The optimal patent val for a regular temperament is the unique patent val that supports the temperament with the lowest error.
Given any temperament, which is characterized by the commas it tempers out, there is a finite list of patent vals that temper out all the commas of the temperament in the same subgroup. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the one which has the lowest TE error; this is the (TE) optimal patent val for the temperament. Note that other definitions of error lead to different results.
On this wiki, the optimal patent val for each temperament is given as the last patent val in the optimal ET sequence, or stated explicitly in case it is not a member of the sequence.
Instructions
By tempering a JI scale using the N-edo found on the list below we automatically temper it to the corresponding temperament. This can be done in Scala using the Quantize command: either type in "Quantize/consistent N" on the bottom, or use the pull-down menu under "Modify", check the box saying "Consistent" and type N (without a decimal point) into "Resolution".
To limit the search range when finding the optimal patent val a useful observation is this: given N-edo, and an odd prime q ≤ p, if d is the absolute value in cents of the difference between the tuning of q given by the POTE tuning and the POTE tuning rounded to the nearest N-edo value, then d < 600/N, from which it follows that N < 600/d. Likewise, if e is the absolute value of the error of q in the patent val tuning, then e < 600/N and so N < 600/e. If N-edo defines an optimal patent val, then the patent val will be identical to the val obtained by rounding the POTE tuning to the nearest N-edo value. We have two distances from the patent val, one to the POTE tuning and one to the the JI tuning, both bounded by 600/N, and so by the triangle inequality the distance from the JI tuning to the POTE tuning, which is the error of the prime q in the POTE tuning, is bounded by 1200/N. Hence, N < 1200/error(q). If now we take the minimum value for 1200/error(prime) for all the odd primes up to p, we obtain an upper bound for N.
Examples
Below are tabulated some values. In each case an identifier which uniquely identifies the temperament in question is given. In the codimension one case, where the temperament is defined by a single comma, the comma is given and used as a name. In other cases, for a temperament of rank n, n independent vals are given. Normally this is by way of integers conjoined by ampersands, such as 2&10 for 7-limit pajara. This tells us we can use the 7-limit patent vals for 2 and 10 to define the temperament. In case n independent patent vals cannot be found, vals using the wart notation are given; this adjusts the nth prime mapping to its second-best value by appending the n-th lower-case letter in alphabetical order. Thus, "12f" adjusts a patent val for 12 in the 13-limit or above, for instance ⟨12 19 28 34 42 44], to ⟨12 19 28 34 42 45] (which is actually a better mapping, and hence more useful for this purpose.)
5-limit rank two
Comma: ET w/ optimal patent val: 1000 * badness
16/15: 8et 14.884
648/625: 12et 47.231
27/25: 14et 32.801
25/24: 17et 13.028
250/243: 22et 30.778
135/128: 23et 39.556
128/125: 39et 22.315
3125/3072: 60et 39.163
2048/2025: 80et 19.915
81/80: 81et 7.381
20000/19683: 109et 48.518
393216/390625: 164et 40.603
2109375/2097152: 296et 40.807
15625/15552: 458et 13.234
78732/78125: 539et 35.220
32805/32768: 749et 4.259
1600000/1594323: 873et 21.960
6115295232/6103515625: 1400et 31.181
1224440064/1220703125: 1496et 43.729
274877906944/274658203125: 1559et 20.576
31381059609/31250000000: 2760et 82.423
7629394531250/7625597484987: 3501et 17.191
7-limit rank two
Name: ET w/ optimal patent val: Val name: 1000*badness
Pater: 3et 3&11b 53.001
Flat: 4et 3&4 25.381
Father: 5et 3d&5 21.312
Mother: 5et 2&3 24.152
Sharptone: 5et 5&7d 24.848
Baba: 5et 1&5 44.321
Quint: 5et 5&15cd 48.312
Mite: 5et 1cdd&5 54.770
Walid: 6et 2&6 48.978
Dicot: 7et 4&7 19.935
