Shibboleth family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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