Ptolemismic clan

The ptolemismic clan of rank-3 temperaments tempers out the ptolemisma, 100/99. But we can start with the rank-4 temperament.

Temperaments discussed elsewhere include:

• Calliope, {45/44, 81/80} → Didymus rank-3 family
• Jubilee, {50/49, 99/98} → Jubilismic family
• Sonic, {55/54, 100/99} → Porcupine rank-3 family
• Thrasher, {56/55, 100/99} → Starling family
• Ares, {64/63, 100/99} → Archytas family
• Apollo, {100/99, 225/224} → Marvel family
• Nakika, {100/99, 245/242} → Octagar family
• Octarod, {100/99, 245/243} → Sensamagic family
• Supermagic, {100/99, 385/384} → Keemic family
• Androboh, {100/99, 1375/1372} → Gariboh family

Ptolemismic

Subgroup: 2.3.5.7.11

Comma list: 100/99

Mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 -2], ⟨0 0 1 0 2], ⟨0 0 0 1 0]]

POTE generators: ~3/2 = 704.9532, ~5/4 = 384.0675, ~7/4 = 970.8803

Optimal ET sequence: 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e *

* optimal patent val: 104

Badness: 0.0225 × 10^-6

No-7 ptolemismic

Subgroup: 2.3.5.11

Comma list: 100/99

Sval mapping: [⟨1 0 0 2], ⟨0 1 0 -2], ⟨0 0 1 2]]

POTE generators: ~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