Jamesbond: 7et 7&14c 41.714
Oxygen: 8et 7d&8 59.866
Beep: 9et 4&5 18.638
Progression: 9et 9&17c 48.356
Deflated: 9et 3&9 59.079
Fluorine: 9et 9&20bd 55.623
Sharp: 10et 3d&7d 28.942
Decimal: 10et 4&10 28.334
Sodium: 11et 4&11 55.814
Dominant: 12et 5&7 20.690
Diminished: 12et 4&12 22.401
August: 12et 9&12 26.459
Hexe: 12et 6&12 57.730
Schism: 12et 12&29de 56.648
Ripple: 12et 12&23 59.735
Blacksmith: 15et 5&10 25.640
Opossum: 15et 7d&8d 40.650
Inflated: 15et 15&48bc 54.729
Armodue: 16et 7&9 49.038
Dichotic: 17et 3&7 37.565
Octokaidecal: 18et 10&18 36.747
Uncle: 18et 5&18 72.653
Negri: 19et 1&9 26.483
Godzilla: 19et 5&19 26.747
Keemun: 19et 4&15 27.408
Wallaby: 19ccdd 2d&5c 58.468
Gorgo: 21et 5&16 46.385
Pajara: 22et 2&10 20.033
Hedgehog: 22et 14c&22 43.983
Lemba: 26et 10&16 62.208
Augene: 27et 3&12 24.816
Niner: 27et 9&18 67.157
Beatles: 27et 10&27 45.872
Nautilus: 29et 15&29 57.420
Mothra: 31et 5&26 37.146
Squares: 31et 31&45 45.993
Immunity: 34et 5&29 77.631
Injera: 38et 12&26 31.130
Triforce: 39et 6&9 54.988
Magic: 41et 19&41 18.918
Superkleismic: 41et 15&26 47.932
Quasitemp: 41et 4&37 60.269
Flattone: 45et 7&19 38.553
Sensi: 46et 19&27 25.622
Vines: 46et 4&42 78.049
Doublewide: 48et 4&18 43.462
Superpyth: 49et 5&17 32.318
Passion: 49et 12&37 62.327
Porky: 51et 22&51 54.389
Submajor: 53et 10&33 60.533
Liese: 55et 19&55 46.706
Sycamore: 56et 18&19 62.018
Diaschismic: 58et 12&34 37.914
Porcupine: 59et 7&15 41.057
Kumonga: 70et 16&27 87.500
Miracle: 72et 10&21 16.742
Wizard: 72et 22&50 40.846
Unicorn 77et 19&58 40.913
Bidia: 80et 12&56 56.474
Quartonic: 80et 26&27 42.632
Meantone: 81et 12&19 13.707
Myna: 89et 4&27 27.044
Septimin: 91et 9&32 54.502
Sfourth: 91et 45&46 123.291
Garibaldi: 94et 12&29 21.644
Misty: 99et 12&87 36.802
Nusecond: 101et 31&101 50.389
Octacot: 109et 27&41 33.845
Semisept: 111et 18&31 50.472
Buzzard: 111et 5&48 47.963
Guiron: 118et 36&41 47.544
Hemithirds: 118et 25&31 44.284
Hemikleismic: 121et 15&38 52.054
Pluto: 121et 41&80 57.514
Tritonic: 122et 2&29 47.578
Gravid: 123et 58&123 47.283
Slender: 125et 1&31 56.934
Merman: 125et 2&41 55.078
Rodan: 128et 5&41 37.112
Subpental: 130et 19&111 54.303
Bison: 130et 8&38 70.375
Orwell: 137et 9&22 20.375
Tertiaseptal: 171et 31&109 12.995
Septidiasemi: 171et 10&151 44.115
Pontiac: 171et 53&118 14.133
Tsaharuk: 171et 17&77 30.697
Mitonic: 171et 46&125 25.184
Mutt: 171et 3&84 28.406
Fifthplus: 171et 22&149 25.840
Pnict: 171et 15&141 45.660
Tokko: 171et 5&166 44.417
Seniority: 171et 26&145 44.877
Valentine: 185et 15&31 31.056
Sensei: 187et 19&84 59.218
Unidec: 190et 26&46 38.393
Catakleismic: 197et 19&53 21.501
Quadritikleismic: 212et 4&68 39.231
Hemiseven: 221et 5&72 56.557
Octoid: 224et 72&152 42.670
Compton: 228et 12&60 35.686
Tritikleismic: 231et 15&57 56.337
Mirkat: 255et 72&183 59.376
Decoid: 270et 10&120 33.902
Acrokleismic 270et 19&251 56.184
Septisuperfourth: 282et 22&86 59.241
Hemischis: 313et 24&53 45.817
Hemiwürschmidt: 328et 6&31 20.307
Hemififths: 338et 41&58 22.243
Amity: 350et 7&39 23.649
Bischismic: 378et 12&118 54.744
Nessafof: 381et 15&69 45.478
Septiquarter: 391et 5&94 53.760
Parakleismic: 415et 19&80 27.431
Gamera: 422et 26&73 37.648
Sengagen: 446et 49&50 57.978
Chromat: 456et 60&99 57.499
Countercata: 473et 34&53 52.128
Harry: 534et 58&72 34.077
Ennealimmal: 612et 27&45 3.610
Quinmite: 701et 4&95 37.322
Semidimfourth: 875et 91&99 55.245
Quasiorwell: 1111et 31&177 35.832
Amicable: 1131et 99&212 45.473
Vulture: 1133et 53&164 36.985
Emmthird 1255et 58&113 16.736
Septichrome 1308et 60&111 16.814
Sesquiquartififths: 1498et 41&89 11.244
Brahmagupta: 1547et 7&217 29.122
Maviloid: 1614et 76&99 57.632
Osiris: 1696et 157&171 28.307
Term: 1722et 12&159 19.950
Neptune: 1778et 35&68 23.427
Abigail: 1798et 46&132 37.000
Qak: 1831et 50&121 29.267
Enneadecal: 2185et 19&152 10.954
Newt: 2201et 41&188 41.878
Subneutral: 2236et 31&348 45.792
Orga: 2482et 26&244 40.236
Trillium: 4569et 53&441 30.852
Supermajor: 6214et 80&171 10.836
Semidimi: 8419et 171&863 15.075
Domain: 22038et 171&1164 13.979
