241edo: Difference between revisions

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+{{ED intro}}
-: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-06-04 00:19:17 UTC</tt>.<br>
-: The original revision id was <tt>342321938</tt>.<br>
+== Theory ==
-: The revision comment was: <tt></tt><br>
+edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. As an equal temperament, it [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]], [[19683/19600]] and [[3136/3125]] in the [[7-limit]], [[540/539]], 43923/43904, [[65536/65219]], and [[151263/151250]] in the [[11-limit]], and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[subpental]].
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
+=== Prime harmonics ===
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 241 equal temperament divides the octave in 241 parts of 4.979 cents each. It tempers out 78732/78125 in the 5-limit, 19683/19600 and 3136/3125 in the 7-limit, 65536/65219, 540/539, 43923/43904, and 151263/151250 in the 11-limit, and 351/350, 676/675, 729/728, 1001/1000 and 2080/2079 in the 13-limit. It provides the optimal patent val to [[Hemimean clan#Subpental|subpental temperament]]. 241 is the 53rd prime EDO.</pre></div>
+{{Harmonics in equal|241}}
-<h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;241edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 241 equal temperament divides the octave in 241 parts of 4.979 cents each. It tempers out 78732/78125 in the 5-limit, 19683/19600 and 3136/3125 in the 7-limit, 65536/65219, 540/539, 43923/43904, and 151263/151250 in the 11-limit, and 351/350, 676/675, 729/728, 1001/1000 and 2080/2079 in the 13-limit. It provides the optimal patent val to &lt;a class="wiki_link" href="/Hemimean%20clan#Subpental"&gt;subpental temperament&lt;/a&gt;. 241 is the 53rd prime EDO.&lt;/body&gt;&lt;/html&gt;</pre></div>
+=== Subsets and supersets ===
+edo is the 53rd [[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| 382 -241 }}
+| {{mapping| 241 382 }}
+| −0.038
+| 0.038
+| 0.76
+|-
+| 2.3.5
+| 78732/78125, {{monzo| 56 -28 -5 }}
+| {{mapping| 241 382 560 }}
+| −0.322
+| 0.403
+| 8.10
+|-
+| 2.3.5.7
+| 3136/3125, 19683/19600, 829940/823543
+| {{mapping| 241 382 560 677 }}
+| −0.431
+| 0.397
+| 7.97
+|-
+| 2.3.5.7.11
+| 540/539, 3136/3125, 8019/8000, 15488/15435
+| {{mapping| 241 382 560 677 834 }}
+| −0.425
+| 0.355
+| 7.14
+|-
+| 2.3.5.7.11.13
+| 351/350, 540/539, 676/675, 3136/3125, 10648/10647
+| {{mapping| 241 382 560 677 834 892 }}
+| −0.397
+| 0.330
+| 6.63
+|}
+=== 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
+| 20\241
+| 99.59
+| 200/189
+| [[Quintagar]] / [[quinsandric]]
+|-
+| 1
+| 50\241
+| 248.96
+| {{monzo| -26 18 -1 }}
+| [[Monzismic]]
+|-
+| 1
+| 76\241
+| 378.42
+| 56/45
+| [[Subpental]]
+|-
+| 1
+| 89\241
+| 443.15
+| 162/125
+| [[Sensipent]]
+|-
+| 1
+| 100\241
+| 497.93
+| 4/3
+| [[Gary]]
+|}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+[[Category:Subpental]]