Keemic family: Difference between revisions
m Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content" |
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{{Technical data page}} | {{Technical data page}} | ||
The '''keemic family''' is a family of [[rank-3 temperament]]s which [[temper out]] the [[keema]] | The '''keemic family''' is a family of [[rank-3 temperament]]s which [[tempering out|temper out]] the [[keema]] ({{monzo|legend=1| -5 -3 3 1 }}, [[ratio]]: 875/864). | ||
== Supermagic == | == Supermagic == | ||
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{{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }} | {{Mapping|legend=1| 1 0 0 5 | 0 1 0 3 | 0 0 1 -3 }} | ||
: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
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: Angle (6/5, 3/2) = 77.834 | : Angle (6/5, 3/2) = 77.834 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8733{{c}}, ~5/4 = 380.4684{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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{{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }} | {{Optimal ET sequence|legend=1| 7, 12d, 15, 19, 41, 142cd, 183cd, 224ccd }} | ||
[[Badness]]: 0.212 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.212 × 10<sup>-3</sup> | ||
[[Projection pair]]: 7 864/125 | [[Projection pair]]: 7 864/125 | ||
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{{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }} | {{Mapping|legend=1| 1 0 0 5 2 | 0 1 0 3 -2 | 0 0 1 -3 2 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 704.1985{{c}}, ~5/4 = 381.5394{{c}} | ||
{{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }} | {{Optimal ET sequence|legend=1| 7, 15, 19, 22, 37, 41, 104 }} | ||
[[Badness]]: 0.641 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.641 × 10<sup>-3</sup> | ||
Scales: [[supermagic15]] | Scales: [[supermagic15]] | ||
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{{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }} | {{Mapping|legend=1| 1 0 2 -1 0 | 0 5 1 12 0 | 0 0 0 0 1 }} | ||
: mapping generators: ~2, ~5, ~11 | : mapping generators: ~2, ~5, ~11 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~5/4 = 380.3520{{c}}, ~11/8 = 547.5758{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }} | {{Optimal ET sequence|legend=1| 19, 22, 38d, 41, 60e, 101cd, 164c, 224ccde * }} | ||
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<nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | <nowiki>*</nowiki> [[optimal patent val]]: [[104edo|104]] | ||
[[Badness]]: 0.888 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.888 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }} | Mapping: {{mapping| 1 0 2 -1 0 -2 | 0 5 1 12 0 18 | 0 0 0 0 1 0 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~5/4 = 380.0401{{c}}, ~11/8 = 546.6672{{c}} | ||
{{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }} | {{Optimal ET sequence|legend=1| 19, 22f, 38df, 41, 60e, 79d, 101cd }} | ||
Badness: 1.14 × 10<sup>-3</sup> | Badness (Smith): 1.14 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||