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 in March 2019

14 March 2019

Icositritonic (46 & 161)

7-limit
Comma list: 6144/6125, 9920232/9765625
Mapping: [⟨23 37 54 64], ⟨0 -1 -1 1]]
POTE generator: ~64/63 = 29.3586
Vals: 23, 46, 115, 161, 207, 368c
Badness: 0.196622

11-limit
Comma list: 441/440, 6144/6125, 35937/35840
Mapping: [⟨23 37 54 64 79], ⟨0 -1 -1 1 1]]
POTE generator: ~64/63 = 29.3980
Vals: 23, 46, 115, 161, 207, 368c
Badness: 0.064613

13-limit
Comma list: 351/350, 441/440, 847/845, 3584/3575
Mapping: [⟨23 37 54 64 79 84], ⟨0 -1 -1 1 1 2]]
POTE generator: ~64/63 = 29.2830
Vals: 46, 115, 161, 207, 368c
Badness: 0.040484

17-limit
Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
Mapping: [⟨23 37 54 64 79 84 94], ⟨0 -1 -1 1 1 2 0]]
POTE generator: ~64/63 = 29.2800
Vals: 46, 115, 161, 207, 368c
Badness: 0.024676

19-limit
Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
Mapping: [⟨23 37 54 64 79 84 94 96], ⟨0 -1 -1 1 1 2 0 3]]
POTE generator: ~64/63 = 29.3760
Vals: 46, 115, 161, 207, 368c
Badness: 0.021579

23-limit
Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
Mapping: [⟨23 37 54 64 79 84 94 96 104], ⟨0 -1 -1 1 1 2 0 3 0]]
POTE generator: ~64/63 = 29.3471
Vals: 46, 115, 161, 207, 368ci
Badness: 0.017745

Hemicounterpyth (41 & 328)

(Name revised from Tetracontahenatonic (7-limit) and Tetracontahenic (11-limit) on 8 August 2021)
7-limit
Comma list: 2401/2400, 52613349376/52301766015
Mapping: [⟨41 65 95 115], ⟨0 0 2 1]]
POTE generator: ~8/7 = 231.0446
Vals: 41, 328, 369, 779
Badness: 0.134559

11-limit
Comma list: 2401/2400, 16384/16335, 19712/19683
Mapping: [⟨41 65 95 115 142], ⟨0 0 2 1 -1]]
POTE generator: ~8/7 = 230.8276
EDOs: 41, 328, 369
Badness: 0.064400

Hemermapyth (41 & 410)

(Name revised from Tetracontahenatonic on 8 August 2021)
11-limit
Comma list: 2401/2400, 59290/59049, 131072/130977
Mapping: [⟨41 65 95 115 142], ⟨0 0 2 1 -2]]
POTE generator: ~8/7 = 231.3847
EDOs: 41, 328e, 369e, 410, 451, 861e, 2173bcee
Badness: 0.100152

13-limit
Comma list: 2080/2079, 2401/2400, 4096/4095, 59290/59049
Mapping: [⟨41 65 95 115 142 152], ⟨0 0 2 1 -2 -3]]
POTE generator: ~8/7 = 231.3787
EDOs: 41, 410, 451, 861e, 2173bcee
Badness: 0.060512

Pentacontatritonic (53 & 265)

11-limit
Comma list: 540/539, 15625/15552, 32805/32768
Mapping: [⟨53 84 123 149 183], ⟨0 0 0 -1 2]]
POTE generator: ~8/7 = 230.5645
Vals: 53, 159e, 212e, 265, 318, 583c
Badness: 0.115066

13-limit
Comma list: 540/539, 729/728, 4096/4095, 13750/13689
Mapping: [⟨53 84 123 149 183 196], ⟨0 0 0 -1 2 1]]
POTE generator: ~8/7 = 230.4000
Vals: 53, 159ef, 212ef, 265, 318, 583cf
Badness: 0.061158

Hectaheptacontahenatonic (171 & 17442)

7-limit
Comma list: [2 -9 21 -13⟩, [10 -54 12 17⟩
Mapping: [⟨171 271 397 480], ⟨0 3 5 6]]
POTE generator: ~7/5 = 582.5244
Vals: 171, 16416, 16587, 16758, 16929, 17100, 17271, 17442, 17613, 52668, 70281, 87894c, 158175bcd
Badness: 0.286322

15 March 2019

Meridic (258 & 301)

(Name revised from Tetracontatroid on 1 May 2021)
5-limit
Comma: [168 -43 -43⟩
Mapping: [⟨43 68 100], ⟨0 1 -1]]
POTE generator: ~[-68 18 17⟩ = 4.3194
Vals: 43, 172, 215, 258, 559, 1935, 2494, 3053, 3612
Badness: 1.061246

7-limit
Comma list: 5250987/5242880, 2202927104/2197265625
Mapping: [⟨43 68 100 121], ⟨0 1 -1 -2]]
POTE generator: ~703125/702464 = 4.1632
Vals: 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd
Badness: 0.230038

11-limit
Comma list: 41503/41472, 172032/171875, 1240029/1239040
Mapping: [⟨43 68 100 121 148], ⟨0 1 -1 -2 5]]
POTE generator: ~540/539 = 4.1828
Vals: 258, 301, 559, 860
Badness: 0.111149

13-limit
Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325
Mapping: [⟨43 68 100 121 148 159], ⟨0 1 -1 -2 5 1]]
POTE generator: ~540/539 = 4.1765
Vals: 258, 301, 559, 860f
Badness: 0.071435

17-limit
Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011
Mapping: [⟨43 68 100 121 148 159 175], ⟨0 1 -1 -2 5 1 5]]
POTE generator: ~540/539 = 4.1974
Vals: 258, 301, 559, 860f
Badness: 0.047292

Tetracontaheptatonic (94 & 705)

7-limit
Comma list: 242137805625/240518168576, 247669456896/247165842875
Mapping: [⟨47 75 107 133], ⟨0 -1 4 -2]]
POTE generator: ~3/2 = 701.394
Vals: 94, 611, 705, 799
Badness: 1.619046

11-limit
Comma list: 24057/24010, 1366875/1362944, 16808715/16777216
Mapping: [⟨47 75 107 133 161], ⟨0 -1 4 -2 3]]
POTE generator: ~3/2 = 701.406
Vals: 94, 611, 705, 799, 893, 1692bc, 2491bbc
Badness: 0.280814

13-limit
Comma list: 1575/1573, 24057/24010, 41472/41405, 916839/913952
Mapping: [⟨47 75 107 133 161 175], ⟨0 -1 4 -2 3 -2]]
POTE generator: ~3/2 = 701.368
Vals: 94, 611, 705, 799
Badness: 0.144341

24 March 2019

Palladium (46 & 414)

(Name revised from Tetracontahexoid on 29 April 2021)
7-limit
Comma list: 4375/4374, [-51 8 2 12⟩
Mapping: [⟨46 73 107 129], ⟨0 -1 -2 1]]
POTE generator: ~3/2 = 701.6074
Vals: 46, 368, 414, 460, 874d
Badness: 0.308505

11-limit
Comma list: 3025/3024, 9801/9800, 134775333/134217728
Mapping: [⟨46 73 107 129 159], ⟨0 -1 -2 1 1]]
POTE generator: ~3/2 = 701.5951
Vals: 46, 368, 414, 460, 874de
Badness: 0.073783

13-limit
Comma list: 3025/3024, 4225/4224, 4375/4374, 26411/26364
Mapping: [⟨46 73 107 129 159 170], ⟨0 -1 -2 1 1 2]]
POTE generator: ~3/2 = 701.6419
Vals: 46, 368, 414, 460, 874de, 1334de
Badness: 0.040751

17-limit
Comma list: 833/832, 1089/1088, 1225/1224, 1701/1700, 4225/4224
Mapping: [⟨46 73 107 129 159 170 188], ⟨0 -1 -2 1 1 2 0]]
POTE generator: ~3/2 = 701.6425
Vals: 46, 368, 414, 460, 874de, 1334deg
Badness: 0.022441

Proposed in April 2019

1 April 2019

Septisemitonic (128 & 270)

7-limit
Comma list: 102760448/102515625, 200120949/200000000
Mapping: [⟨2 5 0 -1], ⟨0 -13 33 47]]
POTE generator: ~21/20 = 84.446
Vals: 128, 142, 270
Badness: 0.166111

11-limit
Comma list: 3025/3024, 131072/130977, 422576/421875
Mapping: [⟨2 5 0 -1 11], ⟨0 -13 33 47 -29]]
POTE generator: ~21/20 = 84.443
Vals: 128, 142, 270
Badness: 0.058273

13-limit
Comma list: 2080/2079, 3025/3024, 4096/4095, 405769/405000
Mapping: [⟨2 5 0 -1 11 15], ⟨0 -13 33 47 -29 -54]]
POTE generator: ~21/20 = 84.440
Vals: 128, 142, 270
Badness: 0.037612

21 April 2019

Tertiathirds (121 & 270)

7-limit
Comma list: 420175/419904, 29360128/29296875
Mapping: [⟨1 -4 2 -6], ⟨0 52 3 82]]
POTE generator: ~3375/3136 = 128.888
Vals: 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc
Badness: 0.093005

11-limit
Comma list: 3025/3024, 5632/5625, 117649/117612
Mapping: [⟨1 -4 2 -6 -9], ⟨0 52 3 82 116]]
POTE generator: ~264/245 = 128.890
Vals: 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd
Badness: 0.033322

13-limit
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Mapping: [⟨1 -4 2 -6 -9 -5], ⟨0 52 3 82 116 81]]
POTE generator: ~14/13 = 128.890
Vals: 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff
Badness: 0.019494

17-limit
Comma list: 676/675, 715/714, 936/935, 1225/1224, 4225/4224
Mapping: [⟨1 -4 2 -6 -9 -5 -3], ⟨0 52 3 82 116 81 66]]
POTE generator: ~14/13 = 128.891
Vals: 121, 149, 270
Badness: 0.019107

19-limit
Comma list: 676/675, 715/714, 936/935, 1225/1224, 1540/1539, 2128/2125
Mapping: [⟨1 -4 2 -6 -9 -5 -3 5], ⟨0 52 3 82 116 81 66 -7]]
POTE generator: ~14/13 = 128.890
Vals: 121, 149, 270
Badness: 0.015621

22 April 2019

Tertiaschis (94 & 159)

7-limit
Comma list: 32805/32768, 1071875/1062882
Mapping: [⟨1 2 -1 10], ⟨0 -3 24 -52]]
POTE generator: ~192/175 = 166.019
Vals: 65, 94, 159, 253, 412cd
Badness: 0.211859

11-limit
Comma list: 385/384, 4000/3993, 19712/19683
Mapping: [⟨1 2 -1 10 0], ⟨0 -3 24 -52 25]]
POTE generator: ~11/10 = 166.017
Vals: 65, 94, 159, 253, 412cd
Badness: 0.061336

13-limit
Comma list: 325/324, 385/384, 1575/1573, 10985/10976
Mapping: [⟨1 2 -1 10 0 12], ⟨0 -3 24 -52 25 -60]]
POTE generator: ~11/10 = 166.016
Vals: 65f, 94, 159, 253, 412cdf, 665ccdef
Badness: 0.036700

17-limit
Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
Mapping: [⟨1 2 -1 10 0 12 -2], ⟨0 -3 24 -52 25 -60 44]]
POTE generator: ~11/10 = 166.012
Vals: 65f, 94, 159, 253
Badness: 0.026504

Proposed in March 2021

13 March 2021

Trident (53 & 229)

7-limit
Comma list: 6144/6125, 14348907/14336000
Mapping: [⟨1 0 -13 25], ⟨0 3 29 -42]]
POTE generator: ~4096/2835 = 634.048
Vals: 53, 176, 229, 282, 511
Badness: 0.101694

11-limit
Comma list: 3388/3375, 6144/6125, 8019/8000
Mapping: [⟨1 0 -13 25 -33], ⟨0 3 29 -42 69]]
POTE generator: ~231/160 = 634.067
Vals: 53, 176, 229
Badness: 0.074272

13-limit
Comma list: 351/350, 2080/2079, 2197/2187, 3146/3125
Mapping: [⟨1 0 -13 25 -33 0], ⟨0 3 29 -42 69 7]]
POTE generator: ~13/9 = 634.065
Vals: 53, 176, 229
Badness: 0.046593

Trillium (53 & 441)

7-limit
Comma list: 4375/4374, 1099511627776/1098337086315
Mapping: [⟨1 0 -13 53], ⟨0 3 29 -95]]
POTE generator: ~23625/16384 = 634.012
Vals: 53, 441, 494, 935, 1376, 3193, 4569
Badness: 0.030852

11-limit
Comma list: 4375/4374, 131072/130977, 759375/758912
Mapping: [⟨1 0 -13 53 -89], ⟨0 3 29 -95 175]]
POTE generator: ~3888/2695 = 634.009
Vals: 53, 441, 494, 935, 1429
Badness: 0.046758

13-limit
Comma list: 2080/2079, 4096/4095, 4375/4374, 78125/78078
Mapping: [⟨1 0 -13 53 -89 -28], ⟨0 3 29 -95 175 60]]
POTE generator: ~75/52 = 634.010
Vals: 53, 441, 494, 935, 1429
Badness: 0.019393

Pseudotrillium (53 & 388)

11-limit
Comma list: 4375/4374, 5632/5625, 4108797/4096000
Mapping: [⟨1 0 -13 53 -61], ⟨0 3 29 -95 122]]
POTE generator: ~231/160 = 634.019
Vals: 53, 335, 388
Badness: 0.111931

13-limit
Comma list: 847/845, 1001/1000, 4096/4095, 4375/4374
Mapping: [⟨1 0 -13 53 -61 -28], ⟨0 3 29 -95 122 60]]
POTE generator: ~75/52 = 634.018
Vals: 53, 335, 388
Badness: 0.054837

Tritricot (159 & 282)

7-limit
Comma list: 250047/250000, 11785390260224/11767896353375
Mapping: [⟨3 6 19 30], ⟨0 -3 -29 -52]]
POTE generator: ~100352/91125 = 165.984
Vals: 159, 282, 441, 2487, 2928, 3369
Badness: 0.086081

11-limit
Comma list: 4000/3993, 166698/166375, 200704/200475
Mapping: [⟨3 6 19 30 22], ⟨0 -3 -29 -52 -28]]
POTE generator: ~11/10 = 165.984
Vals: 159, 282, 441
Badness: 0.074002

13-limit
Comma list: 1575/1573, 2080/2079, 34398/34375, 43904/43875
Mapping: [⟨3 6 19 30 22 36], ⟨0 -3 -29 -52 -28 -60]]
POTE generator: ~11/10 = 165.984
Vals: 159, 282, 441
Badness: 0.035641

17-limit
Comma list: 936/935, 1575/1573, 1701/1700, 2025/2023, 8624/8619
Mapping: [⟨3 6 19 30 22 36 16], ⟨0 -3 -29 -52 -28 -60 -9]]
POTE generator: ~11/10 = 165.980
Vals: 159, 282, 441
Badness: 0.025972

21 March 2021

Decic (10 & 50)

7-limit
Comma list: 225/224, 16807/16384
Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]
POTE generator: ~3/2 = 698.696
Vals: 10, 30b, 40, 50, 60, 110d, 170cdd
Badness: 0.089135

11-limit
Comma list: 225/224, 385/384, 3087/3025
Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]
POTE generator: ~3/2 = 696.791
Vals: 10, 30be, 40, 50
Badness: 0.063900

13-limit
Comma list: 105/104, 144/143, 196/195, 2200/2197
Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]
POTE generator: ~3/2 = 696.993
Vals: 10, 30be, 40, 50
Badness: 0.036880

17-limit
Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
Mapping: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]
POTE generator: ~3/2 = 697.085
Vals: 10, 30beg, 40, 50
Badness: 0.025064

22 March 2021

Cloudtone (5 & 50)

7-limit
Comma list: 81/80, 16807/16384
Mapping: [⟨5 0 -20 14], ⟨0 1 4 0]]
POTE generator: ~3/2 = 695.720
Vals: 5, 45, 50
Badness: 0.102256

11-limit
Comma list: 81/80, 385/384, 2401/2376
Mapping: [⟨5 0 -20 14 41], ⟨0 1 4 0 -3]]
POTE generator: ~3/2 = 696.536
Vals: 5, 45, 50, 155bdd, 205bddd
Badness: 0.070378

13-limit
Comma list: 81/80, 105/104, 144/143, 2401/2376
Mapping: [⟨5 0 -20 14 41 -21], ⟨0 1 4 0 -3 5]]
POTE generator: ~3/2 = 696.162
Vals: 5, 45f, 50
Badness: 0.048829

Proposed in April 2021

3 April 2021

Pentacloud (5 & 60)

7-limit
Comma list: 245/243, 16807/16384
Mapping: [⟨5 0 -28 14], ⟨0 1 5 0]]
POTE generator: ~3/2 = 700.548
Vals: 5, 60, 65, 125d, 185cdd
Badness: 0.120942

11-limit
Comma list: 245/243, 385/384, 3087/3025
Mapping: [⟨5 0 -28 14 49], ⟨0 1 5 0 -4]]
POTE generator: ~3/2 = 701.377
Vals: 5, 60, 65
Badness: 0.093248

13-limit
Comma list: 105/104, 144/143, 245/243, 3087/3025
Mapping: [⟨5 0 -28 14 49 -29], ⟨0 1 5 0 -4 6]]
POTE generator: ~3/2 = 700.996
Vals: 5, 60, 65, 125de, 190ddef
Badness: 0.067549

Hemipental (125 & 130)

7-limit
Comma list: 19683/19600, 589824/588245
Mapping: [⟨5 8 12 14], ⟨0 -2 -10 1]]
POTE generator: ~8/7 = 230.654
Vals: 5, 125, 130, 255, 385
Badness: 0.104163

11-limit
Comma list: 540/539, 8019/8000, 180224/180075
Mapping: [⟨5 8 12 14 18], ⟨0 -2 -10 1 -18]]
POTE generator: ~8/7 = 230.634
Vals: 5e, 125, 130, 255, 385, 640, 1025b
Badness: 0.047624

13-limit
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000
Mapping: [⟨5 8 12 14 18 18], ⟨0 -2 -10 1 -18 13]]
POTE generator: ~8/7 = 230.668
Vals: 5ef, 125, 130, 255, 385, 515, 900ef
Badness: 0.041043

Sengasec (10 & 55)

7-limit
Comma list: 686/675, 16807/16384
Mapping: [⟨5 7 13 14], ⟨0 2 -3 0]]
POTE generator: ~16/15 = 111.113
Vals: 10, 55, 65, 140dd, 205ddd, 270ddd
Badness: 0.156259

11-limit
Comma list: 243/242, 385/384, 686/675
Mapping: [⟨5 7 13 14 15], ⟨0 2 -3 0 5]]
POTE generator: ~16/15 = 110.659
Vals: 10, 55, 65
Badness: 0.081607

13-limit
Comma list: 105/104, 144/143, 243/242, 686/675
Mapping: [⟨5 7 13 14 15 19], ⟨0 2 -3 0 5 -1]]
POTE generator: ~16/15 = 110.910
Vals: 10, 55, 65
Badness: 0.056390

4 April 2021

Qinto (10 & 75)

11-limit
Comma list: 225/224, 385/384, 332750/321489
Mapping: [⟨5 7 13 15 14], ⟨0 2 -3 -2 7]]
POTE generator: ~15/14 = 112.448
Vals: 10, 75, 160cde
Badness: 0.127732

10 April 2021

Monzism (53 & 559)

7-limit
Comma list: 4375/4374, [-55 30 2 1⟩
Mapping: [⟨1 2 10 -25], ⟨0 -2 -37 134]]
POTE generator: ~310078125/268435456 = 249.0207
Vals: 53, 559, 612, 1277, 1889
Badness: 0.046569

11-limit
Comma list: 4375/4374, 41503/41472, 184549376/184528125
Mapping: [⟨1 2 10 -25 46], ⟨0 -2 -37 134 -205]]
POTE generator: ~231/200 = 249.0193
Vals: 53, 559, 612
Badness: 0.057083

13-limit
Comma list: 2200/2197, 4096/4095, 4375/4374, 40656/40625
Mapping: [⟨1 2 10 -25 46 23], ⟨0 -2 -37 134 -205 -93]]
POTE generator: ~231/200 = 249.0199
Vals: 53, 559, 612
Badness: 0.053780

18 April 2021

Houborizic (53 & 113)

7-limit
Comma list: 225/224, 1250000/1240029
Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]]
POTE generator: ~243/200 = 339.763
Vals: 7d, 46d, 53, 113, 166
Badness: 0.066638

11-limit
Comma list: 225/224, 385/384, 1250000/1240029
Mapping: [⟨1 3 6 13 -9], ⟨0 -5 -13 -36 44]]
POTE generator: ~243/200 = 339.763
Vals: 53, 113, 166
Badness: 0.067891

13-limit
Comma list: 225/224, 325/324, 385/384, 2200/2197
Mapping: [⟨1 3 6 13 -9 2], ⟨0 -5 -13 -36 44 6]]
POTE generator: ~39/32 = 339.764
Vals: 53, 113, 166
Badness: 0.032996

Houbor (7d & 53)

11-limit
Comma list: 121/120, 225/224, 2200/2187
Mapping: [⟨1 3 6 13 6], ⟨0 -5 -13 -36 -9]]
POTE generator: ~11/9 = 339.814
Vals: 7d, 46d, 53, 60e, 113e
Badness: 0.045232

13-limit
Comma list: 121/120, 225/224, 275/273, 325/324
Mapping: [⟨1 3 6 13 6 2], ⟨0 -5 -13 -36 -9 6]]
POTE generator: ~11/9 = 339.784
Vals: 7d, 46d, 53, 60e, 113e
Badness: 0.031331

Gamity (46 & 113)

7-limit
Comma list: 1029/1024, 1071875/1062882
Mapping: [⟨1 -2 -7 4], ⟨0 15 39 -5]]
POTE generator: ~189/160 = 286.787
Vals: 46, 113, 159
Badness: 0.125733

11-limit
Comma list: 385/384, 441/440, 1071875/1062882
Mapping: [⟨1 -2 -7 4 8], ⟨0 15 39 -5 -19]]
POTE generator: ~33/28 = 286.797
Vals: 46, 113, 159
Badness: 0.051111

13-limit
Comma list: 325/324, 364/363, 385/384, 10985/10976
Mapping: [⟨1 -2 -7 4 8 8], ⟨0 15 39 -5 -19 -18]]
POTE generator: ~13/11 = 286.789
Vals: 46, 113, 159
Badness: 0.030297

17-limit
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Mapping: [⟨1 -2 -7 4 8 8 6], ⟨0 15 39 -5 -19 -18 -8]]
POTE generator: ~13/11 = 286.795
Vals: 46, 113, 159
Badness: 0.022036

19 April 2021

Familia (113 & 152)

