Semicanousmic clan: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
+2.3.5.11.17.19 extension to deuteromere |
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Considered below is deuteromere, the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament. | Considered below is deuteromere, the no-7 subgroup temperament, but we can begin by looking at the rank-4 temperament. | ||
== Semicanousmic | == Semicanousmic == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 37: | Line 37: | ||
[[Badness]]: 0.142 × 10<sup>-3</sup> | [[Badness]]: 0.142 × 10<sup>-3</sup> | ||
=== 2.3.5.7.11.17 subgroup === | |||
Subgroup: 2.3.5.11.17 | |||
Comma list: 1089/1088, 14641/14580 | |||
Sval mapping: [{{val| 1 0 2 1 -4 }}, {{val| 0 1 2 2 6 }}, {{val| 0 0 -4 -1 -2 }}] | |||
POTE generators: ~3/2 = 702.3162, ~18/11 = 854.5619 | |||
Optimal GPV sequence: {{val list| 24, 31g, 55g, 56gg, 63, 70c, 80gg, 87, 111, 118, 205, 528e, 733e }} | |||
Badness: 0.481 × 10<sup>-3</sup> | |||
=== 2.3.5.7.11.17.19 subgroup === | |||
Subgroup: 2.3.5.11.17.19 | |||
Comma list: 1089/1088, 1216/1215, 1445/1444 | |||
Sval mapping: [{{val| 1 0 2 1 -4 -4 }}, {{val| 0 1 2 2 6 7 }}, {{val| 0 0 -4 -1 -2 -4 }}] | |||
POTE generators: ~3/2 = 702.2578, ~18/11 = 854.5595 | |||
Optimal GPV sequence: {{val list| 24, 55gh, 63, 70c, 80gghh, 87, 94, 111, 118, 205, 323, 528e }} | |||
Badness: 0.403 × 10<sup>-3</sup> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Semicanousmic clan| ]] <!-- main article --> | [[Category:Semicanousmic clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 21:25, 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
2.3.5.7.11.17 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
2.3.5.7.11.17.19 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