Ptolemismic clan
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The ptolemismic clan of rank-3 temperaments tempers out the ptolemisma, 100/99.
Strong extensions are apollo, supermagic, thrasher, and ares, considered below. Discussed elsewhere are:
- Calliope (+45/44 or 81/80) → Didymus rank-3 family
- Jubilee (+50/49 or 99/98) → Jubilismic family
- Sonic (+55/54) → Porcupine rank-3 family
- Nakika (+245/242) → Octagar family
- Octarod (+245/243) → Sensamagic family
- Androboh (+1375/1372) → Gariboh family
For the rank-4 temperament, see Rank-4 temperament #Ptolemismic (100/99).
Ptolemic
Subgroup: 2.3.5.11
Comma list: 100/99
Sval mapping: [⟨1 0 0 2], ⟨0 1 0 -2], ⟨0 0 1 2]]
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.9532, ~5/4 = 384.0675
Optimal ET sequence: 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e
Badness: 0.0226 × 10-3
Apollo
Supermagic
See Keemic family #Supermagic.
Thrasher
See Starling family #Thrasher.