Bapbo clan: Difference between revisions
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[[Subgroup]]: 2.5.7.11 | [[Subgroup]]: 2.5.7.11 | ||
[[Comma list]]: | [[Comma list]]: 80/77, 176/175 | ||
{{mapping|1 2 3|0 2 -1|legend=2}} | {{mapping|1 2 3 3|0 2 -1 3|legend=2}} | ||
Mapping generators: ~[[2/1]], ~[[8/7]] | Mapping generators: ~[[2/1]], ~[[8/7]] | ||
[[Optimal tuning]] ([[CTE]]): ~[[2/1]] = 1\1, ~[[8/7]] = | [[Optimal tuning]] ([[CTE]]): ~[[2/1]] = 1\1, ~[[8/7]] = 191.779 | ||
[[Support]]ing [[ET]]s: {{EDOs|6, 5, 7, 11, | [[Support]]ing [[ET]]s: {{EDOs|6, 5e, 7, 13e, 11e, 19d, 17[+5, +11], 25[+7, +11], 23[+5, +11], 31[+7, +11], 29[+5, +7, ++11], 37[+7, +11], 35[+5, +7, ++11], 43[+7, +11]}} | ||
[[Badness]]: 0.566 | [[Badness]]: 0.566 | ||
== | == Summary of full 7-limit extensions == | ||
Revision as of 09:06, 8 September 2023
The bapbo clan of temperaments all temper out the comma 256/245, the bapbo comma, all deriving from the no-threes bapbo temperament. This means the generator represents both 35/32 and 8/7 and 2 make 5/4 (a sort of "meantone" but using different seconds than 10/9 and 9/8).
Temperaments discussed elsewhere include dominant, baba and uncle.
Bapbo
Subgroup: 2.5.7
Sval mapping: [⟨1 2 3], ⟨0 2 -1]]
Mapping generators: ~2/1, ~8/7
Optimal tuning (CTE): ~2/1 = 1\1, ~8/7 = 198.709
Supporting ETs: 6, 5, 7, 11, 17c, 13c, 23c, 19d, 29cd, 16c, 25d, 35cd, 31d, 28c
Badness: 0.566
No-threes 11-limit
Subgroup: 2.5.7.11
Comma list: 80/77, 176/175
Sval mapping: [⟨1 2 3 3], ⟨0 2 -1 3]]
Mapping generators: ~2/1, ~8/7
Optimal tuning (CTE): ~2/1 = 1\1, ~8/7 = 191.779
Supporting ETs: 6, 5e, 7, 13e, 11e, 19d, 17[+5, +11], 25[+7, +11], 23[+5, +11], 31[+7, +11], 29[+5, +7, ++11], 37[+7, +11], 35[+5, +7, ++11], 43[+7, +11]
Badness: 0.566