7-limit
Comma list: 16875/16807, 1600000/1594323
Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]]
POTE generator: ~11907/10000 = 307.941
Vals: 39d, 74cd, 113, 152, 265, 417, 986d
Badness: 0.144551

11-limit
Comma list: 540/539, 1375/1372, 1600000/1594323
Mapping: [⟨1 8 19 20 5], ⟨0 -25 -65 -67 -6]]
POTE generator: ~3200/2673 = 307.906
Vals: 39d, 74cd, 113, 152, 417, 569de, 721de
Badness: 0.051740

13-limit
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Mapping: [⟨1 8 19 20 5 25], ⟨0 -25 -65 -67 -6 -83]]
POTE generator: ~143/120 = 307.913
Vals: 39df, 74cdf, 113, 152f, 265, 417f
Badness: 0.038473

25 April 2021

Sabric (53 & 190)

7-limit
Comma list: 4375/4374, 2109375/2097152
Mapping: [⟨1 0 3 -11], ⟨0 7 -3 61]]
POTE generator: ~75/64 = 271.607
Vals: 53, 137d, 190, 243
Badness: 0.088355

Quadrawell (31 & 212)

7-limit
Comma list: 2401/2400, 2109375/2097152
Mapping: [⟨1 7 0 3], ⟨0 -28 12 -1]]
POTE generator: ~8/7 = 232.094
Vals: 31, 119, 150, 181, 212, 243, 698cd, 941cd
Badness: 0.075754

11-limit
Comma list: 385/384, 1375/1372, 14641/14580
Mapping: [⟨1 7 0 3 11], ⟨0 -28 12 -1 -39]]
POTE generator: ~8/7 = 232.083
Vals: 31, 119, 150, 181, 212, 455ee, 667cdee
Badness: 0.036493

Sfour (45 & 46)

11-limit
Comma list: 385/384, 2401/2376, 4375/4374
Mapping: [⟨1 2 3 3 3], ⟨0 -19 -31 -9 21]]
POTE generator: ~49/48 = 26.246
Vals: 45, 46, 91, 137d
Badness: 0.076567

13-limit
Comma list: 196/195, 364/363, 385/384, 4375/4374
Mapping: [⟨1 2 3 3 3 3], ⟨0 -19 -31 -9 21 32]]
POTE generator: ~49/48 = 26.239
Vals: 45, 46, 91, 137d
Badness: 0.051893

26 April 2021

Rainwell (31 & 265)

7-limit
Comma list: 16875/16807, 2100875/2097152
Mapping: [⟨1 14 -3 6], ⟨0 -35 15 -9]]
POTE generator: ~2625/2048 = 425.673
Vals: 31, 172, 203, 234, 265, 296
Badness: 0.143488

11-limit
Comma list: 540/539, 1375/1372, 2100875/2097152
Mapping: [⟨1 14 -3 6 29], ⟨0 -35 15 -9 -72]]
POTE generator: ~2625/2048 = 425.679
Vals: 31, 172e, 203e, 234, 265, 296, 919bc, 1215bcc, 1511bcc
Badness: 0.052774

27 April 2021

Sengage (49f&50)

13-limit
Comma list: 144/143, 196/195, 364/363, 625/624
Mapping: [⟨1 1 2 2 3 3], ⟨0 29 16 40 23 35]]
POTE generator: ~99/98 = 24.234
Vals: 49f, 50, 99ef
Badness: 0.037416

30 April 2021

Marfifths (19 & 140)

7-limit
Comma list: 10976/10935, 15625/15552
Mapping: [⟨1 -6 -4 -17], ⟨0 18 15 47]]
POTE generator: ~75/56 = 505.705
Vals: 19, 121, 140, 579, 719, 859bcd, 999bcd, 1858bbccdd
Badness: 0.063448

11-limit
Comma list: 385/384, 6250/6237, 10976/10935
Mapping: [⟨1 -6 -4 -17 22], ⟨0 18 15 47 -44]]
POTE generator: ~75/56 = 505.684
Vals: 19, 140, 159, 299
Badness: 0.058902

13-limit
Comma list: 325/324, 385/384, 625/624, 10976/10935
Mapping: [⟨1 -6 -4 -17 22 -14], ⟨0 18 15 47 -44 42]]
POTE generator: ~75/56 = 505.686
Vals: 19, 140, 159, 299
Badness: 0.030082

Diatessic (121 & 140)

11-limit
Comma list: 1375/1372, 2200/2187, 5632/5625
Mapping: [⟨1 -6 -4 -17 -37], ⟨0 18 15 47 96]]
POTE generator: ~75/56 = 505.740
Vals: 19e, 121, 140, 261, 401, 662bd
Badness: 0.061172

13-limit
Comma list: 325/324, 352/351, 625/624, 1375/1372
Mapping: [⟨1 -6 -4 -17 -37 -14], ⟨0 18 15 47 96 42]]
POTE generator: ~75/56 = 505.740
Vals: 19e, 121, 140, 261, 401, 662bd
Badness: 0.028671

Marf (19 & 121)

11-limit
Comma list: 540/539, 896/891, 15625/15552
Mapping: [⟨1 -6 -4 -17 14], ⟨0 18 15 47 -25]]
POTE generator: ~75/56 = 505.769
Vals: 19, 102d, 121
Badness: 0.075112

13-limit
Comma list: 325/324, 540/539, 625/624, 896/891
Mapping: [⟨1 -6 -4 -17 14 -14], ⟨0 18 15 47 -25 42]]
POTE generator: ~75/56 = 505.771
Vals: 19, 121
Badness: 0.038317

Proposed in May 2021

1 May 2021

Garistearn (94 & 282)

7-limit
Comma list: 118098/117649, 33554432/33480783
Mapping: [⟨94 149 0 264], ⟨0 0 1 0]]
POTE generator: ~5/4 = 386.7805
Vals: 94, 282, 658d, 940dd
Badness: 0.307043

11-limit
Comma list: 540/539, 4000/3993, 33554432/33480783
Mapping: [⟨94 149 0 264 107], ⟨0 0 1 0 1]]
POTE generator: ~5/4 = 386.5968
Vals: 94, 282, 376, 658de
Badness: 0.082255

13-limit
Comma list: 540/539, 729/728, 1575/1573, 28672/28561
Mapping: [⟨94 149 0 264 107 348], ⟨0 0 1 0 1 0]]
POTE generator: ~5/4 = 386.8141
Vals: 94, 282
Badness: 0.045941

17-limit
Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873
Mapping: [⟨94 149 0 264 107 348 166], ⟨0 0 1 0 1 0 1]]
POTE generator: ~5/4 = 386.8420
Vals: 94, 282
Badness: 0.027608

Decistearn (80 & 130)

7-limit
Comma list: 3136/3125, 118098/117649
Mapping: [⟨10 17 24 30], ⟨0 -3 -2 -5]]
POTE generator: ~6/5 = 313.960
Vals: 50, 80, 130, 470cd, 600cd, 730cd, 860ccd
Badness: 0.095543

11-limit
Comma list: 540/539, 3136/3125, 4000/3993
Mapping: [⟨10 17 24 30 35], ⟨0 -3 -2 -5 -1]]
POTE generator: ~6/5 = 314.079
Vals: 50, 80, 130, 210e, 340ce
Badness: 0.038556

13-limit
Comma list: 351/350, 364/363, 540/539, 3136/3125
Mapping: [⟨10 17 24 30 35 37], ⟨0 -3 -2 -5 -1 0]]
POTE generator: ~6/5 = 313.947
Vals: 50, 80, 130
Badness: 0.026895

17-limit
Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625
Mapping: [⟨10 17 24 30 35 37 42], ⟨0 -3 -2 -5 -1 0 -3]]
POTE generator: ~6/5 = 313.931
Vals: 50, 80, 130
Badness: 0.024234

19-limit
Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475
Mapping: [⟨10 17 24 30 35 37 42 44], ⟨0 -3 -2 -5 -1 0 -3 -4]]
POTE generator: ~6/5 = 313.949
Vals: 50, 80, 130
Badness: 0.018232

Quadrant (12 & 224)

7-limit
Comma list: 32805/32768, 390625/388962
Mapping: [⟨4 6 12 17], ⟨0 1 -8 -17]]
POTE generator: ~28/25 = 198.177
Vals: 12, 200, 212, 224, 436, 660, 1096c
Badness: 0.110242

11-limit
Comma list: 1375/1372, 6250/6237, 32805/32768
Mapping: [⟨4 6 12 17 23], ⟨0 1 -8 -17 -27]]
POTE generator: ~28/25 = 198.181
Vals: 12, 212, 224, 436, 660
Badness: 0.045738

13-limit
Comma list: 625/624, 1375/1372, 2080/2079, 10648/10647
Mapping: [⟨4 6 12 17 23 26], ⟨0 1 -8 -17 -27 -33]]
POTE generator: ~28/25 = 198.184
Vals: 212, 224, 436, 660
Badness: 0.027243

Quintilipyth (12 & 253)

(Name revised from Quintilischis on 6 September 2021)
7-limit
Comma list: 32805/32768, 9765625/9680832
Mapping: [⟨1 2 -1 -4], ⟨0 -5 40 82]]
POTE generator: ~625/588 = 99.625
Vals: 12, 253, 265
Badness: 0.253966

11-limit
Comma list: 1375/1372, 4375/4356, 32805/32768
Mapping: [⟨1 2 -1 -4 -7], ⟨0 -5 40 82 126]]
POTE generator: ~35/33 = 99.616
Vals: 12, 253, 265, 518c, 783cc
Badness: 0.113044

13-limit
Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647
Mapping: [⟨1 2 -1 -4 -7 -9], ⟨0 -5 40 82 126 153]]
POTE generator: ~35/33 = 99.612
Vals: 12f, 253, 518c, 771cc
Badness: 0.069127

17-limit
Comma list: 375/374, 595/594, 833/832, 1375/1372, 8624/8619
Mapping: [⟨1 2 -1 -4 -7 -9 5], ⟨0 -5 40 82 126 153 -11]]
POTE generator: ~18/17 = 99.612
Vals: 12f, 253, 518c, 771cc
Badness: 0.045992

19-limit
Comma list: 375/374, 400/399, 495/494, 595/594, 1375/1372, 3978/3971
Mapping: [⟨1 2 -1 -4 -7 -9 5 4], ⟨0 -5 40 82 126 153 -11 3]]
POTE generator: ~18/17 = 99.615
Vals: 12f, 253, 265, 518ch
Badness: 0.038155

2 May 2021

Helenoid (53 & 118)

11-limit
Comma list: 385/384, 3388/3375, 4375/4374
Mapping: [⟨1 0 15 -59 51], ⟨0 1 -8 39 -30]]
POTE generator: ~3/2 = 701.722
Vals: 53, 118, 289e, 407de
Badness: 0.038863

13-limit
Comma list: 352/351, 385/384, 625/624, 729/728
Mapping: [⟨1 0 15 -59 51 56], ⟨0 1 -8 39 -30 -33]]
POTE generator: ~3/2 = 701.745
Vals: 53, 118, 171e
Badness: 0.033677

17-limit
Comma list: 352/351, 385/384, 561/560, 625/624, 729/728
Mapping: [⟨1 0 15 -59 51 56 -91], ⟨0 1 -8 39 -30 -33 60]]
POTE generator: ~3/2 = 701.742
Vals: 53, 118, 171e, 289ef, 460eef
Badness: 0.028891

Ponta (53 & 224)

11-limit
Comma list: 540/539, 4375/4374, 32805/32768
Mapping: [⟨1 0 15 -59 135], ⟨0 1 -8 39 -83]]
POTE generator: ~3/2 = 701.783
Vals: 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee
Badness: 0.048692

13-limit
Comma list: 540/539, 625/624, 729/728, 2200/2197
Mapping: [⟨1 0 15 -59 135 56], ⟨0 1 -8 39 -83 -33]]
POTE generator: ~3/2 = 701.784
Vals: 53, 171, 224
Badness: 0.023616

17-limit
Comma list: 375/374, 540/539, 625/624, 729/728, 2200/2197
Mapping: [⟨1 0 15 -59 135 56 -91], ⟨0 1 -8 39 -83 -33 60]]
POTE generator: ~3/2 = 701.777
Vals: 53, 171, 224, 395e, 619eg
Badness: 0.022853

Pontic (118 & 171)

11-limit
Comma list: 441/440, 4375/4374, 32805/32768
Mapping: [⟨1 0 15 -59 -136], ⟨0 1 -8 39 88]]
POTE generator: ~3/2 = 701.724
Vals: 53e, 118, 289, 407d, 696d
Badness: 0.049573

13-limit
Comma list: 441/440, 625/624, 729/728, 3584/3575
Mapping: [⟨1 0 15 -59 -136 56], ⟨0 1 -8 39 88 -33]]
POTE generator: ~3/2 = 701.738
Vals: 53e, 118, 171, 289f, 460ef
Badness: 0.045308

17-limit
Comma list: 441/440, 595/594, 625/624, 729/728, 2880/2873
Mapping: [⟨1 0 15 -59 -136 56 -91], ⟨0 1 -8 39 88 -33 60]]
POTE generator: ~3/2 = 701.740
Vals: 53e, 118, 171, 289f, 460ef
Badness: 0.029618

Bipont (118 & 224)

11-limit
Comma list: 3025/3024, 4375/4374, 32805/32768
Mapping: [⟨2 3 6 -1 2], ⟨0 1 -8 39 29]]
POTE generator: ~3/2 = 701.757
Vals: 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde
Badness: 0.014629

13-limit
Comma list: 625/624, 729/728, 1575/1573, 4096/4095
Mapping: [⟨2 3 6 -1 2 13], ⟨0 1 -8 39 29 -33]]
POTE generator: ~3/2 = 701.773
Vals: 106, 118, 224, 566f, 790f
Badness: 0.030172

17-limit
Comma list: 625/624, 729/728, 1089/1088, 1225/1224, 2880/2873
Mapping: [⟨2 3 6 -1 2 13 -2], ⟨0 1 -8 39 29 -33 60]]
POTE generator: ~3/2 = 701.765
Vals: 106g, 118, 224, 342, 566f
Badness: 0.027051

Counterbipont (224 & 566)

13-limit
Comma list: 1716/1715, 2080/2079, 3025/3024, 32805/32768
Mapping: [⟨2 3 6 -1 2 -6], ⟨0 1 -8 39 29 79]]
POTE generator: ~3/2 = 701.769
Vals: 106f, 118f, 224, 342f, 566, 1356cf, 1922cff
Badness: 0.025547

17-limit
Comma list: 715/714, 936/935, 1089/1088, 1225/1224, 32805/32768
Mapping: [⟨2 3 6 -1 2 -6 -2], ⟨0 1 -8 39 29 79 60]]
POTE generator: ~3/2 = 701.764
Vals: 106fg, 118f, 224, 342f, 566, 908fg, 1474cffgg
Badness: 0.025251

Quadrapont (224 & 460)

13-limit
Comma list: 3025/3024, 4225/4224, 4375/4374, 32805/32768
Mapping: [⟨4 6 12 -2 4 7], ⟨0 1 -8 39 29 23]]
POTE generator: ~3/2 = 701.756
Vals: 224, 460, 684, 2276cde, 2960cde, 3644bccddee
Badness: 0.021025

3 May 2021

Decimetra (50 & 140)

7-limit
Comma list: 703125/702464, 823543/820125
Mapping: [⟨10 15 23 27], ⟨0 4 1 5]]
POTE generator: ~5/4 = 385.495
Vals: 50, 90, 140, 330, 470, 800cd
Badness: 0.121818

11-limit
Comma list: 385/384, 9801/9800, 391314/390625
Mapping: [⟨10 15 23 27 35], ⟨0 4 1 5 -2]]
POTE generator: ~5/4 = 385.396
Vals: 50, 90, 140, 190, 330e, 520de
Badness: 0.056915

13-limit
Comma list: 385/384, 625/624, 847/845, 4459/4455
Mapping: [⟨10 15 23 27 35 37], ⟨0 4 1 5 -2 0]]
POTE generator: ~5/4 = 385.419
Vals: 50, 90, 140, 190, 330e
Badness: 0.029297

Stockhausenic (140 & 183)

7-limit
Comma list: 703125/702464, 4096000/4084101
Mapping: [⟨1 4 0 -1], ⟨0 -26 25 41]]
POTE generator: ~16/15 = 111.453
Vals: 43, 97, 140, 183, 323, 786, 1109d, 1432d
Badness: 0.088753

11-limit
Comma list: 1375/1372, 5632/5625, 35937/35840
Mapping: [⟨1 4 0 -1 -1], ⟨0 -26 25 41 48]]
POTE generator: ~16/15 = 111.460
Vals: 43, 97e, 140, 183, 323, 506, 829de, 1335ddee
Badness: 0.056043

13-limit
Comma list: 676/675, 1001/1000, 1375/1372, 4096/4095
Mapping: [⟨1 4 0 -1 -1 5], ⟨0 -26 25 41 48 -14]]
POTE generator: ~16/15 = 111.458
Vals: 43, 97e, 140, 183, 323, 829def, 1152deef
Badness: 0.029947

17-limit
Comma list: 442/441, 561/560, 676/675, 715/714, 4096/4095
Mapping: [⟨1 4 0 -1 -1 5 0], ⟨0 -26 25 41 48 -14 44]]
POTE generator: ~16/15 = 111.459
Vals: 43, 97e, 140, 183, 323, 506, 829defg
Badness: 0.019205

4 May 2021

Decavish (50 & 270)

7-limit
Comma list: 420175/419904, 2202927104/2197265625
Mapping: [⟨10 13 22 24], ⟨0 7 3 10]]
POTE generator: ~25/24 = 71.129
Vals: 50, 220, 270, 1400, 1670, 1940, 2210c, 2480c
Badness: 0.114531

11-limit
Comma list: 9801/9800, 41503/41472, 172032/171875
Mapping: [⟨10 13 22 24 35], ⟨0 7 3 10 -1]]
POTE generator: ~25/24 = 71.141
Vals: 50, 220, 270, 860, 1130, 1400, 3070cd, 4470cde
Badness: 0.036938

13-limit
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
Mapping: [⟨10 13 22 24 35 37], ⟨0 7 3 10 -1 0]]
POTE generator: ~25/24 = 71.151
Vals: 50, 220, 270, 590, 860, 1130
Badness: 0.021906

Bronzoid (109 & 142)

7-limit
Comma list: 2097152/2083725, 52734375/52706752
Mapping: [⟨1 14 -11 -9], ⟨0 -41 44 39]]
POTE generator: ~315/256 = 363.347
Vals: 33, 76b, 109, 142, 251
Badness: 0.382300

11-limit
Comma list: 1331/1323, 1375/1372, 2097152/2083725
Mapping: [⟨1 14 -11 -9 8], ⟨0 -41 44 39 -15]]
POTE generator: ~315/256 = 363.344
Vals: 33, 76b, 109, 142, 251
Badness: 0.152568

5 May 2021

Ennealimmia (171 & 270)

11-limit
Comma list: 2401/2400, 4375/4374, 131072/130977
Mapping: [⟨9 1 1 12 124], ⟨0 2 3 2 -14]]
POTE generator: ~6/5 = 315.591
Vals: 99, 171, 270, 711, 981, 1251, 2232e
Badness: 0.026463

13-limit
Comma list: 2080/2079, 2401/2400, 4096/4095, 4375/4374
Mapping: [⟨9 1 1 12 124 93], ⟨0 2 3 2 -14 -9]]
POTE generator: ~6/5 = 315.600
Vals: 99, 171, 270, 711, 981, 1692e, 2673e
Badness: 0.016607

10 May 2021

Paralytic (118 & 217)

(Name revised from Paraklein by Flora Canou on 13 May 2021)
11-limit
Comma list: 441/440, 3136/3125, 4375/4374
Mapping: [⟨1 5 6 12 25], ⟨0 -13 -14 -35 -82]]
POTE generator: ~6/5 = 315.220
Vals: 19e, 99e, 118, 217, 335, 552d, 887dd
Badness: 0.036027

13-limit
Comma list: 441/440, 1001/1000, 3136/3125, 4375/4374
Mapping: [⟨1 5 6 12 25 -16], ⟨0 -13 -14 -35 -82 75]]
POTE generator: ~6/5 = 315.214
Vals: 99e, 118, 217, 552d, 769de
Badness: 0.044710

11 May 2021

Cotoneum (41 & 217)

7-limit
Comma list: 10976/10935, 823543/819200
Mapping: [⟨1 2 -18 -3], ⟨0 -1 49 14]]
POTE generator: ~3/2 = 702.317
Vals: 41, 135c, 176, 217, 258, 475
Badness: 0.105632

11-limit
Comma list: 441/440, 10976/10935, 16384/16335
Mapping: [⟨1 2 -18 -3 13], ⟨0 -1 49 14 -23]]
POTE generator: ~3/2 = 702.303
Vals: 41, 176, 217
Badness: 0.050966

13-limit
Comma list: 364/363, 441/440, 3584/3575, 10976/10935
Mapping: [⟨1 2 -18 -3 13 29], ⟨0 -1 49 14 -23 -61]]
POTE generator: ~3/2 = 702.306
Vals: 41, 176, 217
Badness: 0.036951

17-limit
Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262
Mapping: [⟨1 2 -18 -3 13 29 41], ⟨0 -1 49 14 -23 -61 -89]]
POTE generator: ~3/2 = 702.307
Vals: 41, 176, 217
Badness: 0.029495

19-limit
Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728
Mapping: [⟨1 2 -18 -3 13 29 41 -14], ⟨0 -1 49 14 -23 -61 -89 44]]
POTE generator: ~3/2 = 702.308
Vals: 41, 176, 217
Badness: 0.021811

12 May 2021

Fog (12 & 63)

7-limit
Comma list: 225/224, 156250/151263
Mapping: [⟨3 5 6 7], ⟨0 -1 4 6]]
POTE generator: ~3/2 = 704.118
Vals: 12, 51, 63, 75
Badness: 0.086866

11-limit
Comma list: 100/99, 225/224, 2420/2401
Mapping: [⟨3 5 6 7 8], ⟨0 -1 4 6 10]]
POTE generator: ~3/2 = 704.411
Vals: 12, 51, 63, 138de
Badness: 0.051348

Countermiracle (31 & 145)

7-limit
Comma list: 6144/6125, 50421/50000
Mapping: [⟨1 4 3 3], ⟨0 -25 -7 -2]]
POTE generator: ~343/320 = 115.917
Vals: 31, 114, 145, 176, 559cc, 735cc
Badness: 0.102326

11-limit
Comma list: 441/440, 3388/3375, 6144/6125
Mapping: [⟨1 4 3 3 8], ⟨0 -25 -7 -2 -47]]
POTE generator: ~77/72 = 115.916
Vals: 31, 114e, 145, 176
Badness: 0.039162

13 May 2021

Paraklein (19e & 118)

13-limit
Comma list: 196/195, 352/351, 625/624, 729/728
Mapping: [⟨1 5 6 12 25 15], ⟨0 -13 -14 -35 -82 -43]]
POTE generator: ~6/5 = 315.225
Vals: 19e, 99ef, 118, 217ff, 335ff
Badness: 0.037618

