Keenanismic family: Difference between revisions
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The '''keenanismic family''' of [[Catalog of rank-4 temperaments|rank-4]] temperaments [[Tempering out|tempers out]] the [[keenanisma]], the 11-limit comma 385/384 = {{monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. | The '''keenanismic family''' of [[Catalog of rank-4 temperaments|rank-4]] temperaments [[Tempering out|tempers out]] the [[keenanisma]], the 11-limit comma 385/384 = {{monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5 | ||
{{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }} | {{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }} | ||
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[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament --> | [[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament --> | ||
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}] | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.11/5.13/5 | ||
{{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }} | {{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Keenanismic family| ]] <!-- main article --> | [[Category:Keenanismic family| ]] <!-- main article --> | ||
[[Category:Keenanismic| ]] <!-- key article --> | [[Category:Keenanismic| ]] <!-- key article --> | ||
[[Category:Rank 4]] | [[Category:Rank 4]] | ||