Yer: Difference between revisions
Cmloegcmluin (talk | contribs) unhyphenate "comma basis" |
Cmloegcmluin (talk | contribs) →Yer as a temperament: join, meet → merge |
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⟨ 0 0 0 1 1 ] ⟩ | ⟨ 0 0 0 1 1 ] ⟩ | ||
Expressed as a [[ | Expressed as a [[map-merge]] of [[ET]]s, that's 13&113&137&194. So one ~19 is up one each of the ~11, ~13, and ~17 here. | ||
Now if you temper out the Blumeyer comma and the yama comma (and therefore also the blume comma; in fact, the [[canonical form]] of the [[comma basis]] appears to be blume and yama, with the Blumeyer comma being a linear combination of them), then you get a [[rank-3 temperament]], with mapping: | Now if you temper out the Blumeyer comma and the yama comma (and therefore also the blume comma; in fact, the [[canonical form]] of the [[comma basis]] appears to be blume and yama, with the Blumeyer comma being a linear combination of them), then you get a [[rank-3 temperament]], with mapping: | ||
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⟨ 0 0 1 0 1 ] ⟩ | ⟨ 0 0 1 0 1 ] ⟩ | ||
Again that's still in the 2.11.13.17.19 subgroup. And this one is the | Again that's still in the 2.11.13.17.19 subgroup. And this one is the map-merge of 13&24&33, with [[generators]] 1200.4457, 4149.8305, 4442.6991 (that 1st generator modulo the [[period]] is 548.4934 and the 2nd generator is 841.362). So one ~17 is down two ~11, and one ~19 is down one ~11 and up a ~13. Cool! This you'd call "Yer temperament" then. It has been registered here: [[Subgroup_temperaments#Yer_.28rank_3.29]] | ||
A 13-note scale with only three scale step sizes is possible here. It's 7L 4M 2s, with the pattern LMLLMLsLMLMLs, where L ≈ 103.4¢, M ≈ 85.9¢, and s ≈ 66.2¢: | A 13-note scale with only three scale step sizes is possible here. It's 7L 4M 2s, with the pattern LMLLMLsLMLMLs, where L ≈ 103.4¢, M ≈ 85.9¢, and s ≈ 66.2¢: | ||