No-threes subgroup temperaments: Difference between revisions

Dummy index (talk | contribs)
grouping No-threes-or-fives subgroup temperaments
Dummy index (talk | contribs)
No edit summary
Line 210: Line 210:


{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }}
{{Optimal ET sequence|legend=1| 6, 23de, 29, 35, 41 }}
== Yer (rank 3) ==
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 209/208, 2057/2048
[[Sval]] [[mapping]]: {{mapping| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
[[Optimal tuning]] ([[TE tuning|TE]]): ~2/1 = 1200.4457, ~11/8 = 548.4934, ~16/13 = 358.638
{{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }}
== Yamablu ==
Yamablu, with a generator of ~17/13, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). The [[Kite's Method of Naming Rank-2 Scales using Mode Numbers|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]].
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 209/208, 2057/2048, 83521/83486
[[Sval]] [[mapping]]: [{{val| 1 5 1 1 0 }}, {{val| 0 -4 7 8 11 }}]
Optimal tuning ([[POTE]]): ~17/13 = 462.9606
{{Optimal ET sequence|legend=1| 13, 44, 57, 70}}
[[Tp tuning #T2 tuning|RMS error]]: 0.4898 cents


== Ostara ==
== Ostara ==
Line 370: Line 344:


{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41e, 66ee }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41e, 66ee }}
== Mavericks ==
[[Subgroup]]: 2.13.19
[[Comma list]]: 47525504/47045881
[[Mapping]]: [{{val|1 1 2}}, {{val|0 6 5}}]
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/19 = 539.886
{{Optimal ET sequence|legend=1| 7fh, 9, 11, 20 }}


== Vengeance ==
== Vengeance ==
Line 477: Line 439:


{{Optimal ET sequence|legend=1|7, 18dg, 25, 32, 57, 488, 545, 602, 659, 716, 773, 830, 887, 1717g}}
{{Optimal ET sequence|legend=1|7, 18dg, 25, 32, 57, 488, 545, 602, 659, 716, 773, 830, 887, 1717g}}
== Yer (rank 3) ==
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 209/208, 2057/2048
[[Sval]] [[mapping]]: {{mapping| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
[[Optimal tuning]] ([[TE tuning|TE]]): ~2/1 = 1200.4457, ~11/8 = 548.4934, ~16/13 = 358.638
{{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }}
== Yamablu ==
Yamablu, with a generator of ~17/13, is named for its tempering of the yama comma (209/208) and the blume comma (2057/2048), which also implies the blumeyer comma (2432/2431). The [[Kite's Method of Naming Rank-2 Scales using Mode Numbers|13th Yamablu[13]]] scale is a linear-temperament version of [[Gjaeck]].
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 209/208, 2057/2048, 83521/83486
[[Sval]] [[mapping]]: [{{val| 1 5 1 1 0 }}, {{val| 0 -4 7 8 11 }}]
Optimal tuning ([[POTE]]): ~17/13 = 462.9606
{{Optimal ET sequence|legend=1| 13, 44, 57, 70}}
[[Tp tuning #T2 tuning|RMS error]]: 0.4898 cents
== Mavericks ==
[[Subgroup]]: 2.13.19
[[Comma list]]: 47525504/47045881
[[Mapping]]: [{{val|1 1 2}}, {{val|0 6 5}}]
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~26/19 = 539.886
{{Optimal ET sequence|legend=1| 7fh, 9, 11, 20 }}


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]