Semicanousmic clan: Difference between revisions
+2.3.5.11.17.19 extension to deuteromere |
m -typos |
||
| Line 38: | Line 38: | ||
[[Badness]]: 0.142 × 10<sup>-3</sup> | [[Badness]]: 0.142 × 10<sup>-3</sup> | ||
=== 2.3.5 | === 2.3.5.11.17 subgroup === | ||
Subgroup: 2.3.5.11.17 | Subgroup: 2.3.5.11.17 | ||
| Line 51: | Line 51: | ||
Badness: 0.481 × 10<sup>-3</sup> | Badness: 0.481 × 10<sup>-3</sup> | ||
=== 2.3.5 | === 2.3.5.11.17.19 subgroup === | ||
Subgroup: 2.3.5.11.17.19 | Subgroup: 2.3.5.11.17.19 | ||
Revision as of 21:26, 2 May 2022
The semicanousmic clan of rank-3 temperaments tempers out the semicanousma, 14641/14580 = [-2 -6 -1 0 4⟩.
Temperaments discussed elsewhere are:
- Urania, {81/80, 121/120} → Didymus rank three family
- Triglav, {3025/3024, 3136/3125} → Hemimean family
- Semicanou, {9801/9800, 14641/14580} → Canou family
Considered below is deuteromere, the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament.
Semicanousmic
Subgroup: 2.3.5.7.11
Comma list: 14641/14580
Mapping: [⟨1 0 2 0 1], ⟨0 1 2 0 2], ⟨0 0 -4 0 -1], ⟨0 0 0 1 0]]
Mapping generators: ~2, ~3, ~18/11, ~7
POTE generators: ~3/2 = 702.2503, ~18/11 = 854.5421, ~7/4 = 968.6866
Badness: 0.351 × 10-6
Deuteromere
Subgroup: 2.3.5.11
Comma list: 14641/14580
Sval mapping: [⟨1 0 2 1], ⟨0 1 2 2], ⟨0 0 -4 -1]]
Sval mapping generators: ~2, ~3, ~18/11
POTE generators: ~3/2 = 702.2503, ~18/11 = 854.5421
Badness: 0.142 × 10-3
2.3.5.11.17 subgroup
Subgroup: 2.3.5.11.17
Comma list: 1089/1088, 14641/14580
Sval mapping: [⟨1 0 2 1 -4], ⟨0 1 2 2 6], ⟨0 0 -4 -1 -2]]
POTE generators: ~3/2 = 702.3162, ~18/11 = 854.5619
Optimal GPV sequence: Template:Val list
Badness: 0.481 × 10-3
2.3.5.11.17.19 subgroup
Subgroup: 2.3.5.11.17.19
Comma list: 1089/1088, 1216/1215, 1445/1444
Sval mapping: [⟨1 0 2 1 -4 -4], ⟨0 1 2 2 6 7], ⟨0 0 -4 -1 -2 -4]]
POTE generators: ~3/2 = 702.2578, ~18/11 = 854.5595
Optimal GPV sequence: Template:Val list
Badness: 0.403 × 10-3