8th-octave temperaments: Difference between revisions

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more prime limit centrism (prioritizing rank-4 full limit over rank-2 subgroup)
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[[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: 2.3.5.7.11
Subgroup: 2.3.11


Comma list: {{monzo|15 8 0 0 -8}}
Comma list: {{monzo|15 8 0 0 -8}}


{{Mapping|legend=1|8 0 0 0 15|0 1 0 0 1|0 0 1 0 0|0 0 0 1 0}}
{{Mapping|legend=1|8 0 15|0 1 1}}


: mapping generators: ~12/11 = 1\8, ~3, ~5, ~7
: 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.