Gamelismic clan: Difference between revisions
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{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }} | {{Optimal ET sequence|legend=1| 36, 77, 113, 190 }} | ||
=== 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 2.3.7.13.17.29 by tempering out [[273/272]], [[378/377]], [[729/728]], and [[833/832]]. | |||
==== 2.3.7.13 ==== | |||
[[Subgroup]]: 2.3.7.13 | |||
[[Comma list]]: 729/728, 1029/1024 | |||
[[Mapping|Sval mapping]]: [{{val|1 1 3 0}}, {{val|0 3 -1 19}}] | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.734 | |||
* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.622 | |||
{{Optimal ET sequence|legend=1| 5, ..., 31f, 36, 77, 113 }} | |||
==== 2.3.7.13.17 ==== | |||
Subgroup: 2.3.7.13.17 | |||
Comma list: 273/272, 729/728, 833/832 | |||
Sval mapping: [{{val|1 1 3 0 0}}, {{val|0 3 -1 19 21}}] | |||
Optimal tunings: | |||
* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.657 | |||
* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.546 | |||
{{Optimal ET sequence|legend=1| 5g, ..., 31fg, 36, 113, 149 }} | |||
==== 2.3.7.13.17.29 ==== | |||
Subgroup: 2.3.7.13.17.29 | |||
Comma list: 273/272, 378/377, 729/728, 833/832 | |||
Sval mapping: [{{val|1 1 3 0 0 7}}, {{val|0 3 -1 19 21 -11}}] | |||
Optimal tunings: | |||
* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.658 | |||
* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.614 | |||
{{Optimal ET sequence|legend=1| 5g, ..., 36, 77, 113 }} | |||
=== Radon === | === Radon === | ||
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Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out {{S|13}} = [[169/168]], which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]]~[[17/12]]. 36edo is an excellent baladic tuning. | Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out {{S|13}} = [[169/168]], which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]]~[[17/12]]. 36edo is an excellent baladic tuning. | ||
==== 2.3.7.13 ==== | |||
[[Subgroup]]: 2.3.7.13 | [[Subgroup]]: 2.3.7.13 | ||