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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 {{val| 12 19 28 34 42 44 }}, to {{val| 12 19 28 34 42 45 }} (which is actually a better mapping, and hence more useful for this purpose.)
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 {{val| 12 19 28 34 42 44 }}, to {{val| 12 19 28 34 42 45 }} (which is actually a better mapping, and hence more useful for this purpose.)


=== 5-limit rank two ===
=== 5-limit rank 2 ===
Comma: ET w/ optimal patent val: 1000 * badness
Comma: ET w/ optimal patent val: 1000 * badness


Line 60: Line 60:
7629394531250/7625597484987: [[3501edo|3501et]] 17.191
7629394531250/7625597484987: [[3501edo|3501et]] 17.191


=== 7-limit rank two ===
=== 7-limit rank 2 ===
Name: ET w/ optimal patent val: Val name: 1000*badness
Name: ET w/ optimal patent val: Val name: 1000*badness


Line 103: Line 103:
[[Meantone family|Dominant]]: [[12edo|12et]] 5&7 20.690
[[Meantone family|Dominant]]: [[12edo|12et]] 5&7 20.690


[[Jubilismic clan|Diminished]]: [[12edo|12et]] 4&12 22.401
[[Diminished family #Septimal diminished|Diminished]]: [[12edo|12et]] 4&12 22.401


[[Augmented family|August]]: [[12edo|12et]] 9&12 26.459
[[Augmented family|August]]: [[12edo|12et]] 9&12 26.459
Line 367: Line 367:
[[Minortonic family#Domain|Domain]]: [[22038edo|22038et]] 171&1164 13.979
[[Minortonic family#Domain|Domain]]: [[22038edo|22038et]] 171&1164 13.979


=== 7-limit rank three ===
=== 7-limit rank 3 ===
Comma: ET w/ optimal patent val: 10^6 * badness
Comma: ET w/ optimal patent val: 10^6 * badness


Line 430: Line 430:
78125000/78121827: [[101654edo|101654et]] 20.457
78125000/78121827: [[101654edo|101654et]] 20.457


=== 11-limit rank two ===
=== 11-limit rank 2 ===
Name: ET w/ optimal patent val: Val name: 1000*badness
Name: ET w/ optimal patent val: Val name: 1000*badness


Line 473: Line 473:
[[Dicot family#Decimal|Decibel]]: [[10edo|10et]] 4&6 32.385
[[Dicot family#Decimal|Decibel]]: [[10edo|10et]] 4&6 32.385


[[Jubilismic clan|Diminished]]: [[12edo|12et]] 4&12 22.132
[[Diminished family #Septimal diminished|Diminished]]: [[12edo|12et]] 4&12 22.132


[[Diaschismic family#Pajara-Pajaric|Pajaric]]: [[12edo|12et]] 2&10 23.798
[[Diaschismic family#Pajara-Pajaric|Pajaric]]: [[12edo|12et]] 2&10 23.798
Line 493: Line 493:
[[Mint temperaments#Ripple|Ripple]]: [[12edo|12et]] 1ce&12 38.811
[[Mint temperaments#Ripple|Ripple]]: [[12edo|12et]] 1ce&12 38.811


[[Jubilismic clan#Diminished-Hemidim|Hemidim]]: [[12edo|12et]] 12&20b 54.965
[Diminished family #Hemidim|Hemidim]]: [[12edo|12et]] 12&20b 54.965


[[Mint temperaments#Smate|Smate]]: [[14edo|14et]] 14&17c 42.518
[[Mint temperaments#Smate|Smate]]: [[14edo|14et]] 14&17c 42.518
Line 530: Line 530:


[[Meantone family#Undevigintone|Undevigintone]]: [[19edo|19et]] 19&38d 36.387
[[Meantone family#Undevigintone|Undevigintone]]: [[19edo|19et]] 19&38d 36.387
[[Meantone family#Septimal meantone-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&19e 31.539


