Quindromeda family: Difference between revisions
Revised explanation of Quintagar (12&217) |
|||
Line 17: | Line 17: | ||
=== Subgroup temperament === | === Subgroup temperament === | ||
The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the password comma ([[1216/1215]]), aureusma ([[1445/1444]]), and 6144/6137. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]]. | The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the password comma ([[1216/1215]]), aureusma ([[1445/1444]]), and 6144/6137. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]]. | ||
==== 2.3.5.17 ==== | |||
Subgroup: 2.3.5.17 | |||
[[Comma list]]: 24576/24565, 295936/295245 | |||
[[Gencom]]: [2 18/17; 24576/24565 295936/295245] | |||
[[Gencom|Gencom mapping]]: [{{val| 1 2 0 0 0 0 5 }}, {{val| 0 -5 28 0 0 0 -11 }}] | |||
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}] | |||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.524 | |||
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }} | |||
[[Tp tuning #T2 tuning|RMS error]]: 0.0757 cents | |||
==== 2.3.5.17.19 ==== | |||
Subgroup: 2.3.5.17.19 | Subgroup: 2.3.5.17.19 | ||
Comma list: 1216/1215, 1445/1444, 6144/6137 | [[Comma list]]: 1216/1215, 1445/1444, 6144/6137 | ||
[[Gencom]]: [2 18/17; 1216/1215 1445/1444 6144/6137] | |||
Gencom: [2 | [[Gencom|Gencom mapping]]: [{{val| 1 2 0 0 0 0 5 4 }}, {{val| 0 -5 28 0 0 0 -11 3 }}] | ||
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}] | |||
[[Tp tuning|POL2 generator]]: ~18/17 = 99.524 | |||
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }} | {{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }} | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents | |||
Badness: 0.007140 | Badness: 0.007140 |