https://en.xen.wiki/index.php?action=history&feed=atom&title=138edo 2026-06-30T21:10:54Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=138edo&diff=181907&oldid=prev 2025-02-20T16:37:57Z

<p></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 16:37, 20 February 2025</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"></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>{{Infobox ET}}</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>{{Infobox ET}}</div></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>{{<del style="font-weight: bold; text-decoration: none;">EDO </del>intro}}</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>{{<ins style="font-weight: bold; text-decoration: none;">ED </ins>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> <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>138 = 3 × 46, <del style="font-weight: bold; text-decoration: none;">and </del>138edo shares its [[3/2|fifth]] with [[46edo]]. Unlike 46edo, it is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 13-limit: {{val| 138 219 320 387 477 511 }} ([[patent val]]), {{val| 138 219 '''321''' '''388''' '''478''' 511 }} (138cde), and {{val| 138 '''218''' 320 387 477 '''510''' }} (138bf). The last mapping uses an alternative flat fifth from [[69edo]].  </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><ins style="font-weight: bold; text-decoration: none;">Since {{nowrap|</ins>138 <ins style="font-weight: bold; text-decoration: none;">{{</ins>=<ins style="font-weight: bold; text-decoration: none;">}} </ins>3 × 46<ins style="font-weight: bold; text-decoration: none;">}}</ins>, 138edo shares its [[3/2|fifth]] with [[46edo]]. Unlike 46edo, it is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 13-limit: {{val| 138 219 320 387 477 511 }} ([[patent val]]), {{val| 138 219 '''321''' '''388''' '''478''' 511 }} (138cde), and {{val| 138 '''218''' 320 387 477 '''510''' }} (138bf). The last mapping uses an alternative flat fifth from [[69edo]].  </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> <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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </div></td></tr> </table>

ArrowHead294 https://en.xen.wiki/index.php?title=138edo&diff=145023&oldid=prev 2024-05-26T09:54:42Z

<p>Note its relation to 46edo and 69edo</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 09:54, 26 May 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</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>{{EDO 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>{{EDO 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> <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>138edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 13-limit: {{val| 138 219 320 387 477 511 }} ([[patent val]]), {{val| 138 '''<del style="font-weight: bold; text-decoration: none;">218</del>''' <del style="font-weight: bold; text-decoration: none;">320 387 477 </del>'''<del style="font-weight: bold; text-decoration: none;">510</del>''' }} (<del style="font-weight: bold; text-decoration: none;">138bf</del>), and {{val| 138 <del style="font-weight: bold; text-decoration: none;">219 </del>'''<del style="font-weight: bold; text-decoration: none;">321</del>''' '''<del style="font-weight: bold; text-decoration: none;">388</del>''' <del style="font-weight: bold; text-decoration: none;">'''478''' 511 </del>}} (<del style="font-weight: bold; text-decoration: none;">138cde</del>).  </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><ins style="font-weight: bold; text-decoration: none;">138 = 3 × 46, and </ins>138edo <ins style="font-weight: bold; text-decoration: none;">shares its [[3/2|fifth]] with [[46edo]]. Unlike 46edo, it </ins>is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 13-limit: {{val| 138 219 320 387 477 511 }} ([[patent val]]), {{val| 138 <ins style="font-weight: bold; text-decoration: none;">219 ''</ins>'<ins style="font-weight: bold; text-decoration: none;">321</ins>''' ''<ins style="font-weight: bold; text-decoration: none;">'388''' </ins>'''<ins style="font-weight: bold; text-decoration: none;">478</ins>''' <ins style="font-weight: bold; text-decoration: none;">511 </ins>}} (<ins style="font-weight: bold; text-decoration: none;">138cde</ins>), and {{val| 138 '''<ins style="font-weight: bold; text-decoration: none;">218</ins>''' <ins style="font-weight: bold; text-decoration: none;">320 387 477 </ins>'''<ins style="font-weight: bold; text-decoration: none;">510</ins>''' }} (<ins style="font-weight: bold; text-decoration: none;">138bf</ins>)<ins style="font-weight: bold; text-decoration: none;">. The last mapping uses an alternative flat fifth from [[69edo]]</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;"><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> <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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </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> <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><del style="font-weight: bold; text-decoration: none;">Using the </del>138cde val, <del style="font-weight: bold; text-decoration: none;">it tempers </del>out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 <del style="font-weight: bold; text-decoration: none;">in the 5-limit; </del>[[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, [[support]]ing the [[echidna]] temperament and giving an excellent tuning.</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><ins style="font-weight: bold; text-decoration: none;">The </ins>138cde val <ins style="font-weight: bold; text-decoration: none;">is [[enfactoring|enfactored]] in the 5-limit</ins>, <ins style="font-weight: bold; text-decoration: none;">with the same tuning as 46edo, tempering </ins>out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125<ins style="font-weight: bold; text-decoration: none;">. However, it tempers out </ins>[[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, [[support]]ing the [[echidna]] temperament and giving an excellent tuning.</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> <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><del style="font-weight: bold; text-decoration: none;">Using the </del>138bf val, <del style="font-weight: bold; text-decoration: none;">it tempers </del>out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }} <del style="font-weight: bold; text-decoration: none;">in the 5-limit; </del>[[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit.  </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><ins style="font-weight: bold; text-decoration: none;">The </ins>138bf val <ins style="font-weight: bold; text-decoration: none;">is also enfactored in the 5-limit</ins>, <ins style="font-weight: bold; text-decoration: none;">with the same tuning as 69edo, tempering </ins>out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }}<ins style="font-weight: bold; text-decoration: none;">. However, it tempers out </ins>[[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit.  </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> <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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14">Line 14:</td> <td colspan="2" class="diff-lineno">Line 14:</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>=== Odd harmonics ===</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>=== Odd harmonics ===</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>{{Harmonics in equal|138}}</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>{{Harmonics in equal|138}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">=== Subsets and supersets ===</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Since 138 factors into {{factorization|138}}, 138edo has subset edos {{EDOs| 2, 3, 6, 23, 46, and 69 }}. </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;"><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> <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>[[Category:Echidna]]</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>[[Category:Echidna]]</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=138edo&diff=145022&oldid=prev 2024-05-26T09:45:04Z

