# User:TallKite/Catalog of thirteen-limit rank two temperaments with Color names

Original version is at https://en.xen.wiki/w/Catalog_of_thirteen-limit_rank_two_temperaments

Below is a complete listing of all 239 13-limit rank-two temperaments with generator complexity less than 40 and TE badness less than 0.025, obtained by the method discussed here. The TE error is multiplied by 1200 so that it can be thought of as cents, and the badness is multiplied by 1000. Some "Junk" temperaments of very low complexity and high error are listed below the main list, which is ordered by increasing generator complexity, with ties broken by TE complexity.

# Temperament list

THIS LIST IS SORTABLE, so you can sort by name or by pergen, and look up a specific temperament. Rules for choosing comma sets: prime limit strictly ascends, no torsion allowed, primes excluded because of downward inheritances are not allowed in other commas, and double-odd-limit is minimized. See: Color Notation/Temperament names.

• Color name column: alternatives or objections are bolded
• Pergen column: all double-splits are false doubles unless otherwise noted.
• Commas column: ratios are grouped by prime limit with actual commas (","), and sorted within prime-limit by double odd limit.
• Cmp = Complexity = corresponds roughly to the odd limit of the commas
• Err = Error = corresponds roughly to the cents discrepancy from JI
• Bad = Badness = a combination of complexity and error
Name Color Name Pergen Commas Mapping Cmp Error Bad
Dicot (extension) Yoyo (& Ruyo & Loru & Thoruru) (P8, P5/2) 25/24, 15/14, 22/21, 52/49 1 1 2 2 2 2
0 2 1 3 5 6
1.6214 27.3134 18.9555
Father (extension) Gubi (& Zo & Loru & Thogugu) (P8, P5) 16/15, 28/27, 22/21, 26/25 1 0 4 -2 -3 7
0 1 -1 3 4 -2
1.6967 21.9084 20.1335
Yoyo & Ruyo & Loru & Thuyo (P8, P5/2) 25/24, 15/14, 22/21, 40/39 1 1 2 2 2 4
0 2 1 3 5 -1
1.7156 27.3628 22.7796
Gu & Zogu & Luzoyo & Thuzo (P8, P5) 81/80, 21/20, 35/33, 14/13 1 0 -4 -2 -6 -1
0 1 4 3 6 3
1.7344 27.8260 21.2719
Gu & Ruyo & Loru & Thu (P8, P5) 81/80, 15/14, 22/21, 27/26 1 0 -4 -5 -6 -1
0 1 4 5 6 3
1.7810 27.5776 24.7359
Gubi & Zogu & Luzoyo & Thuzo (P8, P5) 16/15, 21/20, 35/33, 14/13 1 0 4 6 10 7
0 1 -1 -2 -4 -2
1.7872 36.0627 24.9964
Yoyo & Zogu & Lo & Thuzo (P8, P5/2) 25/24, 21/20, 33/32, 14/13 1 1 2 3 4 4
0 2 1 -1 -2 -1
1.8400 30.6716 23.4200
Yoyo & Ruyo & Lo & Thuyo (P8, P5/2) 25/24, 15/14, 33/32, 40/39 1 1 2 2 4 4
0 2 1 3 -2 -1
1.8400 26.9815 23.8284
Layobi & Ruyo & Loru & Thuyo (P8, P5) 135/128, 15/14, 22/21, 40/39 1 0 7 6 5 10
0 1 -3 -2 -1 -4
1.9230 27.4422 23.2705
Gu & Zogu & Lo & Thuzo (P8, P5) 81/80, 21/20, 33/32, 14/13 1 0 -4 -2 5 -1
0 1 4 3 -1 3
2.0118 27.4831 23.7844
Beep (extension) Gugu (& Zogu & Luyo & Thogugu) (P8, P5/2) 27/25, 21/20, 45/44, 26/25 1 0 0 2 -2 -1
0 2 3 1 7 6
2.0235 19.3072 18.0832
Gubi & Zo & Loru & Thoruru (P8, P5) 16/15, 28/27, 22/21, 52/49 1 0 4 -2 -3 -6
0 1 -1 3 4 6
2.0521 22.3720 21.6827
Gugu & Zogu & Loruru & Thuloyo (P8, P4/2) 27/25, 21/20, 99/98, 66/65 1 0 0 2 5 6
0 2 3 1 -2 -3
2.1027 19.4190 22.7850
Trigu & Rugu & Luyo & Thogugu (P8/3, P5) 128/125, 36/35, 45/44, 26/25 3 0 7 -1 1 11
0 1 0 2 2 0
2.1372 14.5611 22.2357
