Semicanousmic 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 semicanousmic clan of rank-3 temperaments tempers out the semicanousma (monzo: [-2 -6 -1 0 4⟩, ratio: 14641/14580).
Temperaments discussed elsewhere are:
- Urania (+81/80 or 121/120) → Rastmic rank-3 clan
- Triglav (+3025/3024 or 3136/3125) → Hemimean family
- Semicanou (+9801/9800) → Canou family
Considered below are syndeute and hemireiwa, in addition to deuteromere, the no-7 subgroup temperament.
For the rank-4 semicanousmic temperament, see Catalog of rank-4 temperaments #Semicanousmic (14641/14580).
Deuteromere
Subgroup: 2.3.5.11
Comma list: 14641/14580
Subgroup-val mapping: [⟨1 0 2 1], ⟨0 1 2 2], ⟨0 0 -4 -1]]
- mapping generators: ~2, ~3, ~18/11
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.3342 ¢, ~18/11 = 854.5548 ¢
Optimal ET sequence: 7, 17c, 24, 31, 56, 73, 80, 87, 118, 205, 323, 528e
Badness (Smith): 0.142 × 10-3
2.3.5.11.17 subgroup
Subgroup: 2.3.5.11.17
Comma list: 1089/1088, 14641/14580
Subgroup-val mapping: [⟨1 0 2 1 -4], ⟨0 1 2 2 6], ⟨0 0 -4 -1 -2]]
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.3427 ¢, ~18/11 = 854.5587 ¢
Optimal ET sequence: 24, 31g, 55g, 56gg, 63, 70c, 80gg, 87, 111, 118, 205, 528e, 733e
Badness (Smith): 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
Subgroup-val mapping: [⟨1 0 2 1 -4 -4], ⟨0 1 2 2 6 7], ⟨0 0 -4 -1 -2 -4]]
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.2987 ¢, ~18/11 = 854.5520 ¢
Optimal ET sequence: 24, 55gh, 63, 70c, 80gghh, 87, 94, 111, 118, 205, 323, 528e
Badness (Smith): 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]]
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.0812 ¢, ~18/11 = 854.4115 ¢
Optimal ET sequence: 7d, 17c, 24, 77c, 87d, 94, 111, 118, 212, 323, 441e
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~3/2 = 702.1682 ¢, ~18/11 = 854.5074 ¢
Optimal ET sequence: 94, 111, 205, 212, 323, 535ef
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~3/2 = 702.1910 ¢, ~18/11 = 854.4751 ¢
Optimal ET sequence: 94, 111, 205, 212g, 323
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~3/2 = 702.1925 ¢, ~18/11 = 854.4721 ¢
Optimal ET sequence: 94, 111, 205, 212gh, 323
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~400/231 = 951.1975 ¢, ~200/189 = 96.5851 ¢
Optimal ET sequence: 87, 111, 125, 198, 212, 323, 410
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~26/15 = 951.2316 ¢, ~55/52 = 96.6155 ¢
Optimal ET sequence: 87, 111, 198, 323, 410
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~26/15 = 951.2022 ¢, ~55/52 = 96.6006 ¢
Optimal ET sequence: 87, 111, 198g, 212g, 299, 323, 410
Badness (Smith): 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): ~2 = 1200.0000 ¢, ~26/15 = 951.1749 ¢, ~55/52 = 96.5813 ¢
Optimal ET sequence: 87, 111, 198gh, 212gh, 299, 323, 410, 622ef
Badness (Smith): 1.73 × 10-3