8th-octave temperaments
Template:Fractional-octave navigation Discussed elsewhere are:
- Octant, → Schismatic family
- Octoid, → Ragismic microtemperaments
Octatonic
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: 2.3.11
Comma list: [15 8 0 0 -8⟩
Mapping: [⟨8 0 15], ⟨0 1 1]]
- mapping generators: ~12/11 = 1\8, ~3
Supporting ETs: 16, 24, 32, 48, 56, 80, 72, 120, 128, 152, ...
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.
Subgroup: 2.3.19.23.29.31
Comma list: 94221/94208, 419957/419904, 219501/219488, 7997934975003/7996960669696
Subgroup-val mapping: [⟨8 2 35 25 47 2], ⟨0 21 -2 22 -16 74]]
- mapping generators: ~10051/9216 = 1\8, ~24/23 = 76.284
Optimal tuning (CTE): ~24/23 = 76.284