Laconic family: Difference between revisions
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The Laconic family [[ | The Laconic family [[tempering out|tempers out]] the [[Laconic comma]], 2187/2000, which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in [[16edo]] and [[21edo]]. The only 7-limit extension that makes any sense to use is [[gorgo]], which also tempers out 1029/1024. | ||
=Laconic= | = Laconic = | ||
Comma: 2187/2000 | Comma: 2187/2000 | ||
[[ | [[POTE generator]]: ~10/9 = 227.426 | ||
Map: [<1 1 1|, <0 3 7|> | Map: [<1 1 1|, <0 3 7|> | ||
[[ | [[EDO]]s: {{EDOs| 5, 16, 21, 37b }} | ||
[[ | [[Badness]]: 0.1618 | ||
== Gorgo == | |||
{{see also| Gamelismic clan #Gorgo }} | |||
Commas: 36/35, 1029/1024 | Commas: 36/35, 1029/1024 | ||
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Map: [<1 1 1 3|, <0 3 7 -1|> | Map: [<1 1 1 3|, <0 3 7 -1|> | ||
EDOs: 5, 16, 21, 37b | EDOs: {{EDOs| 5, 16, 21, 37b }} | ||
Badness: 0.0607 | Badness: 0.0607 | ||
==11-limit== | == 11-limit == | ||
Commas: 36/35, 45/44, 1029/1024 | Commas: 36/35, 45/44, 1029/1024 | ||
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Map: [<1 1 1 3 1|, <0 3 7 -1 13|> | Map: [<1 1 1 3 1|, <0 3 7 -1 13|> | ||
EDOs: 16, 21, 37b | EDOs: {{EDOs| 16, 21, 37b }} | ||
Badness: 0.0495 | Badness: 0.0495 | ||
==13-limit== | === 13-limit === | ||
Commas: 27/26, 36/35, 45/55, 507/500 | Commas: 27/26, 36/35, 45/55, 507/500 | ||
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Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|> | Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|> | ||
EDOs 16, 21, 37b | EDOs {{EDOs| 16, 21, 37b }} | ||
Badness: 0.0327 | Badness: 0.0327 | ||
=Spartan= | == Spartan == | ||
Commas: 36/35, 56/55, 1029/1024 | Commas: 36/35, 56/55, 1029/1024 | ||
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Map: [<1 1 1 3 5|, <0 3 7 -1 -8|> | Map: [<1 1 1 3 5|, <0 3 7 -1 -8|> | ||
EDOs: 5, 21 | EDOs: {{EDOs| 5, 21 }} | ||
Badness: 0.0627 | Badness: 0.0627 | ||
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[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Laconic]] | [[Category:Laconic]] | ||
[[Category:Rank 2]] | |||
[[Category:Todo:review]] | |||
Revision as of 05:44, 10 December 2020
The Laconic family tempers out the Laconic comma, 2187/2000, which is the difference between three 10/9's and a 3/2. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in 16edo and 21edo. The only 7-limit extension that makes any sense to use is gorgo, which also tempers out 1029/1024.
Laconic
Comma: 2187/2000
POTE generator: ~10/9 = 227.426
Map: [<1 1 1|, <0 3 7|>
Badness: 0.1618
Gorgo
Commas: 36/35, 1029/1024
POTE generator: ~8/7 = 228.334
Map: [<1 1 1 3|, <0 3 7 -1|>
Badness: 0.0607
11-limit
Commas: 36/35, 45/44, 1029/1024
POTE generator: ~8/7 = 227.373
Map: [<1 1 1 3 1|, <0 3 7 -1 13|>
Badness: 0.0495
13-limit
Commas: 27/26, 36/35, 45/55, 507/500
POTE generator: ~8/7 = 227.230
Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|>
Badness: 0.0327
Spartan
Commas: 36/35, 56/55, 1029/1024
POTE generator: ~8/7 = 229.535
Map: [<1 1 1 3 5|, <0 3 7 -1 -8|>
Badness: 0.0627