Hystrix (extension) Triyo & Rugu (& Loru & Thuyo) (P8, P4/3) 250/243, 36/35, 22/21, 40/39 1 2 3 3 4 4
0 -3 -5 -1 -4 -2
2.1534 17.2113 19.8014
Sawa & Zo & Luzoyo & Thuyo (P8/5, ^1) 256/243, 28/27, 35/33, 40/39 5 8 0 14 6 7
0 0 1 0 1 1
2.1534 17.4180 22.5573
Pentoid (extension) Gugu & Zogu & Lo (& Thogugu) (P8, P4/2) 27/25, 21/20, 33/32, 26/25 1 0 0 2 5 -1
0 2 3 1 -2 6
2.1996 18.8797 21.1593
Father variant Gubi & Zo & Luruyo & Thogugu (P8, P5) 16/15, 28/27, 80/77, 26/25 1 0 4 -2 10 7
0 1 -1 3 -4 -2
2.2249 19.9728 21.1254
Pelogic (extension) Layobi (& Zogu & Lo & Thu) (P8, P5) 135/128, 21/20, 33/32, 27/26 1 0 7 9 5 -1
0 1 -3 -4 -1 3
2.2355 17.0065 21.5281
Layobi (& Zogu & Lo) & Thogugu (P8, P5) 135/128, 21/20, 33/32, 26/25 1 0 7 9 5 13
0 1 -3 -4 -1 -6
2.2524 18.4570 22.2116
Yoyo & Zo & Luzoyo & Thuyo (P8, P5/2) 25/24, 28/27, 35/33, 40/39 1 1 2 1 2 4
0 2 1 6 5 -1
2.4075 17.3437 21.8080
Gubi & Zotrigu & Loru & Thogugu (P8, P5) 16/15, 126/125, 22/21, 26/25 1 0 4 11 10 7
0 1 -1 -5 -4 -2
2.4120 22.2679 24.9369
25/24 28/27 35/33 65/63 1 1 2 1 2 1
0 2 1 6 5 9
2.4321 17.9441 23.0236
August 27/26 36/35 45/44 56/55 3 0 7 -1 1 -3
0 1 0 2 2 3
2.4321 11.6244 18.4482
Arnold 22/21 27/26 33/32 40/39 1 0 -4 6 5 -1
0 1 4 -2 -1 3
2.4351 20.2444 23.3005
Dominatrix 27/26 36/35 45/44 64/63 1 0 -4 6 -6 -1
0 1 4 -2 6 3
2.4468 13.7371 18.2887
Jamesbond 25/24 27/26 33/32 45/44 7 11 16 0 24 26
0 0 0 1 0 0
2.4935 16.1224 23.0035
Septimal 25/24 33/32 45/44 65/63 7 11 16 0 24 6
0 0 0 1 0 1
2.4935 13.2598 22.5694
Diminished variant 22/21 26/25 36/35 50/49 4 0 3 5 1 2
0 1 1 1 2 2
2.5237 17.3415 21.6035
Diminished variant 26/25 36/35 50/49 56/55 4 0 3 5 14 2
0 1 1 1 0 2
2.5237 15.0507 23.8852
Diminished variant 36/35 40/39 50/49 66/65 4 0 3 5 14 15
0 1 1 1 0 0
2.5237 11.9675 19.5087
Octokaidecal variant 22/21 28/27 40/39 50/49 2 0 -5 -4 -6 1
0 1 3 3 4 2
2.5841 16.7342 22.5814
Octokaidecal (extension) 28/27 40/39 50/49 55/54 2 0 -5 -4 7 1
0 1 3 3 0 2
2.5841 13.2207 20.6424
22/21 25/24 33/32 40/39 1 1 2 4 4 4
0 2 1 -4 -2 -1
2.6867 18.7092 22.7413
Dichotic (extension) 25/24 40/39 45/44 65/63 1 1 2 4 2 4
0 2 1 -4 5 -1
2.8702 14.1529 21.6740
Decimal (extension) 25/24 45/44 49/48 78/77 2 0 3 4 -1 1
0 2 1 1 5 4
2.8906 12.3389 21.3256
Blacksmith variant 28/27 40/39 49/48 66/65 5 8 0 14 -6 7
0 0 1 0 2 1
2.8906 11.1408 22.3247
Pajaric 40/39 45/44 50/49 56/55 2 0 11 12 7 17
0 1 -2 -2 0 -3
2.9846 11.0657 20.4605
Armodue (extension) 27/26 33/32 36/35 45/44 1 0 7 -5 5 -1
0 1 -3 5 -1 3
3.0731 12.8903 19.3512
Progression 26/25 36/35 56/55 66/65 1 1 2 2 3 3
0 5 3 7 4 6
3.1546 11.1466 18.1575
Opossum variant 26/25 28/27 55/54 65/63 1 2 3 4 4 5
0 -3 -5 -9 -4 -10
3.2059 14.1496 24.4605
Opossum 28/27 40/39 55/54 66/65 1 2 3 4 4 4
0 -3 -5 -9 -4 -2
3.2059 10.9238 19.3894
12 & 12f 36/35 45/44 50/49 56/55 12 19 28 34 42 0
0 0 0 0 0 1
3.2429 11.5467 24.8352
Diminished variant 27/26 36/35 45/44 50/49 4 0 3 5 -5 -4
0 1 1 1 3 3
3.4688 11.0754 22.8374
Godzilla 45/44 49/48 78/77 81/80 1 0 -4 2 -6 -5
0 2 8 1 12 11
3.4688 8.1712 22.5029
Meanundec 27/26 40/39 45/44 56/55 1 0 -4 -13 -6 -1
0 1 4 10 6 3
3.5621 12.3475 24.2428
Blacksmith (extension) 28/27 40/39 49/48 55/54 5 8 0 14 29 7
0 0 1 0 -1 1
3.5987 10.3814 20.4976
Triforce 49/48 56/55 66/65 77/75 3 0 7 6 8 4
