8th-octave temperaments: Difference between revisions
more prime limit centrism (prioritizing rank-4 full limit over rank-2 subgroup) |
|||
| Line 6: | Line 6: | ||
[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. | [[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. | ||
Subgroup: 2.3 | Subgroup: 2.3.11 | ||
Comma list: {{monzo|15 8 0 0 -8}} | Comma list: {{monzo|15 8 0 0 -8}} | ||
{{Mapping|legend=1|8 | {{Mapping|legend=1|8 0 15|0 1 1}} | ||
: mapping generators: ~12/11 = 1\8, ~3 | : mapping generators: ~12/11 = 1\8, ~3 | ||
[[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 80, 72, 120, 128, 152}}, ... | [[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 80, 72, 120, 128, 152}}, ... | ||
== Octium == | == Octium == | ||
Octium temperament is named after an "extended provisional" name for oxygen, the 8th element. The term [[oxygen]] itself is already the name of an exotemperament. It reaches [[24/23]] in one generator and [[19/16]] in two. | Octium temperament is named after an "extended provisional" name for oxygen, the 8th element. The term [[oxygen]] itself is already the name of an exotemperament. It reaches [[24/23]] in one generator and [[19/16]] in two. | ||