Ptolemismic clan

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

See Marvel family #Apollo.

Supermagic

See Keemic family #Supermagic.

Thrasher

See Starling family #Thrasher.

Ares

Main article: Archytas_and_ares

See Archytas family #Ares.