Countermiraculous (31 & 145)

13-limit
Comma list: 196/195, 352/351, 1001/1000, 6144/6125
Mapping: [⟨1 4 3 3 8 1], ⟨0 -25 -7 -2 -47 28]]
POTE generator: ~77/72 = 115.880
Vals: 31, 83e, 114e, 145, 321ceff
Badness: 0.039271

Counterbenediction (31 & 176)

13-limit
Comma list: 351/350, 441/440, 3146/3125, 3584/3575
Mapping: [⟨1 4 3 3 8 -2], ⟨0 -25 -7 -2 -47 59]]
POTE generator: ~77/72 = 115.933
Vals: 31, 145f, 176, 207, 383c, 590cc
Badness: 0.045569

Counterrevelation (31 & 114)

11-limit
Comma list: 121/120, 176/175, 50421/50000
Mapping: [⟨1 4 3 3 5], ⟨0 -25 -7 -2 -16]]
POTE generator: ~343/320 = 115.919
Vals: 31, 114, 145e, 176e
Badness: 0.064070

13-limit
Comma list: 121/120, 176/175, 196/195, 13750/13689
Mapping: [⟨1 4 3 3 5 1], ⟨0 -25 -7 -2 -16 28]]
POTE generator: ~273/256 = 115.862
Vals: 31, 83, 114, 145e
Badness: 0.057497

Septant (224 & 301)

7-limit
Comma list: 32805/32768, 516560652/514714375
Mapping: [⟨7 11 17 19], ⟨0 1 -8 7]]
POTE generator: ~3/2 = 701.702
Vals: 77, 147, 224, 301, 525, 826, 1351
Badness: 0.111142

11-limit
Comma list: 3025/3024, 24057/24010, 32805/32768
Mapping: [⟨7 11 17 19 23], ⟨0 1 -8 7 13]]
POTE generator: ~3/2 = 701.719
Vals: 77, 147, 224, 301, 525
Badness: 0.044122

13-limit
Comma list: 729/728, 1716/1715, 2200/2197, 3025/3024
Mapping: [⟨7 11 17 19 23 26], ⟨0 1 -8 7 13 -1]]
POTE generator: ~3/2 = 701.724
Vals: 77, 147, 224, 525
Badness: 0.024706

15 May 2021

Terminal (12 & 159)

11-limit
Comma list: 441/440, 4375/4356, 32805/32768
Mapping: [⟨3 5 5 4 4], ⟨0 -1 8 18 26]]
POTE generator: ~35/33 = 98.176
Vals: 12, 147de, 159, 330
Badness: 0.059502

13-limit
Comma list: 364/363, 441/440, 625/624, 13720/13689
Mapping: [⟨3 5 5 4 4 3], ⟨0 -1 8 18 26 33]]
POTE generator: ~35/33 = 98.179
Vals: 12f, 147def, 159, 330
Badness: 0.037082

17-limit
Comma list: 364/363, 375/374, 441/440, 595/594, 8624/8619
Mapping: [⟨3 5 5 4 4 3 13], ⟨0 -1 8 18 26 33 -3]]
POTE generator: ~18/17 = 98.190
Vals: 12f, 147def, 159, 171, 330
Badness: 0.027073

Semiterm (12 & 342)

(Name revised from Hemiterm by Flora Canou on 16 October 2021)
11-limit
Comma list: 9801/9800, 32805/32768, 151263/151250
Mapping: [⟨6 10 10 8 7], ⟨0 -1 8 18 28]]
POTE generator: ~35/33 = 98.254
Vals: 12, 342, 1380, 1722, 2064, 2406c
Badness: 0.029438

18 May 2021

Sedia (10 & 161)

11-limit
Comma list: 243/242, 441/440, 939524096/935859375
Mapping: [⟨1 -1 6 4 -3], ⟨0 26 -37 -12 65]]
POTE generator: ~15/14 = 119.279
Vals: 10, 151, 161, 171, 332
Badness: 0.090687

13-limit
Comma list: 243/242, 441/440, 2200/2197, 3584/3575
Mapping: [⟨1 -1 6 4 -3 4], ⟨0 26 -37 -12 65 -3]]
POTE generator: ~15/14 = 119.281
Vals: 10, 151, 161, 171, 332, 835eeff
Badness: 0.045773

17-limit
Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
Mapping: [⟨1 -1 6 4 -3 4 2], ⟨0 26 -37 -12 65 -3 21]]
POTE generator: ~15/14 = 119.281
Vals: 10, 151, 161, 171, 332, 503ef, 835eeff
Badness: 0.027322

21 May 2021

Marthirds (19 & 193)

7-limit
Comma list: 15625/15552, 2460375/2458624
Mapping: [⟨1 -6 -4 -19], ⟨0 24 20 69]]
POTE generator: ~56/45 = 379.252
Vals: 19, 193, 212, 617c, 829c
Badness: 0.104253

11-limit
Comma list: 1375/1372, 15625/15552, 19712/19683
Mapping: [⟨1 -6 -4 -19 -43], ⟨0 24 20 69 147]]
POTE generator: ~56/45 = 379.257
Vals: 19e, 193, 212, 405, 617c, 1022cce
Badness: 0.075624

13-limit
Comma list: 325/324, 625/624, 1375/1372, 19712/19683
Mapping: [⟨1 -6 -4 -19 -43 -14], ⟨0 24 20 69 147 56]]
POTE generator: ~56/45 = 379.256
Vals: 19e, 193, 212, 405f, 617cff
Badness: 0.043728

22 May 2021

Counterkleismic (19 & 224)

7-limit
Comma list: 4375/4374, 158203125/157351936
Mapping: [⟨1 -5 -4 -18], ⟨0 25 24 79]]
POTE generator: ~6/5 = 316.060
Vals: 19, 205, 224, 243, 467
Badness: 0.090553

11-limit
Comma list: 540/539, 4375/4374, 2097152/2096325
Mapping: [⟨1 -5 -4 -18 19], ⟨0 25 24 79 -59]]
POTE generator: ~6/5 = 316.071
Vals: 19, 205, 224
Badness: 0.070952

13-limit
Comma list: 540/539, 625/624, 729/728, 10985/10976
Mapping: [⟨1 -5 -4 -18 19 -15], ⟨0 25 24 79 -59 71]]
POTE generator: ~6/5 = 316.070
Vals: 19, 205, 224, 1587cde, 1811ccdef, 2035ccddeef, 2259ccddeef, 2483ccddeef, 2707ccddeef
Badness: 0.033874

Counterlytic (19e & 224)

11-limit
Comma list: 1375/1372, 4375/4374, 496125/495616
Mapping: [⟨1 -5 -4 -18 -40], ⟨0 25 24 79 165]]
POTE generator: ~6/5 = 316.065
Vals: 19e, 205e, 224
Badness: 0.065400

13-limit
Comma list: 625/624, 729/728, 1375/1372, 10985/10976
Mapping: [⟨1 -5 -4 -18 -40 -15], ⟨0 25 24 79 165 71]]
POTE generator: ~6/5 = 316.065
Vals: 19e, 205e, 224
Badness: 0.029782

24 May 2021

Geb (171 & 506)

5-limit
Comma list: [-31 43 -16⟩
Mapping: [⟨1 -3 -10], ⟨0 16 43]]
POTE generator: ~8000/6561 = 343.868
Vals: 7, 143c, 150c, 157, 164, 171, 506, 677, 848
Badness: 0.118577

7-limit
Comma list: 703125/702464, 14348907/14336000
Mapping: [⟨1 -3 -10 -29], ⟨0 16 43 111]]
POTE generator: ~8000/6561 = 343.863
Vals: 171, 1190, 1361, 1532, 1703, 1874, 2045, 2216, 4603bc
Badness: 0.048770

26 May 2021

Hemidimfi (130 & 193)

7-limit
Comma list: 589824/588245, 2460375/2458624
Mapping: [⟨1 -4 14 -1], ⟨0 22 -46 15]]
POTE generator: ~343/288 = 304.639
Vals: 63, 130, 323, 453, 776
Badness: 0.083491

11-limit
Comma list: 540/539, 12005/11979, 16384/16335
Mapping: [⟨1 -4 14 -1 6], ⟨0 22 -46 15 -10]]
POTE generator: ~105/88 = 304.641
Vals: 63, 130, 193, 323e
Badness: 0.052236

13-limit
Comma list: 364/363, 540/539, 676/675, 4096/4095
Mapping: [⟨1 -4 14 -1 6 7], ⟨0 22 -46 15 -10 -13]]
POTE generator: ~105/88 = 304.639
Vals: 63, 130, 193, 323e, 453e, 776eef
Badness: 0.030433

29 May 2021

Maquiloid (9 & 56)

7-limit
Comma list: 686/675, 65625/65536
Mapping: [⟨1 -6 5 -3], ⟨0 17 -6 13]]
POTE generator: ~175/128 = 535.482
Vals: 9, 38b, 47b, 56, 65, 121d, 186dd
Badness: 0.188977

11-limit
Comma list: 245/242, 385/384, 686/675
Mapping: [⟨1 -6 5 -3 -1], ⟨0 17 -6 13 10]]
POTE generator: ~15/11 = 535.485
Vals: 9, 38be, 47b, 56, 65, 121d, 186dde
Badness: 0.066234

13-limit
Comma list: 91/90, 169/168, 245/242, 385/384
Mapping: [⟨1 -6 5 -3 -1 -3], ⟨0 17 -6 13 10 15]]
POTE generator: ~15/11 = 535.501
Vals: 9, 38be, 47b, 56, 65f, 121df, 186ddeff
Badness: 0.041850

30 May 2021

Paramity (53 & 311)

7-limit
Comma list: 65625/65536, 1600000/1594323
Mapping: [⟨1 3 6 -17], ⟨0 -5 -13 70]]
POTE generator: ~243/200 = 339.553
Vals: 53, 205d, 258, 311, 675, 986, 1297c, 2283bc
Badness: 0.113655

11-limit
Comma list: 6250/6237, 19712/19683, 41503/41472
Mapping: [⟨1 3 6 -17 36], ⟨0 -5 -13 70 -115]]
POTE generator: ~243/200 = 339.554
Vals: 53, 205de, 258, 311, 675, 986
Badness: 0.064853

13-limit
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Mapping: [⟨1 3 6 -17 36 17], ⟨0 -5 -13 70 -115 -47]]
POTE generator: ~243/200 = 339.554
Vals: 53, 205de, 258, 311, 675, 986, 1661cf
Badness: 0.030347

17-limit
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
Mapping: [⟨1 3 6 -17 36 17 -31], ⟨0 -5 -13 70 -115 -47 124]]
POTE generator: ~243/200 = 339.555
Vals: 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf
Badness: 0.024118

19-limit
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
Mapping: [⟨1 3 6 -17 36 17 -31 15], ⟨0 -5 -13 70 -115 -47 124 -38]]
POTE generator: ~208/171 = 339.555
Vals: 53, 205deg, 258g, 311, 675, 986, 1661cfh
Badness: 0.017420

Proposed in June 2021

1 June 2021

Schisennealimmal (171 & 342)

11-limit
Comma list: 2401/2400, 4375/4374, 32805/32768
Mapping: [⟨171 271 397 480 0], ⟨0 0 0 0 1]]
POTE generator: ~11/8 = 550.954
Vals: 171, 342
Badness: 0.031739

13-limit
Comma list: 625/624, 729/728, 2205/2197, 2401/2400
Mapping: [⟨171 271 397 480 0 633], ⟨0 0 0 0 1 0]]
POTE generator: ~11/8 = 551.322
Vals: 171, 342, 855ff, 1197fff
Badness: 0.054029

17-limit
Comma list: 625/624, 729/728, 833/832, 1225/1224, 2205/2197
Mapping: [⟨171 271 397 480 0 633 699], ⟨0 0 0 0 1 0 0]]
POTE generator: ~11/8 = 551.365
Vals: 171, 342, 855ff, 1197fff
Badness: 0.031323

Schisennealimmic (171 & 513)

13-limit
Comma list: 2080/2079, 2401/2400, 4375/4374, 32805/32768
Mapping: [⟨171 271 397 480 0 41], ⟨0 0 0 0 1 1]]
POTE generator: ~11/8 = 551.625
Vals: 171, 342f, 513, 855f
Badness: 0.046843

17-limit
Comma list: 936/935, 1225/1224, 1701/1700, 2025/2023, 11271/11264
Mapping: [⟨171 271 397 480 0 41 699], ⟨0 0 0 0 1 1 0]]
POTE generator: ~11/8 = 551.756
Vals: 171, 342f, 513, 855f
Badness: 0.030622

2 June 2021

Decades (36 & 72)

7-limit
Comma list: 1029/1024, 118098/117649
Mapping: [⟨36 57 0 101], ⟨0 0 1 0]]
POTE generator: ~5/4 = 384.764
Vals: 36, 72, 252, 324bd, 396bd
Badness: 0.108016

11-limit
Comma list: 540/539, 1029/1024, 4000/3993
Mapping: [⟨36 57 0 101 41], ⟨0 0 1 0 1]]
POTE generator: ~5/4 = 384.150
Vals: 36, 72, 396bd, 468bcd, 540bcd, 612bccdd, 684bbccdd, 756bbccdd
Badness: 0.043088

3 June 2021

Undecentic (99 & 198)

11-limit
Comma list: 2401/2400, 3136/3125, 4375/4374
Mapping: [⟨99 157 230 278 0], ⟨0 0 0 0 1]]
POTE generator: ~11/8 = 552.756
Vals: 99e, 198, 297e, 495ce
Badness: 0.058801

13-limit
Comma list: 352/351, 847/845, 2401/2400, 3136/3125
Mapping: [⟨99 157 230 278 0 24], ⟨0 0 0 0 1 1]]
POTE generator: ~11/8 = 552.024
Vals: 99ef, 198
Badness: 0.042547

5 June 2021

Pentadecal (15 & 60)

7-limit
Comma list: 875/864, 16807/16384
Mapping: [⟨15 0 11 42], ⟨0 1 1 0]]
POTE generator: ~3/2 = 700.223
Vals: 15, 45, 60
Badness: 0.114833

11-limit
Comma list: 100/99, 385/384, 1372/1331
Mapping: [⟨15 0 11 42 52], ⟨0 1 1 0 0]]
POTE generator: ~3/2 = 702.733
Vals: 15, 45, 60, 75de, 135de
Badness: 0.077420

13-limit
Comma list: 100/99, 105/104, 144/143, 1372/1331
Mapping: [⟨15 0 11 42 52 8], ⟨0 1 1 0 0 2]]
POTE generator: ~3/2 = 701.715
Vals: 15, 45f, 60, 135de, 195cddee
Badness: 0.051740

9 June 2021

Quinkee (15 & 55)

7-limit
Comma list: 1029/1000, 6144/6125
Mapping: [⟨5 9 12 14], ⟨0 -3 -1 0]]
POTE generator: ~5/4 = 393.439
Vals: 15, 40, 55, 125cd, 180ccdd
Badness: 0.184222

11-limit
Comma list: 121/120, 176/175, 1029/1000
Mapping: [⟨5 9 12 14 18], ⟨0 -3 -1 0 -2]]
POTE generator: ~5/4 = 393.438
Vals: 15, 40, 55, 125cd, 180ccdde
Badness: 0.065192

13-limit
Comma list: 66/65, 105/104, 121/120, 637/625
Mapping: [⟨5 9 12 14 18 20], ⟨0 -3 -1 0 -2 -4]]
POTE generator: ~5/4 = 392.798
Vals: 15, 40, 55
Badness: 0.048440

10 June 2021

Coditonic (3de & 53)

(Proposed name for disambiguation of coditone extension)
11-limit
Comma list: 99/98, 176/175, 6655/6561
Mapping: [⟨1 6 3 13 15], ⟨0 -13 -2 -30 -34]]
POTE generator: ~242/189 = 407.567
Vals: 3de, 50e, 53
Badness: 0.063876

13-limit
Comma list: 99/98, 176/175, 325/324, 847/845
Mapping: [⟨1 6 3 13 15 20], ⟨0 -13 -2 -30 -34 -48]]
POTE generator: ~33/26 = 407.541
Vals: 3def, 53
Badness: 0.043989

27 June 2021

Terture (111 & 159)

7-limit
Comma list: 250047/250000, 359661568/358722675
Mapping: [⟨3 4 3 2], ⟨0 4 21 34]]
POTE generator: ~392/375 = 75.555
Vals: 111, 159, 270
Badness: 0.087156

11-limit
Comma list: 3025/3024, 19712/19683, 102487/102400
Mapping: [⟨3 4 3 2 10], ⟨0 4 21 34 2]]
POTE generator: ~392/375 = 75.550
Vals: 111, 159, 270, 1239, 1509, 1779, 2049, 2319
Badness: 0.029326

13-limit
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Mapping: [⟨3 4 3 2 10 6], ⟨0 4 21 34 2 27]]
POTE generator: ~117/112 = 75.553
Vals: 111, 159, 270
Badness: 0.018647

17-limit
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
Mapping: [⟨3 4 3 2 10 6 10], ⟨0 4 21 34 2 27 12]]
POTE generator: ~117/112 = 75.560
Vals: 111, 159, 270
Badness: 0.018705

19-limit
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
Mapping: [⟨3 4 3 2 10 6 10 5], ⟨0 4 21 34 2 27 12 41]]
POTE generator: ~95/91 = 75.560
Vals: 111, 159, 270
Badness: 0.013902

23-limit
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
Mapping: [⟨3 4 3 2 10 6 10 5 13], ⟨0 4 21 34 2 27 12 41 3]]
POTE generator: ~24/23 = 75.548
Vals: 111, 159, 270
Badness: 0.014915

Semivulture (106 & 164)

11-limit
Comma list: 3025/3024, 4375/4374, 33554432/33480783
Mapping: [⟨2 4 9 -6 -2], ⟨0 -4 -21 56 43]]
POTE generator: ~275/256 = 124.450
Vals: 106, 164, 270
Badness: 0.040799

13-limit
Comma list: 676/675, 3025/3024, 4096/4095, 4375/4374
Mapping: [⟨2 4 9 -6 -2 13], ⟨0 -4 -21 56 43 -27]]
POTE generator: ~275/256 = 124.447
Vals: 106, 164, 270
Badness: 0.035458

Eagle (58 & 212)

7-limit
Comma list: 2401/2400, 10485760000/10460353203
Mapping: [⟨2 4 9 8], ⟨0 -8 -42 -23]]
POTE generator: ~28/27 = 62.229
Vals: 58, 212, 270, 752, 1022, 1292, 2854b
Badness: 0.059498

11-limit
Comma list: 2401/2400, 9801/9800, 19712/19683
Mapping: [⟨2 4 9 8 12], ⟨0 -8 -42 -23 -49]]
POTE generator: ~28/27 = 62.224
Vals: 58, 212, 270
Badness: 0.024885

13-limit
Comma list: 676/675, 1001/1000, 1716/1715, 10648/10647
Mapping: [⟨2 4 9 8 12 13], ⟨0 -8 -42 -23 -49 -54]]
POTE generator: ~28/27 = 62.220
Vals: 58, 212, 270
Badness: 0.016282

Quindromeda (12 & 193)

5-limit
Comma: [56 -28 -5⟩
Mapping: [⟨1 2 0], ⟨0 -5 28]]
POTE generator: ~4428675/4194304 = 99.526
Vals: 12, 169, 181, 193, 205, 217, 422
Badness: 0.399849

Quintakwai (12 & 193)

7-limit
Comma list: 5120/5103, 9765625/9680832
Mapping: [⟨1 2 0 -2], ⟨0 -5 28 58]]
POTE generator: ~625/588 = 99.483
Vals: 12, 169, 181, 193
Badness: 0.155536

11-limit
Comma list: 1375/1372, 4375/4356, 5120/5103
Mapping: [⟨1 2 0 -2 -4], ⟨0 -5 28 58 90]]
POTE generator: ~35/33 = 99.472
Vals: 12, 181, 193, 374, 567ce
Badness: 0.073158

13-limit
Comma list: 325/324, 1375/1372, 1575/1573, 4096/4095
Mapping: [⟨1 2 0 -2 -4 10], ⟨0 -5 28 58 90 -76]]
POTE generator: ~35/33 = 99.468
Vals: 12, 181, 193, 374, 567ce, 941bce
Badness: 0.062737

17-limit
Comma list: 325/324, 375/374, 595/594, 1275/1274, 4096/4095
Mapping: [⟨1 2 0 -2 -4 10 5], ⟨0 -5 28 58 90 -76 -11]]
POTE generator: ~18/17 = 99.469
Vals: 12, 181, 193, 374, 567ce, 941bceg
Badness: 0.037855

19-limit
Comma list: 325/324, 375/374, 400/399, 595/594, 1216/1215, 1275/1274
Mapping: [⟨1 2 0 -2 -4 10 5 4], ⟨0 -5 28 58 90 -76 -11 3]]
POTE generator: ~18/17 = 99.469
Vals: 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh
Badness: 0.025861

Quintagar (12 & 217)

(Name revised from Quintoneum on 30 June 2021)
7-limit
Comma list: 3136/3125, 33554432/33480783
Mapping: [⟨1 2 0 -3], ⟨0 -5 28 70]]
POTE generator: ~200/189 = 99.555
Vals: 12, 217, 229, 446, 675c
Badness: 0.142897

Quintoneum (12 & 217)

11-limit
Comma list: 441/440, 3136/3125, 7168000/7144929
Mapping: [⟨1 2 0 -3 -5], ⟨0 -5 28 70 102]]
POTE generator: ~35/33 = 99.539
Vals: 12, 205d, 217
Badness: 0.087157

13-limit
Comma list: 364/363, 441/440, 3136/3125, 13720/13689
Mapping: [⟨1 2 0 -3 -5 -7], ⟨0 -5 28 70 102 129]]
POTE generator: ~35/33 = 99.541
Vals: 12f, 205df, 217
Badness: 0.052361

17-limit
Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750
Mapping: [⟨1 2 0 -3 -5 -7 5], ⟨0 -5 28 70 102 129 -11]]
POTE generator: ~18/17 = 99.540
Vals: 12f, 205df, 217
Badness: 0.035653

19-limit
Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750
Mapping: [⟨1 2 0 -3 -5 -7 5 4], ⟨0 -5 28 70 102 129 -11 3]]
POTE generator: ~18/17 = 99.541
Vals: 12f, 205df, 217
Badness: 0.025782

Quinsandra (217 & 229)

(Name revised from Quintasandra on 20 January 2022)
11-limit
Comma list: 3136/3125, 19712/19683, 41503/41472
Mapping: [⟨1 2 0 -3 13], ⟨0 -5 28 70 -115]]
POTE generator: ~200/189 = 99.551
Vals: 12e, 217, 446
Badness: 0.109908

13-limit
Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683
Mapping: [⟨1 2 0 -3 13 11], ⟨0 -5 28 70 -115 -88]]
POTE generator: ~55/52 = 99.548
Vals: 12e, 217, 446, 663c
Badness: 0.067730

