22nd-octave temperaments: Difference between revisions
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Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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Optimal tuning (CTE): ~3/2 = 701.942 | Optimal tuning (CTE): ~3/2 = 701.942 | ||
{{Optimal ET sequence|legend=1|176, 336, 506, 836, 1342, 1848}}, ... | |||
=== 7-limit === | === 7-limit === | ||
Revision as of 18:24, 7 May 2023
22edo is a notable tuning system, and as such it gives rise to some fractional-octave temperaments.
Icosidillic
Main article: Porwell temperaments#Icosidillic
Major Arcana
Named after a subset of Tarot cards of which there is 22. Tempers out the [-193 154 -22⟩ comma in the 5-limit. Can be conceptualized as a more precise version of icosidillic in the 5-limit and the 7-limit, however there's no single way to extend it to the 11-limit due to inconsistency.
Subgroup: 2.3.5
Comma list: [-193 154 -22⟩
Mapping: [⟨22 22 -39], ⟨0 1 7]]
Mapping generators: ~[79 -63 9⟩, ~3/2
Optimal tuning (CTE): ~3/2 = 701.942
Optimal ET sequence: 176, 336, 506, 836, 1342, 1848, ...
7-limit
Subgroup: 2.3.5.7
Comma list: [51 -24 -8 2⟩, [-20 41 -23 3⟩
Mapping: [⟨22 22 -39 -453], ⟨0 1 7 40]]
Mapping generators: ~16128/15625, ~3/2
Optimal tuning (CTE): ~3/2 = 701.948