Augmented family: Difference between revisions

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@@ Line 580: / Line 580: @@
 It was named by [[User:Overthink|Overthink]] in 2026, since it splits every Pythagorean interval in three.
-{{Todo|review|comment=Last digits in ~8/7 for WE may be wrong. Also, comma lists could potentially be simplified.}}
 [[Subgroup]]: 2.3.5.7
@@ Line 586: / Line 585: @@
 [[Comma list]]: 128/125, 1029/1000
-{{Mapping|legend=1| 3 3 7 9 | 0 3 0 -1 }}
+{{Mapping|legend=1| 3 0 7 10 | 0 3 0 -1 }}
+: mapping generators: ~5/4, ~10/7
-: mapping generators: ~5/4, ~8/7
 [[Optimal tuning]]s:
-* [[WE]]: ~5/4 = 399.520{{c}}, ~8/7 = 234.195{{c}}
+* [[WE]]: ~5/4 = 399.5199{{c}}, ~10/7 = 633.7146{{c}}
-: [[error map]]: {{val| -1.440 -0.811 10.325 -7.342 }}
+: [[error map]]: {{val| -1.440 -0.811 +10.325 -7.342 }}
+* [[CWE]]: ~5/4 = 400.0000{{c}}, ~10/7 = 634.3393{{c}}
-* [[CWE]]: ~5/4 = 400.000{{c}}, ~8/7 = 234.339{{c}}
 : error map: {{val| 0.000 +1.063 +13.686 -3.165 }}
@@ Line 602: / Line 599: @@
 === 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: {{Mapping| 3 0 7 10 12 | 0 3 0 -1 -1 }}
-: mapping generators: ~5/4, ~8/7
 Optimal tunings:
-* WE: ~5/4 = 399.305{{c}}, ~8/7 = 234.484{{c}}
+* WE: ~5/4 = 399.3049{{c}}, ~10/7 = 633.7891{{c}}
+* CWE: ~5/4 = 400.0000{{c}}, ~10/7 = 634.7695{{c}}
-* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.769{{c}}
-{{Optimal ET sequence|legend=1| 15, 36, 51ce }}
+{{Optimal ET sequence|legend=0| 15, 36, 51ce }}
-[[Badness]] (Sintel): 1.60
+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: {{Mapping| 3 0 7 10 12 0 | 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}}
+* WE: ~5/4 = 399.3194{{c}}, ~10/7 = 634.0637{{c}}
+* CWE: ~5/4 = 400.0000{{c}}, ~10/7 = 634.9907{{c}}
-* CWE: ~5/4 = 400.000{{c}}, ~8/7 = 234.991{{c}}
-{{Optimal ET sequence|legend=1| 15, 36, 51ce }}
+{{Optimal ET sequence|legend=0| 15, 36, 51ce }}
-[[Badness]] (Sintel): 1.70
+Badness (Sintel): 1.70
 == Niner ==