7-limit rank three
Comma: ET w/ optimal patent val: 10^6 * badness
36/35: 12et 63.675
49/48: 19et 115.514
875/864: 41et 212.413
525/512: 45et 476.454
686/675: 46et 320.094
50/49: 48et 127.208
64/63: 49et 98.719
1029/1000: 55et 678.164
3125/3087: 94et 613.731
1728/1715: 111et 187.341
2430/2401: 137et 518.625
65625/65536: 171et 172.601
126/125: 185et 69.867
1029/1024: 190et 176.105
225/224: 197et 36.517
4000/3969: 215et 215.550
16875/16807: 224et 341.931
245/243: 283et 121.191
6144/6125: 381et 142.375
5120/5103: 391et 153.052
3136/3125: 446et 160.039
19683/19600: 587et 300.987
10976/10935: 695et 199.139
4802000/4782969: 1131et 1121.894
703125/702464: 2185et 149.828
2401/2400: 2749et 15.288
420175/419904: 4306et 86.449
4375/4374: 8419et 11.665
250047/250000: 12555et 21.301
78125000/78121827: 101654et 20.457
11-limit rank two
Name: ET w/ optimal patent val: Val name: 1000*badness
Fervor: 2et 2&27e 52.054
Decimated: 4et 4&10e 31.456
Coleto: 4et 4&27e 48.687
Semafour: 5et 5&14c 28.510
Neutrominant: 7et 7&10c 40.240
Arnold: 7et 5&7 26.141
Hystrix: 7et 7&15d 44.944
Dicot: 7et 4e&7 19.854
Jamesbond: 7et 7&14c 23.524
Modus: 7et 7&27e 35.149
Ptolemy: 7et 7&38d 58.785
Negric: 9et 1&9 30.617
Progression: 9et 8d&9 26.050
Superpelog: 9et 9&14c 28.535
Octokaidecal: 10et 10&18e 30.235
Decimal: 10et 10&14c 26.712
Sharp: 10et 10&17d 22.366
Ringo: 10et 10&17c 32.863
Dichosis: 10et 3&10 41.361
Decibel: 10et 4&6 32.385
Diminished: 12et 4&12 22.132
Pajaric: 12et 2&10 23.798
Dominant: 12et 5&12 24.180
Domineering: 12et 7&12 21.978
Lahoh: 12et 12&14ce 43.062
Duodecim: 12et 12&24d 30.536
Schism: 12et 12&41d 37.482
Injerous: 12e 12e&14c 38.577
Hexe: 12et 6&12 38.412
Ripple: 12et 1ce&12 38.811
Hemidim: 12et 12&20b 54.965
Smate: 14et 14&17c 42.518
Opossum: 15et 7d&8d 22.325
Kangaroo: 15et 2cde&15 43.195
Augene: 15et 3&12 19.613
Progress: 15et 2&13 31.036
Darjeeling: 15et 15&19e 27.648
Ferrier: 15et 5e&15 29.200
Inflated: 15et 15&48bce 31.171
Armodue: 16et 7&9 27.211
Bipelog: 16et 2&16 35.694
Dichotic: 17et 7&10 30.680
Sidi: 17et 14c&17 32.957
Domination: 17c 5e&12e 36.562
Negri: 19et 9&10 26.190
Meanenneadecal: 19et 12&19 21.182
Flattone 19et 7&19 33.839
Godzilla: 19et 14c&19 28.947
Undevigintone: 19et 19&38d 36.387
Meanundeci: 19e 12e&19e 31.539
Lisa: 19et 2cde&19 54.829
Horcrux: 19et 19&60e 39.282
Spell: 19et 6&19 59.791
Rhinoceros: 19et 1ce&19 59.319
Triton: 19et 2&19 45.675
Qeema: 19et 4e&19 40.056
Cataleptic: 19et 19&34d 44.335
Oodako: 21et 6&21 59.192
Pajara: 22et 12&22 20.343
Pajarous: 22et 10&22 28.349
Telepathy: 22et 19e&22 27.109
Hedgehog: 22et 14c&22 23.095
Ceratitid: 22et 1ce&22 51.319
Vigintiduo: 22et 22&66de 48.372
Astrology: 22et 22&60de 39.151
Divination: 22et 22&38d 35.864
Fleetwood: 22et 22&26e 35.202
Quasisupra: 22et 17c&22 32.203
Comic: 22et 2cde&22 45.052
Hemipaj: 22et 2&20 38.890
Mohamaq: 24et 17c&24 36.207
Baragon: 24et 5&19 35.673
Varan: 24et 19e&24 39.647
Hemiaug: 24et 24&27e 38.232
Hemidim: 24et 4e&24 56.576
Semidim: 24et 24&32c 30.597
Injera: 26et 12&26 23.124
Lemba: 26et 10&16 41.563
Secund: 26et 9&17 42.562
Crepuscular: 26et 26&34d 40.758
Quarto: 26et 26&27e 41.786
Cynder: 26et 5e&26 55.706
Cavalier: 26et 4e&26 52.899
Sensa: 27et 19e&27 36.835
Demolished: 28et 12&28 26.574
Nautilus: 29et 15&29 26.023
Negril: 29et 19&29 38.679
Negroni: 29et 10&29 35.296
Coendou: 29et 7&29 49.669
Wilsec: 29et 9&20 41.886
Impunity: 29et 5e&29 55.243
Immunity: 29et 5&29 52.661
Mohajira: 31et 7&24 26.064
Squares: 31et 31&45e 21.636
Cuboctahedra: 31et 31&45 56.826
Migration: 31et 31&100de 25.516
Tritonic: 31et 2&29 23.659
Casablanca: 31et 31&42 67.291
Myno: 31et 4&27 33.434
Cypress: 31et 20cde&31 42.719
Revelation: 31et 21&31 32.946
Diesic: 31et 1ce&31 44.186
Slurpee: 33et 16&33 50.514
Keemun: 34et 4&15 27.410
Wollemia: 34et 27e&34 37.551
Anguirus: 34et 10&24 49.253
Muggles: 35et 16&19 48.038
Greenwood: 35et 21&35 57.471
Liesel: 36et 19&36 40.721
Elisa: 36e 19e&36e 41.592
Catnip: 36et 12&24 34.478
Niner: 36et 9&36 34.861
Beatles: 37et 27e&37 45.639