0 2 0 1 1 3
3.7856 7.9575 20.2480
Darjeeling (extension) 49/48 55/54 66/65 77/75 1 0 1 2 0 0
0 6 5 3 13 14
3.7856 7.3788 21.4453
Negri 45/44 49/48 56/55 78/77 1 2 2 3 4 4
0 -4 3 -2 -5 -3
3.8157 8.6891 17.8329
Negric 33/32 49/48 65/64 91/90 1 2 2 3 3 4
0 -4 3 -2 4 -3
3.8157 8.5618 20.2047
Superpelog (extension) 33/32 45/44 49/48 78/77 1 0 7 2 5 6
0 2 -6 1 -2 -3
3.8459 10.9415 22.4731
33/32 49/48 55/54 91/90 1 0 -4 2 5 -5
0 2 8 1 -2 11
4.0235 8.0673 23.5937
Augene 40/39 56/55 64/63 66/65 3 0 7 18 20 16
0 1 0 -2 -2 -1
4.0300 8.4291 20.7855
Meanenneadecal 45/44 56/55 78/77 81/80 1 0 -4 -13 -6 -20
0 1 4 10 6 15
4.0536 7.5265 21.1818
Dominant 36/35 56/55 64/63 66/65 1 0 -4 6 13 18
0 1 4 -2 -6 -9
4.1548 9.0031 24.1076
Porcupine variant 40/39 55/54 64/63 66/65 1 2 3 2 4 4
0 -3 -5 6 -4 -2
4.2906 7.7242 21.2764
Hedgehog (extension) 50/49 55/54 65/63 99/98 2 1 1 2 4 3
0 3 5 5 4 6
4.3068 7.9361 21.5156
Keemun variant 49/48 56/55 91/90 625/624 1 0 1 2 4 0
0 6 5 3 -2 14
4.3637 6.3766 22.7494
Sensi variant 55/54 66/65 77/75 143/140 1 6 8 11 11 10
0 -7 -9 -13 -12 -10
4.6307 7.4628 23.2580
Sensis 56/55 78/77 91/90 100/99 1 6 8 11 6 10
0 -7 -9 -13 -4 -10
4.6307 5.5229 20.0172
Meanenneadecal variant 45/44 56/55 65/64 81/80 1 0 -4 -13 -6 10
0 1 4 10 6 -4
4.6430 8.6347 24.7630
Pajara variant 40/39 50/49 64/63 99/98 2 0 11 12 26 17
0 1 -2 -2 -6 -3
4.7306 7.8062 22.6765
Injera 45/44 50/49 78/77 99/98 2 0 -8 -7 -12 -21
0 1 4 4 6 9
4.8643 6.7024 21.5655
Flattone variant 33/32 55/54 65/64 105/104 1 0 -4 17 5 10
0 1 4 -9 -1 -4
4.9286 8.2456 24.9444
Flattone (extension) 45/44 65/64 78/77 81/80 1 0 -4 17 -6 10
0 1 4 -9 6 -4
4.9403 6.1445 22.2597
Nautilus 49/48 55/54 91/90 100/99 1 2 3 3 4 5
0 -6 -10 -3 -8 -19
5.1345 5.6901 22.2846
Meantone 66/65 81/80 99/98 105/104 1 0 -4 -13 -25 -20
0 1 4 10 18 15
5.2032 4.3643 18.0484
Ringo 56/55 64/63 78/77 91/90 1 1 5 4 2 4
0 2 -9 -4 5 -1
5.3214 5.7998 22.6194
Superpyth (extension) 64/63 78/77 91/90 100/99 1 0 -12 6 -22 -17
0 1 9 -2 16 13
5.3375 5.1055 24.6725
Ogene 56/55 64/63 91/90 100/99 3 0 7 18 20 -8
0 1 0 -2 -2 4
5.3801 5.4596 22.8903
Undevigintone 49/48 65/64 81/80 91/90 19 30 44 53 0 70
0 0 0 0 1 0
5.4922 4.8990 22.9331
Negroni 49/48 55/54 65/64 91/90 1 2 2 3 5 4
0 -4 3 -2 -15 -3
5.6280 5.5412 21.5588
56/55 78/77 91/90 128/125 9 0 21 11 17 19
0 1 0 1 1 1
5.6784 5.4793 24.1428
Blair 65/64 78/77 91/90 99/98 1 0 3 1 3 3
0 7 -3 8 2 3
5.7085 5.5776 23.0863
Winston 66/65 99/98 105/104 121/120 1 0 3 1 3 1
0 7 -3 8 2 12
5.7085 4.3658 19.9306
Agene 56/55 64/63 78/77 100/99 3 0 7 18 20 35
0 1 0 -2 -2 -5
5.9464 5.4878 23.1130
Pajara 50/49 64/63 99/98 975/968 2 0 11 12 26 36
0 1 -2 -2 -6 -9
6.1261 4.7671 22.3268
Cassandra 100/99 105/104 196/195 245/242 1 0 15 25 32 37
0 1 -8 -14 -18 -21
6.3059 3.2191 20.7493
Crepuscular 50/49 78/77 99/98 144/143 2 2 3 4 6 6
0 5 7 7 4 6
6.3093 4.5686 24.3679
Negril 49/48 65/64 91/90 875/858 1 2 2 3 2 4
0 -4 3 -2 14 -3
6.5706 5.1756 24.3832
Modus 64/63 78/77 100/99 144/143 1 1 1 4 2 4
0 4 9 -8 10 -2
6.7257 4.1699 23.8059
Lupercalia 66/65 105/104 121/120 126/125 1 1 2 3 3 3
0 9 5 -3 7 11
6.7470 4.1905 21.3278
Superkleismic 100/99 105/104 245/242 1188/1183 1 4 5 2 4 8
0 -9 -10 3 -2 -16
6.7470 3.2749 21.4777