17-limit
Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095
Mapping: [⟨1 2 0 -3 13 11 5], ⟨0 -5 28 70 -115 -88 -11]]
POTE generator: ~18/17 = 99.548
Vals: 12e, 217, 446, 663c
Badness: 0.038153

19-limit
Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728
Mapping: [⟨1 2 0 -3 13 11 5 4], ⟨0 -5 28 70 -115 -88 -11 3]]
POTE generator: ~18/17 = 99.547
Vals: 12e, 217, 446, 663ch
Badness: 0.026654

Quinsandric (12 & 229)

(Name revised from Quintasandroid on 20 January 2022)
11-limit
Comma list: 3136/3125, 8019/8000, 15488/15435
Mapping: [⟨1 2 0 -3 -6], ⟨0 -5 28 70 114]]
POTE generator: ~200/189 = 99.570
Vals: 12, 217e, 229, 470cd, 699cd
Badness: 0.093971

13-limit
Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647
Mapping: [⟨1 2 0 -3 -6 -8], ⟨0 -5 28 70 114 141]]
POTE generator: ~55/52 = 99.578
Vals: 12f, 217ef, 229, 241, 470cd, 711ccd
Badness: 0.065701

17-limit
Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735
Mapping: [⟨1 2 0 -3 -6 -8 5], ⟨0 -5 28 70 114 141 -11]]
POTE generator: ~18/17 = 99.574
Vals: 12f, 217ef, 229, 241, 470cd
Badness: 0.046624

19-limit
Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137
Mapping: [⟨1 2 0 -3 -6 -8 5 4], ⟨0 -5 28 70 114 141 -11 3]]
POTE generator: ~18/17 = 99.575
Vals: 12f, 217ef, 229, 241, 470cd
Badness: 0.033145

Quinsandro (12 & 229)

(Name revised from Quintasand on 20 January 2022)
13-limit
Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455
Mapping: [⟨1 2 0 -3 -6 11], ⟨0 -5 28 70 114 -88]]
POTE generator: ~200/189 = 99.556
Vals: 12, 217e, 229, 446e, 675ceef
Badness: 0.100195

17-limit
Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095
Mapping: [⟨1 2 0 -3 -6 11 5], ⟨0 -5 28 70 114 -88 -11]]
POTE generator: ~18/17 = 99.556
Vals: 12, 217e, 229, 446e, 675ceef
Badness: 0.057851

19-limit
Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728
Mapping: [⟨1 2 0 -3 -6 11 5 4], ⟨0 -5 28 70 114 -88 -11 3]]
POTE generator: ~18/17 = 99.557
Vals: 12, 217e, 229, 446e, 675ceefh
Badness: 0.040410

Semiquindromeda (12 & 422)

7-limit
Comma list: 102760448/102515625, 1220703125/1219784832
Mapping: [⟨2 4 0 -5], ⟨0 -5 28 64]]
POTE generator: ~1323/1250 = 99.521
Vals: 12, 398, 410, 422, 832, 1254d, 2086bd
Badness: 0.233140

11-limit
Comma list: 5632/5625, 9801/9800, 85937500/85766121
Mapping: [⟨2 4 0 -5 -10], ⟨0 -5 28 64 102]]
POTE generator: ~1323/1250 = 99.525
Vals: 12, 410, 422
Badness: 0.093926

13-limit
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466
Mapping: [⟨2 4 0 -5 -10 -13], ⟨0 -5 28 64 102 123]]
POTE generator: ~1323/1250 = 99.523
Vals: 12f, 410, 422, 1254df, 1676bdff, 2098bcddff
Badness: 0.053361

17-limit
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
Mapping: [⟨2 4 0 -5 -10 -13 10], ⟨0 -5 28 64 102 123 -11]]
POTE generator: ~18/17 = 99.522
Vals: 12f, 410, 422, 832, 1254df, 1676bdff
Badness: 0.034659

19-limit
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
Mapping: [⟨2 4 0 -5 -10 -13 10 8], ⟨0 -5 28 64 102 123 -11 3]]
POTE generator: ~18/17 = 99.523
Vals: 12f, 410, 422, 1254dfhh, 1676bdffhh
Badness: 0.025439

28 June 2021

Quintoneoid (12 & 217)

13-limit
Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049
Mapping: [⟨1 2 0 -3 -5 11], ⟨0 -5 28 70 102 -88]]
POTE generator: ~35/33 = 99.537
Vals: 12, 205d, 217
Badness: 0.072826

17-limit
Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125
Mapping: [⟨1 2 0 -3 -5 11 5], ⟨0 -5 28 70 102 -88 -11]]
POTE generator: ~18/17 = 99.537
Vals: 12, 205d, 217
Badness: 0.042339

19-limit
Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600
Mapping: [⟨1 2 0 -3 -5 11 5 4], ⟨0 -5 28 70 102 -88 -11 3]]
POTE generator: ~18/17 = 99.537
Vals: 12, 205d, 217
Badness: 0.028983

Proposed in July 2021

4 July 2021

Mineral (46 & 171)

11-limit
Comma list: 441/440, 4375/4374, 16384/16335
Mapping: [⟨1 -1 -3 6 10], ⟨0 17 35 -21 -43]]
POTE generator: ~10/9 = 182.482
Vals: 46, 125e, 171, 217, 605ee, 822dee
Badness: 0.059060

13-limit
Comma list: 364/363, 441/440, 3584/3575, 4375/4374
Mapping: [⟨1 -1 -3 6 10 11], ⟨0 17 35 -21 -43 -48]]
POTE generator: ~10/9 = 182.481
Vals: 46, 125e, 171, 217, 605ee, 822dee
Badness: 0.033140

17-limit
Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575
Mapping: [⟨1 -1 -3 6 10 11 5], ⟨0 17 35 -21 -43 -48 -6]]
POTE generator: ~10/9 = 182.481
Vals: 46, 125e, 171, 217, 605ee, 822dee
Badness: 0.019792

Ore (46 & 125)

11-limit
Comma list: 385/384, 1331/1323, 4375/4374
Mapping: [⟨1 -1 -3 6 3], ⟨0 17 35 -21 3]]
POTE generator: ~10/9 = 182.449
Vals: 46, 125, 171e
Badness: 0.053662

13-limit
Comma list: 352/351, 385/384, 1331/1323, 3267/3250
Mapping: [⟨1 -1 -3 6 3 11], ⟨0 17 35 -21 3 -48]]
POTE generator: ~10/9 = 182.470
Vals: 46, 125, 171e, 388ee
Badness: 0.046170

17-limit
Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445
Mapping: [⟨1 -1 -3 6 3 11 5], ⟨0 17 35 -21 3 -48 -6]]
POTE generator: ~10/9 = 182.471
Vals: 46, 125, 171e, 388ee
Badness: 0.028423

12 July 2021

Quintaleap (12 & 121)

(Name revised from Quintupole on 9 September 2021)
5-limit
Comma: [37 -16 -5⟩
Mapping: [⟨1 2 1], ⟨0 -5 16]]
POTE generator: ~135/128 = 99.267
Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc
Badness: 0.444506

Quintupole (12 & 121)

7-limit
Comma list: 4000/3969, 458752/455625
Mapping: [⟨1 2 1 0], ⟨0 -5 16 34]]
POTE generator: ~135/128 = 99.175
Vals: 12, 97, 109, 121
Badness: 0.111620

11-limit
Comma list: 896/891, 1375/1372, 4375/4356
Mapping: [⟨1 2 1 0 -1], ⟨0 -5 16 34 54]]
POTE generator: ~35/33 = 99.156
Vals: 12, 109, 121, 351bde, 472bdee
Badness: 0.056501

13-limit
Comma list: 352/351, 364/363, 625/624, 2704/2695
Mapping: [⟨1 2 1 0 -1 -2], ⟨0 -5 16 34 54 69]]
POTE generator: ~35/33 = 99.165
Vals: 12f, 109, 121
Badness: 0.038431

17-limit
Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
Mapping: [⟨1 2 1 0 -1 -2 5], ⟨0 -5 16 34 54 69 -11]]
POTE generator: ~18/17 = 99.172
Vals: 12f, 109, 121
Badness: 0.028721

19-limit
Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374
Mapping: [⟨1 2 1 0 -1 -2 5 4], ⟨0 -5 16 34 54 69 -11 3]]
POTE generator: ~18/17 = 99.164
Vals: 12f, 109, 121
Badness: 0.023818

17 July 2021

Quinticosiennic (12 & 145)

7-limit
Comma list: 5120/5103, 395136/390625
Mapping: [⟨1 2 1 -1], ⟨0 -5 16 46]]
POTE generator: ~135/128 = 99.345
Vals: 12, 133, 145, 157, 302c, 459bcc
Badness: 0.158041

11-limit
Comma list: 441/440, 896/891, 78408/78125
Mapping: [⟨1 2 1 -1 -2], ⟨0 -5 16 46 66]]
POTE generator: ~35/33 = 99.318
Vals: 12, 133, 145
Badness: 0.080674

13-limit
Comma list: 196/195, 352/351, 364/363, 78408/78125
Mapping: [⟨1 2 1 -1 -2 -3], ⟨0 -5 16 46 66 81]]
POTE generator: ~35/33 = 99.307
Vals: 12f, 133, 145
Badness: 0.052464

17-limit
Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750
Mapping: [⟨1 2 1 -1 -2 -3 5], ⟨0 -5 16 46 66 81 -11]]
POTE generator: ~18/17 = 99.308
Vals: 12f, 133, 145
Badness: 0.037108

19-limit
Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475
Mapping: [⟨1 2 1 -1 -2 -3 5 4], ⟨0 -5 16 46 66 81 -11 3]]
POTE generator: ~18/17 = 99.303
Vals: 12f, 133, 145
Badness: 0.028440

Quintapole (12 & 85)

7-limit
Comma list: 225/224, 7812500/7411887
Mapping: [⟨1 2 1 1], ⟨0 -5 16 22]]
POTE generator: ~21/20 = 98.994
Vals: 12, 73c, 85, 97d
Badness: 0.192498

11-limit
Comma list: 100/99, 225/224, 85184/84035
Mapping: [⟨1 2 1 1 0], ⟨0 -5 16 22 42]]
POTE generator: ~21/20 = 98.954
Vals: 12, 73ce, 85, 97d
Badness: 0.104353

18 July 2021

Hemiseptisix (103 & 121)

7-limit
Comma list: 16875/16807, 95703125/95551488
Mapping: [⟨1 -19 -7 -17], ⟨0 53 24 51]]
POTE generator: ~98/75 = 466.071
Vals: 18, 103, 121, 224
Badness: 0.162826

11-limit
Comma list: 540/539, 1375/1372, 2734375/2725888
Mapping: [⟨1 -19 -7 -17 -28], ⟨0 53 24 51 81]]
POTE generator: ~55/42 = 466.070
Vals: 103, 121, 224
Badness: 0.043381

13-limit
Comma list: 540/539, 625/624, 1375/1372, 2200/2197
Mapping: [⟨1 -19 -7 -17 -28 -13], ⟨0 53 24 51 81 43]]
POTE generator: ~55/42 = 466.071
Vals: 103, 121, 224
Badness: 0.021127

17-limit
Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
Mapping: [⟨1 -19 -7 -17 -28 -13 -13], ⟨0 53 24 51 81 43 44]]
POTE generator: ~17/13 = 466.074
Vals: 103, 121, 224
Badness: 0.018611

Proposed in August 2021

2 August 2021

Goldmine (46 & 79)

13-limit
Comma list: 169/168, 325/324, 385/384, 1331/1323
Mapping: [⟨1 -1 -3 6 3 4], ⟨0 17 35 -21 3 -2]]
POTE generator: ~10/9 = 182.437
Vals: 46, 79, 125f, 171ef, 296eff
Badness: 0.039302

17-limit
Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323
Mapping: [⟨1 -1 -3 6 3 4 5], ⟨0 17 35 -21 3 -2 -6]]
POTE generator: ~10/9 = 182.444
Vals: 46, 125f, 171ef
Badness: 0.027440

8 August 2021

Gamelapyth (41 & 164)

7-limit
Comma list: 1029/1024, 537824/531441
Mapping: [⟨41 65 0 115], ⟨0 0 1 0]]
POTE generator: ~5/4 = 385.731
Vals: 41, 123, 164, 205d, 246d, 451dd
Badness: 0.161056

11-limit
Comma list: 385/384, 441/440, 537824/531441
Mapping: [⟨41 65 0 115 237], ⟨0 0 1 0 -1]]
POTE generator: ~5/4 = 385.871
Vals: 41, 123e, 164, 205d, 451dd
Badness: 0.076537

Mermapyth (41 & 205)

7-limit
Comma list: 5120/5103, 2500000/2470629
Mapping: [⟨41 65 0 20], ⟨0 0 1 1]]
POTE generator: ~5/4 = 385.667
Vals: 41, 123d, 164d, 205, 246, 451d, 697dd
Badness: 0.142344

11-limit
Comma list: 540/539, 5120/5103, 75625/75264
Mapping: [⟨41 65 0 20 237], ⟨0 0 1 1 -1]]
POTE generator: ~5/4 = 385.309
Vals: 41, 164d, 205, 246
Badness: 0.076588

13 August 2021

Undesemi (15 & 224)

7-limit
Comma list: 4096000/4084101, 95703125/95551488
Mapping: [⟨1 5 5 1], ⟨0 -51 -40 27]]
POTE generator: ~8575/8192 = 80.347
Vals: 15, 194, 209, 224, 463, 687, 1150d
Badness: 0.178777

11-limit
Comma list: 3025/3024, 4000/3993, 180224/180075
Mapping: [⟨1 5 5 1 5], ⟨0 -51 -40 27 -23]]
POTE generator: ~22/21 = 80.347
Vals: 15, 194, 209, 224, 463, 1150de
Badness: 0.042318

Decipentic (43 & 56)

7-limit
Comma list: 3136/3125, 2097152/2083725
Mapping: [⟨1 6 0 -3], ⟨0 -19 10 25]]
POTE generator: ~75/64 = 278.800
Vals: 13, 43, 56, 99
Badness: 0.087325

11-limit
Comma list: 441/440, 1344/1331, 3136/3125
Mapping: [⟨1 6 0 -3 3], ⟨0 -19 10 25 2]]
POTE generator: ~75/64 = 278.799
Vals: 13, 43, 56, 99e
Badness: 0.061413

13-limit
Comma list: 169/168, 441/440, 832/825, 975/968
Mapping: [⟨1 6 0 -3 3 3], ⟨0 -19 10 25 2 3]]
POTE generator: ~13/11 = 278.802
Vals: 13, 43, 56, 99e
Badness: 0.047611

17-limit
Comma list: 169/168, 221/220, 256/255, 273/272, 375/374
Mapping: [⟨1 6 0 -3 3 3 2], ⟨0 -19 10 25 2 3 9]]
POTE generator: ~13/11 = 278.798
Vals: 13, 43, 56, 99e
Badness: 0.031191

19-limit
Comma list: 169/168, 210/209, 221/220, 256/255, 273/272, 286/285
Mapping: [⟨1 6 0 -3 3 3 2 1], ⟨0 -19 10 25 2 3 9 14]]
POTE generator: ~13/11 = 278.790
Vals: 13, 43, 56, 99e
Badness: 0.023899

Quasijerome (43 & 198)

11-limit
Comma list: 3136/3125, 15488/15435, 16384/16335
Mapping: [⟨1 6 0 -3 3], ⟨0 -38 20 50 47]]
POTE generator: ~896/825 = 139.403
Vals: 43, 112, 155, 198, 439cd, 637cd
Badness: 0.092996

13-limit
Comma list: 676/675, 1001/1000, 3136/3125, 15488/15435
Mapping: [⟨1 6 0 -3 3 8], ⟨0 -38 20 50 47 -37]]
POTE generator: ~13/12 = 139.403
Vals: 43, 155, 198, 439cdf, 637cdf
Badness: 0.044328

14 August 2021

Septendesemi (80 & 103)

7-limit
Comma list: 16875/16807, 1959552/1953125
Mapping: [⟨1 -2 -1 -2], ⟨0 41 38 55]]
POTE generator: ~343/324 = 104.916
Vals: 80, 103, 183
Badness: 0.146795

11-limit
Comma list: 540/539, 1375/1372, 43923/43750
Mapping: [⟨1 -2 -1 -2 -1], ⟨0 41 38 55 51]]
POTE generator: ~35/33 = 104.916
Vals: 80, 103, 183
Badness: 0.041554

13-limit
Comma list: 351/350, 540/539, 1375/1372, 4225/4224
Mapping: [⟨1 -2 -1 -2 -1 3], ⟨0 41 38 55 51 8]]
POTE generator: ~35/33 = 104.908
Vals: 80, 103, 183, 469f, 652def
Badness: 0.027908

17-limit
Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
Mapping: [⟨1 -2 -1 -2 -1 3 4], ⟨0 41 38 55 51 8 1]]
POTE generator: ~17/16 = 104.909
Vals: 80, 103, 183, 469f, 652def
Badness: 0.020128

15 August 2021

Witch (99 & 265)

7-limit
Comma list: 420175/419904, 1600000/1594323
Mapping: [⟨1 -7 -20 -2], ⟨0 25 65 14]]
POTE generator: ~80/63 = 412.098
Vals: 99, 265, 364, 463, 562, 1025
Badness: 0.080608

11-limit
Comma list: 540/539, 4375/4356, 1240029/1239040
Mapping: [⟨1 -7 -20 -2 -35], ⟨0 25 65 14 112]]
POTE generator: ~80/63 = 412.079
Vals: 99e, 166, 265
Badness: 0.082607

13-limit
Comma list: 540/539, 729/728, 4375/4356, 10648/10647
Mapping: [⟨1 -7 -20 -2 -35 -43], ⟨0 25 65 14 112 136]]
POTE generator: ~33/26 = 412.070
Vals: 99ef, 166, 265, 431c, 696cc
Badness: 0.057980

Semiwitch (166 & 198)

11-limit
Comma list: 9801/9800, 41503/41472, 585640/583443
Mapping: [⟨2 11 25 10 16], ⟨0 -25 -65 -14 -29]]
POTE generator: ~49/44 = 187.904
Vals: 166, 198, 364, 562, 926, 1488bd, 2414bdd
Badness: 0.088189

13-limit
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
Mapping: [⟨2 11 25 10 16 24], ⟨0 -25 -65 -14 -29 -53]]
POTE generator: ~39/35 = 187.904
Vals: 166, 198, 364, 562, 926
Badness: 0.038009

Hitch (198 & 463)

11-limit
Comma list: 3025/3024, 117649/117612, 1600000/1594323
Mapping: [⟨1 18 45 12 -10], ⟨0 -50 -130 -28 41]]
POTE generator: ~1120/891 = 393.950
Vals: 198, 463, 661, 1124bde
Badness: 0.093482

13-limit
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
Mapping: [⟨1 18 45 12 -10 71], ⟨0 -50 -130 -28 41 -205]]
POTE generator: ~1120/891 = 393.948
Vals: 198, 463, 661
Badness: 0.060716

Hitcher (198 & 265)

13-limit
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
Mapping: [⟨1 18 45 12 -10 6], ⟨0 -50 -130 -28 41 -7]]
POTE generator: ~49/39 = 393.949
Vals: 198, 463f, 661ff
Badness: 0.059591

16 August 2021

Quinwell (22 & 243)

7-limit
Comma list: 420175/419904, 2109375/2097152
Mapping: [⟨1 0 3 0], ⟨0 35 -15 62]]
POTE generator: ~405/392 = 54.324
Vals: 22, 221, 243, 751c, 994cd, 1237bccd, 1480bccd
Badness: 0.168897

11-limit
Comma list: 540/539, 4375/4356, 2109375/2097152
Mapping: [⟨1 0 3 0 5], ⟨0 35 -15 62 -34]]
POTE generator: ~33/32 = 54.334
Vals: 22, 221, 243, 265, 773ce, 1038ccee, 1303ccee
Badness: 0.097202

17 August 2021

Septiquarschis (89 & 94)

7-limit
Comma list: 32805/32768, 829440/823543
Mapping: [⟨1 3 -9 2], ⟨0 -7 -56 4]]
POTE generator: ~147/128 = 242.614
Vals: 89, 94, 183, 460d, 643d, 1103dd
Badness: 0.187047

11-limit
Comma list: 540/539, 15488/15435, 32805/32768
Mapping: [⟨1 3 -9 2 -2], ⟨0 -7 -56 4 27]]
POTE generator: ~147/128 = 242.616
Vals: 89, 94, 183, 460d, 643d, 826dd
Badness: 0.052002

13-limit
Comma list: 540/539, 729/728, 1573/1568, 4096/4095
Mapping: [⟨1 3 -9 2 -2 13], ⟨0 -7 -56 4 27 -46]]
POTE generator: ~147/128 = 242.610
Vals: 89, 94, 183, 277, 460d
Badness: 0.035315

21 August 2021

Quinbetter (22 & 221e)

11-limit
Comma list: 385/384, 24057/24010, 43923/43750
Mapping: [⟨1 0 3 0 4], ⟨0 35 -15 62 -12]]
POTE generator: ~405/392 = 54.316
Vals: 22, 199d, 221e, 243e
Badness: 0.078657

22 August 2021

Ultramarine (5e & 37)

(Name revised from Counterultrapyth on 8 January 2022)
11-limit
Comma list: 64/63, 100/99, 3773/3645
Mapping: [⟨1 0 -20 6 -38], ⟨0 1 14 -2 26]]
POTE generator: ~3/2 = 713.791
Vals: 5e, 32e, 37, 79bce, 116bbce
Badness: 0.078068

13-limit
Comma list: 64/63, 91/90, 100/99, 847/845
Mapping: [⟨1 0 -20 6 -38 -25], ⟨0 1 14 -2 26 18]]
POTE generator: ~3/2 = 713.811
Vals: 5e, 32e, 37, 79bcef, 116bbcef
Badness: 0.045653

28 August 2021

Mowglic (19 & 161)

7-limit
Comma list: 3136/3125, 177147/175000
Mapping: [⟨1 0 0 -3], ⟨0 15 22 55]]
POTE generator: ~27/25 = 126.706
Vals: 19, 123d, 142, 161
Badness: 0.129915

11-limit
Comma list: 540/539, 3136/3125, 72171/71680
Mapping: [⟨1 0 0 -3 8], ⟨0 15 22 55 -43]]
POTE generator: ~27/25 = 126.711
Vals: 19, 123de, 142, 161
Badness: 0.094032

13-limit
Comma list: 351/350, 540/539, 1701/1690, 3136/3125
Mapping: [⟨1 0 0 -3 8 -2], ⟨0 15 22 55 -43 54]]
POTE generator: ~14/13 = 126.705
Vals: 19, 123def, 142f, 161
Badness: 0.051571

17-limit
Comma list: 351/350, 540/539, 833/832, 1701/1690, 3136/3125
Mapping: [⟨1 0 0 -3 8 -2 10], ⟨0 15 22 55 -43 54 -56]]
POTE generator: ~14/13 = 126.703
Vals: 19, 123defg, 142f, 161
Badness: 0.041918