[[Meantone family#Liese-Lisa|Lisa]]: [[19edo|19et]] 2cde&19 54.829
[[Meantone family#Liese-Lisa|Lisa]]: [[19edo|19et]] 2cde&19 54.829
Line 581: Line 579:
[[Augmented family#Hemiaug|Hemiaug]]: [[24edo|24et]] 24&27e 38.232
[[Augmented family#Hemiaug|Hemiaug]]: [[24edo|24et]] 24&27e 38.232


[[Dimipent family#Hemidim|Hemidim]]: [[24edo|24et]] 4e&24 56.576
[[Diminished family #Hemidim|Hemidim]]: [[24edo|24et]] 4e&24 56.576


[[Dimipent family#Semidim|Semidim]]: [[24edo|24et]] 24&32c 30.597
[[Diminished family #Octonion|Octonion]]: [[24edo|24et]] 24&32c 30.597


[[Meantone family#Injera-11-limit|Injera]]: [[26edo|26et]] 12&26 23.124
[[Meantone family#Injera-11-limit|Injera]]: [[26edo|26et]] 12&26 23.124
Line 601: Line 599:
[[Sensipent family#Sensi-Sensa|Sensa]]: [[27edo|27et]] 19e&27 36.835
[[Sensipent family#Sensi-Sensa|Sensa]]: [[27edo|27et]] 19e&27 36.835


[[Jubilismic clan#Diminished-Demolished|Demolished]]: [[28edo|28et]] 12&28 26.574
[[Diminished family #Demolished|Demolished]]: [[28edo|28et]] 12&28 26.574


[[Porcupine family|Nautilus]]: [[29edo|29et]] 15&29 26.023
[[Porcupine family|Nautilus]]: [[29edo|29et]] 15&29 26.023
Line 1,071: Line 1,069:
[[Ragismic microtemperaments#Supermajor-Semisupermajor|Semisupermajor]]: [[2554edo|2554et]] 80&342 12.773
[[Ragismic microtemperaments#Supermajor-Semisupermajor|Semisupermajor]]: [[2554edo|2554et]] 80&342 12.773


=== 11-limit rank three ===
=== 11-limit rank 3 ===
Name: ET w/ optimal patent val: Val name: 10^5 * badness
Name: ET w/ optimal patent val: Val name: 10^5 * badness


Line 1,086: Line 1,084:
[[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 4&5&10 66.5377
[[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 4&5&10 66.5377


[[Didymus rank three family #Calliope|Calliope]]: [[45edo|45et]] 7&12&19 52.9778
[[Didymus rank-3 family #Calliope|Calliope]]: [[45edo|45et]] 7&12&19 52.9778


[[Jubilismic family #Jubilee|Jubilee]]: [[48edo|48et]] 4&12&22 55.9842
[[Jubilismic family #Jubilee|Jubilee]]: [[48edo|48et]] 4&12&22 55.9842
Line 1,092: Line 1,090:
[[Archytas family #Ares|Ares]]: [[49edo|49et]] 3&7&12 46.8874
[[Archytas family #Ares|Ares]]: [[49edo|49et]] 3&7&12 46.8874


[[Porcupine rank three family #Sonic|Sonic]]: [[51edo|51et]] 7&15&51 52.3158
[[Porcupine rank-3 family #Sonic|Sonic]]: [[51edo|51et]] 7&15&51 52.3158


[[Nuwell family #Big Brother|Big Brother]]: [[53edo|53et]] 9&22&70 50.6556
[[Biyatismic clan #Big Brother|Big Brother]]: [[53edo|53et]] 9&22&70 50.6556


[[Orwellismic family #Orwellian|Orwellian]]: [[53edo|53et]] 4&5&17 71.513
[[Orwellismic family #Orwellian|Orwellian]]: [[53edo|53et]] 4&5&17 71.513
Line 1,100: Line 1,098:
[[Marvel family #Prodigy|Prodigy]]: [[72edo|72et]] 2&10&29 33.4745
[[Marvel family #Prodigy|Prodigy]]: [[72edo|72et]] 2&10&29 33.4745