Nusecond 66/65 99/98 121/120 126/125 1 3 4 5 5 5
0 -11 -13 -17 -12 -10
6.9402 4.0097 23.3231
Magic 100/99 105/104 144/143 196/195 1 0 2 -1 6 -2
0 5 1 12 -8 18
7.1768 3.2665 21.5095
Miraculous 105/104 144/143 196/195 275/273 1 1 3 3 2 4
0 6 -7 -2 15 -3
7.3507 2.7371 18.6685
Mohajira 66/65 105/104 121/120 512/507 1 1 0 6 2 4
0 2 8 -11 5 -1
7.3637 4.3193 23.3878
Mothra 81/80 99/98 105/104 144/143 1 1 0 3 5 1
0 3 12 -1 -8 14
7.4806 3.6713 23.9543
Würschmidt 99/98 144/143 176/175 275/273 1 7 3 15 17 1
0 -8 -1 -18 -20 4
7.4927 2.7652 23.5928
Meanpop 81/80 105/104 144/143 196/195 1 0 -4 -13 24 -20
0 1 4 10 -13 15
7.8114 3.1263 20.8828
Agora 81/80 99/98 105/104 121/120 1 3 8 6 7 14
0 -4 -16 -9 -10 -29
7.8369 3.4913 24.5215
Tritonic 105/104 121/120 196/195 275/273 1 4 -3 -3 2 -5
0 -5 11 12 3 18
8.0189 2.8102 22.9934
Dwynwen 91/90 121/120 126/125 176/175 1 1 2 3 3 2
0 9 5 -3 7 26
8.0948 2.9858 23.4609
Bohpier 100/99 144/143 245/243 275/273 1 0 0 0 2 2
0 13 19 23 12 14
8.2021 2.7870 24.8637
Myna 126/125 144/143 176/175 196/195 1 9 9 8 22 0
0 -10 -9 -7 -25 5
8.5778 1.9478 17.1255
Octacot 100/99 144/143 243/242 245/242 1 1 1 2 2 4
0 8 18 11 20 -4
8.8331 2.6029 23.2762
Sensus 91/90 126/125 169/168 352/351 1 6 8 11 23 10
0 -7 -9 -13 -31 -10
8.9610 2.9616 20.7887
Leapday 91/90 121/120 169/168 441/440 1 0 -31 -21 -14 -9
0 1 21 15 11 8
9.0442 2.8672 24.7316
Cataclysmic 99/98 169/168 176/175 275/273 1 0 1 -3 -5 0
0 6 5 22 32 14
9.2501 2.4818 22.5549
Diaschismic 126/125 176/175 196/195 364/363 2 0 11 31 45 55
0 1 -2 -8 -12 -15
9.3690 1.7525 18.9259
Septimin 105/104 144/143 196/195 245/242 1 4 1 5 5 7
0 -11 6 -10 -7 -15
9.5243 2.7176 23.1168
Witchcraft 105/104 196/195 245/243 1188/1183 1 0 2 -1 -7 -2
0 5 1 12 33 18
9.5391 2.5946 23.5472
Orwell 99/98 121/120 176/175 275/273 1 0 3 1 3 8
0 7 -3 8 2 -19
9.5510 2.3097 19.7181
Bunya 100/99 144/143 243/242 275/273 1 1 1 -1 2 4
0 4 9 26 10 -2
9.8019 2.6925 24.8861
Thuja 126/125 144/143 176/175 364/363 1 8 5 -2 4 16
0 -12 -5 9 -1 -23
10.7770 1.9835 22.8384
Alicorn 126/125 144/143 196/195 676/675 1 2 3 4 3 5
0 -8 -13 -23 9 -25
10.7943 1.9579 23.6666
Hemififths 144/143 196/195 243/242 364/363 1 1 -5 -1 2 4
0 2 25 13 5 -1
11.0372 1.5814 19.0896
Valentino 121/120 126/125 176/175 196/195 1 1 2 3 3 5
0 9 5 -3 7 -20
11.0831 2.0505 20.6653
Hendec 169/168 325/324 364/363 1716/1715 2 5 8 5 6 8
0 -6 -11 2 3 -2
11.2093 1.1966 17.7067
Bisemidim 126/125 144/143 196/195 364/363 2 1 2 2 5 5
0 9 11 15 8 10
11.3567 1.8575 23.8769
Infraorwell 144/143 176/175 196/195 364/363 1 14 0 16 12 20
0 -16 3 -17 -11 -21
11.3869 1.9483 23.6834
Garibaldi 225/224 275/273 325/324 385/384 1 0 15 25 -33 -28
0 1 -8 -14 23 20
11.6354 1.4775 20.6757
Hitchcock 121/120 169/168 176/175 325/324 1 3 6 -2 6 2
0 -5 -13 17 -9 6
11.6543 1.9118 22.4484
Quartonic 169/168 176/175 325/324 540/539 1 2 3 3 5 4
0 -11 -18 -5 -41 -8
11.8517 1.7776 23.8747
Buzzard 176/175 351/350 676/675 847/845 1 0 -6 4 -12 -7
0 4 21 -3 39 27
12.3421 1.1747 18.8425
Echidna 176/175 351/350 364/363 540/539 2 1 9 2 12 19
0 3 -6 5 -7 -16
12.4332 1.4956 23.6786
Mystery 196/195 352/351 364/363 676/675 29 46 0 14 33 40
0 0 1 1 1 1
12.4896 1.0869 18.5912
Sruti 144/143 176/175 351/350 676/675 2 0 11 -15 -1 9
