Diaschismic rank three family: Difference between revisions
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The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. | The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| -1/8 3/2 -5/4 0 1 }}, {{monzo| 11/8 -1/2 -1/4 0 1 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| -1/8 3/2 -5/4 0 1 }}, {{monzo| 11/8 -1/2 -1/4 0 1 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/3 | ||
{{Optimal ET sequence|legend=1| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }} | {{Optimal ET sequence|legend=1| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }} | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo| 45/16 3/4 -3/8 -1/2 1/2 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo| 45/16 3/4 -3/8 -1/2 1/2 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/7 | ||
{{Optimal ET sequence|legend=1| 10, 12e, 22, 46, 68, 114, 170b }} | {{Optimal ET sequence|legend=1| 10, 12e, 22, 46, 68, 114, 170b }} | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| -3 2 -1 2 0 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/8 1/2 -1/4 0 0 }}, {{monzo| 11/4 -1 1/2 0 0 }}, {{monzo| 0 0 0 1 0 }}, {{monzo| -3 2 -1 2 0 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.7 | ||
{{Optimal ET sequence|legend=1| 46, 58, 104c, 160, 162ce, 172ce, 218ce }} | {{Optimal ET sequence|legend=1| 46, 58, 104c, 160, 162ce, 172ce, 218ce }} | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 9/7 0 -3/7 2/7 1/7 }}, {{monzo| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo| 41/14 0 -1/7 -4/7 5/7 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 9/7 0 -3/7 2/7 1/7 }}, {{monzo| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo| 41/14 0 -1/7 -4/7 5/7 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5 | ||
{{Optimal ET sequence|legend=1| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }} | {{Optimal ET sequence|legend=1| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Diaschismic rank-3 family| ]] <!-- main article --> | [[Category:Diaschismic rank-3 family| ]] <!-- main article --> | ||
[[Category:Diaschismic| ]] <!-- key article --> | [[Category:Diaschismic| ]] <!-- key article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||