Optimal patent val: Difference between revisions
Cassandra and Andromeda named according to Erv Wilson's original |
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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 Keenan 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 Keenan 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 two = | ||
Comma: Optimal patent val: 1000 * badness | Comma: Optimal patent val: 1000 * badness | ||
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2109375/2097152: [[296edo]] 40.807 | 2109375/2097152: [[296edo]] 40.807 | ||
15625/15552: [[458edo]] 13.234 | 15625/15552: [[458edo]] 13.234 | ||
78732/78125: [[539edo]] 35.220 | 78732/78125: [[539edo]] 35.220 | ||
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[[Marvel temperaments|Septimin]]: [[91edo]] 9&32 54.502 | [[Marvel temperaments|Septimin]]: [[91edo]] 9&32 54.502 | ||
[[Ragismic microtemperaments|Sfourth]]: [[91edo]] 45&46 123.291 | |||
[[Schismatic family|Garibaldi]]: [[94edo]] 12&29 21.644 | [[Schismatic family|Garibaldi]]: [[94edo]] 12&29 21.644 | ||
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[[Ragismic microtemperaments|Mitonic]]: [[171edo]] 46&125 25.184 | [[Ragismic microtemperaments|Mitonic]]: [[171edo]] 46&125 25.184 | ||
[[Mutt | [[Horwell temperaments#Mutt|Mutt]]: [[171edo]] 3&84 28.406 | ||
[[Horwell temperaments#Fifthplus|Fifthplus]]: [[171edo]] 22&149 25.840 | [[Horwell temperaments#Fifthplus|Fifthplus]]: [[171edo]] 22&149 25.840 | ||
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[[Ragismic microtemperaments#Orga|Orga]]: [[2482edo]] 26&244 40.236 | [[Ragismic microtemperaments#Orga|Orga]]: [[2482edo]] 26&244 40.236 | ||
[[Tricot family|Trillium]]: [[4569edo]] 53&441 30.852 | |||
[[Ragismic microtemperaments|Supermajor]]: [[6214edo]] 80&171 10.836 | [[Ragismic microtemperaments|Supermajor]]: [[6214edo]] 80&171 10.836 | ||
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[[Minortonic family#Domain|Domain]]: [[22038edo]] 171&1164 13.979 | [[Minortonic family#Domain|Domain]]: [[22038edo]] 171&1164 13.979 | ||
=7-limit rank three= | = 7-limit rank three = | ||
Comma: Optimal patent val: 10^6 * badness | Comma: Optimal patent val: 10^6 * badness | ||
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78125000/78121827: [[101654edo]] 20.457 | 78125000/78121827: [[101654edo]] 20.457 | ||
=11-limit rank two= | = 11-limit rank two = | ||
Name: Optimal patent val: Val name: 1000*badness | Name: Optimal patent val: Val name: 1000*badness | ||
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[[Ragismic microtemperaments#Ennealimmal-Trinealimmal|Trinealimmal]]: [[1323edo]] 27&243 29.812 | [[Ragismic microtemperaments#Ennealimmal-Trinealimmal|Trinealimmal]]: [[1323edo]] 27&243 29.812 | ||
[[Tricot family#Trillium|Trillium]]: [[1429edo]] 53&441 46.758 | |||
[[Ragismic microtemperaments#Quasithird-11-limit|Quasithird]]: [[1448edo]] 164&224 21.125 | [[Ragismic microtemperaments#Quasithird-11-limit|Quasithird]]: [[1448edo]] 164&224 21.125 | ||
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[[Ragismic microtemperaments#Supermajor-Semisupermajor|Semisupermajor]]: [[2554edo]] 80&342 12.773 | [[Ragismic microtemperaments#Supermajor-Semisupermajor|Semisupermajor]]: [[2554edo]] 80&342 12.773 | ||
=11-limit rank three= | = 11-limit rank three = | ||
Name: Optimal patent val: Val name: 10^5 * badness | Name: Optimal patent val: Val name: 10^5 * badness | ||
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[[Kalismic temperaments|Odin]]: [[7464edo]] 12&42&72 11.6151 | [[Kalismic temperaments|Odin]]: [[7464edo]] 12&42&72 11.6151 | ||
=13-limit rank two= | = 13-limit rank two = | ||
Name: Optimal patent val: Val name: 1000*badness | Name: Optimal patent val: Val name: 1000*badness | ||
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[[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&178 8.856 | [[Ragismic microtemperaments|Abigail]]: [[1258edo]] 46&178 8.856 | ||
[[Tricot family#Trillium|Trillium]]: [[1429edo]] 53&441 19.393 | |||
[[Vishnuzmic family#Vishnu-Ananta|Ananta]]: [[1468edo]] 118&152 23.678 | [[Vishnuzmic family#Vishnu-Ananta|Ananta]]: [[1468edo]] 118&152 23.678 | ||
=13-limit rank three= | = 13-limit rank three = | ||
Name: Optimal patent val: Val name: 10^5 * badness | Name: Optimal patent val: Val name: 10^5 * badness | ||