0 2 -4 13 5 -1
12.7068 1.8820 23.7911
Compton 225/224 351/350 364/363 441/440 12 19 0 -22 -42 -67
0 0 1 2 3 4
12.9714 1.2359 21.8524
Lizard 225/224 351/350 364/363 385/384 2 1 5 2 8 11
0 6 -1 10 -3 -10
12.9759 1.3242 21.7807
Ennealimnic 169/168 243/242 325/324 441/440 9 1 1 12 -2 20
0 2 3 2 5 2
13.0079 1.3158 20.6966
Marvolo 169/168 225/224 364/363 441/440 1 2 1 1 2 3
0 -6 19 26 21 10
13.0470 1.3528 21.4699
Rodan 196/195 245/243 352/351 364/363 1 1 -1 3 6 8
0 3 17 -1 -13 -22
13.2667 1.3261 18.4483
Manna 225/224 243/242 325/324 385/384 1 1 3 3 2 0
0 6 -7 -2 15 38
13.2838 1.1773 17.0122
Tritikleismic 325/324 364/363 441/440 625/624 3 0 3 10 8 0
0 6 5 -2 3 14
13.4940 .8133 15.6523
Benediction 225/224 243/242 351/350 441/440 1 1 3 3 2 7
0 6 -7 -2 15 -34
13.5241 1.0143 15.7152
Catakleismic 169/168 225/224 325/324 385/384 1 0 1 -3 9 0
0 6 5 22 -21 14
13.9069 1.1908 16.8832
Qilin 126/125 176/175 196/195 2200/2197 1 2 3 4 6 5
0 -8 -13 -23 -49 -25
14.1642 1.6395 22.8419
Harry 243/242 351/350 441/440 676/675 2 4 7 7 9 11
0 -6 -17 -10 -15 -26
14.6430 .7511 13.0465
Semimiracle 169/168 225/224 243/242 385/384 2 2 6 6 4 7
0 6 -7 -2 15 2
14.7014 1.3334 24.6222
Catalytic 169/168 225/224 325/324 1716/1715 1 0 1 -3 -10 0
0 6 5 22 51 14
14.7423 1.3244 22.3368
Octopus 169/168 325/324 364/363 540/539 8 1 3 3 16 14
0 3 4 5 3 4
15.1423 1.1002 21.6786
Enneaportent 169/168 225/224 364/363 1716/1715 9 0 28 11 24 19
0 2 -1 2 1 2
15.2328 1.3133 22.3223
Bikleismic 169/168 225/224 243/242 325/324 2 0 2 -6 -1 0
0 6 5 22 15 14
15.6731 1.3198 21.8142
Hemithirds 196/195 352/351 1001/1000 1029/1024 1 4 2 2 7 0
0 -15 2 5 -22 23
15.6794 1.1293 21.7376
Gizzard 225/224 325/324 385/384 1573/1568 2 1 5 2 8 -2
0 6 -1 10 -3 26
15.7868 .9255 20.2519
Coditone 225/224 351/350 385/384 847/845 1 6 3 13 -3 2
0 -13 -2 -30 19 5
16.1784 1.1526 24.3522
Bison 351/350 364/363 441/440 10985/10976 2 5 7 3 3 4
0 -7 -9 10 15 13
17.5050 .7645 23.5039
Mirkat 351/350 540/539 676/675 1375/1372 3 2 1 2 9 1
0 6 13 14 3 22
17.8357 .6381 18.6316
Subfourth 352/351 364/363 540/539 676/675 1 0 17 4 11 16
0 4 -37 -3 -19 -31
18.4588 .9671 23.7996
Mintone 243/242 351/350 441/440 1188/1183 1 5 9 7 12 11
0 -22 -43 -27 -55 -47
18.5191 .9414 21.8493
Hemiseven 351/350 385/384 441/440 676/675 1 4 14 2 -5 19
0 -6 -29 2 21 -38
18.5600 .8367 21.9005
Quadritikleismic 325/324 385/384 625/624 1573/1568 4 0 4 7 17 0
0 6 5 4 -3 14
18.6111 .6278 18.7309
Sqrtphi 325/324 364/363 625/624 1375/1372 1 12 11 16 17 28
0 -30 -25 -38 -39 -70
18.9279 .7746 20.0402
Supers 352/351 540/539 729/728 1575/1573 2 1 -12 2 -9 -2
0 3 23 5 22 13
19.8111 .7880 21.6449
Kwai 352/351 540/539 729/728 1375/1372 1 0 -50 -40 32 37
0 1 33 27 -18 -21
19.8873 .7677 24.5550
Metakleismic 325/324 352/351 364/363 625/624 1 0 1 -12 -5 0
0 6 5 56 32 14
19.9476 .8865 24.3714
Catafourth 243/242 351/350 441/440 10985/10976 1 13 17 13 32 9
0 -28 -36 -25 -70 -13
20.2345 .6664 21.6939
Countercata 325/324 352/351 385/384 625/624 1 0 1 11 -5 0
0 6 5 -31 32 14
20.2925 .8135 20.1564
Ketchup 325/324 352/351 847/845 1331/1323 2 3 4 6 7 8
0 4 15 -9 -2 -14
20.4870 .8412 24.8236
Semihemi 352/351 676/675 847/845 1716/1715 2 0 -35 -15 -47 -37
0 2 25 13 34 28
21.5338 .5670 21.1879
