22nd-octave temperaments: Difference between revisions

Eliora (talk | contribs)
Major arcana: 330, not 336 - there
Eliora (talk | contribs)
Major arcana: rework: apply simpler mapping in the 7-limit (6 gensteps vs. 40)
Line 40: Line 40:
Mapping: [{{val|22 22 -39}}, {{val|0 1 7}}]
Mapping: [{{val|22 22 -39}}, {{val|0 1 7}}]


Mapping generators: ~{{monzo|79 -63 9}}, ~3/2
: mapping generators: ~{{monzo|79 -63 9}}, ~3/2


Optimal tuning (CTE): ~3/2 = 701.942
Optimal tuning (CTE): ~3/2 = 701.942


{{Optimal ET sequence|legend=1|176, 330, 506, 836, 1342, 1848}}, ...
[[Support]]ing [[ET]]s: {{EDOs|176, 330, 506, 836, 1342, 1848}}, ...


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: {{monzo|51 -24 -8 2}}, {{monzo|-20 41 -23 3}}
Comma list: 14348907/14336000, {{monzo|39 11 -11 -11}}


Mapping: [{{val|22 22 -39 -453}}, {{val|0 1 7 40}}]
Mapping: [{{val|22 0 -193 271}}, {{val|0 1 7 -6}}]


Mapping generators: ~16128/15625, ~3/2
: mapping generators: ~8388608/8103375, ~3/2


Optimal tuning (CTE): ~3/2 = 701.948
Optimal tuning (CTE): ~3/2 = 702.014


{{Optimal ET sequence|legend=1|506}}
[[Support]]ing [[ET]]s: {{EDOs|176, 506, 682}}


== Bibium ==
== Bibium ==