Triforce: 39et 6&9 20.248
Andromeda: 41et 12&29 23.556
Superkleismic: 41et 15&26 25.659
Hemimiracle: 41et 20&21 59.232
Monkey: 41et 7&34 38.836
Bunya: 41et 7d&41 31.332
Hocus: 41et 38d&41 38.519
Witchcraft: 41et 41&60e 30.706
Trismegistus: 41et 16&41 45.623
Salsa: 41et 17&24 39.444
Varan: 41et 41&46e 44.937
Bohpier: 41et 41&49 33.949
Octacot: 41et 27e&41 24.078
Quato: 41et 4e&41 41.170
Plutino: 41et 2cde&41 57.966
Eugene: 42et 15&27 35.554
Amavil: 43et 9&43 42.649
Kumonga: 43et 16&43 43.336
Flattone: 45et 7&19 33.839
Sensor: 46et 19&27 37.942
Sensus: 46et 46&73 29.486
Leapday: 46et 29&46 38.624
Twothirdtonic: 46et 9&37 40.768
Aerodino: 46et 5e&46 54.294
Bamity: 46et 14c&46 35.504
Accord: 46et 7d&46 42.468
Vines: 46et 4&42 44.499
Doublewide: 48et 4&18 32.058
Superpyth: 49et 22&49 24.976
Passion: 49et 12&37 40.809
Catalan: 49et 15&49 36.894
Bimeantone: 50et 12&50 38.122
Porky: 51et 22&51 27.268
Orwell: 53et 9&22 15.231
Tricot: 53et 53&70 56.134
Cataclysmic: 53et 53&140d 39.954
Hamity: 53et 14c&53 42.947
Kleiboh: 53et 49&53 52.805
Maja: 53et 45e&53 49.991
Helenus: 53et 12&53 35.637
Hemigari: 53et 29&53 50.681
Quartz: 53et 26&53 53.285
Sycamore: 56et 18&19 55.940
Diaschismic: 58et 12&46 25.034
Hemififths: 58et 41&58 23.498
Thuja: 58et 15&43 33.078
Alicorn: 58et 19&58 39.156
Secant: 58et 26&58 46.373
Infraorwell: 58et 9&49 40.721
Sruti: 58et 24&58 41.459
Qilin: 58et 58&77 41.426
Gorgik: 58et 21&37 59.260
Porcupine: 59et 7&15 21.562
Worschmidt: 65et 31&65 33.436
Hemisensi: 65et 27e&65 48.714
Ammonite: 66et 29&37 45.694
Hemikleismic: 68et 15&38 38.023
Miracle: 72et 10&31 10.684
Catakleismic: 72et 19&53 21.849
Compton: 72et 12&72 22.235
Hours: 72et 24&48 36.248
Bikleismic: 72et 72&106 29.319
Ennealimnic: 72et 27e&72 20.697
Ennealiminal: 72et 27&45 31.123
Marvolo: 72et 29&43 28.965
Catalytic: 72et 53e&72 30.422
Enneaportent: 72et 9&54 30.426
Marrakesh: 73et 31&73 40.539
Valentine: 77et 15&31 16.687
Camahueto 77et 19&77 65.940
Keen: 78et 22&56 45.270
Sentinel: 79et 14&17 39.595
Echidna: 80et 22&58 25.987
Paradigmic: 80et 19&80 41.720
Bidia: 80et 12&68 40.191
Quartonic: 80et 53&80 34.031
Meanpop: 81et 19&31 21.543
Newspeak: 81et 31&84 31.438
Merman: 84et 2&41 36.383
Rodan: 87et 5&41 23.093
Clyde: 87et 19&68 47.41686
Misty: 87et 12&87 35.932
Emka: 87et 37&50 54.744
Mothra: 88et 5&26 25.642
Myna: 89et 31&58 16.842
Amigo: 89et 43&46 43.438
Septimin: 91et 9&32 31.309
Prajapati: 93et 31&93 42.959
Cassandra: 94et 41&53 27.396
Sanjaab: 94et 29&94 58.040
Magus: 95et 46&95 45.108
Interpental: 96et 43&53 51.806
Hitchcock: 99et 7&39 35.187
Hemiwur: 99et 6&31 29.270
Hendecatonic: 99et 22&55 46.088
Nusecond: 101et 31&101 25.621
Magic: 104et 19&22 25.621
Meantone: 105et 12&31 17.027
Bisemidim: 108et 50&58 41.190
Leapweek: 109et 17&46 50.679
Buzzard: 111et 53&58 34.484
Shrutar: 114et 22&46 26.489
Submajor: 116et 10&53 50.582
Hemithirds: 118et 31&87 19.003
Parakleismic: 118et 19&99 49.711
Quasitemp: 119et 4&37 43.209
Pluto: 121et 41&80 29.844
Subfourth: 121et 58&121 45.323
Tritoni: 122et 31&91 45.456
Slender: 125et 31&63 25.342
Srutal: 126et 46&80 35.315
Würschmidt: 127et 31&96 24.413
Mosura: 129et 31&129 31.334
Hemiwürschmidt: 130et 31&130 21.069
Sesquart: 130et 41&89 29.306
Bosonic: 130et 26&130 65.219
Hemimaquila: 130et 9&121 47.440
Borwell: 137et 31&106 38.377
Tertia: 140et 31&109 30.171
Fibo: 140et 37&103 56.514
Ketchup: 140et 46&94 39.555
Mystery: 145et 29&58 34.291
Echidnic: 148et 10&46 45.127
Heinz: 149et 46&103 42.412
Hemiseven: 149et 5&72 28.467
Grendel: 152et 31&121 19.845
Kwai: 152et 41&111 26.219
Supers: 152et 58&94 28.240
Amity: 152et 53&152 31.506
Whoops: 152et 15&137 43.743
Monocerus: 154et 58&154 52.757
Guiron: 159et 41&77 26.648
Mintone: 161et 58&103 39.962
Wizard: 166et 22&50 18.539
Polypyth: 167et 46&121 51.131
Parkleismic: 179et 80&179 55.844
Unidec: 190et 26&46 15.479
Triwell: 190et 31&97 29.807
Widefourth: 190et 16&71 40.785
Semihemi: 198et 58&140 42.487
Harry: 202et 58&72 15.867
Tertiaseptal: 202et 31&171 35.576
Swetneus: 207et 58&149 55.163
