, 2100875/2097152
POTE generator: ~2625/2048 = 425.679
Map: [<1 14 -3 6 29|, <0 -35 15 -9 -72|]
EDOs: 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc
Badness: 0.052774
Commas which this user proposed names
This user proposed new names for following commas.
Proposed on 4 April 2021
- hewuermera: 589824/588245, satribiru-agu
- triwellisma: 235298/234375, tribizo-asepgu (name revised on 24 April 2021)
Proposed on 25 April 2021
- quadrawellisma: 67528125/67108864, lalaquadzo-aquinyo