Ptolemismic clan
(Redirected from Ptolemismic temperaments)
- 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
- 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