https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AFrancium%2F3919edo 2026-06-27T04:41:15Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Francium/3919edo&diff=211819&oldid=prev 2025-10-03T20:29:23Z

<p>Created page with &quot;{{Infobox ET}} {{ED intro}} == Theory == 3919edo is only <a href="/w/Consistent" class="mw-redirect" title="Consistent">consistent</a> to the <a href="/w/3-limit" title="3-limit">3-limit</a> and its <a href="/w/Harmonic" title="Harmonic">harmonic</a> <a href="/w/3/1" title="3/1">3</a> is about halfway its steps. It is a strong 2.9.15.7.13.23 <a href="/w/Subgroup" class="mw-redirect" title="Subgroup">subgroup</a> tuning, <a href="/w/Tempering_out" title="Tempering out">tempering out</a> 76545/76544, 287500/287469, 66560000/66548223, 2951690625/2951578112 and 743115202375/743008370688. === Odd harmonics === {{Harmonics in equal|3919}} === Subsets and supersets === 3919edo is the 543rd <a href="/w/Prime_edo" class="mw-redirect" title="Prime edo">prime edo</a>. <a href="/index.php?title=7838edo&amp;action=edit&amp;redlink=1" class="new" title="7838edo (page does not exist)">7838edo</a>, which doubles it, gives...&quot;</p> <p><b>New page</b></p><div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 3919edo is only [[consistent]] to the [[3-limit]] and its [[harmonic]] [[3/1|3]] is about halfway its steps. It is a strong 2.9.15.7.13.23 [[subgroup]] tuning, [[tempering out]] 76545/76544, 287500/287469, 66560000/66548223, 2951690625/2951578112 and 743115202375/743008370688.<br /> <br /> === Odd harmonics ===<br /> {{Harmonics in equal|3919}}<br /> <br /> === Subsets and supersets ===<br /> 3919edo is the 543rd [[prime edo]]. [[7838edo]], which doubles it, gives a good correction to its harmonic 3.<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 /> | 2.9<br /> | {{monzo|12423 -3919}}<br /> | {{mapping|3919 12423}}<br /> | −0.0031<br /> | 0.0031<br /> | 1.01<br /> |-<br /> | 2.9.5<br /> | {{monzo|146 -38 -11}}, {{monzo|105 35 -93}}<br /> | {{mapping|3919 12423 9100}}<br /> | −0.0181<br /> | 0.0213<br /> | 6.96<br /> |-<br /> | 2.9.5.7<br /> | 4398046511104/4395357421875, 96889010407/96855122250, 40041913260899432169/40000000000000000000<br /> | {{mapping|3919 12423 9100 11002}}<br /> | −0.0129<br /> | 0.0205<br /> | 6.69<br /> |}</div>

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