Augmented family: Difference between revisions

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 Badness (Sintel): 2.67
+== Trisected ==
+{{Main|Trisected}}
+{{See also|Subgroup temperaments #Trisect}}
+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 0 7 10 | 0 3 0 -1 }}
+: mapping generators: ~5/4, ~10/7
+[[Optimal tuning]]s:
+* [[WE]]: ~5/4 = 399.5199{{c}}, ~10/7 = 633.7146{{c}}
+: [[error map]]: {{val| -1.440 -0.811 +10.325 -7.342 }}
+* [[CWE]]: ~5/4 = 400.0000{{c}}, ~10/7 = 634.3393{{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 ===
+This extension also tempers out [[4000/3993]], equating 3 intervals of [[11/10]] with [[4/3]].
+Subgroup: 2.3.5.7.11
+Comma list: 56/55, 128/125, 1029/1000
+Mapping: {{Mapping| 3 0 7 10 12 | 0 3 0 -1 -1 }}
+Optimal tunings:
+* WE: ~5/4 = 399.3049{{c}}, ~10/7 = 633.7891{{c}}
+* CWE: ~5/4 = 400.0000{{c}}, ~10/7 = 634.7695{{c}}
+{{Optimal ET sequence|legend=0| 15, 36, 51ce }}
+Badness (Sintel): 1.60
+=== 13-limit ===
+This extension is natural since it equates the [[10/7]], which is 1/3 of [[3/1]] since 1029/1000 is tempered out, with [[13/9]], thus tempering out [[91/90]] and [[2197/2187]].
+Subgroup: 2.3.5.7.11.13
+Comma list: 56/55, 91/90, 128/125, 1029/1000
+Mapping: {{Mapping| 3 0 7 10 12 0 | 0 3 0 -1 -1 7 }}
+Optimal tunings:
+* WE: ~5/4 = 399.3194{{c}}, ~10/7 = 634.0637{{c}}
+* CWE: ~5/4 = 400.0000{{c}}, ~10/7 = 634.9907{{c}}
+{{Optimal ET sequence|legend=0| 15, 36, 51ce }}
+Badness (Sintel): 1.70
 == Niner ==