<p>Note it as an excellent tuning of echidna</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 09:45, 26 May 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6">Line 6:</td> <td colspan="2" class="diff-lineno">Line 6:</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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </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>Using the patent val, it [[tempering out|tempers out]] 1953125/1889568 ([[shibboleth comma]]) and 67108864/66430125 ([[misty comma]]) in the 5-limit; [[875/864]], [[1029/1024]], and 1647086/1594323 in the 7-limit; [[896/891]], 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; [[196/195]], [[275/273]], and [[1575/1573]] in the 13-limit.  </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> <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>Using the 138cde val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, <del style="font-weight: bold; text-decoration: none;">supporting </del>the [[echidna]] temperament.</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>Using the 138cde val, it tempers out the [[diaschisma]], 2048/2025 and the [[sensipent comma]], 78732/78125 in the 5-limit; [[1728/1715]], [[10976/10935]], and [[250047/250000]] in the 7-limit; [[176/175]], [[540/539]], [[896/891]], and 85184/84375 in the 11-limit; [[351/350]], [[352/351]], [[364/363]], [[640/637]], and [[2197/2187]] in the 13-limit, <ins style="font-weight: bold; text-decoration: none;">[[support]]ing </ins>the [[echidna]] temperament <ins style="font-weight: bold; text-decoration: none;">and giving an excellent tuning</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;"><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> <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>Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }} in the 5-limit; [[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit.  </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>Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and {{monzo| -41 1 17 }} in the 5-limit; [[2401/2400]], [[2430/2401]], and 9765625/9633792 in the 7-limit; [[385/384]], [[1375/1372]], 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament; [[625/624]], 975/968, [[1001/1000]], and [[1188/1183]] in the 13-limit.  </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14">Line 14:</td> <td colspan="2" class="diff-lineno">Line 14:</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>=== Odd harmonics ===</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>=== Odd harmonics ===</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>{{Harmonics in equal|138}}</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>{{Harmonics in equal|138}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">[[Category:Echidna]]</ins></div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=138edo&diff=145021&oldid=prev 2024-05-26T09:43:15Z

