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241edo: Difference between revisions

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**Imported revision 338139240 - Original comment: **
 
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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:genewardsmith|genewardsmith]] and made on <tt>2012-05-21 22:14:35 UTC</tt>.<br>
 
: The original revision id was <tt>338139240</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
241edo 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]].</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;.&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
241edo 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]]
Retrieved from "https://en.xen.wiki/w/241edo"