Quindromeda family: Difference between revisions

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Revised explanation of Quintagar (12&217)
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=== Subgroup temperament ===
=== Subgroup temperament ===
{{see also| No-sevens subgroup temperaments #Quindromeda }}


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


Sval mapping: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]
[[Gencom]]: [2 18/17; 1216/1215 1445/1444 6144/6137]


Gencom: [2 18/17; 1216/1215 1445/1444 6144/6137]
[[Gencom|Gencom mapping]]: [{{val| 1 2 0 0 0 0 5 4 }}, {{val| 0 -5 28 0 0 0 -11 3 }}]


POTE generator: ~18/17 = 99.524
[[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