<p>Adopt template: EDO intro; group the vals by similarity; -redundant categories; misc. cleanup</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 09:43, 26 May 2024</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"></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>{{Infobox ET}}</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>{{Infobox ET}}</div></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><del style="font-weight: bold; text-decoration: none;">'''138edo''' is the [[</del>EDO<del style="font-weight: bold; text-decoration: none;">|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. </del></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><ins style="font-weight: bold; text-decoration: none;">{{</ins>EDO <ins style="font-weight: bold; text-decoration: none;">intro}}</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;"><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> <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><del style="font-weight: bold; text-decoration: none;">It </del>is <del style="font-weight: bold; text-decoration: none;">inconsistent </del>to the 5-limit and higher <del style="font-weight: bold; text-decoration: none;">limit</del>, with three mappings possible for the 13-limit: <del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>138 219 320 387 477 511<del style="font-weight: bold; text-decoration: none;">| </del>(patent val), <del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>138 218 320 387 477 510<del style="font-weight: bold; text-decoration: none;">| </del>(138bf), and <del style="font-weight: bold; text-decoration: none;">&amp;lt;</del>138 219 321 388 478 511<del style="font-weight: bold; text-decoration: none;">| </del>(138cde).  </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><ins style="font-weight: bold; text-decoration: none;">138edo </ins>is <ins style="font-weight: bold; text-decoration: none;">in[[consistent]] </ins>to the <ins style="font-weight: bold; text-decoration: none;">[[</ins>5<ins style="font-weight: bold; text-decoration: none;">-odd</ins>-limit<ins style="font-weight: bold; text-decoration: none;">]] </ins>and higher <ins style="font-weight: bold; text-decoration: none;">limits</ins>, with three mappings possible for the 13-limit: <ins style="font-weight: bold; text-decoration: none;">{{val| </ins>138 219 320 387 477 511 <ins style="font-weight: bold; text-decoration: none;">}} </ins>(<ins style="font-weight: bold; text-decoration: none;">[[</ins>patent val<ins style="font-weight: bold; text-decoration: none;">]]</ins>), <ins style="font-weight: bold; text-decoration: none;">{{val| </ins>138 <ins style="font-weight: bold; text-decoration: none;">'''</ins>218<ins style="font-weight: bold; text-decoration: none;">''' </ins>320 387 477 <ins style="font-weight: bold; text-decoration: none;">'''</ins>510<ins style="font-weight: bold; text-decoration: none;">''' }} </ins>(138bf), and <ins style="font-weight: bold; text-decoration: none;">{{val| </ins>138 219 <ins style="font-weight: bold; text-decoration: none;">'''</ins>321<ins style="font-weight: bold; text-decoration: none;">''' '''</ins>388<ins style="font-weight: bold; text-decoration: none;">''' '''</ins>478<ins style="font-weight: bold; text-decoration: none;">''' </ins>511 <ins style="font-weight: bold; text-decoration: none;">}} </ins>(138cde).  </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> <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>Using the patent val, it tempers out <del style="font-weight: bold; text-decoration: none;">the shibboleth comma, </del>1953125/1889568 and <del style="font-weight: bold; text-decoration: none;">the misty comma, </del>67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit.  </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>Using the patent val, it <ins style="font-weight: bold; text-decoration: none;">[[tempering out|</ins>tempers out<ins style="font-weight: bold; text-decoration: none;">]] </ins>1953125/1889568 <ins style="font-weight: bold; text-decoration: none;">([[shibboleth comma]]) </ins>and 67108864/66430125 <ins style="font-weight: bold; text-decoration: none;">([[misty comma]]) </ins>in the 5-limit; <ins style="font-weight: bold; text-decoration: none;">[[</ins>875/864<ins style="font-weight: bold; text-decoration: none;">]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[</ins>1029/1024<ins style="font-weight: bold; text-decoration: none;">]]</ins>, and 1647086/1594323 in the 7-limit; <ins style="font-weight: bold; text-decoration: none;">[[</ins>896/891<ins style="font-weight: bold; text-decoration: none;">]]</ins>, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; <ins style="font-weight: bold; text-decoration: none;">[[</ins>196/195<ins style="font-weight: bold; text-decoration: none;">]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[</ins>275/273<ins style="font-weight: bold; text-decoration: none;">]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[</ins>1575/1573<ins style="font-weight: bold; text-decoration: none;">]] </ins>in the 13-limit.  </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> <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>Using the <del style="font-weight: bold; text-decoration: none;">138bf </del>val, it tempers out the [[<del style="font-weight: bold; text-decoration: none;">syntonic comma</del>]], <del style="font-weight: bold; text-decoration: none;">81</del>/<del style="font-weight: bold; text-decoration: none;">80 </del>and <del style="font-weight: bold; text-decoration: none;">2288818359375</del>/<del style="font-weight: bold; text-decoration: none;">2199023255552 </del>in the 5-limit; <del style="font-weight: bold; text-decoration: none;">2401</del>/<del style="font-weight: bold; text-decoration: none;">2400</del>, <del style="font-weight: bold; text-decoration: none;">2430</del>/<del style="font-weight: bold; text-decoration: none;">2401</del>, and <del style="font-weight: bold; text-decoration: none;">9765625</del>/<del style="font-weight: bold; text-decoration: none;">9633792 </del>in the 7-limit; <del style="font-weight: bold; text-decoration: none;">385</del>/<del style="font-weight: bold; text-decoration: none;">384</del>, <del style="font-weight: bold; text-decoration: none;">1375</del>/<del style="font-weight: bold; text-decoration: none;">1372</del>, <del style="font-weight: bold; text-decoration: none;">1944</del>/<del style="font-weight: bold; text-decoration: none;">1925</del>, and <del style="font-weight: bold; text-decoration: none;">9375</del>/<del style="font-weight: bold; text-decoration: none;">9317 </del>in the 11-limit, <del style="font-weight: bold; text-decoration: none;">supporting the </del>[[<del style="font-weight: bold; text-decoration: none;">Meantone family|cuboctahedra temperament</del>]]<del style="font-weight: bold; text-decoration: none;">; 625/624</del>, <del style="font-weight: bold; text-decoration: none;">975</del>/<del style="font-weight: bold; text-decoration: none;">968</del>, <del style="font-weight: bold; text-decoration: none;">1001</del>/<del style="font-weight: bold; text-decoration: none;">1000</del>, and <del style="font-weight: bold; text-decoration: none;">1188</del>/<del style="font-weight: bold; text-decoration: none;">1183 </del>in the 13-limit.  </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>Using the <ins style="font-weight: bold; text-decoration: none;">138cde </ins>val, it tempers out the [[<ins style="font-weight: bold; text-decoration: none;">diaschisma</ins>]], <ins style="font-weight: bold; text-decoration: none;">2048</ins>/<ins style="font-weight: bold; text-decoration: none;">2025 </ins>and <ins style="font-weight: bold; text-decoration: none;">the [[sensipent comma]], 78732</ins>/<ins style="font-weight: bold; text-decoration: none;">78125 </ins>in the 5-limit; <ins style="font-weight: bold; text-decoration: none;">[[1728</ins>/<ins style="font-weight: bold; text-decoration: none;">1715]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[10976</ins>/<ins style="font-weight: bold; text-decoration: none;">10935]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[250047</ins>/<ins style="font-weight: bold; text-decoration: none;">250000]] </ins>in the 7-limit; <ins style="font-weight: bold; text-decoration: none;">[[176</ins>/<ins style="font-weight: bold; text-decoration: none;">175]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[540</ins>/<ins style="font-weight: bold; text-decoration: none;">539]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[896</ins>/<ins style="font-weight: bold; text-decoration: none;">891]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">85184</ins>/<ins style="font-weight: bold; text-decoration: none;">84375 </ins>in the 11-limit<ins style="font-weight: bold; text-decoration: none;">; [[351/350]]</ins>, [[<ins style="font-weight: bold; text-decoration: none;">352/351</ins>]], <ins style="font-weight: bold; text-decoration: none;">[[364</ins>/<ins style="font-weight: bold; text-decoration: none;">363]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[640</ins>/<ins style="font-weight: bold; text-decoration: none;">637]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[2197</ins>/<ins style="font-weight: bold; text-decoration: none;">2187]] </ins>in the 13-limit<ins style="font-weight: bold; text-decoration: none;">, supporting the [[echidna]] temperament</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;"><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> <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>Using the <del style="font-weight: bold; text-decoration: none;">138cde </del>val, it tempers out the [[<del