Augmented family: Difference between revisions

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 === Overview to extensions ===
 The second comma of the [[Normal lists #Normal interval list|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds [[36/35]], augene [[64/63]], hexe [[256/245]], hemiaug [[245/243]], and triforce [[49/48]]. Hexe splits the [[period]] to 1/6 octave, and hemiaug the [[generator]], giving quartertones instead of semitones.
-== August ==
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 36/35, 128/125
-{{Mapping|legend=1| 3 0 7 -1 | 0 1 0 2 }}
-[[Optimal tuning]]s:
-* [[WE]]: ~5/4 = 399.1036{{c}}, ~3/2 = 694.4509{{c}} (~16/15 = 103.7564{{c}})
-: [[error map]]: {{val| -2.689 -10.193 +7.412 +15.594 }}
-* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 694.6812{{c}} (~16/15 = 105.3188{{c}})
-: error map: {{val| 0.000 -7.274 +13.686 +20.537 }}
-{{Optimal ET sequence|legend=1| 9, 12, 45cd }}
-[[Badness]] (Sintel): 0.670
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 36/35, 45/44, 56/55
-Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}
-Optimal tunings:
-* WE: ~5/4 = 398.9225{{c}}, ~3/2 = 690.6486{{c}} (~16/15 = 107.1966{{c}})
-* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 690.8519{{c}} (~16/15 = 109.1481{{c}})
-{{Optimal ET sequence|legend=0| 9, 12, 21, 33e }}
-Badness (Sintel): 0.668
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 27/26, 36/35, 45/44, 56/55
-Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }}
-Optimal tunings:
-* WE: ~5/4 = 399.0956{{c}}, ~3/2 = 687.2261{{c}} (~16/15 = 110.9651{{c}})
-* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 687.5057{{c}} (~16/15 = 112.4943{{c}})
-{{Optimal ET sequence|legend=0| 9, 12f, 21, 33ef }}
-Badness (Sintel): 0.762
-==== Augustus ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 26/25, 36/35, 45/44, 56/55
-Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }}
-Optimal tunings:
-* WE: ~5/4 = 400.4230{{c}}, ~3/2 = 686.0809{{c}} (~16/15 = 114.7650{{c}})
-* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 685.8446{{c}} (~16/15 = 114.1554{{c}})
-{{Optimal ET sequence|legend=0| 9, 12 }}
-Badness (Sintel): 0.919
 == Augene ==
@@ Line 185: / Line 123: @@
 Badness (Sintel): 1.18
+== August ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 36/35, 128/125
+{{Mapping|legend=1| 3 0 7 -1 | 0 1 0 2 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~5/4 = 399.1036{{c}}, ~3/2 = 694.4509{{c}} (~16/15 = 103.7564{{c}})
+: [[error map]]: {{val| -2.689 -10.193 +7.412 +15.594 }}
+* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 694.6812{{c}} (~16/15 = 105.3188{{c}})
+: error map: {{val| 0.000 -7.274 +13.686 +20.537 }}
+{{Optimal ET sequence|legend=1| 9, 12, 45cd }}
+[[Badness]] (Sintel): 0.670
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 36/35, 45/44, 56/55
+Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}
+Optimal tunings:
+* WE: ~5/4 = 398.9225{{c}}, ~3/2 = 690.6486{{c}} (~16/15 = 107.1966{{c}})
+* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 690.8519{{c}} (~16/15 = 109.1481{{c}})
+{{Optimal ET sequence|legend=0| 9, 12, 21, 33e }}
+Badness (Sintel): 0.668
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 27/26, 36/35, 45/44, 56/55
+Mapping: {{mapping| 3 0 7 -1 1 -3 | 0 1 0 2 2 3 }}
+Optimal tunings:
+* WE: ~5/4 = 399.0956{{c}}, ~3/2 = 687.2261{{c}} (~16/15 = 110.9651{{c}})
+* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 687.5057{{c}} (~16/15 = 112.4943{{c}})
+{{Optimal ET sequence|legend=0| 9, 12f, 21, 33ef }}
+Badness (Sintel): 0.762
+==== Augustus ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 26/25, 36/35, 45/44, 56/55
+Mapping: {{mapping| 3 0 7 -1 1 11 | 0 1 0 2 2 0 }}
+Optimal tunings:
+* WE: ~5/4 = 400.4230{{c}}, ~3/2 = 686.0809{{c}} (~16/15 = 114.7650{{c}})
+* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 685.8446{{c}} (~16/15 = 114.1554{{c}})
+{{Optimal ET sequence|legend=0| 9, 12 }}
+Badness (Sintel): 0.919
 == Inflated ==