Hemimean clan: Difference between revisions
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== Tremka == | == Tremka == | ||
The name ''tremka'' was initially used for [[No-sevens subgroup temperaments|no-sevens version]] of 50 & 111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka. | The name ''tremka'' was initially used for the [[No-sevens subgroup temperaments|no-sevens version]] of 50 & 111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka. | ||
=== 2.3.5.11 subgroup === | |||
Subgroup: 2.3.5.11 | |||
[[Comma list]]: 6912/6875, 526153617/524288000 | |||
[[Gencom]]: [2 363/320; 6912/6875 526153617/524288000] | |||
[[Gencom|Gencom mapping]]: [{{val|1 -4 -2 0 4}}, {{val|0 31 24 0 -3}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 -4 -2 4}}, {{val|0 31 24 -3}}] | |||
[[Tp tuning|POL2 generator]]: ~363/320 = 216.182 | |||
{{Optimal ET sequence|legend=1| 11b, 28bbcc, 39bc, 50, 111, 161, 272 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3717 cents | |||
==== 2.3.5.11.13 ==== | |||
Subgroup: 2.3.5.11.13 | |||
[[Comma list]]: 2200/2197, 3267/3250, 6656/6655 | |||
[[Gencom]]: [2 192/169; 2200/2197 3267/3250 6656/6655] | |||
[[Gencom|Gencom mapping]]: [{{val|1 -4 -2 0 4 1}}, {{val|0 31 24 0 -3 15}}] | |||
[[Mapping|Sval mapping]]: [{{val|1 -4 -2 4 1}}, {{val|0 31 24 -3 15}}] | |||
[[Tp tuning|POL2 generator]]: ~192/169 = 216.186 | |||
{{Optimal ET sequence|legend=1| 11b, 28bbccf, 39bc, 50, 111, 272, 383cf }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.3705 cents | |||
=== Septimal tremka === | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 782: | Line 817: | ||
[[Badness]]: 0.179925 | [[Badness]]: 0.179925 | ||
=== 11-limit === | ==== 11-limit ==== | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 795: | Line 830: | ||
Badness: 0.068825 | Badness: 0.068825 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 808: | Line 843: | ||
Badness: 0.036070 | Badness: 0.036070 | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||