Keenanismic family: Difference between revisions
Logging zaxa = 13-limit[352/351, 385/384], a temperament designed to interpret the Zil series of scales as 13-limit. |
Complete the data, update keys and normalize the mapping |
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== Keenanismic == | == Keenanismic == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 385/384 | [[Comma list]]: 385/384 | ||
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Transpose]]: [2 3 5 7 385/35] | [[Transpose]]: [2 3 5 7 385/35] | ||
| Line 19: | Line 19: | ||
{{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 }} | ||
[[Badness]]: 15. | [[Badness]]: 15.2 × 10<sup>-9</sup> | ||
== Martwin == | == Martwin == | ||
Subgroup: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
[[Comma list]]: 325/324, 385/384 | [[Comma list]]: 325/324, 385/384 | ||
{{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }} | |||
[[Transpose]]: [2 3 5 7 385/35 324/25] | [[Transpose]]: [2 3 5 7 385/35 324/25] | ||
| Line 34: | Line 32: | ||
[[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 (unchanged-interval) 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 }} | ||
[[Badness]]: 2. | [[Badness]]: 2.21 × 10<sup>-6</sup> | ||
== Ancient == | == Ancient == | ||
Subgroup: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
[[Comma list]]: 385/384, 625/624 | [[Comma list]]: 385/384, 625/624 | ||
{{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }} | |||
[[Transpose]]: [2 3 5 7 385/35 625/48] | [[Transpose]]: [2 3 5 7 385/35 625/48] | ||
| Line 53: | Line 49: | ||
{{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }} | {{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }} | ||
[[Badness]]: 2. | [[Badness]]: 2.57 × 10<sup>-6</sup> | ||
== Zaxa == | == Zaxa == | ||
Subgroup: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
[[Comma list]]: 352/351, 385/384 | [[Comma list]]: 352/351, 385/384 | ||
{{Mapping|legend=1| 1 0 0 0 7 12 |0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829 | |||
{{Optimal ET sequence|legend=1| 7, 10, 15f, 17, 19f, 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }} | |||
[[Badness]]: 3.35 × 10<sup>-6</sup> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Keenanismic family| ]] <!-- main article --> | [[Category:Keenanismic family| ]] <!-- main article --> | ||
[[Category:Keenanismic| ]] <!-- key article --> | |||
[[Category:Rank 4]] | [[Category:Rank 4]] | ||