https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AFrancium%2F4597edo 2026-07-19T13:27:41Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Francium/4597edo&diff=234346&oldid=prev 2026-07-19T03:04:39Z

<p>Userspace -&gt; remove from EDO categories</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 03:04, 19 July 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Infobox ET<ins style="font-weight: bold; text-decoration: none;">|debug=1</ins>}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ED intro}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ED intro}}</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <!-- diff cache key xenwiki_en:diff:1.41:old-234328:rev-234346:php=table --> </table>

Fredg999 https://en.xen.wiki/index.php?title=User:Francium/4597edo&diff=234328&oldid=prev 2026-07-18T15:43:43Z

<p>Created page with &quot;{{Infobox ET}} {{ED intro}} == Theory == 4597edo is <a href="/w/Consistent" class="mw-redirect" title="Consistent">consistent</a> to the <a href="/w/5-limit" title="5-limit">5-limit</a>, its <a href="/w/Harmonic" title="Harmonic">harmonic</a> <a href="/w/7/1" title="7/1">7</a> is about halfway its steps. It is strong in the 2.3.5.11.13.17.23.29 <a href="/w/Subgroup" class="mw-redirect" title="Subgroup">subgroup</a>, <a href="/w/Tempering_out" title="Tempering out">tempering out</a> 20736/20735, 359424/359375, 3408075/3407872, 13311/13310, 486243/486200, 2460375/2460172, 1069056/1068925. Using the 2.5.11.29.37 subgroup, it tempers out <a href="/w/9251/9250" title="9251/9250">9251/9250</a>. === Prime harmonics === {{Harmonics in equal|4597}} === Subsets and supersets === 4597e...&quot;</p> <p><b>New page</b></p><div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 4597edo is [[consistent]] to the [[5-limit]], its [[harmonic]] [[7/1|7]] is about halfway its steps. It is strong in the 2.3.5.11.13.17.23.29 [[subgroup]], [[tempering out]] 20736/20735, 359424/359375, 3408075/3407872, 13311/13310, 486243/486200, 2460375/2460172, 1069056/1068925. Using the 2.5.11.29.37 subgroup, it tempers out [[9251/9250]].<br /> <br /> === Prime harmonics ===<br /> {{Harmonics in equal|4597}}<br /> <br /> === Subsets and supersets ===<br /> 4597edo is the 622nd [[prime edo]]. [[9194edo]], which doubles it, gives a good correction to its harmonic 7.<br /> <br /> == Regular temperament properties ==<br /> {| class=&quot;wikitable center-4 center-5 center-6&quot;<br /> ! rowspan=&quot;2&quot; |[[Subgroup]]<br /> ! rowspan=&quot;2&quot; |[[Comma list|Comma List]]<br /> ! rowspan=&quot;2&quot; |[[Mapping]]<br /> ! rowspan=&quot;2&quot; |Optimal&lt;br&gt;8ve Stretch (¢)<br /> ! colspan=&quot;2&quot; |Tuning Error<br /> |- <br /> ![[TE error|Absolute]] (¢)<br /> ![[TE simple badness|Relative]] (%)<br /> |-<br /> | 2.3<br /> | {{monzo|-7286 4597}}<br /> | {{mapping|4597 7286}}<br /> | 0.0060<br /> | 0.0060<br /> | 2.30<br /> |-<br /> | 2.3.5<br /> | {{monzo|-16 35 -17}}, {{monzo|342 -81 -92}}<br /> | {{mapping|4597 7286 10674}}<br /> | 0.0004<br /> | 0.0093<br /> | 3.56<br /> |-<br /> | 2.3.5.7<br /> | 200120949/200000000, {{monzo|-7 30 -9 -7}}, {{monzo|47 -18 -14 5}}<br /> | {{mapping|4597 7286 10674 12905}}<br /> | 0.0098<br /> | 0.0183<br /> | 7.01<br /> |-<br /> | 2.3.5.7.11<br /> | 117649/117612, 50014503/50000000, 14348907/14348180, 6576668672/6576582375<br /> | {{mapping|4597 7286 10674 12905 15903}}<br /> | 0.0080<br /> | 0.0167<br /> | 6.40<br /> |-<br /> | 2.3.5.7.11.13<br /> | 123201/123200, 1990656/1990625, 117649/117612, 1574640/1574573, 3195731/3194880<br /> | {{mapping|4597 7286 10674 12905 15903 17011}}<br /> | 0.0057<br /> | 0.0161<br /> | 6.17<br /> |-<br /> | 2.3.5.7.11.13.17<br /> | 12376/12375, 123201/123200, 1990656/1990625, 790272/790075, 637637/637500, 163863/163840<br /> | {{mapping|4597 7286 10674 12905 15903 17011 18790}}<br /> | 0.0055<br /> | 0.0149<br /> | 5.71<br /> |-<br /> | 2.3.5.7.11.13.17.19<br /> | 12376/12375, 10241/10240, 5929/5928, 123201/123200, 1549184/1549125, 203148/203125, 1285956/1285625<br /> | {{mapping|4597 7286 10674 12905 15903 17011 18790 19528}}<br /> | 0.0027<br /> | 0.0158<br /> | 4.44<br /> |}<br /> <br /> === Rank-2 temperaments ===<br /> {| class=&quot;wikitable center-all left-5&quot;<br /> |+Table of rank-2 temperaments by generator<br /> ! Periods&lt;br&gt;per 8ve<br /> ! Generator*<br /> ! Cents*<br /> ! Associated&lt;br&gt;Ratio*<br /> ! Temperaments<br /> |-<br /> | 1<br /> | 699\4597<br /> | 182.4668<br /> | 10/9<br /> | [[Minortone]]<br /> |}</div>

Francium