19-limit
Comma list: 351/350, 476/475, 495/494, 513/512, 540/539, 1701/1690
Mapping: [⟨1 0 0 -3 8 -2 10 9], ⟨0 15 22 55 -43 54 -56 -45]]
POTE generator: ~14/13 = 126.705
Vals: 19, 123defg, 142f, 161
Badness: 0.032168

23-limit
Comma list: 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: [⟨1 0 0 -3 8 -2 10 9 6], ⟨0 15 22 55 -43 54 -56 -45 -14]]
POTE generator: ~14/13 = 126.703
Vals: 19, 123defg, 142f, 161
Badness: 0.026117

29-limit
Comma list: 261/260, 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: [⟨1 0 0 -3 8 -2 10 9 6 0], ⟨0 15 22 55 -43 54 -56 -45 -14 46]]
POTE generator: ~14/13 = 126.704
Vals: 19, 123defg, 142f, 161
Badness: 0.021398

31-limit
Comma list: 261/260, 276/275, 351/350, 435/434, 476/475, 495/494, 513/512, 529/528, 540/539
Mapping: [⟨1 0 0 -3 8 -2 10 9 6 0 2], ⟨0 15 22 55 -43 54 -56 -45 -14 46 28]]
POTE generator: ~14/13 = 126.703
Vals: 19, 123defgk, 142fk, 161
Badness: 0.019331

Proposed in September 2021

4 September 2021

Terminator (171 & 183)

11-limit
Comma list: 540/539, 32805/32768, 137781/137500
Mapping: [⟨3 5 5 4 18], ⟨0 -1 8 18 -31]]
POTE generator: ~1323/1250 = 98.315
Vals: 12e, 159e, 171, 183, 354, 537, 891de
Badness: 0.066968

13-limit
Comma list: 540/539, 729/728, 4096/4095, 31250/31213
Mapping: [⟨3 5 5 4 18 17], ⟨0 -1 8 18 -31 -24]]
POTE generator: ~55/52 = 98.311
Vals: 171, 183, 354, 891de, 1245dee, 1599ddee
Badness: 0.035487

17-limit
Comma list: 540/539, 729/728, 936/935, 1156/1155, 4096/4095
Mapping: [⟨3 5 5 4 18 17 13], ⟨0 -1 8 18 -31 -24 -3]]
POTE generator: ~18/17 = 98.312
Vals: 171, 183, 354, 891de, 1245dee, 1599ddee
Badness: 0.020434

6 September 2021

Quintaschis (12 & 289)

7-limit
Comma list: 32805/32768, 49009212/48828125
Mapping: [⟨1 2 -1 -5], ⟨0 -5 40 94]]
POTE generator: ~200/189 = 99.664
Vals: 12, 277d, 289
Badness: 0.132890

11-limit
Comma list: 441/440, 32805/32768, 1953125/1951488
Mapping: [⟨1 2 -1 -5 -8], ⟨0 -5 40 94 138]]
POTE generator: ~35/33 = 99.653
Vals: 12, 277d, 289
Badness: 0.111477

13-limit
Comma list: 364/363, 441/440, 32805/32768, 109512/109375
Mapping: [⟨1 2 -1 -5 -8 -11], ⟨0 -5 40 94 138 177]]
POTE generator: ~35/33 = 99.658
Vals: 12f, 277df, 289
Badness: 0.074218

17-limit
Comma list: 364/363, 441/440, 595/594, 3757/3750, 32805/32768
Mapping: [⟨1 2 -1 -5 -8 -11 5], ⟨0 -5 40 94 138 177 -11]]
POTE generator: ~18/17 = 99.656
Vals: 12f, 277df, 289
Badness: 0.050571

19-limit
Comma list: 364/363, 441/440, 476/475, 595/594, 3757/3750, 6885/6859
Mapping: [⟨1 2 -1 -5 -8 -11 5 4], ⟨0 -5 40 94 138 177 -11 3]]
POTE generator: ~18/17 = 99.659
Vals: 12f, 277df, 289
Badness: 0.042120

Quintahelenic (12 & 301)

11-limit
Comma list: 5632/5625, 8019/8000, 151263/151250
Mapping: [⟨1 2 -1 -5 -9], ⟨0 -5 40 94 150]]
POTE generator: ~200/189 = 99.671
Vals: 12, 289e, 301, 915, 1216ce
Badness: 0.082225

13-limit
Comma list: 847/845, 1716/1715, 5632/5625, 8019/8000
Mapping: [⟨1 2 -1 -5 -9 -11], ⟨0 -5 40 94 150 177]]
POTE generator: ~200/189 = 99.661
Vals: 12f, 289e, 301
Badness: 0.055570

17-limit
Comma list: 561/560, 833/832, 847/845, 1701/1700, 3757/3750
Mapping: [⟨1 2 -1 -5 -9 -11 5], ⟨0 -5 40 94 150 177 -11]]
POTE generator: ~18/17 = 99.665
Vals: 12f, 289e, 301
Badness: 0.040412

19-limit
Comma list: 476/475, 495/494, 561/560, 833/832, 847/845, 1701/1700
Mapping: [⟨1 2 -1 -5 -9 -11 5 4], ⟨0 -5 40 94 150 177 -11 3]]
POTE generator: ~18/17 = 99.668
Vals: 12f, 289e, 301
Badness: 0.036840

Quintahelenoid (12 & 301)

13-limit
Comma list: 729/728, 1001/1000, 4096/4095, 86515/86436
Mapping: [⟨1 2 -1 -5 -9 14], ⟨0 -5 40 94 150 -124]]
POTE generator: ~200/189 = 99.672
Vals: 12, 301, 614, 915
Badness: 0.066108

17-limit
Comma list: 561/560, 729/728, 1001/1000, 4096/4095, 14161/14157
Mapping: [⟨1 2 -1 -5 -9 14 5], ⟨0 -5 40 94 150 -124 -11]]
POTE generator: ~18/17 = 99.671
Vals: 12, 301, 915gg, 1216cegg
Badness: 0.047908

19-limit
Comma list: 476/475, 561/560, 729/728, 1001/1000, 4096/4095, 6144/6137
Mapping: [⟨1 2 -1 -5 -9 14 5 4], ⟨0 -5 40 94 150 -124 -11 3]]
POTE generator: ~18/17 = 99.672
Vals: 12, 301, 614gh, 915gghh
Badness: 0.039542

11 September 2021

Semihemiwür (68 & 130)

(Proposed name for disambiguation of hemiwürschmidt extension)
11-limit
Comma list: 2401/2400, 3136/3125, 9801/9800
Mapping: [⟨2 14 6 9 -10], ⟨0 -16 -2 -5 25]]
POTE generator: ~28/25 = 193.902
Vals: 62e, 68, 130, 198, 328
Badness: 0.044848

13-limit
Comma list: 676/675, 1001/1000, 1716/1715, 3136/3125
Mapping: [⟨2 14 6 9 -10 25], ⟨0 -16 -2 -5 25 -26]]
POTE generator: ~28/25 = 193.903
Vals: 62e, 68, 130, 198, 328
Badness: 0.023388

Semihemiwürat (68 & 130)

(Name revised from Semihemiwür by Flora Canou on 3 October 2021)
17-limit
Comma list: 289/288, 442/441, 561/560, 676/675, 1632/1625
Mapping: [⟨2 14 6 9 -10 25 19], ⟨0 -16 -2 -5 25 -26 -16]]
POTE generator: ~28/25 = 193.911
Vals: 62e, 68, 130, 198, 328g, 526cfgg
Badness: 0.028987

19-limit
Comma list: 289/288, 442/441, 456/455, 476/475, 561/560, 627/625
Mapping: [⟨2 14 6 9 -10 25 19 20], ⟨0 -16 -2 -5 25 -26 -16 -17]]
POTE generator: ~19/17 = 193.915
Vals: 62e, 68, 130, 198, 328g, 526cfgg
Badness: 0.021707

Beetle (10 & 27)

11-limit
Comma list: 55/54, 64/63, 686/675
Mapping: [⟨1 1 5 4 -1], ⟨0 2 -9 -4 15]]
POTE generator: ~49/40 = 356.710
Vals: 10, 27, 37
Badness: 0.058084

13-limit
Comma list: 55/54, 64/63, 91/90, 169/168
Mapping: [⟨1 1 5 4 -1 4], ⟨0 2 -9 -4 15 -1]]
POTE generator: ~16/13 = 356.701
Vals: 10, 27, 37
Badness: 0.033971

Subsedia (10 & 111)

7-limit
Comma list: 16875/16807, 65536/64827
Mapping: [⟨1 0 5 4], ⟨0 16 -27 -12]]
POTE generator: ~15/14 = 118.965
Vals: 10, 101, 111, 121, 232d
Badness: 0.157658

11-limit
Comma list: 540/539, 1375/1372, 65536/64827
Mapping: [⟨1 0 5 4 -1], ⟨0 16 -27 -12 45]]
POTE generator: ~15/14 = 118.968
Vals: 10, 101, 111, 121, 232d
Badness: 0.066838

13-limit
Comma list: 352/351, 540/539, 676/675, 1375/1372
Mapping: [⟨1 0 5 4 -1 4], ⟨0 16 -27 -12 45 -3]]
POTE generator: ~15/14 = 118.968
Vals: 10, 101, 111, 121, 232d
Badness: 0.031635

17-limit
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
Mapping: [⟨1 0 5 4 -1 4 3], ⟨0 16 -27 -12 45 -3 11]]
POTE generator: ~15/14 = 118.968
Vals: 10, 101, 111, 121, 232dg
Badness: 0.019707

19-limit
Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
Mapping: [⟨1 0 5 4 -1 4 3 10], ⟨0 16 -27 -12 45 -3 11 -58]]
POTE generator: ~15/14 = 118.964
Vals: 10, 101h, 111, 121, 232dg
Badness: 0.017935

12 September 2021

Quinkwai (12f & 181)

13-limit
Comma list: 352/351, 847/845, 1375/1372, 4375/4356
Mapping: [⟨1 2 0 -2 -4 -5], ⟨0 -5 28 58 90 105]]
POTE generator: ~35/33 = 99.456
Vals: 12f, 169e, 181
Badness: 0.061873

17-limit
Comma list: 352/351, 375/374, 595/594, 833/832, 1375/1372
Mapping: [⟨1 2 0 -2 -4 -5 5], ⟨0 -5 28 58 90 105 -11]]
POTE generator: ~18/17 = 99.458
Vals: 12f, 169e, 181, 374ff, 555cff
Badness: 0.043506

19-limit
Comma list: 352/351, 375/374, 400/399, 495/494, 595/594, 1375/1372
Mapping: [⟨1 2 0 -2 -4 -5 5 4], ⟨0 -5 28 58 90 105 -11 3]]
POTE generator: ~18/17 = 99.459
Vals: 12f, 169e, 181, 374ff, 555cff
Badness: 0.031313

Quintakwoid (12f & 193)

13-limit
Comma list: 364/363, 625/624, 1375/1372, 5120/5103
Mapping: [⟨1 2 0 -2 -4 -6], ⟨0 -5 28 58 90 117]]
POTE generator: ~35/33 = 99.484
Vals: 12f, 181f, 193
Badness: 0.057357

17-limit
Comma list: 364/363, 375/374, 442/441, 595/594, 5120/5103
Mapping: [⟨1 2 0 -2 -4 -6 5], ⟨0 -5 28 58 90 117 -11]]
POTE generator: ~18/17 = 99.484
Vals: 12f, 181f, 193
Badness: 0.039289

19-limit
Comma list: 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
Mapping: [⟨1 2 0 -2 -4 -6 5 4], ⟨0 -5 28 58 90 117 -11 3]]
POTE generator: ~18/17 = 99.485
Vals: 12f, 181f, 193
Badness: 0.028101

18 September 2021

Passionate (12 & 61)

7-limit
Comma list: 126/125, 131072/127575
Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]
POTE generator: ~16/15 = 98.817
Vals: 12, 61, 73, 85c
Badness: 0.121293

11-limit
Comma list: 126/125, 176/175, 8192/8019
Mapping: [⟨1 2 2 1 1], ⟨0 -5 4 22 30]]
POTE generator: ~16/15 = 98.721
Vals: 12, 61, 73, 158bccee
Badness: 0.068322

13-limit
Comma list: 126/125, 176/175, 343/338, 364/363
Mapping: [⟨1 2 2 1 1 1], ⟨0 -5 4 22 30 33]]
POTE generator: ~16/15 = 98.627
Vals: 12f, 61, 73f
Badness: 0.052302

Pash (12 & 73)

13-limit
Comma list: 126/125, 176/175, 196/195, 1352/1331
Mapping: [⟨1 2 2 1 1 0], ⟨0 -5 4 22 30 45]]
POTE generator: ~16/15 = 98.791
Vals: 12f, 61f, 73, 85ce
Badness: 0.056386

25 September 2021

Majvamic (183 & 217)

7-limit
Comma list: 1959552/1953125, 67108864/66976875
Mapping: [⟨1 10 5 -32], ⟨0 -22 -7 91]]
POTE generator: ~125/96 = 459.001
Vals: 34, 149d, 183, 217, 400
Badness: 0.188996

11-limit
Comma list: 5632/5625, 46656/46585, 131072/130977
Mapping: [⟨1 10 5 -32 31], ⟨0 -22 -7 91 -72]]
POTE generator: ~125/96 = 459.002
Vals: 34, 149d, 183, 400, 983c, 1383ce, 1783cce
Badness: 0.055046

13-limit
Comma list: 676/675, 1001/1000, 4096/4095, 39366/39325
Mapping: [⟨1 10 5 -32 31 19], ⟨0 -22 -7 91 -72 -40]]
POTE generator: ~125/96 = 459.000
Vals: 34, 149d, 183, 217, 400
Badness: 0.033963

17-limit
Comma list: 676/675, 936/935, 1001/1000, 1156/1155, 4096/4095
Mapping: [⟨1 10 5 -32 31 19 6], ⟨0 -22 -7 91 -72 -40 -5]]
POTE generator: ~125/96 = 459.000
Vals: 34, 149d, 183, 217, 400
Badness: 0.019543

Majvamoid (149 & 183)

7-limit
Comma list: 19683/19600, 29360128/29296875
Mapping: [⟨1 10 5 38], ⟨0 -22 -7 -92]]
POTE generator: ~125/96 = 459.031
Vals: 34d, 115d, 149, 183, 332, 515, 847, 1362bc
Badness: 0.207280

11-limit
Comma list: 3025/3024, 5632/5625, 19683/19600
Mapping: [⟨1 10 5 38 31], ⟨0 -22 -7 -92 -72]]
POTE generator: ~125/96 = 459.027
Vals: 34d, 149, 183, 332e, 515e, 698e
Badness: 0.065874

13-limit
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
Mapping: [⟨1 10 5 38 31 19], ⟨0 -22 -7 -92 -72 -40]]
POTE generator: ~125/96 = 459.028
Vals: 34d, 149, 183, 332ef, 515ef
Badness: 0.034696

17-limit
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
Mapping: [⟨1 10 5 38 31 19 6], ⟨0 -22 -7 -92 -72 -40 -5]]
POTE generator: ~125/96 = 459.027
Vals: 34d, 149, 183, 332ef, 515ef, 698ef
Badness: 0.023302

Narayana (84 & 118)

7-limit
Comma list: 65625/65536, 321489/320000
Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]
POTE generator: ~25/24 = 71.265
Vals: 34, 84, 118, 202, 320, 522
Badness: 0.094295

11-limit
Comma list: 441/440, 8019/8000, 65625/65536
Mapping: [⟨2 4 5 3 3], ⟨0 -7 -3 22 33]]
POTE generator: ~25/24 = 71.248
Vals: 34e, 84, 118, 202, 320
Badness: 0.045908

26 September 2021

Turkey (212 & 217)

7-limit
Comma list: 4802000/4782969, 5250987/5242880
Mapping: [⟨1 8 36 0], ⟨0 -16 -84 7]]
POTE generator: ~1715/1296 = 481.120
Vals: 5, 207c, 212, 429
Badness: 0.210964

11-limit
Comma list: 19712/19683, 42875/42768, 160083/160000
Mapping: [⟨1 8 36 0 64], ⟨0 -16 -84 7 -151]]
POTE generator: ~33/25 = 481.120
Vals: 212, 429
Badness: 0.079694

13-limit
Comma list: 676/675, 1001/1000, 19712/19683, 31213/31104
Mapping: [⟨1 8 36 0 64 47], ⟨0 -16 -84 7 -151 -108]]
POTE generator: ~33/25 = 481.118
Vals: 212, 217, 429
Badness: 0.043787

Proposed in October 2021

2 October 2021

Lunennealimmal (441 & 882)

11-limit
Comma list: 2401/2400, 4375/4374, 274877906944/274658203125
Mapping: [⟨441 699 1024 1238 1526], ⟨0 0 0 0 -1]]
POTE generator: ~11/8 = 551.3584
Vals: 441, 882, 1323, 2205, 3528
Badness: 0.091939

13-limit
Comma list: 2401/2400, 4096/4095, 4375/4374, 85750/85683
Mapping: [⟨441 699 1024 1238 1526 1632], ⟨0 0 0 0 -1 0]]
POTE generator: ~11/8 = 551.4043
Vals: 441, 882, 1323, 3528f, 4851ff, 6174dff
Badness: 0.042975

17-limit
Comma list: 2401/2400, 4096/4095, 4375/4374, 8624/8619, 14161/14157
Mapping: [⟨441 699 1024 1238 1526 1632 1803], ⟨0 0 0 0 -1 0 -1]]
POTE generator: ~11/8 = 551.3688
Vals: 441, 882, 1323, 2205f, 3528f
Badness: 0.029334

3 October 2021

Hexadecoid (80 & 144)

13-limit
Comma list: 540/539, 1375/1372, 4000/3993, 4225/4224
Mapping: [⟨16 26 38 46 56 59], ⟨0 -3 -4 -5 -3 1]]
POTE generator: ~13/8 = 841.015
Vals: 80, 144, 224
Badness: 0.030818

17-limit
Comma list: 540/539, 715/714, 936/935, 4000/3993, 4225/4224
Mapping: [⟨16 26 38 46 56 59 65], ⟨0 -3 -4 -5 -3 1 2]]
POTE generator: ~13/8 = 840.932
Vals: 80, 144, 224, 528dg
Badness: 0.028611

19-limit
Comma list: 400/399, 540/539, 715/714, 936/935, 1331/1330, 1445/1444
Mapping: [⟨16 26 38 46 56 59 65 68], ⟨0 -3 -4 -5 -3 1 2 0]]
POTE generator: ~13/8 = 840.896
Vals: 80, 144, 224, 304dh, 528dghh
Badness: 0.023731

9 October 2021

Undetrita (111 & 118)

7-limit
Comma list: 3136/3125, 14348907/14336000
Mapping: [⟨1 0 -2 -8], ⟨0 11 30 75]]
POTE generator: ~448/405 = 172.917
Vals: 111, 118, 229, 347, 576c
Badness: 0.114188

11-limit
Comma list: 3025/3024, 3136/3125, 8019/8000
Mapping: [⟨1 0 -2 -8 0], ⟨0 11 30 75 24]]
POTE generator: ~400/363 = 172.912
Vals: 111, 118, 229, 347
Badness: 0.043883

13-limit
Comma list: 352/351, 729/728, 1001/1000, 3025/3024
Mapping: [⟨1 0 -2 -8 0 5], ⟨0 11 30 75 24 -9]]
POTE generator: ~72/65 = 172.930
Vals: 111, 229f
Badness: 0.038771

12 October 2021

Rubidium (37 & 111)

7-limit
Comma list: 3136/3125, 4194304/4117715
Mapping: [⟨37 0 86 104], ⟨0 1 0 0]]
POTE generator: ~3/2 = 703.3903
Vals: 37, 74, 111
Badness: 0.312105

11-limit
Comma list: 176/175, 1375/1372, 65536/65219
Mapping: [⟨37 0 86 104 128], ⟨0 1 0 0 0]]
POTE generator: ~3/2 = 703.0355
Vals: 37, 74, 111
Badness: 0.101001

13-limit
Comma list: 176/175, 640/637, 847/845, 1375/1372
Mapping: [⟨37 0 86 104 128 137], ⟨0 1 0 0 0 0]]
POTE generator: ~3/2 = 703.0520
Vals: 37, 74, 111
Badness: 0.048732

Terbium (65 & 130)

7-limit
Comma list: 32805/32768, 78732/78125
Mapping: [⟨65 103 151 0], ⟨0 0 0 1]]
POTE generator: ~8/7 = 230.8641
Vals: 65, 130
Badness: 0.169778

11-limit
Comma list: 243/242, 4000/3993, 5632/5625
Mapping: [⟨65 103 151 0 225], ⟨0 0 0 1 0]]
POTE generator: ~8/7 = 230.4285
Vals: 65d, 130
Badness: 0.059966

13-limit
Comma list: 243/242, 351/350, 2080/2079, 3584/3575
Mapping: [⟨65 103 151 0 225 58], ⟨0 0 0 1 0 1]]
POTE generator: ~8/7 = 230.0388
Vals: 65d, 130
Badness: 0.036267

Parakleischis (118 & 354)

7-limit
Comma list: 32805/32768, 1224440064/1220703125
Mapping: [⟨118 187 274 0], ⟨0 0 0 1]]
POTE generator: ~8/7 = 231.2765
Vals: 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b
Badness: 0.145166

11-limit
Comma list: 9801/9800, 32805/32768, 137781/137500
Mapping: [⟨118 187 274 0 77], ⟨0 0 0 1 1]]
POTE generator: ~8/7 = 231.4883
Vals: 118, 354, 472
Badness: 0.049316

13 October 2021

Triacontaheptoid (37 & 296)

7-limit
Comma list: 244140625/242121642, 283115520/282475249
Mapping: [⟨37 23 74 92], ⟨0 3 1 1]]
POTE generator: ~5/4 = 385.3041
Vals: 37, 259b, 296, 629, 925c
Badness: 0.784746

11-limit
Comma list: 1375/1372, 4000/3993, 226492416/226474325
Mapping: [⟨37 23 74 92 128], ⟨0 3 1 1 0]]
POTE generator: ~5/4 = 385.3281
Vals: 37, 259b, 296, 629
Badness: 0.167327

13-limit
Comma list: 625/624, 1375/1372, 4000/3993, 15379/15360
Mapping: [⟨37 23 74 92 128 125], ⟨0 3 1 1 0 1]]
POTE generator: ~5/4 = 385.3067
Vals: 37, 259b, 296, 629f, 925cf
Badness: 0.076183

17-limit
Comma list: 625/624, 715/714, 1225/1224, 4000/3993, 11271/11264
Mapping: [⟨37 23 74 92 128 125 175], ⟨0 3 1 1 0 1 -2]]
POTE generator: ~5/4 = 385.3427
Vals: 37, 259b, 296, 629f
Badness: 0.052475

18 October 2021

Octogintic (80 & 320)

