Gamelismic clan: Difference between revisions
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=== Euslendric === | === Euslendric === | ||
Forms of slendric in the most optimal range for the 2.3.7 temperament (36 & 77) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to | Forms of slendric in the most optimal range for the 2.3.7 temperament (36 & 77) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. | ||
==== 2.3.7.13 ==== | ==== 2.3.7.13 ==== | ||
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{{Optimal ET sequence|legend=1| 5, ..., 31f, 36, 77, 113 }} | {{Optimal ET sequence|legend=1| 5, ..., 31f, 36, 77, 113 }} | ||
Badness (Dirichlet): 0.339 | |||
==== 2.3.7.13.17 ==== | ==== 2.3.7.13.17 ==== | ||
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{{Optimal ET sequence|legend=1| 5g, ..., 31fg, 36, 113, 149 }} | {{Optimal ET sequence|legend=1| 5g, ..., 31fg, 36, 113, 149 }} | ||
Badness (Dirichlet): 0.332 | |||
==== 2.3.7.13.17.19 ==== | ==== 2.3.7.13.17.19 ==== | ||
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{{Optimal ET sequence|legend=1| 5g, ..., 36, 77, 113 }} | {{Optimal ET sequence|legend=1| 5g, ..., 36, 77, 113 }} | ||
==== 2.3.7.13.17.19.29 ==== | Badness (Dirichlet): 0.380 | ||
Subgroup: 2.3.7.13.17.19.29 | |||
==== 2.3.7.13.17.19.23 ==== | |||
Subgroup: 2.3.7.13.17.19.23 | |||
Comma list: 273/272, 343/342, 392/391, 513/512, 729/728 | |||
Sval mapping: [{{val|1 1 3 0 0 6 9}}, {{val|0 3 -1 19 21 -9 -23}}] | |||
Optimal tunings: | |||
* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.624 | |||
* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.607 | |||
{{Optimal ET sequence|legend=1| 5gi, ..., 36, 77, 113 }} | |||
Badness (Dirichlet): 0.474 | |||
==== 2.3.7.13.17.19.23.29 ==== | |||
Subgroup: 2.3.7.13.17.19.23.29 | |||
Comma list: 273/272, 343/342, 378/377, 513/512, 609/608 | Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608 | ||
Sval mapping: [{{val|1 1 3 0 0 6 7}}, {{val|0 3 -1 19 21 -9 -11}}] | Sval mapping: [{{val|1 1 3 0 0 6 9 7}}, {{val|0 3 -1 19 21 -9 -23 -11}}] | ||
Optimal tunings: | Optimal tunings: | ||
* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233. | * [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.626 | ||
* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233. | * [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.620 | ||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 5gi, ..., 36, 77, 113 }} | ||
Badness (Dirichlet): 0.473 | |||
=== Radon === | === Radon === | ||