Ptolemismic clan

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The ptolemismic clan of rank-3 temperaments tempers out the ptolemisma, 100/99.

Strong extensions are apollo, keemic, 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

Subgroup-val mapping: [⟨1 0 0 2], ⟨0 1 0 -2], ⟨0 0 1 2]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

• WE: ~2 = 1199.2633 ¢, ~3/2 = 704.5205 ¢, ~5/4 = 383.8317 ¢

error map: ⟨-0.737 +1.829 -3.955 +4.358]

• CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.4751 ¢, ~5/4 = 383.0756 ¢

error map: ⟨0.000 +2.520 -3.238 +5.883]

Optimal ET sequence: 7, 12, 15, 19, 22, 34, 41, 56, 75e, 97, 131e

Badness (Sintel): 0.187

Apollo

See Marvel family #Apollo.

Keemic

See Keemic family #Keemic.

Thrasher

See Starling family #Thrasher.

Ares

Main article: Archytas and ares

See Archytas family #Ares.