Grendel 352/351 540/539 625/624 1375/1372 1 9 2 7 17 -5
0 -23 1 -13 -42 27
21.8078 .7473 24.8390
Hemiwürschmidt 243/242 351/350 441/440 3584/3575 1 15 4 7 37 -29
0 -16 -2 -5 -40 39
22.1019 .7291 23.0740
Ekadash 385/384441/440 625/624 729/728 2 5 8 5 6 19
0 -6 -11 2 3 -38
22.2725 .5694 20.3814
Arch 364/363 441/440 676/675 3136/3125 1 2 2 2 3 4
0 -18 14 35 20 -13
23.8240 .5728 19.5041
Sesquart 243/242 364/363 441/440 105644/105625 1 1 7 5 2 -2
0 4 -32 -15 10 39
24.3209 .6708 22.3961
Ennealimnic 243/242 364/363 441/440 625/624 9 1 1 12 -2 -33
0 2 3 2 5 10
24.3214 .7265 23.2502
Subpental 351/350 540/539 676/675 3136/3125 1 6 8 17 -6 16
0 -14 -18 -45 30 -39
24.7013 .6592 23.9401
Widefourth 385/384 441/440 625/624 847/845 1 16 8 -2 17 12
0 -33 -13 11 -31 -19
24.7390 .6202 21.6356
Hemimist 352/351 676/675 847/845 3025/3024 3 0 26 56 8 23
0 2 -8 -20 1 -5
25.1580 .5751 22.9233
Quincy 364/363 441/440 676/675 4375/4374 1 2 3 3 4 5
0 -30 -49 -14 -39 -94
25.4024 .5479 23.8618
Decal 441/440 729/728 1001/1000 4225/4224 10 0 -56 -67 -108 37
0 1 5 6 9 0
26.0158 .4227 23.9484
Hemischis 351/350 540/539 676/675 40656/40625 1 0 15 -17 51 14
0 2 -16 25 -60 -13
26.2491 .5658 20.8155
Hemimaquila 364/363 540/539 676/675 3584/3575 1 28 -7 30 19 34
0 -34 12 -35 -20 -39
26.6197 .5984 24.4449
Septisuperfourth 540/539 729/728 4000/3993 21168/21125 2 4 4 7 6 11
0 -9 7 -15 10 -39
27.1080 .4537 22.8872
Pogo 540/539 729/728 4000/3993 10985/10976 2 1 22 2 25 -2
0 3 -24 5 -25 13
27.6987 .3280 17.5141
Octoid 540/539 625/624 1375/1372 4000/3993 8 1 3 3 16 -21
0 3 4 5 3 13
28.1048 .3789 15.2738
Hemiennealimmal 676/675 1001/1000 1716/1715 3025/3024 18 0 -1 22 48 -19
0 2 3 2 1 6
29.1857 .2310 12.5045
Quanharuk 540/539 1375/1372 4096/4095 6656/6655 1 0 15 12 -7 -15
0 5 -40 -29 33 59
33.1711 .3531 21.3919
540/539 625/624 1375/1372 2200/2197 1 34 17 34 53 30
0 -53 -24 -51 -81 -43
33.4393 .3824 21.1266
676/675 1716/1715 3025/3024 4225/4224 1 48 5 76 107 76
0 -52 -3 -82 -116 -81
33.5315 .2302 19.4943
540/539 729/728 1375/1372 2200/2197 1 11 38 37 -1 26
0 -19 -72 -69 9 -45
33.6103 .3698 24.8815
540/539 729/728 1575/1573 2200/2197 2 1 -5 2 -2 -2
0 9 40 15 37 39
34.4541 .3541 20.1941
676/675 1001/1000 1716/1715 3136/3125 2 14 6 9 -10 25
0 -16 -2 -5 25 -26
34.6430 .3993 23.3876
Abigail 1716/1715 2080/2079 3025/3024 4096/4095 2 7 13 -1 1 -2
0 -11 -24 19 17 27
35.2653 .1098 8.8558
Decoid 676/675 1001/1000 1716/1715 4225/4224 10 0 47 36 98 37
0 2 -3 -1 -8 0
35.7438 .2238 13.4746
676/675 1001/1000 1716/1715 10648/10647 2 4 9 8 12 13
0 -8 -42 -23 -49 -54
36.1768 .2313 16.2821
676/675 1001/1000 3025/3024 10985/10976 3 0 -18 -32 8 -21
0 4 21 34 2 27
36.3331 .2325 18.6469
1716/1715 2080/2079 2200/2197 3025/3024 2 12 20 6 5 17
0 -23 -40 -1 5 -25
37.3448 .2265 20.4161
540/539 625/624 729/728 2200/2197 1 0 15 -59 135 56
0 1 -8 39 -83 -33
37.8845 .3814 23.6158
729/728 1001/1000 1716/1715 3025/3024 1 27 54 35 6 124
0 -30 -61 -38 -3 -142
38.3738 .2790 22.4115
676/675 1001/1000 3025/3024 4096/4095 3 2 8 16 9 8
0 8 -3 -22 4 9
38.6520 .2333 15.5572
Deca 1001/1000 3025/3024 4225/4224 4375/4374 10 4 9 2 18 37
0 5 6 11 7 0
39.1828 .1817 16.8103
625/624 1575/1573 2080/2079 2401/2400 1 29 33 25 25 99
0 -42 -47 -34 -33 -146
39.4548 .2872 20.8877

