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 tunings:

• CTE: ~2 = 1\1, ~6/5 = 321.773
• POTE: ~2 = 1\1, ~6/5 = 321.852

Optimal ET sequence: 15, 26, 41, 179c, 220c, 261cc, 302cc

Badness: 0.227553

Superkleismic

Main article: 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 tunings:

• CTE: ~2 = 1\1, ~6/5 = 321.798
• POTE: ~2 = 1\1, ~6/5 = 321.930

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 tunings:

• CTE: ~2 = 1\1, ~6/5 = 321.109
• POTE: ~2 = 1\1, ~6/5 = 321.423

Optimal ET sequence: 11cd, 15, 41dd, 56dd

Badness: 0.115292