Optimal patent val: Difference between revisions
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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 | === 5-limit rank 2 === | ||
Comma: ET w/ optimal patent val: 1000 * badness | Comma: ET w/ optimal patent val: 1000 * badness | ||
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7629394531250/7625597484987: [[3501edo|3501et]] 17.191 | 7629394531250/7625597484987: [[3501edo|3501et]] 17.191 | ||
=== 7-limit rank | === 7-limit rank 2 === | ||
Name: ET w/ optimal patent val: Val name: 1000*badness | Name: ET w/ optimal patent val: Val name: 1000*badness | ||
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[[Minortonic family#Domain|Domain]]: [[22038edo|22038et]] 171&1164 13.979 | [[Minortonic family#Domain|Domain]]: [[22038edo|22038et]] 171&1164 13.979 | ||
=== 7-limit rank | === 7-limit rank 3 === | ||
Comma: ET w/ optimal patent val: 10^6 * badness | Comma: ET w/ optimal patent val: 10^6 * badness | ||
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78125000/78121827: [[101654edo|101654et]] 20.457 | 78125000/78121827: [[101654edo|101654et]] 20.457 | ||
=== 11-limit rank | === 11-limit rank 2 === | ||
Name: ET w/ optimal patent val: Val name: 1000*badness | Name: ET w/ optimal patent val: Val name: 1000*badness | ||
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[[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 | === 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 | ||
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[[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 4&5&10 66.5377 | [[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 4&5&10 66.5377 | ||
[[Didymus rank | [[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 | ||
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[[Archytas family #Ares|Ares]]: [[49edo|49et]] 3&7&12 46.8874 | [[Archytas family #Ares|Ares]]: [[49edo|49et]] 3&7&12 46.8874 | ||
[[Porcupine rank | [[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 | [[Nuwell family #Big Brother|Big Brother]]: [[53edo|53et]] 9&22&70 50.6556 | ||
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[[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 | [[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 | [[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 | ||
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[[Marvel family #Minerva|Minerva]]: [[127edo|127et]] 1&9&12 38.1064 | [[Marvel family #Minerva|Minerva]]: [[127edo|127et]] 1&9&12 38.1064 | ||
[[Didymus rank | [[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 | ||
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[[Breed family #Agni|Agni]]: [[284edo|284et]] 4&6&27 49.3790 | [[Breed family #Agni|Agni]]: [[284edo|284et]] 4&6&27 49.3790 | ||
[[Kleismic rank | [[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 | ||
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[[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 | === 13-limit rank 2 === | ||
Name: ET w/ optimal patent val: Val name: 1000*badness | Name: ET w/ optimal patent val: Val name: 1000*badness | ||
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[[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 | === 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 | ||
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[[Werckismic temperaments #History|History]]: [[289edo|289et]] 15&29&43 53.955 | [[Werckismic temperaments #History|History]]: [[289edo|289et]] 15&29&43 53.955 | ||
[[Kleismic rank | [[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 | ||