Metakleismic: 208et 87&121 48.570
Marvo: 209et 72&137 26.882
Kleischismic: 212et 24&94 36.749
Slithy: 215et 94&121 45.895
Arch: 217et 43&87 36.541
Octoid: 224et 72&152 14.097
Quanharuk: 224et 41&142 31.549
Countercata: 227et 34&53 39.770
Tritikleismic: 231et 15&57 19.333
Subpental: 241et 19&111 45.352
Ennealimnic: 243et 72&171 20.347
Bischismic: 248et 12&118 28.160
Birds: 248et 31&217 39.921
Essence: 248et 58&190 46.447
Mirkat: 255et 72&183 22.126
Sqrtphi: 265et 49&72 25.515
Quasiorwell: 270et 31&208 17.540
Counteracro: 270et 270&1061e 42.572
Marvo: 281et 72&281 31.685
Septisuperfourth: 282et 22&86 24.619
Sensa: 283et 22&65 35.844
Quadritikleismic: 284et 4&68 23.406
Quincy: 289et 72&217 30.875
Commatic: 294et 58&118 30.461
Neominor: 305et 72&161 27.958
Bison: 306et 46&84 37.132
Unthirds: 311et 72&167 22.926
Hemischis: 313et 53&130 36.289
Semiparakleismic: 316et 80&118 34.208
Octowerck: 320et 72&176 30.159
Decal: 320et 130&190 40.633
Hemitert: 342et 31&280 15.633
Hemiamity: 350et 46&106 31.307
Stearnscape: 354et 72&282 32.096
Degrees: 360et 80&140 46.770
Catafourth: 363et 103&130 36.785
Neusec: 388et 190&388 59.127
Alphaquarter: 391et 87&152 29.638
Novemkleismic: 405et 72&261 51.730
Subsemifourth: 407et 49&103 34.276
Semiennealimmal: 441et 72&441 34.196
Emkay: 535et 87&137 35.586
Pogo: 578et 36&94 31.857
Quatracot: 638et 190&224 41.043
Hemigamera: 646et 26&198 40.955
Brahmagupta: 665et 7&217 52.190
Eris: 703et 31&193 27.621
Abigail: 764et 46&132 12.860
Sextile: 1092et 12&270 29.677
Orga: 1106et 26&244 16.188
Octant: 1168et 24&224 44.778
Decoid: 1210et 130&270 18.735
Deca: 1270et 80&190 24.329
Trinealimmal: 1323et 27&243 29.812
Trillium: 1429et 53&441 46.758
Quasithird: 1448et 164&224 21.125
Bisesqui: 1498et 130&212 16.968
Vishnu: 1502et 118&152 14.180
Hemiennealimmal: 1566et 72&198 6.283
Acrokleismic: 1639et 19&251 36.878
Quadraennealimmal: 1737et 342&1053 21.320
Newt: 1972et 41&188 19.461
Semisupermajor: 2554et 80&342 12.773
11-limit rank three
Name: ET w/ optimal patent val: Val name: 10^5 * badness
Vulcan: 15et 2&3&10 57.7113
Potassium: 19et 2&9&10 46.3665
Festival: 26et 2&10&26 68.8510
Nickel: 28et 7&9&12 46.3463
Thrasher: 34et 3&4&12 48.0188
Selenium: 34et 4&5&10 66.5377
Calliope: 45et 7&12&19 52.9778
Jubilee: 48et 4&12&22 55.9842
Ares: 49et 3&7&12 46.8874
Sonic: 51et 7&15&51 52.3158
Big Brother: 53et 9&22&70 50.6556
Orwellian: 53et 4&5&17 71.513
Prodigy: 72et 2&10&29 33.4745
Mirwomo: 72et 7&10&24 64.0943
Gamel: 72et 5e&31&72 85.266
Oxpecker: 77et 8d&15&31 69.945
Starling: 77et 4&15&27 67.680
Erato: 81et 12&19&31 55.7521
Sensawer: 87et 41&46&73 79.632
Euterpe: 88et 5&12&26 53.5809
Thrush: 89et 3&12&31 35.2591
Aplonis: 89et 19&31&58 64.7511
Mandos: 89et 7&24&58 75.1090
Malcolm: 94et 19e&41&53 124.957
Shrusus: 95et 22&46&95 87.6795
Zeus: 99et 6&7&9 39.9882
Apollo: 104et 12&19&22 52.9766
Supermagic: 104et 4&7&15 64.0789
Supernatural: 104et 19&22&82e 88.8164
Octarod: 104et 19&22&49 58.0664
Guanyin: 111et 9&22&58 41.1252
Manwe: 111et 15&31&80 67.9150
Bisector : 114et 14c&22&46 108.9026
Zelda: 118et: 9&22&87 64.1882
Parahemif: 123et 17&24&58 134.547
Varda: 126et 12&22&46 72.8125
Minerva: 127et 1&9&12 38.1064
Clio: 129et 7&12&24 73.7590
Pele: 145et 5&12&29 64.8199
Laka: 152et 41&53&58 82.5317
Marvel: 166et 9&10&22 25.5033
Fantastic: 166et 12&22&50 74.3439
Portent: 190et 5&10&26 23.4092
Beyla: 190et 7&19&46 72.097
Jove: 202et 10&31&58 24.1055
Tolerant: 208et 5&41&80 103.923
Belobog: 248et 12&31&87 60.9402
Spectacle: 281et 10&31&281 49.8669
Jupiter: 282et 9&22&108 56.2368
Sensamagic: 283et 5&17&19 72.231
Agni: 284et 4&6&27 49.3790
Enlil: 284et 4&15&38 79.8062
Trimyna: 294et 2&29&58 81.4047
Triglav: 316et 31&80&87 81.896
Varuna: 320et 12&26&46 41.8714
Hera: 359et 46&53&84 223.1795
Semicanou: 410et 24&80&94 219.7478
Semiporwell: 480et 22&24&84 125.3053
History: 491et 15&29&43 60.3636
Hades: 578et 22&50&58 36.1398
Albus: 640et 19&53&58 62.1100
Indra: 703et 10&31&152 26.6020
Hanuman: 998et 15&57&152 49.965
Loki: 1092et 12&22&86 49.2550
