22nd-octave temperaments

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