# Alphaxenic rank three clan

The alphaxenic rank-3 clan of temperaments tempers out the Alpharabian comma, [-17 2 0 0 4 = 131769/131072. Both no-5 alphaxenic and no-7 alphaxenic can be the head of this clan, but we can begin with the rank-4 temperament.

Temperaments discussed elsewhere include:

## Alphaxenic

Subgroup: 2.3.5.7.11

Comma list: 131769/131072

Mapping[2 1 0 0 8], 0 2 0 0 -1], 0 0 1 0 0], 0 0 0 1 0]]

mapping generators: ~363/256, ~16/11, ~5, ~7

Optimal tuning (POTE): ~363/256 = 1\2, ~16/11 = 650.6784, ~5/4 = 385.5751, ~7/4 = 967.9328

## Rabic

Whenever the rastma is added to the list of commas tempered out among alphaxenic temperaments, you end up with rabic, which splits the octave into 24 equal parts. This temperament is named as such because tempering out both the Alpharabian comma and the rastma automatically tempers out the Betarabian comma.

Subgroup: 2.3.5.7.11

Comma list: 243/242, 131769/131072

Mapping[24 38 0 0 83], 0 0 1 0 0], 0 0 0 1 0]]

mapping generators: ~33/32, ~5, ~7

Wedgie⟨⟨⟨0 0 0 24 0 0 38 0 0 83]]]

Optimal tuning (POTE): ~33/32 = 1\24, ~5/4 = 385.0647, ~7/4 = 967.3158