7-limit
Comma list: 1959552/1953125, 645700815/645657712
Mapping: [⟨80 127 186 225], ⟨0 -1 -1 -2]]
POTE generator: ~3/2 = 701.940
Vals: 80, 320, 400
Badness: 0.307033

11-limit
Comma list: 9801/9800, 46656/46585, 391314/390625
Mapping: [⟨80 127 186 225 277], ⟨0 -1 -1 -2 -1]]
POTE generator: ~3/2 = 701.982
Vals: 80, 320, 400
Badness: 0.067939

13-limit
Comma list: 1001/1000, 4225/4224, 4459/4455, 46656/46585
Mapping: [⟨80 127 186 225 277 296], ⟨0 -1 -1 -2 -1 0]]
POTE generator: ~3/2 = 701.796
Vals: 80, 320, 400, 720, 1120
Badness: 0.046158

17-limit
Comma list: 936/935, 1001/1000, 1377/1375, 4225/4224, 4459/4455
Mapping: [⟨80 127 186 225 277 296 327], ⟨0 -1 -1 -2 -1 0 0]]
POTE generator: ~3/2 = 701.800
Vals: 80, 320, 400, 720, 1120
Badness: 0.029279

19-limit
Comma list: 936/935, 969/968, 1001/1000, 1377/1375, 1521/1520, 3136/3135
Mapping: [⟨80 127 186 225 277 296 327 340], ⟨0 -1 -1 -2 -1 0 0 -1]]
POTE generator: ~3/2 = 701.784
Vals: 80, 320, 400, 720h, 1120h
Badness: 0.021470

19 October 2021

Senator (26 & 145)

11-limit
Comma list: 441/440, 4375/4374, 65536/65219
Mapping: [⟨1 11 19 2 4], ⟨0 -35 -62 3 -2]]
POTE generator: ~77/64 = 322.793
Vals: 26, 119c, 145, 171, 316e, 487ee
Badness: 0.092238

13-limit
Comma list: 364/363, 441/440, 2200/2197, 4375/4374
Mapping: [⟨1 11 19 2 4 15], ⟨0 -35 -62 3 -2 -42]]
POTE generator: ~77/64 = 322.793
Vals: 26, 119c, 145, 171, 316ef, 487eef
Badness: 0.044662

17-limit
Comma list: 364/363, 441/440, 595/594, 1156/1155, 2200/2197
Mapping: [⟨1 11 19 2 4 15 17], ⟨0 -35 -62 3 -2 -42 -48]]
POTE generator: ~77/64 = 322.793
Vals: 26, 119c, 145, 171, 316ef, 487eef
Badness: 0.026562

20 October 2021

Hemivalentine (30 & 31)

13-limit
Comma list: 121/120, 126/125, 176/175, 343/338
Mapping: [⟨1 1 2 3 3 4], ⟨0 18 10 -6 14 -9]]
POTE generator: ~40/39 = 39.044
Vals: 30, 31, 61, 92f, 123f
Badness: 0.047059

Hemivalentino (31 & 123)

11-limit
Comma list: 126/125, 243/242, 1029/1024
Mapping: [⟨1 1 2 3 2], ⟨0 18 10 -6 45]]
POTE generator: ~45/44 = 38.921
Vals: 31, 92e, 123, 154, 185
Badness: 0.061275

13-limit
Comma list: 126/125, 196/195, 243/242, 1029/1024
Mapping: [⟨1 1 2 3 2 5], ⟨0 18 10 -6 45 -40]]
POTE generator: ~45/44 = 38.948
Vals: 31, 92e, 123, 154
Badness: 0.057919

Hemivalentoid (31 & 61e)

13-limit
Comma list: 126/125, 144/143, 243/242, 343/338
Mapping: [⟨1 1 2 3 2 4], ⟨0 18 10 -6 45 -9]]
POTE generator: ~40/39 = 38.993
Vals: 31, 92ef, 123f
Badness: 0.057931

23 October 2021

Undetritoid (111 & 229)

13-limit
Comma list: 351/350, 1573/1568, 2080/2079, 3136/3125
Mapping: [⟨1 0 -2 -8 0 -11], ⟨0 11 30 75 24 102]]
POTE generator: ~400/363 = 172.933
Vals: 111, 229
Badness: 0.042744

Biquartonic (26 & 80)

11-limit
Comma list: 1728/1715, 2420/2401, 2560/2541
Mapping: [⟨2 4 6 6 7], ⟨0 -11 -18 -5 -1]]
POTE generator: ~36/35 = 45.129
Vals: 26, 54c, 80, 186de, 266dde
Badness: 0.060737

13-limit
Comma list: 169/168, 325/324, 364/363, 640/637
Mapping: [⟨2 4 6 6 7 8], ⟨0 -11 -18 -5 -1 -8]]
POTE generator: ~36/35 = 45.153
Vals: 26, 54c, 80, 106, 186de
Badness: 0.039891

27 October 2021

Quindro (205 & 217)

7-limit
Comma list: 4375/4374, 72057594037927936/71489976421753125
Mapping: [⟨1 2 0 15], ⟨0 -5 28 -147]]
POTE generator: ~4428675/4194304 = 99.529
Vals: 205, 217, 422, 639, 1061
Badness: 0.316850

11-limit
Comma list: 4375/4374, 5632/5625, 25165824/25109315
Mapping: [⟨1 2 0 15 -5], ⟨0 -5 28 -147 102]]
POTE generator: ~17325/16384 = 99.529
Vals: 205, 217, 422, 639, 1061e
Badness: 0.085219

13-limit
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449
Mapping: [⟨1 2 0 15 -5 11], ⟨0 -5 28 -147 102 -88]]
POTE generator: ~4096/3861 = 99.529
Vals: 205, 217, 422, 639, 1061ef
Badness: 0.039203

17-limit
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625
Mapping: [⟨1 2 0 15 -5 11 5], ⟨0 -5 28 -147 102 -88 -11]]
POTE generator: ~18/17 = 99.529
Vals: 205, 217, 422, 639, 1061ef
Badness: 0.024110

19-limit
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430
Mapping: [⟨1 2 0 15 -5 11 5 4], ⟨0 -5 28 -147 102 -88 -11 3]]
POTE generator: ~18/17 = 99.529
Vals: 205, 217, 422, 639h, 1061efh
Badness: 0.016764

Proposed in November 2021

21 November 2021

Tridecatonic (26 & 39)

5-limit
Comma: 2541865828329/2500000000000
Mapping: [⟨13 21 31], ⟨0 -1 -2]]
POTE generator: ~3/2 = 701.0837
Vals: 26, 39, 65, 286, 351, 416, 481, 546
Badness: 0.437494

7-limit
Comma list: 4000/3969, 8748/8575
Mapping: [⟨13 21 31 37], ⟨0 -1 -2 -1]]
POTE generator: ~3/2 = 701.9605
Vals: 26, 39d, 65d
Badness: 0.139213

11-limit
Comma list: 99/98, 1944/1925, 2560/2541
Mapping: [⟨13 21 31 37 45], ⟨0 -1 -2 -1 0]]
POTE generator: ~3/2 = 701.7028
Vals: 26, 39d, 65d
Badness: 0.063257

13-limit
Comma list: 99/98, 144/143, 275/273, 1040/1029
Mapping: [⟨13 21 31 37 45 49], ⟨0 -1 -2 -1 0 -2]]
POTE generator: ~3/2 = 701.3573
Vals: 26, 39df, 65d
Badness: 0.037851

Trideci (26 & 65)

7-limit
Comma list: 4375/4374, 83349/81920
Mapping: [⟨13 21 31 36], ⟨0 -1 -2 1]]
POTE generator: ~3/2 = 699.1410
Vals: 26, 65, 91, 156d, 247cdd
Badness: 0.184585

11-limit
Comma list: 245/242, 385/384, 4375/4374
Mapping: [⟨13 21 31 36 45], ⟨0 -1 -2 1 0]]
POTE generator: ~3/2 = 699.6179
Vals: 26, 65, 91, 156d, 247cdde
Badness: 0.084590

13-limit
Comma list: 169/168, 245/242, 325/324, 385/384
Mapping: [⟨13 21 31 36 45 48], ⟨0 -1 -2 1 0 0]]
POTE generator: ~3/2 = 699.2969
Vals: 26, 65f, 91f, 156dff
Badness: 0.052366

28 November 2021

Decimaleap (24 & 121)

7-limit
Comma list: 6144/6125, 393379840/387420489
Mapping: [⟨1 2 1 5], ⟨0 -10 32 -53]]
POTE generator: ~36/35 = 49.621
Vals: 24, 97d, 121, 145, 266
Badness: 0.314227

11-limit
Comma list: 896/891, 6144/6125, 14700/14641
Mapping: [⟨1 2 1 5 4], ⟨0 -10 32 -53 -13]]
POTE generator: ~36/35 = 49.622
Vals: 24, 97d, 121, 145, 266e
Badness: 0.084612

13-limit
Comma list: 352/351, 364/363, 676/675, 6144/6125
Mapping: [⟨1 2 1 5 4 3], ⟨0 -10 32 -53 -13 17]]
POTE generator: ~36/35 = 49.620
Vals: 24, 97d, 121, 266ef
Badness: 0.041763

17-limit
Comma list: 256/255, 352/351, 364/363, 676/675, 1156/1155
Mapping: [⟨1 2 1 5 4 3 5], ⟨0 -10 32 -53 -13 17 -22]]
POTE generator: ~34/33 = 49.621
Vals: 24, 97dg, 121, 266efg
Badness: 0.025552

19-limit
Comma list: 256/255, 352/351, 361/360, 364/363, 456/455, 665/663
Mapping: [⟨1 2 1 5 4 3 5 4], ⟨0 -10 32 -53 -13 17 -22 6]]
POTE generator: ~34/33 = 49.624
Vals: 24, 97dg, 121, 145, 266efg
Badness: 0.021208

Hemiquindromeda (24 & 193)

7-limit
Comma list: 4802000/4782969, 67108864/66976875
Mapping: [⟨1 2 0 6], ⟨0 -10 56 -77]]
POTE generator: ~36/35 = 49.756
Vals: 24, 169d, 193, 217, 410
Badness: 0.244589

11-limit
Comma list: 14700/14641, 16384/16335, 19712/19683
Mapping: [⟨1 2 0 6 4], ⟨0 -10 56 -77 -13]]
POTE generator: ~36/35 = 49.757
Vals: 24, 169d, 193, 217, 410e
Badness: 0.093130

13-limit
Comma list: 364/363, 676/675, 4096/4095, 19712/19683
Mapping: [⟨1 2 0 6 4 2], ⟨0 -10 56 -77 -13 41]]
POTE generator: ~36/35 = 49.759
Vals: 24, 169d, 193, 217, 410e, 627e
Badness: 0.048715

17-limit
Comma list: 364/363, 595/594, 676/675, 1156/1155, 4096/4095
Mapping: [⟨1 2 0 6 4 2 5], ⟨0 -10 56 -77 -13 41 -22]]
POTE generator: ~34/33 = 49.759
Vals: 24, 169d, 193, 217, 410e, 627e
Badness: 0.028155

19-limit
Comma list: 364/363, 595/594, 676/675, 1156/1155, 1216/1215, 1729/1728
Mapping: [⟨1 2 0 6 4 2 5 4], ⟨0 -10 56 -77 -13 41 -22 6]]
POTE generator: ~34/33 = 49.759
Vals: 24, 169d, 193, 217, 410e
Badness: 0.019364

29 November 2021

Triboh (49 & 123)

11-limit
Comma list: 245/243, 1331/1323, 3125/3087
Mapping: [⟨1 0 0 0 0], ⟨0 39 57 69 85]]
POTE generator: ~77/75 = 48.828
Vals: 49, 123ce, 172
Badness: 0.162592

13-limit
Comma list: 245/243, 275/273, 847/845, 1331/1323
Mapping: [⟨1 0 0 0 0 0], ⟨0 39 57 69 85 91]]
POTE generator: ~77/75 = 48.822
Vals: 49f, 123ce, 172f, 295ce, 467bccef
Badness: 0.082158

Proposed in December 2021

7 December 2021

Hemimabila (9 & 68)

7-limit
Comma list: 6144/6125, 117649/116640
Mapping: [⟨1 6 1 7], ⟨0 -20 6 -19]]
POTE generator: ~7/6 = 264.825
Vals: 9, 59, 68, 77, 145
Badness: 0.111130

11-limit
Comma list: 121/120, 176/175, 67228/66825
Mapping: [⟨1 6 1 7 5], ⟨0 -20 6 -19 -7]]
POTE generator: ~7/6 = 264.849
Vals: 9, 59, 68, 77, 145e
Badness: 0.061426

13-limit
Comma list: 121/120, 176/175, 196/195, 676/675
Mapping: [⟨1 6 1 7 5 9], ⟨0 -20 6 -19 -7 -24]]
POTE generator: ~7/6 = 264.861
Vals: 9, 59f, 68, 77, 145e, 222cef
Badness: 0.034531

17-limit
Comma list: 121/120, 154/153, 176/175, 196/195, 676/675
Mapping: [⟨1 6 1 7 5 9 1], ⟨0 -20 6 -19 -7 -24 14]]
POTE generator: ~7/6 = 264.839
Vals: 9, 59f, 68, 77, 145e
Badness: 0.027851

19-limit
Comma list: 121/120, 154/153, 176/175, 196/195, 209/208, 361/360
Mapping: [⟨1 6 1 7 5 9 1 8], ⟨0 -20 6 -19 -7 -24 14 -17]]
POTE generator: ~7/6 = 264.839
Vals: 9, 59f, 68, 77, 145e
Badness: 0.020053

Sedecic (16 & 32)

7-limit
Comma list: 50/49, 546875/524288
Mapping: [⟨16 25 37 45], ⟨0 1 0 0]]
POTE generator: ~3/2 = 700.554
Vals: 16, 32, 48
Badness: 0.265972

11-limit
Comma list: 50/49, 385/384, 1331/1323
Mapping: [⟨16 25 37 45 55], ⟨0 1 0 0 1]]
POTE generator: ~3/2 = 700.331
Vals: 16, 32, 48
Badness: 0.092774

11 December 2021

Hyperkleismic (26 & 37)

7-limit
Comma list: 875/864, 51200/50421
Mapping: [⟨1 -3 -2 2], ⟨0 17 16 3]]
POTE generator: ~6/5 = 323.780
Vals: 26, 37, 63
Badness: 0.157830

11-limit
Comma list: 100/99, 385/384, 2420/2401
Mapping: [⟨1 -3 -2 2 4], ⟨0 17 16 3 -2]]
POTE generator: ~6/5 = 323.796
Vals: 26, 37, 63
Badness: 0.065356

13-limit
Comma list: 100/99, 169/168, 275/273, 385/384
Mapping: [⟨1 -3 -2 2 4 1], ⟨0 17 16 3 -2 10]]
POTE generator: ~6/5 = 323.790
Vals: 26, 37, 63
Badness: 0.035724

Proposed in January 2022

2 January 2022

Cobalt (27 & 81)

(Name revised from Enneaplonic on 5 January 2022)
7-limit
Comma list: 126/125, 40353607/40310784
Mapping: [⟨27 43 63 76], ⟨0 -1 -1 -1]]
POTE generator: ~3/2 = 701.244
Vals: 27, 81, 108, 135c, 243c
Badness: 0.173308

11-limit
Comma list: 126/125, 540/539, 21609/21296
Mapping: [⟨27 43 63 76 94], ⟨0 -1 -1 -1 -2]]
POTE generator: ~3/2 = 700.001
Vals: 27e, 81, 108
Badness: 0.078060

13-limit
Comma list: 126/125, 144/143, 196/195, 21609/21296
Mapping: [⟨27 43 63 76 94 100], ⟨0 -1 -1 -1 -2 0]]
POTE generator: ~3/2 = 700.867
Vals: 27e, 81, 108, 243ceef
Badness: 0.057145

Cobaltous (27 & 81)

17-limit
Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445
Mapping: [⟨27 43 63 76 94 100 111], ⟨0 -1 -1 -1 -2 0 -2]]
POTE generator: ~3/2 = 700.397
Vals: 27eg, 81, 108g
Badness: 0.042106

19-limit
Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968
Mapping: [⟨27 43 63 76 94 100 111 115], ⟨0 -1 -1 -1 -2 0 -2 -1]]
POTE generator: ~3/2 = 700.429
Vals: 27eg, 81, 108g
Badness: 0.030415

Cobaltic (27 & 108)

17-limit
Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968
Mapping: [⟨27 43 63 76 94 100 111], ⟨0 -1 -1 -1 -2 0 -3]]
POTE generator: ~3/2 = 701.595
Vals: 27eg, 81gg, 108, 135ce
Badness: 0.047163

19-limit
Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083
Mapping: [⟨27 43 63 76 94 100 111 115], ⟨0 -1 -1 -1 -2 0 -3 -1]]
POTE generator: ~3/2 = 701.673
Vals: 27eg, 81gg, 108, 135ceh
Badness: 0.034176

Cobaltite (27 & 81)

(Name revised from Enneaplonoid on 5 January 2022)
(Name revised from Cobalat on 6 March 2022)
13-limit
Comma list: 126/125, 169/168, 540/539, 975/968
Mapping: [⟨27 43 63 76 94 100], ⟨0 -1 -1 -1 -2 -1]]
POTE generator: ~3/2 = 699.179
Vals: 27e, 54bdef, 81f, 108f
Badness: 0.052732

3 January 2022

Pontoid (171 & 289)

13-limit
Comma list: 364/363, 441/440, 4375/4374, 32805/32768
Mapping: [⟨1 2 -1 19 40 61], ⟨0 -1 8 -39 -88 -138]]
POTE generator: ~3/2 = 701.735
Vals: 53ef, 118f, 171, 289, 460e, 749def
Badness: 0.050188

17-limit
Comma list: 364/363, 441/440, 595/594, 1156/1155, 32805/32768
Mapping: [⟨1 2 -1 19 40 61 29], ⟨0 -1 8 -39 -88 -138 -60]]
POTE generator: ~3/2 = 701.735
Vals: 53ef, 118f, 171, 289, 460e, 749defg
Badness: 0.029383

Grackle (12 & 77)

11-limit
Comma list: 126/125, 176/175, 32805/32768
Mapping: [⟨1 0 15 44 70], ⟨0 1 -8 -26 -42]]
POTE generator: ~3/2 = 701.172
Vals: 12, 53dee, 65e, 77, 89, 166c, 255c
Badness: 0.048887

13-limit
Comma list: 126/125, 176/175, 196/195, 5445/5408
Mapping: [⟨1 0 15 44 70 75], ⟨0 1 -8 -26 -42 -45]]
POTE generator: ~3/2 = 701.226
Vals: 12f, 53deeff, 65ef, 77, 166cf, 243cf
Badness: 0.037859

17-limit
Comma list: 126/125, 176/175, 196/195, 256/255, 2904/2873
Mapping: [⟨1 0 15 44 70 75 -7], ⟨0 1 -8 -26 -42 -45 7]]
POTE generator: ~3/2 = 701.206
Vals: 12f, 53deeff, 65ef, 77, 89f, 166cf
Badness: 0.029864

19-limit
Comma list: 126/125, 171/170, 176/175, 196/195, 209/208, 324/323
Mapping: [⟨1 0 15 44 70 75 -7 9], ⟨0 1 -8 -26 -42 -45 7 -3]]
POTE generator: ~3/2 = 701.217
Vals: 12f, 53deeff, 65ef, 77, 166cf
Badness: 0.023096

Grackloid (12 & 77)

13-limit
Comma list: 126/125, 176/175, 729/728, 1287/1280
Mapping: [⟨1 0 15 44 70 -47], ⟨0 1 -8 -26 -42 32]]
POTE generator: ~3/2 = 701.217
Vals: 12, 53deef, 65e, 77, 166c
Badness: 0.048511

Grack (12 & 65)

11-limit
Comma list: 126/125, 245/242, 896/891
Mapping: [⟨1 0 15 44 51], ⟨0 1 -8 -26 -30]]
POTE generator: ~3/2 = 701.401
Vals: 12, 53d, 65, 77e, 142de
Badness: 0.055908

13-limit
Comma list: 126/125, 196/195, 245/242, 832/825
Mapping: [⟨1 0 15 44 51 75], ⟨0 1 -8 -26 -30 -45]]
POTE generator: ~3/2 = 701.348
Vals: 12f, 53dff, 65f, 77e
Badness: 0.044458

Catahelenic (12 & 65)

13-limit
Comma list: 105/104, 126/125, 245/242, 352/351
Mapping: [⟨1 0 15 44 51 56], ⟨0 1 -8 -26 -30 -33]]
POTE generator: ~3/2 = 701.529
Vals: 12f, 53df, 65
Badness: 0.048524

6 January 2022

Countriton (53 & 157)

5-limit
Comma list: 16777216000000000/16677181699666569
Mapping: [⟨1 6 19], ⟨0 -9 -34]]
POTE generator: ~14348907/10240000 = 588.636
Vals: 53, 263, 316, 369, 422, 475, 528
Badness: 0.255594

7-limit
Comma list: 5120/5103, 7558272/7503125
Mapping: [⟨1 6 19 -7], ⟨0 -9 -34 20]]
POTE generator: ~1728/1225 = 588.582
Vals: 53, 157, 210
Badness: 0.131191

11-limit
Comma list: 176/175, 5120/5103, 41503/41472
Mapping: [⟨1 6 19 -7 27], ⟨0 -9 -34 20 -48]]
POTE generator: ~108/77 = 588.545
Vals: 53, 104c, 157
Badness: 0.084782

13-limit
Comma list: 176/175, 351/350, 847/845, 2197/2187
Mapping: [⟨1 6 19 -7 27 14], ⟨0 -9 -34 20 -48 -21]]
POTE generator: ~108/77 = 588.544
Vals: 53, 104c, 157
Badness: 0.042321

Aufic (53 & 161)

11-limit
Comma list: 540/539, 5632/5625, 72171/71680
Mapping: [⟨1 6 -7 19 -25], ⟨0 -9 19 -33 58]]
POTE generator: ~45/32 = 588.800
Vals: 53, 108, 161, 214, 375
Badness: 0.075149

13-limit
Comma list: 351/350, 540/539, 847/845, 4096/4095
Mapping: [⟨1 6 -7 19 -25 -12], ⟨0 -9 19 -33 58 32]]
POTE generator: ~45/32 = 588.796
Vals: 53, 108, 161, 214, 375, 589be
Badness: 0.039050

8 January 2022

Pajarina (12 & 22)

13-limit
Comma list: 50/49, 64/63, 78/77, 99/98
Mapping: [⟨2 0 11 12 26 36], ⟨0 1 -2 -2 -6 -9]]
POTE generator: ~3/2 = 706.133
Vals: 12f, 22, 34d
Badness: 0.022327

17-limit
Comma list: 50/49, 64/63, 78/77, 85/84, 99/98
Mapping: [⟨2 0 11 12 26 36 5], ⟨0 1 -2 -2 -6 -9 1]]
POTE generator: ~3/2 = 706.410
Vals: 12f, 22, 34d
Badness: 0.018375

