https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AFrancium%2F7297edo 2026-06-27T19:03:35Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Francium/7297edo&diff=222918&oldid=prev 2026-01-30T15:24:10Z

<p>Created page with &quot;{{Infobox ET}} {{ED intro}} == Theory == 7297edo is <a href="/w/Consistent" class="mw-redirect" title="Consistent">consistent</a> to the <a href="/w/7-limit" title="7-limit">7-limit</a>, although 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 strong in the 2.9.5.13.19 <a href="/w/Subgroup" class="mw-redirect" title="Subgroup">subgroup</a>, <a href="/w/Tempering_out" title="Tempering out">tempering out</a> 1220703125/1220607063, 41864013671875/41856138215424, 882632959197184/882592301503125 and 90647705078125/90628500150792. === Odd harmonics === {{Harmonics in equal|7297}} === Subsets and supersets === 7297edo is the 930th <a href="/w/Prime_edo" class="mw-redirect" title="Prime edo">prime edo</a>. <a href="/index.php?title=14594edo&amp;action=edit&amp;redlink=1" class="new" title="14594edo (page does not exist)">14594edo</a>, which...&quot;</p> <p><b>New page</b></p><div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 7297edo is [[consistent]] to the [[7-limit]], although its [[harmonic]] [[3/1|3]] is about halfway its steps. It is strong in the 2.9.5.13.19 [[subgroup]], [[tempering out]] 1220703125/1220607063, 41864013671875/41856138215424, 882632959197184/882592301503125 and 90647705078125/90628500150792.<br /> <br /> === Odd harmonics ===<br /> {{Harmonics in equal|7297}}<br /> <br /> === Subsets and supersets ===<br /> 7297edo is the 930th [[prime edo]]. [[14594edo]], which doubles it, gives a good correction to its harmonic 3, but it is only consistent to the [[5-limit]]. [[43782edo]], which is the sixfold of 7297edo, ensures its consistency.<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|23131 -7297}}<br /> | {{mapping|7297 23131}}<br /> | −0.0015<br /> | 0.0015<br /> | 0.91<br /> |-<br /> | 2.9.5<br /> | {{monzo|-34 -53 87}}, {{monzo|269 -79 -8}}<br /> | {{mapping|7297 23131 16943}}<br /> | +0.0016<br /> | 0.0045<br /> | 2.73<br /> |-<br /> | 2.9.5.7<br /> | 96889010407/96855122250, 193119049072265625/193091834023510016, {{monzo|57 -25 12 -2}}<br /> | {{mapping|7297 23131 16943 20485}}<br /> | +0.0051<br /> | 0.0073<br /> | 4.44<br /> |-<br /> | 2.9.5.7.11<br /> | 3294225/3294172, 6576668672/6576582375, 1722499009/1721868840, 19073486328125/19070548180992<br /> | {{mapping|7297 23131 16943 20485 25243}}<br /> | +0.0086<br /> | 0.0095<br /> | 5.77<br /> |-<br /> | 2.9.5.7.11.13<br /> | 10648/10647, 3764768/3764475, 19140625/19140264, 708883245/708837376, 120955835/120932352<br /> | {{mapping|7297 23131 16943 20485 25243 27002}}<br /> | +0.0080<br /> | 0.0088<br /> | 5.35<br /> |-<br /> | 2.9.5.7.11.13.17<br /> | 426496/426465, 194481/194480, 10648/10647, 3408075/3407872, 66406250/66405339, 406174769/406093824<br /> | {{mapping|7297 23131 16943 20485 25243 27002 29826}}<br /> | +0.0081<br /> | 0.0081<br /> | 4.92<br /> |-<br /> | 2.9.5.7.11.13.17.19<br /> | 10241/10240, 426496/426465, 194481/194480, 1549184/1549125, 10648/10647, 1484406/1484375, 739375/739328<br /> | {{mapping|7297 23131 16943 20485 25243 27002 29826 30997}}<br /> | +0.0077<br /> | 0.0077<br /> | 4.68<br /> |}</div>

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