[[Rastmic temperaments #Mirwomo|Mirwomo]]: [[72edo|72et]] 7&10&24 64.0943
[[Rastmic rank-3 clan #Mirwomo|Mirwomo]]: [[72edo|72et]] 7&10&24 64.0943


[[Gamelismic family #Gamel|Gamel]]: [[72edo|72et]] 5e&31&72 85.266
[[Gamelismic family #Gamel|Gamel]]: [[72edo|72et]] 5e&31&72 85.266


[[Starling family #Oxpecker|Oxpecker]]: [[77edo|77et]] 8d&15&31 69.945
[[Biyatismic clan #Oxpecker|Oxpecker]]: [[77edo|77et]] 8d&15&31 69.945


[[Starling family #Undecimal starling|Starling]]: [[77edo|77et]] 4&15&27 67.680
[[Starling family #Undecimal starling|Starling]]: [[77edo|77et]] 4&15&27 67.680


[[Didymus rank three family #Erato|Erato]]: [[81edo|81et]] 12&19&31 55.7521
[[Didymus rank-3 family #Erato|Erato]]: [[81edo|81et]] 12&19&31 55.7521


[[Sensamagic family #Sensawer|Sensawer]]: [[87edo|87et]] 41&46&73 79.632
[[Sensamagic family #Sensawer|Sensawer]]: [[87edo|87et]] 41&46&73 79.632


[[Didymus rank three family #Euterpe|Euterpe]]: [[88edo|88et]] 5&12&26 53.5809
[[Didymus rank-3 family #Euterpe|Euterpe]]: [[88edo|88et]] 5&12&26 53.5809


[[Starling family #Thrush|Thrush]]: [[89edo|89et]] 3&12&31 35.2591
[[Starling family #Thrush|Thrush]]: [[89edo|89et]] 3&12&31 35.2591
Line 1,128: Line 1,126:
[[Marvel family #Apollo|Apollo]]: [[104edo|104et]] 12&19&22 52.9766
[[Marvel family #Apollo|Apollo]]: [[104edo|104et]] 12&19&22 52.9766


[[Keemic family #Supermagic|Supermagic]]: [[104edo|104et]] 4&7&15 64.0789
[[Keemic family #Keemic|Keemic]]: [[104edo|104et]] 4&7&15 64.0789


[[Keemic family #Supernatural|Supernatural]]: [[104edo|104et]] 19&22&82e 88.8164
[[Keemic family #Supernatural|Supernatural]]: [[104edo|104et]] 19&22&82e 88.8164
Line 1,142: Line 1,140:
[[Horwell family #Zelda|Zelda]]: [[118edo|118et]]: 9&22&87 64.1882
[[Horwell family #Zelda|Zelda]]: [[118edo|118et]]: 9&22&87 64.1882


[[Rastmic temperaments #Parahemif|Parahemif]]: [[123edo|123et]] 17&24&58 134.547
[[Rastmic rank-3 clan #Parahemif|Parahemif]]: [[123edo|123et]] 17&24&58 134.547


[[Valinorismic temperaments #Varda|Varda]]: [[126edo|126et]] 12&22&46 72.8125
[[Valinorismic temperaments #Varda|Varda]]: [[126edo|126et]] 12&22&46 72.8125
Line 1,148: Line 1,146:
[[Marvel family #Minerva|Minerva]]: [[127edo|127et]] 1&9&12 38.1064
[[Marvel family #Minerva|Minerva]]: [[127edo|127et]] 1&9&12 38.1064


[[Didymus rank three family|Clio]]: [[129edo|129et]] 7&12&24 73.7590
[[Didymus rank-3 family|Clio]]: [[129edo|129et]] 7&12&24 73.7590


[[Hemifamity family #Pele|Pele]]: [[145edo|145et]] 5&12&29 64.8199
[[Hemifamity family #Pele|Pele]]: [[145edo|145et]] 5&12&29 64.8199
Line 1,176: Line 1,174:
[[Breed family #Agni|Agni]]: [[284edo|284et]] 4&6&27 49.3790
[[Breed family #Agni|Agni]]: [[284edo|284et]] 4&6&27 49.3790


