Keemic family: Difference between revisions
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The '''keemic family''' of rank-3 | {{Technical data page}} | ||
The '''keemic family''' is a family of [[rank-3 temperament]]s which [[temper out]] the [[keema]], 875/864 = {{monzo| -5 -3 3 1 }}. | |||
== Supermagic | == Supermagic == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 875/864 | [[Comma list]]: 875/864 | ||
{{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }} | |||
: mapping generators: ~2, ~3, ~5 | |||
[[Mapping to lattice]]: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}] | [[Mapping to lattice]]: [{{val| 0 0 -1 3 }}, {{val| 0 1 1 0 }}] | ||
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: Angle (6/5, 3/2) = 77.834 | : Angle (6/5, 3/2) = 77.834 | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.8733, ~5/4 = 380.4684 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and [[9-odd-limit]] | * [[7-odd-limit|7-]] and [[9-odd-limit]] | ||
: | : {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/4 3/4 1/4 -1/4 | 5/4 3/4 -3/4 3/4 }} | ||
: | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }} | ||
[[Badness]]: 0.212 × 10<sup>-3</sup> | |||
[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
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== Undecimal supermagic == | == Undecimal supermagic == | ||
Subgroup: 2.3.5.7.11 | {{See also| Ptolemismic clan #Supermagic }} | ||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 100/99, 385/384 | [[Comma list]]: 100/99, 385/384 | ||
{{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.1985, ~5/4 = 381.5394 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }} | ||
[[Badness]]: 0.641 × 10<sup>-3</sup> | [[Badness]]: 0.641 × 10<sup>-3</sup> | ||
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== Supernatural == | == Supernatural == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 225/224, 245/243 | [[Comma list]]: 225/224, 245/243 | ||
{{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }} | |||
: mapping generators: ~2, ~5, ~11 | |||
{{ | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 380.3520, ~11/8 = 547.5758 | ||
{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }} | |||
<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | <nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | ||
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[[Badness]]: 0.888 × 10<sup>-3</sup> | [[Badness]]: 0.888 × 10<sup>-3</sup> | ||
[[Category: | === 13-limit === | ||
[[Category: | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 105/104, 196/195, 245/243 | |||
Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 380.0401, ~11/8 = 546.6672 | |||
{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }} | |||
Badness: 1.14 × 10<sup>-3</sup> | |||
[[Category:Temperament families]] | |||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Keemic family| ]] <!-- main article --> | [[Category:Keemic family| ]] <!-- main article --> | ||
[[Category:Supermagic]] | [[Category:Supermagic]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||