Ganesha: 1502et 31&87&152 39.0462
Freya: 1566et 10&31&167 16.9702
Tyr: 1566et 15&57&183 25.8374
Baldur: 1696et 4&58&72 16.6115
Skadi: 2014et 31&97&121 34.8944
Thor: 2554et 26&46&152 8.8834
Lux: 2603et 41&46&137 50.834
Ennealimmic: 2619et 27&45&171 27.4685
Galaxy: 2665et 46&103&121 84.057
Van Gogh: 6992et 22&58&284 29.7565
Odin: 7464et 12&42&72 11.6151
13-limit rank two
Name: ET w/ optimal patent val: Val name: 1000*badness
Diminished: 4et 4&8d 19.509
Neutrominant: 7et 7&10c 27.214
Modus: 7et 7&27e 23.806
Arnold: 7et 5&7 23.300
Dominatrix: 7et 7&12f 18.289
Jamesbond: 7et 7&14c 23.003
Septimal: 7et 7&14cf 22.569
Ptolemy: 7et 7&38df 34.316
Progression: 9et 8d&9 18.158
Negric: 9et 1&9 20.205
Pentoid: 9et 5&9 21.159
Ringo: 10et 10&17c 22.619
Pajaric: 10et 10&12f 20.461
Pajaro: 10et 10&22f 27.355
Augustus: 12et 9&12 22.236
Dominion: 12et 5&12 27.295
Hexe: 12et 6f&12f 35.946
Ripple: 12f 1ce&12f 31.639
Smate: 14et 14&17c 36.836
Opossum: 15et 7d&8d 19.389
Kangaroo: 15et 2cde&15 32.653
Blacksmith: 15et 5&10 20.498
Archytas clan: 15et 5e&15 22.325
Progress: 15et 2&15 26.214
Porcupine: 15et 7&15 21.276
Belauensis: 15et 14c&15 29.816
Kumbaya: 15et 4&15 31.633
Darjeeling: 15et 15&19e 21.445
Augene: 15et 3&15 20.785
Ogene: 15et 12&15 22.890
Armodue: 16et 7&9 19.351
Domination: 17c 5e&12e 27.435
Dominant: 17c 12f&17c 24.108
Progressive: 17c 2f&15f 32.721
Negri: 19et 9&10 17.833
Sensis: 19et 8d&19 20.017
Meanenneadecal: 19et 12f&19 21.182
Meanplop: 19et 12e&19 27.666
Godzilla: 19et 14cf&19 22.503
Undevigintone: 19et 19&38df 22.933
Lisa: 19et 2cde&19 36.144
Keemun: 19et 4&19 29.749
Qeema: 19et 4ef&19 29.419
Cataleptic: 19et 19&34d 27.343
Rhinoceros: 19et 1ce&19 39.343
Spell: 19et 6&19 45.591
Cantrip: 19et 6f&19 41.603
Muggles: 19et 16&19 30.386
August: 21et 9&21 18.448
Oodako: 21et 6&21 42.323
Telepathy: 22et 19e&22 25.522
Sorcery: 22et 19&22 25.829
Divination: 22et 22f&60e 34.551
Blair: 22et 9&22 23.086
Hedgehog: 22et 14cf&22
Pajarous: 22et 10&22 25.176
Pajara: 22et 12&22 27.642
Porkpie: 22et 7&22 26.043
Ceratitid: 22et 1ce&22 44.739
Urchin: 22et 14c&22f 25.233
Fleetwood: 22et 22&84bdf 31.835
Suprapyth: 22et 17&22 36.336
Comic: 22et 2cde&22 41.470
Astrology: 22et 6&16 34.376
Quasisupra: 22et 17c&22 30.219
Catnip: 24et 12f&24 28.363
Triforce: 24et 9&15 20.248
Hemiaug: 24et 3de&24 30.159
Hemidim: 24et 4ef&24 39.030
Semidim: 24et 24&32c 30.597
Mohamaq: 24et 17c&24 28.738
Varan: 24et 19e&24 25.676
Injera: 26et 26&104bcf 21.565
Flattone: 26et 7&19 22.260
Lemba: 26et 10&16 25.477
Crepuscular: 26et 26&34d 24.368
Quarto: 26et 26&27e 27.692
Cynder: 26et 5e&26 34.124
Secundly: 26et 9&17 26.212
Cavalier: 26et 4ef&26 35.040
Sensa: 27et 19e&27 23.258
Ponens: 27et 7&27 39.043
Fervor: 27e 2f&27e 39.705
Octocat: 27e 14cf&27e 27.601
Minah: 27e 4ef&27e 27.568
Roman: 29et 3&23 30.043
Porky: 29et 22&29 26.543
Coendou: 29et 7&29 30.233
Nautilus: 29et 15&29 22.285
Negril: 29et 19&29 24.383
Negroni: 29et 10&29 21.559
Wilsec: 29et 9&20 25.192
Impunity: 29et 5e&29 33.196
Immunity: 29et 5&29 37.078
Quindecic: 30et 15&30 28.944
Meantone: 31et 12f&31 18.048
Squares: 31et 17c&31 25.514
Agora: 31et 31&76e 24.522
Mohajira: 31et 7&24 23.388
Winston: 31et 9&31 19.931
Revelation: 31et 21&31 29.452
Tritonic: 31et 29&31 22.993
Lupercalia: 31et 15&31 21.328
Murakuc: 31et 31&73f 41.394
Nusecond: 31et 31&70f 23.323
Cypress: 31et 11cdeef&31 37.849
Maneh: 31et 4ef&31 29.868
Prajapati: 31et 31&93f 37.885
Würschmidt: 31et 31&65d 23.593
Worseschmidt: 31et 3def&31 34.382
Hemithir: 31et 31&68e 31.199
Hemiwar: 31et 6f&31 44.886
Sentinel: 31et 14&17 37.408
Diesic: 31et 1ce&31 38.116
Semishly: 31et 31&49f 28.408
Slurpee: 33et 16&33 33.102
Kema: 34et 15&19 22.749
Wollemia: 34et 27e&34 31.219
Anguirus: 34et 10&24 30.829
Secund: 35et 9&35 49.684
Greenwood: 35et 21&35 54.009
Liesel: 36et 19&36 27.304
Niner: 36et 9&36 24.143
Beatles: 37et 27e&37 30.161
Enjera: 38et 12f&26f 26.542
Horoscope: 38et 16&38 35.284
Miraculous: 41et 10&31 18.669
Superkleismic: 41et 15&26 21.478
Varan: 41et 5e&41 32.284
Hemimiracle: 41et 20&21 43.151
