22nd-octave temperaments: Difference between revisions
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| Line 11: | Line 11: | ||
Mapping: [{{val|22 22 -39}}, {{val|0 1 7}}] | Mapping: [{{val|22 22 -39}}, {{val|0 1 7}}] | ||
Mapping generators: ~{{monzo| | Mapping generators: ~{{monzo|79 -63 9}}, ~3/2 | ||
Optimal tuning (CTE): ~3/2 = 701.942 | Optimal tuning (CTE): ~3/2 = 701.942 | ||
| Line 21: | Line 21: | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: {{monzo|}}}} | Comma list: {{monzo|51 -24 -8 2}}, {{monzo|-20 41 -23 3}} | ||
Mapping: [{{val|22 22 -39 -453}}, {{val|0 1 7 40}}] | |||
Mapping generators: ~16128/15625, ~3/2 | |||
Optimal tuning (CTE): ~3/2 = 701.948 | |||
[[Category:22edo]] | |||
[[Category:Temperament collections]] | |||
[[Category:Rank 2]] | |||
Revision as of 14:00, 8 January 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
Vals: Template:Val list, ...
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