Augmented family: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 574: / Line 574: @@
 Badness (Sintel): 2.67
+== Trisected ==
+Trisected tempers out [[1029/1024]] and [[1029/1000]], so it is the intersection of augmented and [[slendric]]. It can be described as the {{nowrap| 15 & 36 }} temperament.
+It was named by [[User:Overthink|Overthink]] in 2026, since it splits every Pythagorean interval in three.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 128/125, 1029/1000
+{{Mapping|legend=1| 3 3 7 9 | 0 3 0 -1 }}
+: mapping generators: ~5/4, ~8/7
+[[Optimal tuning]]s:
+* [[WE]]: ~5/4 = 399.520{{c}}, ~8/7 = 234.195{{c}}
+: [[error map]]: {{val| -1.440 -0.811 10.325 -7.342 }}
+* [[CWE]]: ~5/4 = 400.000{{c}}, ~8/7 = 234.339{{c}}
+: error map: {{val| 0.000 +1.063 +13.686 -3.165 }}
+{{Optimal ET sequence|legend=1| 15, 36, 51c }}
+[[Badness]] (Sintel): 2.61
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 56/55, 128/125, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 | 0 3 0 -1 -1 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.305{{c}}, ~8/7 = 234.484{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.769{{c}}
+{{Optimal ET sequence|legend=1| 15, 36, 51ce }}
+[[Badness]] (Sintel): 1.60
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 56/55, 91/90, 128/125, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 7 | 0 3 0 -1 -1 7 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.319{{c}}, ~8/7 = 234.745{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.991{{c}}
+{{Optimal ET sequence|legend=1| 15, 36, 51ce }}
+[[Badness]] (Sintel): 1.70
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 56/55, 91/90, 128/125, 136/135, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 7 7 | 0 3 0 -1 -1 7 9 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.317{{c}}, ~8/7 = 234.609{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.852{{c}}
+{{Optimal ET sequence|legend=1| 15g, 36, 51ceg }}
+[[Badness]] (Sintel): 1.83
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 56/55, 76/75, 91/90, 128/125, 136/135, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 7 7 10 | 0 3 0 -1 -1 7 9 3 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.328{{c}}, ~8/7 = 234.614{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.852{{c}}
+{{Optimal ET sequence|legend=1| 15g, 36, 51ceg }}
+[[Badness]] (Sintel): 1.62
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 56/55, 76/75, 91/90, 128/125, 136/135, 161/160, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 7 7 10 13 | 0 3 0 -1 -1 7 9 3 1 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.353{{c}}, ~8/7 = 234.601{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.843{{c}}
+{{Optimal ET sequence|legend=1| 15g, 36, 51ceg }}
+[[Badness]] (Sintel): 1.54
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 56/55, 76/75, 91/90, 128/125, 136/135, 161/160, 203/200, 1029/1000
+Mapping: {{Mapping| 3 3 7 9 11 7 7 10 13 14 | 0 3 0 -1 -1 7 9 3 1 1 }}
+: mapping generators: ~5/4, ~8/7
+Optimal tunings:
+* WE: ~5/4 = 399.388{{c}}, ~8/7 = 234.581{{c}}
+* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.819{{c}}
+{{Optimal ET sequence|legend=1| 15g, 36, 51ceg }}
+[[Badness]] (Sintel): 1.52
 == Niner ==