Andromeda: 41et 29&41 20.749
Octacot: 41et 27e&41 23.276
Octopod: 41et 14cf&41 28.326
Monkey: 41et 7&34 28.410
Bunya: 41et 7d&41 24.886
Magic: 41et 19&41 21.509
Hocus: 41et 41&79d 30.280
Witchcraft: 41et 41&60e 23.547
Trismegistus: 41et 16&41 33.081
Bohpier: 41et 41&90ef 24.864
Salsa: 41et 17&24 30.793
Plutino: 41et 2cde&41 40.182
Quato: 41et 4ef&41 30.081
Slendi: 41et 41&124ef 43.644
Jerome: 43et 26&43 29.285
Amavil: 43et 9&43 25.791
Meridetone: 43et 43&117df 26.421
Kumonga: 43et 16&43 28.920
Vigin: 44et 22&44 29.849
Sensor: 46et 19&27 25.474
Sensus: 46et 46&73 20.789
Dwynwen: 46et 15&46 23.461
Leapday: 46et 29&46 24.732
Twothirdtonic: 46et 9&37 25.941
Bamity: 46et 14cf&46 30.885
Magus: 46et 3de&46 43.024
Aerodactyl: 46et 5&46 33.986
Aerodino: 46et 5e&46 35.836
Vines: 46et 4&42 29.693
Superpyth: 49et 22&49 24.673
Bimeantone: 50et 12f&50 28.817
Cataclysmic: 53et 53&140d 22.554
Hemikleismic: 53et 15&53 26.005
Orwell: 53et 22&31 19.718
Doublethink: 53et 9&44 27.120
Tricot: 53et 53&70 32.102
Hamity: 53et 14cf&53 29.753
Kleiboh: 53et 4ef&53 31.074
Maja: 53et 45ef&53 27.532
Helenus: 53et 53&118d 26.284
Hemigari: 53et 29&53 27.464
Quartz: 53et 26&53 28.818
Sycamore: 56et 18&19 34.295
Diaschismic: 58et 46&58 18.926
Myna: 58et 31&58 17.125
Hemififths: 58et 41&58 19.090
Infraorwell: 58et 9&58 23.683
Thuja: 58et 15&43 22.838
Alicorn: 58et 19&58 23.667
Bisemidim: 58et 50&58 23.877
Sruti: 58et 24&58 23.791
Qilin: 58et 58&77 22.842
Gorgik: 58et 21&37 32.205
Gallium: 62et 31&62 25.484
Semivalentine: 62et 16&30 32.749
Hemimeantone: 62et 43&62 31.433
Ammonite: 66et 29&37 27.168
Hemiwur: 68et 6&31 28.432
Manna: 72et 41&72 17.012
Hendec: 72et 26&46 17.707
Catakleismic: 72et 19&53 16.883
Lizard: 72et 22&50 21.781
Neominor: 72et 72&161f 26.942
Compton: 72et 72&228f 21.852
Comptone: 72et 12&72 25.144
Hours: 72et 24&72 26.931
Bikleismic: 72et 72&106 21.814
Marvolo: 72et 29&43 21.470
Semimiracle: 72et 10&62 24.622
Catalytic: 72et 19e&72 22.337
Enneaportent: 72et 9&54 22.322
Ennealim: 72et 27e&72 20.697
Ennealiminal: 72et 27&72 30.325
Marrakesh: 73et 31&73 40.774
Grosstone: 74et 12&31 25.899
Valentino: 77et 31&46 20.665
Camahueto 77et 19&77 36.155
Echidna: 80et 22&58 23.679
Bidia: 80et 12&68 41.137
Paradigmic: 80et 19&80 35.781
Quartonic: 80et 53&80 23.875
Meanpop: 81et 19&31 20.883
Soothsaying: 82et 22&60 55.443
Secant: 84et 26&58 46.373
Rodan: 87et 41&46 18.448
Clyde: 87et 19&68 26.842
Misty: 87et 12f&87 27.820
Emka: 87et 37&50 29.741
Mothra: 88et 5&26 23.954
Amigo: 89et 43&46 30.666
Septimin: 91et 9&41 23.117
Kumhar: 93et 31&93 48.582
Slender: 94et 31&63 25.913
Sanjaab: 94et 29&94 33.849
Supers: 94et 58&94 21.644
Interpental: 96et 43&53 29.680
Mosura: 98et 31&67 36.857
Hitchcock: 99et 7&39 22.448
Echidnic: 102et 10&46 28.874
Benediction: 103et 31&72 15.715
Phicordial: 103et 10&103 33.198
Hemisecordite: 103et 41&62 25.589
Necromancy: 104et 22&41 25.275
Leapweek: 109et 17&46 32.727
Buzzard: 111et 53&58 18.842
Semisept: 111et 31&80 25.204
Kwai: 111et 41&111 24.555
Shrutar: 114et 46&68 28.057
Submajor: 116et 10&53 27.689
Guiron: 118et 41&77 28.444
Hemithirds: 118et 31&56 21.738
Kleischismic: 118et 24&94 37.640
Grendel: 121et 31&121 24.839
Pluto: 121et 41&80 25.717
Subfourth: 121et 58&121 23.800
Harry: 130et 58&72 13.046
Bosonic: 130et 26&130 32.946
Bison: 130et 46&84 23.504
Sesquart: 130et 41&89 22.396
Septisuperquad: 130et 22&108 33.038
Hemimaquila: 130et 9&121 24.445
Countercata: 140et 34&53 20.156
Degrees: 140et 80&140 32.718
Ketchup: 140et 46&94 24.824
Fibo: 140et 37&103 27.429
Omicronbeta: 144et 72&144 29.956
Heinz: 149et 46&103 25.779
Hemiseven: 149et 5&72 21.900
Octopus: 152et 72&152 21.679
Monocerus: 154et 58&154 28.795
Tritikleismic: 159et 15&72 15.652
Mintone: 161et 58&103 21.849
Gizzard: 166et 72&166 20.252
Polypyth: 167et 46&121 30.292
Tertiaseptal: 171et 31&171 36.876
Parkleismic: 179et 80&179 36.559
Mirkat: 183et 72&111 18.632
Ekadash: 190et 72&118 20.381
Widefourth: 190et 16&71 21.636
Sqrtphi: 193et 72&121 20.040
Hemimist: 198et 87&111 22.923