[[Kleismic rank three family #Enlil|Enlil]]: [[284edo|284et]] 4&15&38 79.8062
[[Kleismic rank-3 family #Enlil|Enlil]]: [[284edo|284et]] 4&15&38 79.8062


[[Werckismic temperaments #Trimyna|Trimyna]]: [[294edo|294et]] 2&29&58 81.4047
[[Werckismic temperaments #Trimyna|Trimyna]]: [[294edo|294et]] 2&29&58 81.4047
Line 1,224: Line 1,222:
[[Kalismic temperaments #Odin|Odin]]: [[7464edo|7464et]] 12&42&72 11.6151
[[Kalismic temperaments #Odin|Odin]]: [[7464edo|7464et]] 12&42&72 11.6151


=== 13-limit rank two ===
=== 13-limit rank 2 ===
Name: ET w/ optimal patent val: Val name: 1000*badness
Name: ET w/ optimal patent val: Val name: 1000*badness


[[Jubilismic clan#Diminished-13-limit|Diminished]]: [[4edo|4et]] 4&8d 19.509
[[Diminished family #Septimal diminished|Diminished]]: [[4edo|4et]] 4&8d 19.509


[[Meantone family#Neutrominant-13-limit|Neutrominant]]: [[7edo|7et]] 7&10c 27.214
[[Meantone family#Neutrominant-13-limit|Neutrominant]]: [[7edo|7et]] 7&10c 27.214


[[Tetracot family#Modus|Modus]]: [[7edo|7et]] 7&27e 23.806
[[Tetracot family#Modus|Modus]]: [[7edo|7et]] 7&27e 23.806
[[Meantone family#Dominant-Arnold|Arnold]]: [[7edo|7et]] 5&7 23.300
[[Meantone family#Dominant-Dominatrix|Dominatrix]]: [[7edo|7et]] 7&12f 18.289


[[Dicot family#Jamesbond|Jamesbond]]: [[7edo|7et]] 7&14c 23.003
[[Dicot family#Jamesbond|Jamesbond]]: [[7edo|7et]] 7&14c 23.003
Line 1,300: Line 1,294:


[[Meantone family|Meanenneadecal]]: [[19edo|19et]] 12f&19 21.182
[[Meantone family|Meanenneadecal]]: [[19edo|19et]] 12f&19 21.182
[[Meantone family#Septimal meantone-Meanpop-Meanplop|Meanplop]]: [[19edo|19et]] 12e&19 27.666


[[Meantone family#Godzilla-13-limit|Godzilla]]: [[19edo|19et]] 14cf&19 22.503
[[Meantone family#Godzilla-13-limit|Godzilla]]: [[19edo|19et]] 14cf&19 22.503
Line 1,363: Line 1,355:
[[Augmented family#Hemiaug-13-limit|Hemiaug]]: [[24edo|24et]] 3de&24 30.159
[[Augmented family#Hemiaug-13-limit|Hemiaug]]: [[24edo|24et]] 3de&24 30.159


[[Dimipent family#Hemidim|Hemidim]]: [[24edo|24et]] 4ef&24 39.030
[[Diminished family #Hemidim|Hemidim]]: [[24edo|24et]] 4ef&24 39.030


[[Dimipent family#Semidim|Semidim]]: [[24edo|24et]] 24&32c 30.597
[[Diminished family #Octonion|Octonion]]: [[24edo|24et]] 24&32c 30.597


[[Meantone family#Mohamaq-13-limit|Mohamaq]]: [[24edo|24et]] 17c&24 28.738
[[Meantone family#Mohamaq-13-limit|Mohamaq]]: [[24edo|24et]] 17c&24 28.738
Line 1,417: Line 1,409:
[[Trienstonic clan#Quindecic|Quindecic]]: [[30edo|30et]] 15&30 28.944
[[Trienstonic clan#Quindecic|Quindecic]]: [[30edo|30et]] 15&30 28.944


