251edo: Difference between revisions

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 {{Infobox ET}}
-'''251edo''' is the [[EDO|equal division of the octave]] into 251 parts of 4.7809 [[cent]]s each.
+{{ED intro}}
-It tempers out 1600000/1594323 (amity comma) and 562949953421312/556182861328125 (maquila comma) in the 5-limit; 4375/4374, 5120/5103, and 40500000/40353607 in the 7-limit.
+== Theory ==
+et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]].
-Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit.
+Using the [[patent val]] {{val| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.
-Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit.
+Using the 251e val  {{val| 251 398 583 705 '''869''' }}, it tempers out [[540/539]], [[5632/5625]], [[6250/6237]], and 12005/11979 in the 11-limit; [[364/363]], [[676/675]], [[1716/1715]], and 3584/3575 in the 13-limit.
-edo is the 54th [[prime EDO]].
+=== Odd harmonics ===
+{{Harmonics in equal|251}}
+=== Subsets and supersets ===
+edo is the 54th [[prime edo]].
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo| 398 -251 }}
+| {{mapping| 251 398 }}
+| −0.2630
+| 0.2630
+| 5.50
+|-
+| 2.3.5
+| {{monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }}
+| {{mapping| 251 398 583 }}
+| −0.3099
+| 0.2247
+| 4.70
+|-
+| 2.3.5.7
+| 4375/4374, 5120/5103, 40500000/40353607
+| {{mapping| 251 398 583 705 }}
+| −0.3830
+| 0.2322
+| 4.86
+|}
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
+|-
+| 1
+| 66\251
+| 315.54
+| 6/5
+| [[Acrokleismic]]
+|-
+| 1
+| 71\251
+| 339.44
+| 243/200
+| [[Amity]]
+|-
+| 1
+| 91\251
+| 435.06
+| 9/7
+| [[Supermajor]]
+|-
+| 1
+| 96\251
+| 458.96
+| 125/96
+| [[Majvam]]
+|-
+| 1
+| 112\251
+| 535.46
+| 512/375
+| [[Maquila]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-{{Harmonics in equal|251}}
+== Music ==
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+; [[Francium]]
-[[Category:Prime EDO]]
+* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]
+[[Category:Listen]]