Jubilismic family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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The '''jubilismic family''' contains temperaments that temper out the [[jubilisma|jubilisma (50/49)]] (also called tritonic diesis, or septimal sixth-tone). It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While most rank-three temperaments are planar, a jubilismic temperament divides the octave in two. | The '''jubilismic family''' contains temperaments that temper out the [[jubilisma|jubilisma (50/49)]] (also called tritonic diesis, or septimal sixth-tone). It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While most rank-three temperaments are planar, a jubilismic temperament divides the octave in two. | ||
== Jubilismic | == Jubilismic == | ||
[[Subgroup]]: 2.3.5.7 | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 50/49 | [[Comma list]]: 50/49 | ||
{{Mapping|legend=1| 2 0 0 1 | 0 1 0 0 | 0 0 1 1 }} | |||
: mapping generators: ~7/5, ~3, ~5 | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 702.9804, ~5/4 = 380.8399 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and [[9-odd-limit]] | * 7- and [[9-odd-limit]] | ||
: | : {{monzo list| 1 0 0 0 | 0 1 0 0 | -1/4 0 1/2 1/2 | 1/4 0 1/2 1/2 }} | ||
: [[Eigenmonzo | : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.35 | ||
{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }} | {{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }} | ||
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== Jubilee == | == Jubilee == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 50/49, 99/98 | [[Comma list]]: 50/49, 99/98 | ||
{{Mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 703.4155, ~5/4 = 380.6973 | ||
{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }} | {{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }} | ||
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== Festival == | == Festival == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 45/44, 50/49 | [[Comma list]]: 45/44, 50/49 | ||
{{Mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 693.6257, ~5/4 = 371.2658 | ||
{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }} | {{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }} | ||
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== Fiesta == | == Fiesta == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 50/49, 56/55 | [[Comma list]]: 50/49, 56/55 | ||
{{Mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 713.5853, ~5/4 = 397.6952 | ||
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }} | {{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }} | ||
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== Jamboree == | == Jamboree == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 50/49, 55/54 | [[Comma list]]: 50/49, 55/54 | ||
{{Mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }} | |||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 706.6559, ~5/4 = 376.8308 | ||
{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22 }} | {{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22 }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Jubilismic]] | [[Category:Jubilismic family| ]] <!-- main article --> | ||
[[Category:Jubilismic| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||