style="font-weight: bold; text-decoration: none;">Diaschismic family|diaschisma</del>]], <del style="font-weight: bold; text-decoration: none;">2048</del>/<del style="font-weight: bold; text-decoration: none;">2025 </del>and <del style="font-weight: bold; text-decoration: none;">the [[Sensipent family</del>|<del style="font-weight: bold; text-decoration: none;">sensipent comma]], 78732/78125 </del>in the 5-limit; <del style="font-weight: bold; text-decoration: none;">1728</del>/<del style="font-weight: bold; text-decoration: none;">1715</del>, <del style="font-weight: bold; text-decoration: none;">10976</del>/<del style="font-weight: bold; text-decoration: none;">10935</del>, and <del style="font-weight: bold; text-decoration: none;">250047</del>/<del style="font-weight: bold; text-decoration: none;">250000 </del>in the 7-limit; <del style="font-weight: bold; text-decoration: none;">176</del>/<del style="font-weight: bold; text-decoration: none;">175</del>, <del style="font-weight: bold; text-decoration: none;">540</del>/<del style="font-weight: bold; text-decoration: none;">539</del>, <del style="font-weight: bold; text-decoration: none;">896</del>/<del style="font-weight: bold; text-decoration: none;">891</del>, and <del style="font-weight: bold; text-decoration: none;">85184</del>/<del style="font-weight: bold; text-decoration: none;">84375 </del>in the 11-limit; <del style="font-weight: bold; text-decoration: none;">351</del>/<del style="font-weight: bold; text-decoration: none;">350</del>, <del style="font-weight: bold; text-decoration: none;">352</del>/<del style="font-weight: bold; text-decoration: none;">351</del>, <del style="font-weight: bold; text-decoration: none;">364</del>/<del style="font-weight: bold; text-decoration: none;">363, 640/637</del>, and <del style="font-weight: bold; text-decoration: none;">2197</del>/<del style="font-weight: bold; text-decoration: none;">2187 </del>in the 13-limit<del style="font-weight: bold; text-decoration: none;">, supporting the [[Diaschismic family|echidna temperament]]</del>.</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>Using the <ins style="font-weight: bold; text-decoration: none;">138bf </ins>val, it tempers out the [[<ins style="font-weight: bold; text-decoration: none;">syntonic comma</ins>]], <ins style="font-weight: bold; text-decoration: none;">81</ins>/<ins style="font-weight: bold; text-decoration: none;">80 </ins>and <ins style="font-weight: bold; text-decoration: none;">{{monzo</ins>| <ins style="font-weight: bold; text-decoration: none;">-41 1 17 }} </ins>in the 5-limit; <ins style="font-weight: bold; text-decoration: none;">[[2401</ins>/<ins style="font-weight: bold; text-decoration: none;">2400]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[2430</ins>/<ins style="font-weight: bold; text-decoration: none;">2401]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">9765625</ins>/<ins style="font-weight: bold; text-decoration: none;">9633792 </ins>in the 7-limit; <ins style="font-weight: bold; text-decoration: none;">[[385</ins>/<ins style="font-weight: bold; text-decoration: none;">384]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[1375</ins>/<ins style="font-weight: bold; text-decoration: none;">1372]]</ins>, <ins style="font-weight: bold; text-decoration: none;">1944</ins>/<ins style="font-weight: bold; text-decoration: none;">1925</ins>, and <ins style="font-weight: bold; text-decoration: none;">9375</ins>/<ins style="font-weight: bold; text-decoration: none;">9317 </ins>in the 11-limit<ins style="font-weight: bold; text-decoration: none;">, supporting the [[Meantone family #Cuboctahedra|cuboctahedra]] temperament</ins>; <ins style="font-weight: bold; text-decoration: none;">[[625</ins>/<ins style="font-weight: bold; text-decoration: none;">624]]</ins>, <ins style="font-weight: bold; text-decoration: none;">975</ins>/<ins style="font-weight: bold; text-decoration: none;">968</ins>, <ins style="font-weight: bold; text-decoration: none;">[[1001</ins>/<ins style="font-weight: bold; text-decoration: none;">1000]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[1188</ins>/<ins style="font-weight: bold; text-decoration: none;">1183]] </ins>in the 13-limit.  </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> <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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">=== Odd harmonics ===</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>{{Harmonics in equal|138}}</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>{{Harmonics in equal|138}}</div></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><del style="font-weight: bold; text-decoration: none;">[[Category:Equal divisions of the octave|###]] &lt;!-- 3-digit number --&gt;</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=138edo&diff=117535&oldid=prev 2023-06-24T07:15:43Z

