User:Francium/Temperament research: Difference between revisions

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-== Introduction ==
 Since my site about the miscellaneous rank-2 temperaments gets too messy and some temperaments even are repeated, I decided to create a structured page, in which I explain the temperaments I have worked with. I am very cautious about giving names, since I'm bad at it, plus it might be an emotional subject for some people (not as controversial as naming commas, but I still get haunted by the sayings of some people who called me Xenllium 2.0).
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 Badness: 2.592
+== Horwell extensions ==
+I noticed, that 31 & 53 & 277 is the [[horwell]] temperament, I have found 11- and 13-limit extensions of it, before I even knew that this temperament already was documented in the wiki.
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 3388/3375
+Mapping: <br>
+{| class="right-all"
+| [⟨ || 1 || 0 || 1 || 11 || -5 || ],
+|-
+| ⟨ || 0 || 1 || 1 || -6 || 6 || ],
+|-
+| ⟨ || 0 || 0 || 2 || -10 || 8 || ]
+|}
+CTE generators:  ~2 = 1200.000, ~3/2 = 702.121, ~5/4 = 386.112
+{{Optimal ET sequence|legend=1|9, 22, 31, 53, 84e, 87, 118, 258e, 376de, 547dee}}
+Badness: 0.771
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 385/384, 352/351, 1001/1000
+Mapping: <br>
+{| class="right-all"
+| [⟨ || 1 || 0 || 1 || 11 || -5 || 0 || ],
+|-
+| ⟨ || 0 || 1 || 1 || -6 || 6 || 3 || ],
+|-
+| ⟨ || 0 || 0 || 2 || -10 || 8 || 8 || ]
+|}
+CTE generators: ~2 = 1200.000, ~3/2 = 702.608, ~5/4 = 385.917
+{{Optimal ET sequence|legend=1|9f, 22, 31, 53, 84e, 87, 118, 140, 258e}}
+Badness: 0.986