# Junk temperaments

Some of these contain the trivial commas 1-edo, Yobi, Rubi, Loquad and Thutri, which set some prime to some number of octaves, and in effect remove the prime from the subgroup. These trivial commas can be omitted from the temperament name if desired.

Name Commas Pergen Generator Mapping Comp Error Badness
1-edo (& Yobi & Rubi & Loquad) + tha

or Tha nowa (2.13 JI)

4/3, 5/4, 8/7, 11/8 (P8, M3) 16/13 1 2 2 3 3 0
0 0 0 0 0 1
.2702 336.2129 17.8545
1-edo (& Yobi & Rubi & Thutri) + ila

or iLa nowa (2.11 JI)

4/3, 5/4, 8/7, 16/13 (P8, P4) 11/8 1 2 2 3 0 4
0 0 0 0 1 0
.2891 283.7695 17.6578
1-edo (& Yobi & Rubi) & Tholutri

or Tholutri nowa

4/3, 5/4, 8/7, 13/11 (P8, P4) 11/8 = 13/8 1 2 2 3 0 0
0 0 0 0 1 1
.2891 287.8202 24.1056
2-edo (& Gutri & Rubi & Lu) + tha 9/8, 6/5, 8/7, 12/11 (P8/2, ^1) 16/13 2 3 5 6 7 0
0 0 0 0 0 1
.5405 108.8851 16.3368
2-edo (& Gutri & Rubi & Tho) + ila 9/8, 6/5, 8/7, 13/12 (P8/2, ^1) 11/8 2 3 5 6 0 7
0 0 0 0 1 0
.5781 130.7392 21.2974
Gutri & Zobi & Lu & Tho 6/5, 7/6, 12/11, 13/12 (P8, P5) 3/2 = 5/4 = 7/4

= 11/8 = 13/8

1 0 1 1 2 2
0 1 1 1 1 1
.6309 149.7414 19.8124
(Yobi &) Zobi & Lu & Tho 5/4, 7/6, 12/11, 13/12 (P8, P5) 3/2 = 7/4

= 11/8 = 13/8

1 0 2 1 2 2
0 1 0 1 1 1
.6309 145.2377 21.5971
(Yobi &) Zobi (& Loquad) & Tho 5/4, 7/6, 11/8, 13/12 (P8, P5) 3/2 = 7/4 = 13/8 1 0 2 1 3 2
0 1 0 1 0 1
.6309 135.7653 21.7806
Gutri (& Rubi) & Lu & Tho 6/5, 8/7, 12/11, 13/12 (P8, P5) 3/2 = 5/4

= 11/8 = 13/8

1 0 1 3 2 2
0 1 1 0 1 1
.6309 118.9826 21.3636
Gutri (& Rubi) & Lu & Thuquad 6/5, 8/7, 12/11, 18/13 (P8, P5) 3/2 = 5/4 = 11/8 1 0 1 3 2 1
0 1 1 0 1 2
.6309 118.2399 24.7286
Gutri (& Rubi) & Lu (& Thutri) 6/5, 8/7, 12/11, 16/13 (P8, P5) 3/2 = 5/4 = 11/8 1 0 1 3 2 4
0 1 1 0 1 0
.6309 99.9329 21.2702
Gutri & Rutri & Lu & Thuzo 6/5, 9/7, 12/11, 14/13 (P8, P5) 3/2 = 5/4 = 11/8 1 0 1 0 2 1
0 1 1 2 1 2
.7124 120.1537 22.8145
2-edo (& Gutri & Lu & Tho) + za 9/8, 6/5, 12/11, 13/12 (P8/2, ^1) 8/7 2 3 5 0 7 7
0 0 0 1 0 0
.7124 112.9622 24.7317
3-edo (& Yo & Zobi & Lotri) + tha 32/27, 10/9, 7/6, 11/9 (P8/3, ^1) 16/13 3 5 7 8 10 0
0 0 0 0 0 1
.8107 83.1978 22.0229
Yo & Zobi & Lotri & Tho 10/9, 7/6, 11/9, 13/12 (P8, P5) 3/2 = 7/4 = 13/8 1 0 -1 1 0 2
0 1 2 1 2 1
.8614 81.8009 18.7149
Yo & Zobi & Lu & Tho 10/9, 7/6, 12/11, 13/12 (P8, P5) 3/2 = 7/4

= 11/8 = 13/8

1 0 -1 1 2 2
0 1 2 1 1 1
.8614 93.1286 21.7729
Yo (& Rubi) & Lu & Tho 10/9, 8/7, 12/11, 13/12 (P8, P5) 3/2 = 11/8 = 13/8 1 0 -1 3 2 2
0 1 2 0 1 1
.8614 76.3571 22.8403
2-edo & Ruyo & Logu (& Tho) 9/8, 15/14, 11/10, 13/12 (P8/2, ^1) 5/4 = 7/6 = 11/8 2 3 0 1 2 7
0 0 1 1 1 0
.8614 57.0733 19.3277
2-edo & Ruyo & Lu & Thuzo 9/8, 15/14, 12/11, 14/13 (P8/2, ^1) 5/4 = 7/6 = 13/12 2 3 0 1 7 3
0 0 1 1 0 1
.8614 61.7635 21.4961
2-edo & Ruyo (& Lu & Tho) 9/8, 15/14, 12/11, 13/12 (P8/2, ^1) 5/4 = 7/6 2 3 0 1 7 7
0 0 1 1 0 0
.8614 64.6390 22.8779
3-edo (& Yo & Zobi & Lo) + ila 32/27, 10/9, 7/6, 13/12 (P8/3, P4) 11/8 3 5 7 8 0 11
0 0 0 0 1 0
.8672 75.4782 22.2821
Gubi & Rubi (& Lu) & Tho 16/15, 8/7, 12/11, 13/12 (P8, P5) 3/2 = 8/5