9 January 2022

Muggloid (3 & 16)

11-limit
Comma list: 33/32, 126/125, 176/175
Mapping: [⟨1 0 2 5 5], ⟨0 5 1 -7 -5]]
POTE generator: ~5/4 = 377.832
Vals: 3, 10bd, 13bd, 16, 19e
Badness: 0.046970

13-limit
Comma list: 33/32, 65/64, 105/104, 126/125
Mapping: [⟨1 0 2 5 5 4], ⟨0 5 1 -7 -5 -1]]
POTE generator: ~5/4 = 377.838
Vals: 3, 10bd, 13bd, 16, 19e
Badness: 0.028732

14 January 2022

Gracecord (12 & 113)

11-limit
Comma list: 225/224, 441/440, 109375/107811
Mapping: [⟨1 2 -6 -13 -19], ⟨0 -1 20 38 54]]
POTE generator: ~3/2 = 700.885
Vals: 12, 101cd, 113
Badness: 0.066964

13-limit
Comma list: 225/224, 364/363, 441/440, 6125/6084
Mapping: [⟨1 2 -6 -13 -19 -25], ⟨0 -1 20 38 54 69]]
POTE generator: ~3/2 = 700.890
Vals: 12f, 101cdf, 113
Badness: 0.044196

17-limit
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
Mapping: [⟨1 2 -6 -13 -19 -25 7], ⟨0 -1 20 38 54 69 -7]]
POTE generator: ~3/2 = 700.870
Vals: 12f, 101cdf, 113
Badness: 0.036637

19-limit
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Mapping: [⟨1 2 -6 -13 -19 -25 7 3], ⟨0 -1 20 38 54 69 -7 3]]
POTE generator: ~3/2 = 700.866
Vals: 12f, 101cdf, 113
Badness: 0.027559

15 January 2022

Gaster (111 & 113)

7-limit
Comma list: 16875/16807, 14348907/14336000
Mapping: [⟨1 11 38 37], ⟨0 -19 -72 -69]]
POTE generator: ~800/567 = 594.64130
Vals: 111, 224
Badness: 0.154521

11-limit
Comma list: 540/539, 1375/1372, 14348907/14336000
Mapping: [⟨1 11 38 37 -1], ⟨0 -19 -72 -69 9]]
POTE generator: ~512/363 = 594.63909
Vals: 111, 224, 783d, 1007d, 1231dd
Badness: 0.054060

13-limit
Comma list: 540/539, 729/728, 1375/1372, 2200/2197
Mapping: [⟨1 11 38 37 -1 26], ⟨0 -19 -72 -69 9 -45]]
POTE generator: ~55/39 = 594.63899
Vals: 111, 224, 783df, 1007df, 1231ddf
Badness: 0.024882

17-limit
Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
Mapping: [⟨1 11 38 37 -1 26 14], ⟨0 -19 -72 -69 9 -45 -20]]
POTE generator: ~24/17 = 594.63553
Vals: 111, 224, 559dgg
Badness: 0.021436

19-limit
Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
Mapping: [⟨1 11 38 37 -1 26 14 32], ⟨0 -19 -72 -69 9 -45 -20 -56]]
POTE generator: ~24/17 = 594.63620
Vals: 111, 224
Badness: 0.018370

23-limit
Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: [⟨1 11 38 37 -1 26 14 32 7], ⟨0 -19 -72 -69 9 -45 -20 -56 -5]]
POTE generator: ~24/17 = 594.64147
Vals: 111, 224
Badness: 0.017619

29-limit
Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32]]
POTE generator: ~24/17 = 594.64556
Vals: 111, 113, 224
Badness: 0.016815

31-limit
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10]]
POTE generator: ~24/17 = 594.64392
Vals: 111, 113, 224
Badness: 0.014790

37-limit
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714
Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65]]
POTE generator: ~24/17 = 594.64383
Vals: 111, 113, 224
Badness: 0.014377

41-limit
Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666
Mapping: [⟨1 11 38 37 -1 26 14 32 7 -11 0 -27 45], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80]]
POTE generator: ~24/17 = 594.64299
Vals: 111, 113, 224
Badness: 0.012858

20 January 2022

Tuskaloosa (77 & 111)

7-limit
Comma list: 19683/19600, 110592/109375
Mapping: [⟨1 6 1 24], ⟨0 -10 3 -48]]
POTE generator: ~512/375 = 529.772
Vals: 34d, 77, 111, 188, 299cd
Badness: 0.145058

11-limit
Comma list: 176/175, 1331/1323, 19683/19600
Mapping: [⟨1 6 1 24 22], ⟨0 -10 3 -48 -42]]
POTE generator: ~224/165 = 529.749
Vals: 34d, 77, 111, 299cd, 410ccd, 521ccdd
Badness: 0.061773

13-limit
Comma list: 176/175, 351/350, 676/675, 1331/1323
Mapping: [⟨1 6 1 24 22 9], ⟨0 -10 3 -48 -42 -12]]
POTE generator: ~65/48 = 529.747
Vals: 34d, 77, 111, 410ccdf, 521ccddff
Badness: 0.031480

17-limit
Comma list: 176/175, 256/255, 351/350, 676/675, 715/714
Mapping: [⟨1 6 1 24 22 9 1], ⟨0 -10 3 -48 -42 -12 7]]
POTE generator: ~34/25 = 529.742
Vals: 34d, 77, 111
Badness: 0.022765

19-limit
Comma list: 176/175, 256/255, 286/285, 351/350, 363/361, 476/475
Mapping: [⟨1 6 1 24 22 9 1 25], ⟨0 -10 3 -48 -42 -12 7 -47]]
POTE generator: ~19/14 = 529.749
Vals: 34dh, 77, 111
Badness: 0.017924

Muscogee (43 & 77)

7-limit
Comma list: 126/125, 33756345/33554432
Mapping: [⟨1 6 1 -10], ⟨0 -10 3 29]]
POTE generator: ~512/375 = 529.907
Vals: 34, 43, 77, 274c, 351cc, 428ccd
Badness: 0.162021

11-limit
Comma list: 126/125, 176/175, 264627/262144
Mapping: [⟨1 6 1 -10 -12], ⟨0 -10 3 29 35]]
POTE generator: ~224/165 = 529.955
Vals: 34e, 43, 77, 120, 197ce
Badness: 0.077552

13-limit
Comma list: 126/125, 176/175, 676/675, 1287/1280
Mapping: [⟨1 6 1 -10 -12 9], ⟨0 -10 3 29 35 -12]]
POTE generator: ~65/48 = 529.957
Vals: 34e, 43, 77, 120, 197ce
Badness: 0.043352

17-limit
Comma list: 126/125, 176/175, 256/255, 273/272, 676/675
Mapping: [⟨1 6 1 -10 -12 9 1], ⟨0 -10 3 29 35 -12 7]]
POTE generator: ~34/25 = 529.958
Vals: 34e, 43, 77, 120g, 197ceg
Badness: 0.031217

19-limit
Comma list: 126/125, 171/170, 176/175, 256/255, 273/272, 363/361
Mapping: [⟨1 6 1 -10 -12 9 1 -9], ⟨0 -10 3 29 35 -12 7 30]]
POTE generator: ~19/14 = 529.955
Vals: 34e, 43, 77, 120g, 197ceg
Badness: 0.023670

Cohemimabila (25 & 43)

7-limit
Comma list: 3136/3125, 65536/64827
Mapping: [⟨1 -4 4 7], ⟨0 20 -6 -15]]
POTE generator: ~128/105 = 335.182
Vals: 25, 43, 68, 111, 179, 290cd, 469bccdd
Badness: 0.127451

11-limit
Comma list: 176/175, 1375/1372, 16384/16335
Mapping: [⟨1 -4 4 7 11], ⟨0 20 -6 -15 -27]]
POTE generator: ~40/33 = 335.148
Vals: 25, 43, 68, 111
Badness: 0.064164

13-limit
Comma list: 176/175, 640/637, 676/675, 1375/1372
Mapping: [⟨1 -4 4 7 11 -3], ⟨0 20 -6 -15 -27 24]]
POTE generator: ~40/33 = 335.144
Vals: 25, 43, 68, 111
Badness: 0.035463

17-limit
Comma list: 176/175, 256/255, 442/441, 640/637, 715/714
Mapping: [⟨1 -4 4 7 11 -3 8], ⟨0 20 -6 -15 -27 24 -14]]
POTE generator: ~17/14 = 335.145
Vals: 25, 43, 68, 111
Badness: 0.022728

19-limit
Comma list: 176/175, 256/255, 286/285, 363/361, 442/441, 476/475
Mapping: [⟨1 -4 4 7 11 -3 8 9], ⟨0 20 -6 -15 -27 24 -14 -17]]
POTE generator: ~17/14 = 335.151
Vals: 25, 43, 68, 111
Badness: 0.017450

Trimabila (9 & 111)

7-limit
Comma list: 1728/1715, 268435456/263671875
Mapping: [⟨3 8 6 12], ⟨0 -10 3 -11]]
POTE generator: ~7/6 = 270.269
Vals: 9, 102d, 111
Badness: 0.267168

11-limit
Comma list: 176/175, 540/539, 805255/802816
Mapping: [⟨3 8 6 12 12], ⟨0 -10 3 -11 -5]]
POTE generator: ~7/6 = 270.256
Vals: 9, 102d, 111
Badness: 0.081946

13-limit
Comma list: 176/175, 540/539, 676/675, 1573/1568
Mapping: [⟨3 8 6 12 12 15], ⟨0 -10 3 -11 -5 -12]]
POTE generator: ~7/6 = 270.254
Vals: 9, 102df, 111
Badness: 0.040102

17-limit
Comma list: 176/175, 256/255, 540/539, 676/675, 715/714
Mapping: [⟨3 8 6 12 12 15 10], ⟨0 -10 3 -11 -5 -12 7]]
POTE generator: ~7/6 = 270.266
Vals: 9, 102df, 111
Badness: 0.030657

19-limit
Comma list: 176/175, 256/255, 286/285, 363/361, 476/475, 540/539
Mapping: [⟨3 8 6 12 12 15 10 16], ⟨0 -10 3 -11 -5 -12 7 -10]]
POTE generator: ~7/6 = 270.260
Vals: 9, 102dfh, 111
Badness: 0.022851

22 January 2022

Immune (29 & 34)

7-limit
Comma list: 225/224, 781250/750141
Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]
POTE generator: ~567/500 = 247.583
Vals: 29, 34d, 63
Badness: 0.144835

11-limit
Comma list: 100/99, 225/224, 1331/1323
Mapping: [⟨1 2 5 9 8], ⟨0 -2 -13 -30 -22]]
POTE generator: ~140/121 = 247.589
Vals: 29, 34d, 63
Badness: 0.050990

13-limit
Comma list: 100/99, 169/168, 225/224, 275/273
Mapping: [⟨1 2 5 9 8 7], ⟨0 -2 -13 -30 -22 -16]]
POTE generator: ~15/13 = 247.593
Vals: 29, 34d, 63
Badness: 0.028521

Meantritone (2 & 31)

7-limit
Comma list: 81/80, 16875/16807
Mapping: [⟨1 4 12 12], ⟨0 -5 -20 -19]]
POTE generator: ~7/5 = 580.766
Vals: 2cd, 29cd, 31
Badness: 0.082239

11-limit
Comma list: 81/80, 99/98, 2541/2500
Mapping: [⟨1 4 12 12 17], ⟨0 -5 -20 -19 -28]]
POTE generator: ~7/5 = 580.647
Vals: 2cde, 29cde, 31
Badness: 0.042869

23 January 2022

Aurora (13 & 21)

7-limit
Comma list: 1029/1000, 28672/28125
Mapping: [⟨1 -3 5 7], ⟨0 12 -7 -11]]
POTE generator: ~21/16 = 458.348
Vals: 8bd, 13, 21, 34, 55, 89d, 144cdd
Badness: 0.242134

11-limit
Comma list: 56/55, 1029/1000, 5632/5625
Mapping: [⟨1 -3 5 7 5], ⟨0 12 -7 -11 -4]]
POTE generator: ~21/16 = 458.413
Vals: 8bd, 13, 21, 34, 55e, 89dee
Badness: 0.116654

13-limit
Comma list: 56/55, 105/104, 512/507, 637/625
Mapping: [⟨1 -3 5 7 5 6], ⟨0 12 -7 -11 -4 -6]]
POTE generator: ~13/10 = 458.444
Vals: 8bd, 13, 21, 34, 55e, 89deef
Badness: 0.066541

17-limit
Comma list: 56/55, 105/104, 170/169, 221/220, 375/374
Mapping: [⟨1 -3 5 7 5 6 6], ⟨0 12 -7 -11 -4 -6 -5]]
POTE generator: ~13/10 = 458.444
Vals: 8bd, 13, 21, 34, 55e, 89deef
Badness: 0.044148

19-limit
Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5], ⟨0 12 -7 -11 -4 -6 -5 -2]]
POTE generator: ~13/10 = 458.444
Vals: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.037621

23-limit
Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5 3], ⟨0 12 -7 -11 -4 -6 -5 -2 4]]
POTE generator: ~13/10 = 458.430
Vals: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.030236

29-limit
Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5 3 6], ⟨0 12 -7 -11 -4 -6 -5 -2 4 -3]]
POTE generator: ~13/10 = 458.426
Vals: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.025201

26 January 2022

Leapweeker (17 & 46)

17-limit
Comma list: 136/135, 169/168, 221/220, 245/243, 364/363
Mapping: [⟨1 2 -8 9 8 7 -5], ⟨0 -1 25 -15 -11 -8 22]]
POTE generator: ~3/2 = 704.537
Vals: 17, 29c, 46, 109g, 155fg, 264bfgg
Badness: 0.026774

29 January 2022

Interaufo (159 & 161)

7-limit
Comma list: 235298/234375, 33756345/33554432
Mapping: [⟨1 15 -26 -28], ⟨0 -27 57 62]]
POTE generator: ~10125/7168 = 596.247
Vals: 2, 157cd, 159, 320, 799dd, 1119bdd
Badness: 0.342890

11-limit
Comma list: 441/440, 102487/102400, 235298/234375
Mapping: [⟨1 15 -26 -28 -3], ⟨0 -27 57 62 13]]
POTE generator: ~512/363 = 596.248
Vals: 2, 157cd, 159, 320
Badness: 0.080833

13-limit
Comma list: 441/440, 1001/1000, 6656/6655, 26411/26364
Mapping: [⟨1 15 -26 -28 -3 -44], ⟨0 -27 57 62 13 96]]
POTE generator: ~55/39 = 596.248
Vals: 2f, 157cdf, 159, 320
Badness: 0.041506

17-limit
Comma list: 441/440, 833/832, 1001/1000, 1089/1088, 8624/8619
Mapping: [⟨1 15 -26 -28 -3 -44 18], ⟨0 -27 57 62 13 96 -28]]
POTE generator: ~24/17 = 596.250
Vals: 2f, 157cdf, 159, 320
Badness: 0.028653

19-limit
Comma list: 441/440, 513/512, 833/832, 969/968, 1001/1000, 1521/1520
Mapping: [⟨1 15 -26 -28 -3 -44 18 -36], ⟨0 -27 57 62 13 96 -28 81]]
POTE generator: ~24/17 = 596.250
Vals: 2fh, 157cdfh, 159, 161, 320
Badness: 0.020593

23-limit
Comma list: 441/440, 513/512, 529/528, 833/832, 897/896, 969/968, 1001/1000
Mapping: [⟨1 15 -26 -28 -3 -44 18 -36 8], ⟨0 -27 57 62 13 96 -28 81 -7]]
POTE generator: ~24/17 = 596.249
Vals: 2fh, 157cdfh, 159, 320i
Badness: 0.017242

29-limit
Comma list: 441/440, 513/512, 529/528, 551/550, 609/608, 783/782, 833/832, 969/968
Mapping: [⟨1 15 -26 -28 -3 -44 18 -36 8 -18], ⟨0 -27 57 62 13 96 -28 81 -7 46]]
POTE generator: ~24/17 = 596.249
Vals: 2fh, 157cdfhj, 159, 320ij
Badness: 0.014267

Helena (53 & 118)

13-limit
Comma list: 169/168, 325/324, 385/384, 3146/3125
Mapping: [⟨1 0 15 -59 51 -28], ⟨0 1 -8 39 -30 20]]
POTE generator: ~3/2 = 701.740
Vals: 53, 118f, 171ef
Badness: 0.036281

17-limit
Comma list: 169/168, 273/272, 325/324, 385/384, 3146/3125
Mapping: [⟨1 0 15 -59 51 -28 -91], ⟨0 1 -8 39 -30 20 60]]
POTE generator: ~3/2 = 701.730
Vals: 53, 118f, 171ef, 289eff
Badness: 0.030688

19-limit
Comma list: 169/168, 273/272, 286/285, 325/324, 385/384, 627/625
Mapping: [⟨1 0 15 -59 51 -28 -91 9], ⟨0 1 -8 39 -30 20 60 -3]]
POTE generator: ~3/2 = 701.729
Vals: 53, 118f, 171ef, 289effh
Badness: 0.021892

Proposed in February 2022

1 February 2022

Cohendecatonic (22 & 121)

11-limit
Comma list: 540/539, 896/891, 4375/4356
Mapping: [⟨11 17 26 30 39], ⟨0 1 -1 2 -2]]
POTE generator: ~3/2 = 703.686
Vals: 22, 77e, 99e, 121, 220e
Badness: 0.038042

13-limit
Comma list: 352/351, 364/363, 540/539, 625/624
Mapping: [⟨11 17 26 30 39 43], ⟨0 1 -1 2 -2 -5]]
POTE generator: ~3/2 = 703.888
Vals: 22, 77eff, 99ef, 121, 341bdeeff
Badness: 0.036112

17-limit
Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
Mapping: [⟨11 17 26 30 39 43 45], ⟨0 1 -1 2 -2 -5 0]]
POTE generator: ~3/2 = 703.877
Vals: 22, 77eff, 99ef, 121, 220efg, 341bdeeffgg
Badness: 0.022590

2 February 2022

Nessa (15 & 84)

11-limit
Comma list: 441/440, 1344/1331, 4375/4356
Mapping: [⟨3 2 5 10 10], ⟨0 7 5 -4 1]]
POTE generator: ~35/32 = 157.539
Vals: 15, 54b, 69, 84, 99e
Badness: 0.048836

13-limit
Comma list: 144/143, 364/363, 441/440, 625/624
Mapping: [⟨3 2 5 10 10 6], ⟨0 7 5 -4 1 13]]
POTE generator: ~35/32 = 157.429
Vals: 15, 54bf, 69, 84, 99ef, 183ef, 282eeff
Badness: 0.037409

11 February 2022

Splendecic (10 & 50)

(Name revised from Splendic on 12 February 2022)
11-limit
Comma list: 225/224, 1617/1600, 2401/2376
Mapping: [⟨10 0 39 28 82], ⟨0 1 -1 0 -3]]
POTE generator: ~3/2 = 698.518
Vals: 10e, 30bee, 40e, 50, 60e, 110de
Badness: 0.059802

13-limit
Comma list: 105/104, 196/195, 1001/1000, 1188/1183
Mapping: [⟨10 0 39 28 82 37], ⟨0 1 -1 0 -3 0]]
POTE generator: ~3/2 = 698.365
Vals: 10e, 30bee, 40e, 50, 60e, 110de
Badness: 0.037989

17-limit
Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
Mapping: [⟨10 0 39 28 82 37 25], ⟨0 1 -1 0 -3 0 1]]
POTE generator: ~3/2 = 698.375
Vals: 10e, 30beeg, 40e, 50, 60e, 110deg
Badness: 0.026050

Prodecic (10 & 50)

(Name revised from Prodigic on 12 February 2022)
11-limit
Comma list: 225/224, 441/440, 5929/5832
Mapping: [⟨10 0 39 28 -13], ⟨0 1 -1 0 3]]
POTE generator: ~3/2 = 700.210
Vals: 10, 40ee, 50e, 60e
Badness: 0.066600

13-limit
Comma list: 105/104, 196/195, 275/273, 5929/5832
Mapping: [⟨10 0 39 28 -13 37], ⟨0 1 -1 0 3 0]]
POTE generator: ~3/2 = 700.503
Vals: 10, 40ee, 50e, 60e
Badness: 0.041788

17-limit
Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
Mapping: [⟨10 0 39 28 -13 37 25], ⟨0 1 -1 0 3 0 1]]
POTE generator: ~3/2 = 700.474
Vals: 10, 40ee, 50e, 60e
Badness: 0.027590

12 February 2022

Semimeantone (12 & 62)

13-limit
Comma list: 81/80, 99/98, 126/125, 847/845
Mapping: [⟨2 3 4 4 4 4], ⟨0 1 4 10 18 21]]
POTE generator: ~3/2 = 697.005
Vals: 12f, 50eff, 62, 136b, 198bef, 334bbeef
Badness: 0.040668

17-limit
Comma list: 81/80, 99/98, 126/125, 221/220, 289/288
Mapping: [⟨2 3 4 4 4 4 8], ⟨0 1 4 10 18 21 1]]
POTE generator: ~3/2 = 696.927
Vals: 12f, 50eff, 62, 136bg, 198befgg
Badness: 0.031491

19-limit
Comma list: 81/80, 99/98, 126/125, 153/152, 209/208, 221/220
Mapping: [⟨2 3 4 4 4 4 8 8], ⟨0 1 4 10 18 21 1 3]]
POTE generator: ~3/2 = 696.906
Vals: 12f, 50eff, 62
Badness: 0.024206

Keenic (22 & 34)

13-limit
Comma list: 91/90, 100/99, 352/351, 385/384
Mapping: [⟨2 3 5 4 8 9], ⟨0 1 -2 9 -6 -9]]
POTE generator: ~3/2 = 707.257
Vals: 22, 34, 56
Badness: 0.040351

17-limit
Comma list: 91/90, 100/99, 136/135, 154/153, 256/255
Mapping: [⟨2 3 5 4 8 9 8], ⟨0 1 -2 9 -6 -9 1]]
POTE generator: ~3/2 = 707.252
Vals: 22, 34, 56
Badness: 0.026917

19 February 2022

Warrior (46 & 111)

7-limit
Comma list: 5120/5103, 78732/78125
Mapping: [⟨1 -1 -1 15], ⟨0 7 9 -33]]
POTE generator: ~162/125 = 443.289
Vals: 46, 111, 157, 268cd
Badness: 0.118239

11-limit
Comma list: 176/175, 1331/1323, 5120/5103
Mapping: [⟨1 -1 -1 15 9], ⟨0 7 9 -33 -15]]
POTE generator: ~128/99 = 443.274
Vals: 46, 65d, 111, 268cd, 379cdd
Badness: 0.046383

13-limit
Comma list: 176/175, 351/350, 847/845, 1331/1323
Mapping: [⟨1 -1 -1 15 9 17], ⟨0 7 9 -33 -15 -36]]
POTE generator: ~84/65 = 443.270
Vals: 46, 65d, 111, 268cd, 379cddf
Badness: 0.028735

