Marvel family: Difference between revisions
→Apollo: +link to ptolemismic clan |
→Undecimal marvel (unimarv): extend hecate to the 19-limit via 225/224 = (400/399)(513/512); "17-limit hecate" doesn't deserve the name, changed to "apotropaia"; correct the mapping of enodia |
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== Undecimal marvel (unimarv) == | == Undecimal marvel (unimarv) == | ||
{{Main| Marvel }} | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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{{Mapping|legend=1| 1 0 0 -5 12 | 0 1 0 2 -1 | 0 0 1 2 -3 }} | {{Mapping|legend=1| 1 0 0 -5 12 | 0 1 0 2 -1 | 0 0 1 2 -3 }} | ||
[[ | [[Mapping to lattice]]: [{{val| 0 -1 0 -2 1 }}, {{val| 0 -1 1 0 -2 }}] | ||
Lattice basis: | Lattice basis: | ||
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Complexity spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | Complexity spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11 | ||
==== | ==== 2.3.5.7.11.13.19 subgroup ==== | ||
Subgroup: 2.3.5.7.11.13.19 | |||
Comma list: 225/224, 325/324, 385/384, 400/399 | |||
Sval mapping: {{mapping| 1 0 0 -5 12 2 9 | 0 1 0 2 -1 4 -3 | 0 0 1 2 -3 -2 0 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4245, ~5/4 = 383.0293 | |||
{{Optimal ET sequence|legend=1| 41, 53, 72, 94, 113, 166 }} | |||
Badness: 0.773 × 10<sup>-3</sup> | |||
==== Apotropaia ==== | |||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }} | Mapping: {{mapping| 1 0 0 -5 12 2 18 | 0 1 0 2 -1 4 0 | 0 0 1 2 -3 -2 -6 }} | ||
Optimal tuning ( | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.5860, ~5/4 = 382.7331 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 41, 53g, 72, 166g, 238cfg }} | ||
Badness: 0.869 × 10<sup>-3</sup> | Badness: 0.869 × 10<sup>-3</sup> | ||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 225/224, 325/324, 385/384, 400/399, 595/594 | |||
Mapping: {{mapping| 1 0 0 -5 12 2 18 9 | 0 1 0 2 -1 4 0 -3 | 0 0 1 2 -3 -2 -6 0 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4435, ~5/4 = 382.7395 | |||
{{Optimal ET sequence|legend=1| 41, 53g, 72, 94, 113, 166g }} | |||
Badness: 0.978 × 10<sup>-3</sup> | |||
==== Enodia ==== | ==== Enodia ==== | ||
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Comma list: 225/224, 325/324, 375/374, 385/384 | Comma list: 225/224, 325/324, 375/374, 385/384 | ||
Mapping: {{mapping| 1 0 0 -5 12 2 | Mapping: {{mapping| 1 0 0 -5 12 2 -13 | 0 1 0 2 -1 4 2 | 0 0 1 2 -3 -2 6 }} | ||
Optimal tuning ( | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.6270, ~5/4 = 383.3456 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 41g, 53, 72, 166g, 238cfg }} | ||
Badness: 0.917 × 10<sup>-3</sup> | Badness: 0.917 × 10<sup>-3</sup> | ||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399 | |||
Mapping: {{mapping| 1 0 0 -5 12 2 -13 9 | 0 1 0 2 -1 4 2 -3 | 0 0 1 2 -3 -2 6 0 }} | |||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4791, ~5/4 = 383.3795 | |||
{{Optimal ET sequence|legend=1| 41g, 53, 72, 94, 125f, 166g }} | |||
Badness: 1.03 × 10<sup>-3</sup> | |||
=== Marvell === | === Marvell === | ||