= 11/8 = 13/8

1 0 4 3 2 2
0 1 -1 0 1 1
1.0616 72.2918 22.6134
Gubi (& Rubi) & Lu (& Thutri) 16/15, 8/7, 12/11, 16/13 (P8, P5) 3/2 = 8/5 = 11/8 1 0 4 3 2 4
0 1 -1 0 1 0
1.0616 68.1560 21.3950
3-edo (& Yo) & Loru (& Tho) 32/27, 10/9, 22/21, 13/12 (P8/3, ^1) 8/7 = 12/11 3 5 7 0 2 11
0 0 0 1 1 0
1.0686 48.2352 24.6210
3-edo & Yo & Loru & Thuzo 32/27, 10/9, 22/21, 14/13 (P8/3, ^1) 8/7 = 12/11 3 5 7 0 2 3
0 0 0 1 1 1
1.0686 46.0898 24.1511
2-edo & Yoyo & Ruyo & Lu + tha 9/8, 25/24, 15/14, 12/11 (P8/4, ^1) 16/13 4 6 9 11 14 0
0 0 0 0 0 1
1.0810 54.4751 21.7669
2-edo & Ruyo & Logu & Thogugu 9/8, 15/14, 11/10, 26/25 (P8/2, ^1) 5/4 = 7/6 = 11/8 2 3 0 1 2 -2
0 0 1 1 1 2
1.0810 53.8146 21.8059
Yo & Ruyo & Loru & Tho 10/9, 15/14, 22/21, 13/12 (P8, P5) 3/2 = 13/8 1 0 -1 -2 -3 2
0 1 2 3 4 1
1.1563 51.8815 22.1512
2-edo & Yoyo & Ruyo & Thuzo + ila 9/8, 25/24, 15/14, 14/13 (P8/4, ^1) 11/8 4 6 9 11 0 15
0 0 0 0 1 0
1.1563 55.5099 24.5510
2-edo & Yoyo & Ruyo & Thuloyo + ila 9/8, 25/24, 15/14, 55/52 (P8/4, ^1) 11/8 4 6 9 11 0 1
0 0 0 0 1 1
1.1563 41.3624 24.4943
Gubi & Rubi & Lu & Thogugu 16/15, 8/7, 12/11, 26/25 (P8, P5) 3/2 = 8/5 = 11/8 1 0 4 3 2 7
0 1 -1 0 1 -2
1.1714 53.8501 22.8620
Yoyo & Ruyo & Lu & Tho 25/24, 15/14, 12/11, 13/12 (P8, P5/2) 5/4 1 1 2 2 3 3
0 2 1 3 2 2
1.2619 55.5942 23.7686
Yoyo & Ruyo & Lu & Thuzo 25/24, 15/14, 12/11, 14/13 (P8, P5/2) 5/4 1 1 2 2 3 3
0 2 1 3 2 3
1.2619 53.0408 23.1630
Gugu & Zogu & Logu & Tho 27/25, 21/20, 11/10, 13/12 (P8, P4/2) 6/5 = 8/7 1 0 0 2 1 2
0 2 3 1 3 2
1.2920 43.2424 21.8817
Gugu & Zogu & Lu & Thuzo 27/25, 21/20, 12/11, 14/13 (P8, P4/2) 6/5 = 8/7 1 0 0 2 2 3
0 2 3 1 2 1
1.2920 39.0609 21.8839
Gugu & Zogu & Logu & Thuzo 27/25, 21/20, 11/10, 14/13 (P8, P4/2) 6/5 = 8/7 1 0 0 2 1 3
0 2 3 1 3 1
1.2920 42.8838 24.2613
Gubi & Zogu & Logu & Thuzo 16/15, 21/20, 11/10, 14/13 (P8, P5) 3/2 = 8/5

= 16/11

1 0 4 6 5 7
0 1 -1 -2 -1 -2
1.3433 43.8182 20.8537
Gubi & Zogu & Logu & Tho 16/15, 21/20, 11/10, 13/12 (P8, P5) 3/2 = 8/5

= 16/11 = 13/8

1 0 4 6 5 2
0 1 -1 -2 -1 1
1.3433 48.6247 23.3373
Gubi & Zogu & Lu & Thuzo 16/15, 21/20, 12/11, 14/13 (P8, P5) 3/2 = 8/5 = 11/8 1 0 4 6 2 7
0 1 -1 -2 1 -2
1.3433 41.3652 22.5640
Sawa & Gubi & Zogu & Logu + tha 256/243, 16/15, 21/20, 11/10 (P8/5, ^1) 16/13 5 8 12 14 17 0
0 0 0 0 0 1
1.3512 38.8900 22.4912
Sawa & Gubi & Zogu & Thuzo + ila 256/243, 16/15, 21/20, 14/13 (P8/5, ^1) 11/8 5 8 12 14 0 19
0 0 0 0 1 0
1.4453 33.1105 21.4624
Gubi & Zo & Lu & Thuzo 16/15, 28/27, 12/11, 14/13 (P8, P5) 3/2 = 8/5 = 11/8 1 0 4 -2 2 -1
0 1 -1 3 1 3
1.4993 37.8027 22.5820
Gubi & Zo & Lu & Thogugu 16/15, 28/27, 12/11, 26/25 (P8, P5) 3/2 = 8/5 = 11/8 1 0 4 -2 2 7
0 1 -1 3 1 -2
1.6091 33.9540 24.0271
Yoyo & Zogu & Logu & Tho 25/24, 21/20, 11/10, 13/12 (P8, P5/2) 5/4 = 21/16

= 11/8

1 1 2 3 3 3
0 2 1 -1 1 2
1.6181 43.6565 23.8050