Semihemi: 198et 58&140 21.188
Amity: 205et 53&205 28.008
Quanic: 205et 94&111 32.481
Swetneus: 207et 58&149 28.876
Metakleismic: 208et 87&121 24.371
Quadritikleismic: 212et 68&72 18.731
Slithy: 215et 94&121 28.492
Arch: 217et 43&87 19.504
Octoid: 224et 72&224 15.274
Quanharuk: 224et 41&142 21.392
Mystery: 232et 29&58 18.591
Subpental: 241et 19&111 23.940
Ennealimnic: 243et 72&171 20.250
Essence: 248et 58&190 26.107
Subsemifourth: 255et 103&255 28.387
Hemiennealimmal: 270et 72&198 12.505
Acrokleismic: 270et 19&251 26.818
Counteracro: 270et 270&1331c 26.028
Septisuperfourth: 282et 130&282 22.887
Sensa: 283et 22&65 31.366
Sextilififths: 289et 29&130 25.276
Quincy: 289et 72&145 23.862
Hemiwürschmidt: 291et 31&130 23.074
Hemischis: 313et 53&130 20.816
Octowerck: 320et 72&248 27.632
Decal: 320et 130&190 23.948
Novemkleismic: 333et 72&261 39.072
Catafourth: 363et 103&130 21.694
Bischismic: 378et 12&118 28.722
Neusec: 388et 190&198 30.941
Hemigamera: 422et 26&198 20.416
Semiennealimmal: 441et 72&441 26.122
Birds: 465et 31&217 35.680
Emkay: 535et 87&137 17.853
Fermionic: 546et 130&286 43.581
Pogo: 578et 36&94 17.514
Quatracot: 638et 190&224 22.643
Unthirds: 694et 72&311 20.888
Octant: 696et 24&224 30.425
Quasithird: 836et 164&224 29.501
Newt: 851et 41&229 13.830
Decoid: 940et 130&270 13.475
Semihemiennealimmal 954et 126&144 13.104
Acyuta: 962et 270&692 15.805
Deca: 1000et 80&190 16.810
Quasiorwell: 1111et 31&239 17.921
Abigail: 1258et 46&178 8.856
Trillium: 1429et 53&441 19.393
Ananta: 1468et 118&152 23.678
13-limit rank three
Name: ET w/ optimal patent val: Val name: 10^5 * badness
Mockingbird: 15et 3&4&15 85.942
Catbird: 19et 4&12f&19 90.475
Potassium: 19et 9&10&11 73.346
Nickel: 28et 7&9&21 64.705
Negric: 29et 1&9&10 80.756
Nightingale: 31et 3&15&28 83.714
Thrasher: 34et 12&15&19 87.636
Selenium: 34et 5&9&10 78.368
Krypton: 36et 9&10&36 72.673
Foreboding: 41et 5&10&26 87.267
Prodigy: 41et 10&29&31 73.639
Veery: 46et 12&15&46 99.122
Athene: 53et 12f&22&53 81.781
Thrush: 58et 31&46&58 67.663
Bluebird: 58et 12&15&31 91.548
Aplonis: 58et 19&31&58 82.078
Jofur: 58et 10&31&58 74.932
Parahemif: 58et 17&24&58 119.366
Deecee: 72et 9&22&41 92.048
Prodigious: 72et 2&29&41 89.974
Marvelcat: 72et 9&10&44 99.966
Beyla: 72et 7&19&46 83.962
Varda: 80et 22&46&58 97.041
Sensawer: 87et 41&46&73 92.807
Tripod: 91et 9&10&31 74.546
Isis: 94et 10&22&31 86.583
Malcolm: 94et 19e&41&53 107.452
Marvel: 103et 19&22&31 68.977
Prodigal: 103et 31&72&84 88.910
Mirage: 103et 10&31&62 73.850
Apollo: 104et 22&29&41 103.106
Cerberus: 130et 22&50&58 76.512
Ominous: 149et 5&26&46 75.055
Portending: 159et 15&26&46 62.715
Momentous: 164et 10&31&46 83.202
Hecate: 166et 19&41&53 72.113
Marvell: 166et 9&31&63 86.160
Ulmo: 179et 7&39&80 93.162
Vibhu: 183et 31&72&111 82.598
Portentous: 190et 15&31&56 66.119
Vish: 193et 41&72&121 92.976
Minos: 193et 9&54&58 72.381
Namaka: 198et 29&53&58 78.124
Laka: 205et 41&53&58 82.186
Kujuku 208et 24&29&58 105.976
Tolerant: 208et 41&46&80 102.099
Spectacle: 209et 31&72&209 100.924
Agni: 212et 6&31&72 92.251
Yajna: 224et 31&72&121 69.986
Pele: 232et 29&41&46 70.328
Trimyna: 232et 29&31&56 81.405
Jovial: 243et 41&58&72 62.380
Borneo: 270et 15&72&111 54.937
History: 289et 15&29&43 53.955
Enlil: 299et 15&19&53 68.005
Madagascar: 313et 19&53&58 56.006
Hera: 313et 46&53&84 129.736
Akea: 321et 7&34&46 82.191
Semiporwell: 328et 46&68&84 122.026
Jovis: 363et 31&58&72 54.221
Semicanou: 410et 94&198&212 297.443
Hanuman: 535et 15&72&137 65.278
Hades: 578et 36&58&72 53.531
Vili: 643et 37&93&103 73.821
Shibi: 703et 41&72&111 72.094
Greenland: 940et 58&72&198 44.343
Baffin: 940et 34&43&53 60.443
Ennealimmic: 981et 27&72&171 75.488
Zisa: 1241et 21&31&109 82.974
Thunor: 1258et 26&46&178 34.135
Frigg: 1344et 6&58&103 93.387
Donar: 1448et 46&80&144 32.154
Rym: 1870et 46&106&118 54.933
Galaxy: 2125et 46&103&121 46.311
Lux: 2333et 41&46&137 36.015
Freya: 2615et 10&31&229 85.515
See also
Todo: improve layout, increase applicability
add structure by switching to tables