[[Meantone family|Meantone]]: [[31edo|31et]] 12f&31 18.048
[[Meantone family|Fokkertone]]: [[31edo|31et]] 12f&31 18.048


[[Meantone family|Squares]]: [[31edo|31et]] 17c&31 25.514
[[Meantone family|Squares]]: [[31edo|31et]] 17c&31 25.514
Line 1,807: Line 1,799:
[[Porwell temperaments#Septisuperfourth|Septisuperfourth]]: [[282edo|282et]] 130&282 22.887
[[Porwell temperaments#Septisuperfourth|Septisuperfourth]]: [[282edo|282et]] 130&282 22.887


[[Sensamagic clan|Sensa]]: [[283edo|283et]] 22&65 31.366
[[Escapade family#Escaped|Escaped]]: [[283edo|283et]] 22&65 31.366


[[Schismatic family|Sextilififths]]: [[289edo|289et]] 29&130 25.276
[[Schismatic family#Sextilifourths|Sextilifourths]]: [[289edo|289et]] 29&130 25.276


[[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo|289et]] 72&145 23.862
[[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo|289et]] 72&145 23.862
Line 1,815: Line 1,807:
[[Würschmidt family#Hemiwürschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo|291et]] 31&130 23.074
[[Würschmidt family#Hemiwürschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo|291et]] 31&130 23.074


[[Porwell temperaments|Hemischis]]: [[313edo|313et]] 53&130 20.816
[[Schismatic family#Hemischis|Hemischis]]: [[313edo|313et]] 53&130 20.816


[[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo|320et]] 72&248 27.632
[[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo|320et]] 72&248 27.632


[[Pental family|Decal]]: [[320edo|320et]] 130&190 23.948
[[Quintile family#Decile|Decile]]: [[320edo|320et]] 130&190 23.948


[[Kleismic family#Novemkleismic|Novemkleismic]]: [[333edo|333et]] 72&261 39.072
[[Kleismic family#Novemkleismic|Novemkleismic]]: [[333edo|333et]] 72&261 39.072
Line 1,867: Line 1,859:
[[Vishnuzmic family#Vishnu-Ananta|Ananta]]: [[1468edo|1468et]] 118&152 23.678
[[Vishnuzmic family#Vishnu-Ananta|Ananta]]: [[1468edo|1468et]] 118&152 23.678


=== 13-limit rank three ===
=== 13-limit rank 3 ===
Name: ET w/ optimal patent val: Val name: 10^5 * badness
Name: ET w/ optimal patent val: Val name: 10^5 * badness


Line 1,904: Line 1,896:
[[Breed family #Jofur|Jofur]]: [[58edo|58et]] 10&31&58 74.932
[[Breed family #Jofur|Jofur]]: [[58edo|58et]] 10&31&58 74.932


[[Rastmic temperaments #Parahemif|Parahemif]]: [[58edo|58et]] 17&24&58 119.366
[[Rastmic rank-3 clan #Parahemif|Parahemif]]: [[58edo|58et]] 17&24&58 119.366


[[Marvel family #Deecee|Deecee]]: [[72edo|72et]] 9&22&41 92.048
[[Marvel family #Deecee|Deecee]]: [[72edo|72et]] 9&22&41 92.048
Line 1,978: Line 1,970:
[[Werckismic temperaments #History|History]]: [[289edo|289et]] 15&29&43 53.955
[[Werckismic temperaments #History|History]]: [[289edo|289et]] 15&29&43 53.955


[[Kleismic rank three family #Enlil|Enlil]]: [[299edo|299et]] 15&19&53 68.005
[[Kleismic rank-3 family #Enlil|Enlil]]: [[299edo|299et]] 15&19&53 68.005


[[Cataharry family #Madagascar|Madagascar]]: [[313edo|313et]] 19&53&58 56.006
[[Cataharry family #Madagascar|Madagascar]]: [[313edo|313et]] 19&53&58 56.006
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