87th-octave temperaments: Difference between revisions

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-{{Fractional-octave navigation|87}}
+{{Infobox fractional-octave|87}}
-One step of 87edo is in direct proximity to starling comma, [[126/125]].
+One step of [[87edo]] is in direct proximity to starling comma, [[126/125]].
-==Francium==
+== 87-126/125-commatic ==
-Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts.
+An extremely precise microtemperament provided by tempering the comma which is the difference between a stack of 87 [[126/125]]s and the octave. 87edo itself, notably, does the mapping consistently.
+Subgroup: 2.3.5.7
+Comma list: {{monzo| 86 174 -261 87 }}
+{{Mapping|legend=1| 87 87 174  262 | 0 1 0 -2 | 0 0 1 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~126/125 = 1\87, ~3/2 = 701.955{{c}}, ~5/4 = 386.314
+: [[error map]]: {{val| -0.000, -0.000, 0.000, -0.000 }}
+* [[CWE]]: ~126/125 = 1\87, ~3/2 = 701.955{{c}}, ~5/4 = 386.314
+: error map: {{val| -0.000, -0.000, 0.000, -0.000 }}
+[[Support]]ing [[ET]]s: {{EDOs| 87, 609, 696, 783, 870, 1305, 1479, ... }}
+== Francium ==
+Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit.
 Subgroup: 2.3.5.7
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 Badness: 0.762
-===11-limit===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
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 Badness: 0.352
+{{Navbox fractional-octave}}
 [[Category:87edo]]
-[[Category:Temperament collections]]