# Shibboleth family

The shibboleth family tempers out the shibboleth comma, 1953125/1889568.

Temperaments discussed elsewhere include:

## Shibboleth

Subgroup: 2.3.5

Comma list: 1953125/1889568

Mapping[1 4 5], 0 -9 -10]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.852

## Superkleismic

The S-expression-based comma list of superkleismic is {S5/S6, S7/S8, S10, S12(, S21)}, from which (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 tuning (POTE): ~2 = 1\1, ~6/5 = 321.930

### 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 tuning (POTE): ~2 = 1\1, ~6/5 = 321.847

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 245/243

Mapping: [1 4 5 2 4 8], 0 -9 -10 3 -2 -16]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994