Shibboleth family
The shibboleth family tempers out the shibboleth comma, 1953125/1889568.
Temperaments discussed elsewhere include:
- superthird, {245/243, 78125/76832} → Sensamagic clan #Superthird
Shibboleth
Subgroup: 2.3.5
Comma list: 1953125/1889568
Mapping: [⟨1 4 5], ⟨0 -9 -10]]
Optimal ET sequence: 15, 26, 41, 179c, 220c, 261cc, 302cc
Badness: 0.227553
Superkleismic
The S-expression-based comma list of superkleismic is {S5/S6, S7/S8, S10, S12(, S21)}. Through careful observation of the equivalences therein one can derive that a sharpened ~6/5 is the generator as well as the mapping of the full 13-limit.
Subgroup: 2.3.5.7
Comma list: 875/864, 1029/1024
Mapping: [⟨1 4 5 2], ⟨0 -9 -10 3]]
Wedgie: ⟨⟨ 9 10 -3 -5 -30 -35 ]]
Optimal ET sequence: 11c, 15, 26, 41
Badness: 0.047932
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 385/384
Mapping: [⟨1 4 5 2 4], ⟨0 -9 -10 3 -2]]
Optimal tunings:
- CTE: ~2 = 1\1, ~6/5 = 321.815
- POTE: ~2 = 1\1, ~6/5 = 321.847
Optimal ET sequence: 11c, 15, 26, 41, 179cde, 220cde, 261ccdee
Badness: 0.025659
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 245/242
Mapping: [⟨1 4 5 2 4 8], ⟨0 -9 -10 3 -2 -16]]
Optimal tunings:
- CTE: ~2 = 1\1, ~6/5 = 321.986
- POTE: ~2 = 1\1, ~6/5 = 321.994
Optimal ET sequence: 11cf, 15, 26, 41
Badness: 0.021478
Gilead
Subgroup: 2.3.5.7
Comma list: 126/125, 343/324
Mapping: [⟨1 4 5 6], ⟨0 -9 -10 -12]]
Wedgie: ⟨⟨ 9 10 12 -5 -6 0 ]]
Optimal ET sequence: 11cd, 15, 41dd, 56dd
Badness: 0.115292