Sensamagic clan: Difference between revisions
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{{Technical data page}} | |||
The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]]. | The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], [[sensamagic]], for which [[283edo]] is the [[optimal patent val]]. | ||
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Discussed elsewhere are | Discussed elsewhere are | ||
* [[Father]] (+16/15 or 28/27) → [[Father family #Father|Father family]] | * [[Father]] (+16/15 or 28/27) → [[Father family #Father|Father family]] | ||
* [[Godzilla]] (+49/48 or 81/80) → [[ | * [[Godzilla]] (+49/48 or 81/80) → [[Semaphoresmic clan #Godzilla|Semaphoresmic clan]] | ||
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]] | * ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]] | ||
* ''[[Clyde]]'' (+3136/3125) → [[Kleismic family #Clyde|Kleismic family]] | * ''[[Clyde]]'' (+3136/3125) → [[Kleismic family #Clyde|Kleismic family]] | ||
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{{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }} | {{Mapping|legend=1| 1 0 0 0 | 0 13 19 23 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~27/25 = 146.474 | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~27/25 = 146.474 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]]: ~27/25 = {{monzo| 0 0 1/19 }} | * [[7-odd-limit]]: ~27/25 = {{monzo| 0 0 1/19 }} | ||
: [[eigenmonzo basis| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5 | ||
* [[9-odd-limit]]: ~27/25 = {{monzo| 0 1/13 }} | * [[9-odd-limit]]: ~27/25 = {{monzo| 0 1/13 }} | ||
: [[eigenmonzo basis| | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3 | ||
{{Optimal ET sequence|legend=1| 41, 131, 172, 213c }} | {{Optimal ET sequence|legend=1| 41, 131, 172, 213c }} | ||
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Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }} | * 11-odd-limit: ~12/11 = {{monzo| 1/7 1/7 0 0 -1/14 }} | ||
: | : unchanged-interval (eigenmonzo) basis: 2.11/9 | ||
{{Optimal ET sequence|legend=0| 41, 90e, 131e }} | {{Optimal ET sequence|legend=0| 41, 90e, 131e }} | ||
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Minimax tuning: | Minimax tuning: | ||
* 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }} | * 13- and 15-odd-limit: ~12/11 = {{monzo| 0 0 1/19 }} | ||
: | : Unchanged-interval (eigenmonzo) basis: 2.5 | ||
{{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }} | {{Optimal ET sequence|legend=0| 41, 90ef, 131ef, 221bdeff }} | ||
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{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }} | {{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 351.049 | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~128/105 = 351.049 | ||
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{{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }} | {{Mapping|legend=1| 1 3 -1 8 | 0 -3 7 -11 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~45/32 = 567.720 | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~45/32 = 567.720 | ||
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== Superthird == | == Superthird == | ||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Shibboleth]].'' | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }} | {{Mapping|legend=1| 1 -5 -5 -10 | 0 18 20 35 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 439.076 | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~9/7 = 439.076 | ||
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{{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }} | {{Mapping|legend=1| 1 -2 2 -6 | 0 11 1 27 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 391.465 | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~5/4 = 391.465 | ||
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[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Sensamagic clan| ]] <!-- main article --> | [[Category:Sensamagic clan| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||