17-limit
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
Mapping: [⟨1 -1 -1 15 9 17 10], ⟨0 7 9 -33 -15 -36 -16]]
POTE generator: ~22/17 = 443.270
Vals: 46, 65d, 111, 268cdg, 379cddfg
Badness: 0.018105

Trisensory (27 & 84)

7-limit
Comma list: 1728/1715, 78732/78125
Mapping: [⟨3 4 6 8], ⟨0 7 9 4]]
POTE generator: ~36/35 = 43.147
Vals: 27, 57, 84, 111, 195d, 306d
Badness: 0.089740

11-limit
Comma list: 176/175, 540/539, 78732/78125
Mapping: [⟨3 4 6 8 8], ⟨0 7 9 4 22]]
POTE generator: ~36/35 = 43.292
Vals: 27e, 84e, 111
Badness: 0.058413

13-limit
Comma list: 176/175, 351/350, 540/539, 9295/9261
Mapping: [⟨3 4 6 8 8 11], ⟨0 7 9 4 22 1]]
POTE generator: ~36/35 = 43.288
Vals: 27e, 84e, 111
Badness: 0.034829

17-limit
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
Mapping: [⟨3 4 6 8 8 11 10], ⟨0 7 9 4 22 1 21]]
POTE generator: ~36/35 = 43.276
Vals: 27eg, 84e, 111
Badness: 0.024120

19-limit
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
Mapping: [⟨3 4 6 8 8 11 10 12], ⟨0 7 9 4 22 1 21 7]]
POTE generator: ~36/35 = 43.292
Vals: 27eg, 84e, 111
Badness: 0.018466

20 February 2022

Bisensi (8 & 38)

11-limit
Comma list: 121/120, 126/125, 245/243
Mapping: [⟨2 5 7 9 9], ⟨0 -7 -9 -13 -8]]
POTE generator: ~11/10 = 156.692
Vals: 8d, 38d, 46, 176dde, 222cdde, 268cddee
Badness: 0.041723

13-limit
Comma list: 91/90, 121/120, 126/125, 169/168
Mapping: [⟨2 5 7 9 9 10], ⟨0 -7 -9 -13 -8 -10]]
POTE generator: ~11/10 = 156.725
Vals: 8d, 38df, 46
Badness: 0.026339

25 February 2022

Browser (103 & 111)

7-limit
Comma list: 16875/16807, 78732/78125
Mapping: [⟨1 6 8 10], ⟨0 -35 -45 -57]]
POTE generator: ~49/45 = 151.399
Vals: 103, 111, 214
Badness: 0.180645

11-limit
Comma list: 540/539, 1375/1372, 78732/78125
Mapping: [⟨1 6 8 10 8], ⟨0 -35 -45 -57 -36]]
POTE generator: ~12/11 = 151.405
Vals: 103, 214
Badness: 0.057634

13-limit
Comma list: 351/350, 540/539, 847/845, 1375/1372
Mapping: [⟨1 6 8 10 8 9], ⟨0 -35 -45 -57 -36 -42]]
POTE generator: ~12/11 = 151.403
Vals: 103, 111, 214
Badness: 0.028822

17-limit
Comma list: 351/350, 540/539, 561/560, 715/714, 847/845
Mapping: [⟨1 6 8 10 8 9 8], ⟨0 -35 -45 -57 -36 -42 -31]]
POTE generator: ~12/11 = 151.397
Vals: 103, 111, 214
Badness: 0.020384

19-limit
Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714
Mapping: [⟨1 6 8 10 8 9 8 18], ⟨0 -35 -45 -57 -36 -42 -31 -109]]
POTE generator: ~12/11 = 151.396
Vals: 103h, 111, 214
Badness: 0.017570

Grazer (113 & 121)

7-limit
Comma list: 16875/16807, 1071875/1062882
Mapping: [⟨1 -3 -4 -5], ⟨0 37 51 63]]
POTE generator: ~49/45 = 148.719
Vals: 113, 121, 234
Badness: 0.217166

11-limit
Comma list: 540/539, 1375/1372, 218750/216513
Mapping: [⟨1 -3 -4 -5 -1], ⟨0 37 51 63 36]]
POTE generator: ~12/11 = 148.729
Vals: 113, 121, 234, 355e, 589cee
Badness: 0.076062

13-limit
Comma list: 325/324, 364/363, 540/539, 2200/2197
Mapping: [⟨1 -3 -4 -5 -1 -2], ⟨0 37 51 63 36 46]]
POTE generator: ~12/11 = 148.729
Vals: 113, 121, 234, 355e, 589cee
Badness: 0.036248

17-limit
Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
Mapping: [⟨1 -3 -4 -5 -1 -2 0], ⟨0 37 51 63 36 46 33]]
POTE generator: ~12/11 = 148.735
Vals: 113, 121, 234g, 355eg
Badness: 0.025410

19-limit
Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
Mapping: [⟨1 -3 -4 -5 -1 -2 0 4], ⟨0 37 51 63 36 46 33 2]]
POTE generator: ~12/11 = 148.727
Vals: 113, 121, 234g, 355eg, 589ceegg
Badness: 0.022574

26 February 2022

Quadrasruta (58 & 68)

7-limit
Comma list: 2048/2025, 2401/2400
Mapping: [⟨2 0 11 8], ⟨0 4 -8 -3]]
POTE generator: ~15/14 = 123.784
Vals: 10, 38c, 48c, 58, 68, 126
Badness: 0.073569

11-limit
Comma list: 176/175, 896/891, 2401/2400
Mapping: [⟨2 0 11 8 22], ⟨0 4 -8 -3 -19]]
POTE generator: ~15/14 = 123.882
Vals: 58, 126, 184c, 310bccde
Badness: 0.049018

13-limit
Comma list: 176/175, 196/195, 512/507, 676/675
Mapping: [⟨2 0 11 8 22 9], ⟨0 4 -8 -3 -19 -2]]
POTE generator: ~14/13 = 123.901
Vals: 58, 126f, 184cff
Badness: 0.028463

17-limit
Comma list: 136/135, 170/169, 176/175, 196/195, 256/255
Mapping: [⟨2 0 11 8 22 9 5], ⟨0 4 -8 -3 -19 -2 4]]
POTE generator: ~14/13 = 123.838
Vals: 58, 126f
Badness: 0.023820

Quadrafourths (10 & 58)

11-limit
Comma list: 243/242, 441/440, 2048/2025
Mapping: [⟨2 0 11 8 -1], ⟨0 4 -8 -3 10]]
POTE generator: ~15/14 = 123.983
Vals: 10, 38c, 48c, 58
Badness: 0.049114

13-limit
Comma list: 144/143, 196/195, 243/242, 676/675
Mapping: [⟨2 0 11 8 -1 9], ⟨0 4 -8 -3 10 -2]]
POTE generator: ~14/13 = 123.972
Vals: 10, 38c, 48c, 58
Badness: 0.026743

17-limit
Comma list: 136/135, 144/143, 170/169, 196/195, 221/220
Mapping: [⟨2 0 11 8 -1 9 5], ⟨0 4 -8 -3 10 -2 4]]
POTE generator: ~14/13 = 123.923
Vals: 10, 38c, 48c, 58, 126eef, 184ceeff
Badness: 0.022239

27 February 2022

Pajarita (10 & 12)

13-limit
Comma list: 40/39, 50/49, 64/63, 66/65
Mapping: [⟨2 0 11 12 26 17], ⟨0 1 -2 -2 -6 -3]]
POTE generator: ~3/2 = 707.450
Vals: 10e, 12f, 22f
Badness: 0.022677

17-limit
Comma list: 40/39, 50/49, 64/63, 66/65, 85/84
Mapping: [⟨2 0 11 12 26 17 5], ⟨0 1 -2 -2 -6 -3 1]]
POTE generator: ~3/2 = 707.947
Vals: 10e, 12f, 22f
Badness: 0.019007

Proposed in March 2022

4 March 2022

Catamite (46 & 99)

11-limit
Comma list: 441/440, 896/891, 4375/4374
Mapping: [⟨1 3 6 -2 -7], ⟨0 -5 -13 17 37]]
POTE generator: ~128/105 = 339.340
Vals: 46, 99e, 145, 244e
Badness: 0.040976

13-limit
Comma list: 196/195, 352/351, 364/363, 4375/4374
Mapping: [⟨1 3 6 -2 -7 -11], ⟨0 -5 -13 17 37 52]]
POTE generator: ~128/105 = 339.313
Vals: 46, 99ef, 145
Badness: 0.034215

17-limit
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Mapping: [⟨1 3 6 -2 -7 -11 -1], ⟨0 -5 -13 17 37 52 18]]
POTE generator: ~17/14 = 339.313
Vals: 46, 99ef, 145
Badness: 0.021193

19-limit
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Mapping: [⟨1 3 6 -2 -7 -11 -1 -13], ⟨0 -5 -13 17 37 52 18 61]]
POTE generator: ~17/14 = 339.325
Vals: 46, 99ef, 145
Badness: 0.018864

6 March 2022

Hemikwai (82 & 111)

13-limit
Comma list: 540/539, 676/675, 1375/1372, 5120/5103
Mapping: [⟨1 2 16 14 -4 18], ⟨0 -2 -66 -54 36 -69]]
POTE generator: ~15/13 = 248.686
Vals: 82, 111, 193, 304d
Badness: 0.044108

17-limit
Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
Mapping: [⟨1 2 16 14 -4 18 13], ⟨0 -2 -66 -54 36 -69 -43]]
POTE generator: ~15/13 = 248.686
Vals: 82, 111, 193, 304d
Badness: 0.025806

19-limit
Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
Mapping: [⟨1 2 16 14 -4 18 13 20], ⟨0 -2 -66 -54 36 -69 -43 -76]]
POTE generator: ~15/13 = 248.687
Vals: 82, 111, 193, 304dh
Badness: 0.019146

9 March 2022

Yarm (79 & 80)

11-limit
Comma list: 1331/1323, 1728/1715, 4000/3969
Mapping: [⟨1 2 3 3 4], ⟨0 -33 -54 -15 -43]]
POTE generator: ~100/99 = 15.046
Vals: 79, 80, 239dd, 319dd
Badness: 0.099950

13-limit
Comma list: 169/168, 325/324, 640/637, 1331/1323
Mapping: [⟨1 2 3 3 4 4], ⟨0 -33 -54 -15 -43 -24]]
POTE generator: ~100/99 = 15.060
Vals: 79, 80, 159d, 239dd
Badness: 0.061645

17-limit
Comma list: 169/168, 325/324, 561/560, 640/637, 850/847
Mapping: [⟨1 2 3 3 4 4 4], ⟨0 -33 -54 -15 -43 -24 7]]
POTE generator: ~100/99 = 15.066
Vals: 79, 80, 159d, 239dd
Badness: 0.046718

10 March 2022

Cohedim (8bce & 12)

(Proposed name for disambiguation of diminished extension)
11-limit
Comma list: 36/35, 50/49, 125/121
Mapping: [⟨4 7 10 12 15], ⟨0 -2 -2 -2 -3]]
POTE generator: ~12/11 = 101.679
Vals: 8bce, 12
Badness: 0.054965

13-limit
Comma list: 36/35, 50/49, 66/65, 125/121
Mapping: [⟨4 7 10 12 15 16], ⟨0 -2 -2 -2 -3 -3]]
POTE generator: ~12/11 = 102.299
Vals: 8bcef, 12f
Badness: 0.041707

12 March 2022

October (41 & 68)

11-limit
Comma list: 245/243, 385/384, 1375/1372
Mapping: [⟨1 1 1 2 5], ⟨0 8 18 11 -21]]
POTE generator: ~21/20 = 88.035
Vals: 27, 41, 68, 109, 150, 259
Badness: 0.039643

13-limit
Comma list: 196/195, 245/243, 275/273, 385/384
Mapping: [⟨1 1 1 2 5 4], ⟨0 8 18 11 -21 -4]]
POTE generator: ~21/20 = 88.075
Vals: 27, 41, 68, 109f
Badness: 0.031136

17-limit
Comma list: 154/153, 170/169, 196/195, 245/243, 256/255
Mapping: [⟨1 1 1 2 5 4 6], ⟨0 8 18 11 -21 -4 -26]]
POTE generator: ~21/20 = 88.104
Vals: 27, 41, 68, 109f
Badness: 0.026833

19-limit
Comma list: 154/153, 170/169, 190/189, 196/195, 209/208, 245/243
Mapping: [⟨1 1 1 2 5 4 6 3], ⟨0 8 18 11 -21 -4 -26 17]]
POTE generator: ~19/18 = 88.113
Vals: 27, 41, 68, 109f, 177ffg
Badness: 0.020511

16 March 2022

Dichotomic (3 & 7)

11-limit
Comma list: 22/21, 25/24, 33/32
Mapping: [⟨1 1 2 4 4], ⟨0 2 1 -4 -2]]
POTE generator: ~5/4 = 354.073
Vals: 3, 7, 10e, 17e
Badness: 0.031719

13-limit
Comma list: 22/21, 25/24, 33/32, 40/39
Mapping: [⟨1 1 2 4 4 4], ⟨0 2 1 -4 -2 -1]]
POTE generator: ~5/4 = 354.313
Vals: 3, 7, 10e, 17e
Badness: 0.022741

19 March 2022

Seminar (46 & 296)

11-limit
Comma list: 3025/3024, 4375/4374, 2100875/2097152
Mapping: [⟨2 -2 -6 12 13], ⟨0 17 35 -21 -20]]
POTE generator: ~10/9 = 182.457
Vals: 46, 204c, 250, 296, 342
Badness: 0.026808

Chromat (99 & 159)

11-limit
Comma list: 441/440, 4375/4356, 10976/10935
Mapping: [⟨3 4 5 6 6], ⟨0 5 13 16 29]]
POTE generator: ~28/27 = 60.430
Vals: 60e, 99e, 159, 258, 417d
Badness: 0.050379

13-limit
Comma list: 364/363, 441/440, 625/624, 10976/10935
Mapping: [⟨3 4 5 6 6 4], ⟨0 5 13 16 29 47]]
POTE generator: ~28/27 = 60.428
Vals: 99ef, 159, 258, 417d
Badness: 0.046006

17-limit
Comma list: 364/363, 375/374, 441/440, 595/594, 3773/3757
Mapping: [⟨3 4 5 6 6 4 10], ⟨0 5 13 16 29 47 15]]
POTE generator: ~28/27 = 60.438
Vals: 99ef, 159, 258, 417dg
Badness: 0.031678

Catachrome (60 & 99)

13-limit
Comma list: 325/324, 441/440, 1001/1000, 10976/10935
Mapping: [⟨3 4 5 6 6 12], ⟨0 5 13 16 29 -6]]
POTE generator: ~28/27 = 60.378
Vals: 60e, 99e, 159
Badness: 0.043844

17-limit
Comma list: 273/272, 325/324, 375/374, 441/440, 4928/4913
Mapping: [⟨3 4 5 6 6 12 10], ⟨0 5 13 16 29 -6 15]]
POTE generator: ~28/27 = 60.377
Vals: 60e, 99e, 159
Badness: 0.030218

Chromic (60 & 99)

13-limit
Comma list: 196/195, 352/351, 729/728, 1875/1859
Mapping: [⟨3 4 5 6 6 9], ⟨0 5 13 16 29 14]]
POTE generator: ~27/26 = 60.456
Vals: 60e, 99ef, 159f, 258ff
Badness: 0.049857

17-limit
Comma list: 170/169, 196/195, 352/351, 375/374, 595/594
Mapping: [⟨3 4 5 6 6 9 10], ⟨0 5 13 16 29 14 15]]
POTE generator: ~27/26 = 60.459
Vals: 60e, 99ef, 159f, 258ff
Badness: 0.031043

20 March 2022

Trinity (152 & 159)

7-limit
Comma list: 703125/702464, 1600000/1594323
Mapping: [⟨1 8 19 46], ⟨0 -15 -39 -101]]
POTE generator: ~168/125 = 513.178
Vals: 152, 311, 463, 774
Badness: 0.119453

11-limit
Comma list: 3025/3024, 4000/3993, 19712/19683
Mapping: [⟨1 8 19 46 18], ⟨0 -15 -39 -101 -34]]
POTE generator: ~121/90 = 513.177
Vals: 152, 311, 463, 774, 1237e
Badness: 0.031296

13-limit
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
Mapping: [⟨1 8 19 46 18 64], ⟨0 -15 -39 -101 -34 -141]]
POTE generator: ~35/26 = 513.182
Vals: 152f, 311
Badness: 0.026418

17-limit
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
Mapping: [⟨1 8 19 46 18 64 -22], ⟨0 -15 -39 -101 -34 -141 61]]
POTE generator: ~35/26 = 513.186
Vals: 152f, 159, 311, 1092cdg, 1403cdg, 1714cdeg
Badness: 0.025588

19-limit
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
Mapping: [⟨1 8 19 46 18 64 -22 53], ⟨0 -15 -39 -101 -34 -141 61 -114]]
POTE generator: ~35/26 = 513.185
Vals: 152f, 159, 311, 1403cdgh, 1714cdegh, 2025cdefgghh, 2336bccdefgghh
Badness: 0.018412

23-limit
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
Mapping: [⟨1 8 19 46 18 64 -22 53 49], ⟨0 -15 -39 -101 -34 -141 61 -114 -104]]
POTE generator: ~35/26 = 513.185
Vals: 152f, 159, 311, 1092cdgh, 1403cdgh, 1714cdeghi
Badness: 0.014343

29-limit
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
Mapping: [⟨1 8 19 46 18 64 -22 53 49 72], ⟨0 -15 -39 -101 -34 -141 61 -114 -104 -157]]
POTE generator: ~35/26 = 513.186
Vals: 152fj, 159, 311, 781dh, 1092cdgh, 1403cdgh
Badness: 0.012038

21 March 2022

Poseidon (68 & 274)

11-limit
Comma list: 2401/2400, 9801/9800, 9453125/9437184
Mapping: [⟨2 2 4 5 8], ⟨0 40 22 21 -37]]
POTE generator: ~99/98 = 17.545
Vals: 68, 206b, 274, 342
Badness: 0.041727

23 March 2022

Salacia (103 & 171)

11-limit
Comma list: 243/242, 441/440, 9765625/9732096
Mapping: [⟨1 21 13 13 52], ⟨0 -40 -22 -21 -100]]
POTE generator: ~7/5 = 582.478
Vals: 68e, 103, 171, 274, 719be, 993bcde, 1267bbcde
Badness: 0.069721

13-limit
Comma list: 243/242, 441/440, 625/624, 2200/2197
Mapping: [⟨1 21 13 13 52 27], ⟨0 -40 -22 -21 -100 -48]]
POTE generator: ~7/5 = 582.477
Vals: 68e, 103, 171, 274, 719be, 993bcde
Badness: 0.034977

17-limit
Comma list: 243/242, 375/374, 441/440, 625/624, 2200/2197
Mapping: [⟨1 21 13 13 52 27 7], ⟨0 -40 -22 -21 -100 -48 -6]]
POTE generator: ~7/5 = 582.475
Vals: 68e, 103, 171, 274, 445e, 719be, 1164bcdeef
Badness: 0.024577

Commas which this user proposed names

This user proposed new names for following commas.

Proposed in April 2021

4 April 2021

• hewuermera: 589824/588245, satribiru-agu
• triwellisma: 235298/234375, tribizo-asepgu (name revised on 24 April 2021)

25 April 2021

• quadrawellisma: 67528125/67108864, lalaquadzo-aquinyo

26 April 2021

• catasyc comma: 390625/387072, laruquadbiyo

28 April 2021

• mistisma: 458752/455625, sazoquadgu

Proposed in May 2021

3 May 2021

• hemfiness comma: 4096000/4084101, saquinru-atriyo
• marvelfifths comma: 158203125/157351936, laquadru-atritriyo (name revised on 13 May 2021)
• chromatisma: 640000000000000000/635585924776181463, trisa-triru-aquadquadyo

4 May 2021

• bronzisma: 2097152/2083725, satriru-agugu

6 May 2021

• sesquiquartisma: 2460375/2458624, laquadru-atruyo
• mitonisma: 5250987/5242880, laquadzo-agu
• olympia: 131072/130977, salururu (name revised on 2 August 2021)

13 May 2021

• sensamagicfifths comma: [-11 42 -7 -14⟩, trila-seprurugu

19 May 2021

• secanticornisma: 177147/175000, laruquingu

23 May 2021

• supermatertisma: 52734375/52706752, lasepru-atritriyo
• supermasesquartisma: 184528125/184473632, laquadbiru-aquinyo

27 May 2021

• septimirod comma: 84035/82944, quinzo-ayo

Proposed in June 2021

8 June 2021

• vorwell comma: 134217728/133984375, sasatriru-aquadbigu
• maitri comma: 40353607/40000000, tritrizo-asepgu

28 June 2021

• compass comma: 9765625/9680832, quinruyoyo

Proposed in July 2021

12 July 2021

• fantares comma: 4375/4356, luluzoquadyo

13 July 2021

• septiness comma: 67108864/66706983, sasasepru
• decovulture comma: 67108864/66976875, sasabirugugu

18 July 2021

• pontiqak comma: 95703125/95551488, lazozotritriyo

Proposed in August 2021

7 August 2021

• slither comma: 40960000/40353607, satritriru-aquadyo

8 August 2021

• mermisma: 2500000/2470629, sepruyo

13 August 2021

• valenwuer comma: 110592/109375, sarutribigu
• negricorn comma: 153664/151875, saquadzogu

14 August 2021

• parkleiness comma: 1959552/1953125, zotritrigu

19 August 2021

• mynaslender comma: 829440/823543, sepru-ayo

Proposed in September 2021

11 September 2021

• buzzardisma: 65536/64827, saquadru

15 September 2021

• neptunisma: 48828125/48771072, laruruleyo

Proposed in October 2021

16 October 2021

• domicomp comma: 413343/409600, lazogugu

Proposed in November 2021

5 November 2021

• trienstonisma: 43046721/43025920, laquinru-agu

7 November 2021

• lokisma: 102760448/102515625, sasazozo-atribigu

Proposed in January 2022

6 January 2022

• countriton comma: 16777216000000000 / 16677181699666569, quadsa-tritriyo

11 January 2022

• diagassormisma: 3042/3025, bitholugu

15 January 2022

• gaster comma: [-70 72 -19⟩, quadbila-negu

22 January 2022

• mabilisma: 1071875/1048576, latrizo-aquinyo
• pentonisma: 281974669312/281950621875, saquinthuzogu

Proposed in February 2022

22 February 2022

• diahuntmisma: 8281/8192, labithozo

25 February 2022

• schismean comma: 3645/3584, laruyo

Proposed in March 2022

6 March 2022

• acrodec comma: 7710244864/7688671875, sasatribizo-aquadbigu

19 March 2022

• lynchisma: 120/119, suruyo

Documents

• Rank-two regular temperament