<p>Added &quot;harmonics in equal&quot; table</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 07:15, 24 June 2023</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"></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>{{Infobox ET}}</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>{{Infobox ET}}</div></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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each.  </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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>It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde).  </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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>Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit.  </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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>Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit.  </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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>Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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> <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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{Harmonics in equal|138}}</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>[[Category:Equal divisions of the octave|###]] &lt;!-- 3-digit number --&gt;</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>[[Category:Equal divisions of the octave|###]] &lt;!-- 3-digit number --&gt;</div></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=138edo&diff=96243&oldid=prev 2022-10-04T19:05:39Z

<p></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 19:05, 4 October 2022</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 colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{{Infobox ET}}</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>&#039;&#039;&#039;138edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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>&#039;&#039;&#039;138edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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> </table>

Aura https://en.xen.wiki/index.php?title=138edo&diff=92948&oldid=prev 2022-07-02T16:35:07Z

<p>Sort key</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 16:35, 2 July 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3">Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <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>[[Category:Equal divisions of the octave]]</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>[[Category:Equal divisions of the octave<ins style="font-weight: bold; text-decoration: none;">|###</ins>]] <ins style="font-weight: bold; text-decoration: none;">&lt;!-- 3-digit number --&gt;</ins></div></td></tr> </table>

Fredg999 category edits https://en.xen.wiki/index.php?title=138edo&diff=54990&oldid=prev 2020-12-04T23:13:08Z

<p>Moving from <a href="/w/Category:Edo" title="Category:Edo">Category:Edo</a> to <a href="/w/Category:Equal_divisions_of_the_octave" title="Category:Equal divisions of the octave">Category:Equal divisions of the octave</a> using <a href="/w/C:Help:Cat-a-lot" class="mw-redirect" title="C:Help:Cat-a-lot">Cat-a-lot</a></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 23:13, 4 December 2020</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3">Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <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>[[Category:<del style="font-weight: bold; text-decoration: none;">Edo</del>]]</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>[[Category:<ins style="font-weight: bold; text-decoration: none;">Equal divisions of the octave</ins>]]</div></td></tr> </table>

Keenan Pepper category edits https://en.xen.wiki/index.php?title=138edo&diff=39063&oldid=prev 2018-12-16T12:39:53Z

<p></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 12:39, 16 December 2018</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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (<del style="font-weight: bold; text-decoration: none;">optimal </del>patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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> <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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <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>[[Category:Edo]]</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>[[Category:Edo]]</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=138edo&diff=39035&oldid=prev 2018-12-14T01:34:08Z

<p>minor edit</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 01:34, 14 December 2018</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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (optimal patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the <del style="font-weight: bold; text-decoration: none;">optimal </del>patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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>'''138edo''' is the [[EDO|equal division of the octave]] into 138 parts of 8.6957 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: &amp;lt;138 219 320 387 477 511| (optimal patent val), &amp;lt;138 218 320 387 477 510| (138bf), and &amp;lt;138 219 321 388 478 511| (138cde). Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit. Using the 138bf val, it tempers out the [[syntonic comma]], 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the [[Meantone family|cuboctahedra temperament]]; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit. Using the 138cde val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and the [[Sensipent family|sensipent comma]], 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the [[Diaschismic family|echidna temperament]].</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> <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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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>138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.</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> <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>[[Category:Edo]]</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>[[Category:Edo]]</div></td></tr> </table>

Xenllium