Semicanousmic clan
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 are syndeute and hemireiwa, in addition to deuteromere, the no-7 subgroup temperament.
For the rank-4 semicanousmic temperament, see Rank-4 temperament #Semicanousmic (14641/14580).
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
Optimal tuning (CTE): ~3/2 = 702.3342, ~18/11 = 854.5548
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]]
Optimal tuning (CTE): ~3/2 = 702.3427, ~18/11 = 854.5587
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]]
Optimal tuning (CTE): ~3/2 = 702.2987, ~18/11 = 854.5520
Optimal GPV sequence: Template:Val list
Badness: 0.403 × 10-3
Syndeute
Subgroup: 2.3.5.7.11
Comma list: 14641/14580, 19712/19683
Mapping: [⟨1 0 2 -9 1], ⟨0 1 2 7 2], ⟨0 0 -4 1 -1]]
Mapping generators: ~2, ~3, ~18/11
Optimal tuning (CTE): ~3/2 = 702.0812, ~18/11 = 854.4115
Badness: 3.26 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1573/1568, 2080/2079, 14641/14580
Mapping: [⟨1 0 2 -9 1 -15], ⟨0 1 2 7 2 10], ⟨0 0 -4 1 -1 4]]
Optimal tuning (CTE): ~3/2 = 702.1682, ~18/11 = 854.5074
Optimal GPV sequence: Template:Val list
Badness: 3.01 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 442/441, 561/560, 715/714, 14641/14580
Mapping: [⟨1 0 2 -9 1 -15 -4], ⟨0 1 2 7 2 10 6], ⟨0 0 -4 1 -1 4 -2]]
Optimal tuning (CTE): ~3/2 = 702.1910, ~18/11 = 854.4751
Optimal GPV sequence: Template:Val list
Badness: 1.69 × 10-3
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 442/441, 561/560, 715/714, 1216/1215, 1445/1444
Mapping: [⟨1 0 2 -9 1 -15 -4 -4], ⟨0 1 2 7 2 10 6 7], ⟨0 0 -4 1 -1 4 -2 -4]]
Optimal tuning (CTE): ~3/2 = 702.1925, ~18/11 = 854.4721
Optimal GPV sequence: Template:Val list
Badness: 1.27 × 10-3
Hemireiwa
Hemireiwa is in a certain sense dual to semicanou. It splits the perfect twelfth into two, whereas semicanou splits the octave.
Subgroup: 2.3.5.7.11
Comma list: 14641/14580, 160083/160000
Mapping: [⟨1 0 2 7 1], ⟨0 2 0 -6 3], ⟨0 0 4 7 1]]
Mapping generators: ~2, ~400/231, ~200/189
Optimal tuning (CTE): ~400/231 = 951.1975, ~200/189 = 96.5851
Badness: 3.95 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 14641/14580
Mapping: [⟨1 0 2 7 1 1], ⟨0 2 0 -6 3 3], ⟨0 0 4 7 1 4]]
Optimal tuning (CTE): ~26/15 = 951.2316, ~55/52 = 96.6155
Optimal GPV sequence: Template:Val list
Badness: 1.89 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 1001/1000, 14641/14580
Mapping: [⟨1 0 2 7 1 1 -4], ⟨0 2 0 -6 3 3 10], ⟨0 0 4 7 1 4 2]]
Optimal tuning (CTE): ~26/15 = 951.2022, ~55/52 = 96.6006
Optimal GPV sequence: Template:Val list
Badness: 1.90 × 10-3
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 1001/1000, 1216/1215, 1445/1444
Mapping: [⟨1 0 2 7 1 1 -4 -4], ⟨0 2 0 -6 3 3 10 10], ⟨0 0 4 7 1 4 2 4]]
Optimal tuning (CTE): ~26/15 = 951.1749, ~55/52 = 96.5813
Optimal GPV sequence: Template:Val list
Badness: 1.73 × 10-3