https://en.xen.wiki/index.php?action=history&feed=atom&title=136edo 2026-06-26T21:48:03Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=136edo&diff=182073&oldid=prev 2025-02-20T19:28:35Z

<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 19:28, 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"></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>136edo is closely related to [[68edo]], but the [[patent val]]s differ on the [[mapping]] for 13. Using this val, it is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[121/120]], [[176/175]], [[245/243]], and [[1375/1372]]. It tempers out [[169/168]] and [[847/845]] in the 13-limit; [[136/135]], [[154/153]], [[256/255]], [[561/560]], and [[1089/1088]] in the 17-limit; [[190/189]], [[343/342]], [[361/360]], 363/361, and [[400/399]] in the 19-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>136edo is closely related to [[68edo]], but the [[patent val]]s differ on the [[mapping]] for 13. Using this val, it is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[121/120]], [[176/175]], [[245/243]], and [[1375/1372]]. It tempers out [[169/168]] and [[847/845]] in the 13-limit; [[136/135]], [[154/153]], [[256/255]], [[561/560]], and [[1089/1088]] in the 17-limit; [[190/189]], [[343/342]], [[361/360]], 363/361, and [[400/399]] in the 19-limit.  </div></td></tr> </table>

ArrowHead294 https://en.xen.wiki/index.php?title=136edo&diff=148378&oldid=prev 2024-07-23T07:42:26Z

<p>Formatting fix</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 07:42, 23 July 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 136e val, it tempers out 2560/2541 in the 11-limit; [[169/168]], [[352/351]], [[832/825]], [[1001/1000]], and [[1716/1715]] in the 13-limit. Using the 136ef val, it tempers out [[196/195]], [[325/324]], [[364/363]], [[512/507]], and [[625/624]] 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 136e val, it tempers out 2560/2541 in the 11-limit; [[169/168]], [[352/351]], [[832/825]], [[1001/1000]], and [[1716/1715]] in the 13-limit. Using the 136ef val, it tempers out [[196/195]], [[325/324]], [[364/363]], [[512/507]], and [[625/624]] 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 136b val, it tempers out [[81/80]], [[99/98]], [[126/125]], and 136410197/134217728 in the 11-limit; [[847/845]], 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit [[meantone]] tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx <del style="font-weight: bold; text-decoration: none;">| </del>by some metrics].  </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 136b val, it tempers out [[81/80]], [[99/98]], [[126/125]], and 136410197/134217728 in the 11-limit; [[847/845]], 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit [[meantone]] tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx by some metrics].  </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 136bcd val, it tempers out [[540/539]], [[1375/1372]], 2079/2048, and [[3125/3072]] in the 11-limit; [[105/104]], 847/845, [[1188/1183]], [[1287/1280]], and 6561/6500 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 136bcd val, it tempers out [[540/539]], [[1375/1372]], 2079/2048, and [[3125/3072]] in the 11-limit; [[105/104]], 847/845, [[1188/1183]], [[1287/1280]], and 6561/6500 in the 13-limit.  </div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=136edo&diff=147122&oldid=prev 2024-07-06T16:58:22Z

<p>Internal links</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 16:58, 6 July 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4">Line 4:</td> <td colspan="2" class="diff-lineno">Line 4:</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>136edo is closely related to [[68edo]], but the [[patent val]]s differ on the [[mapping]] for 13. Using this val, it is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[121/120]], [[176/175]], [[245/243]], and [[1375/1372]]. It tempers out [[169/168]] and [[847/845]] in the 13-limit; [[136/135]], [[154/153]], [[256/255]], [[561/560]], and [[1089/1088]] in the 17-limit; [[190/189]], [[343/342]], [[361/360]], 363/361, and [[400/399]] in the 19-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>136edo is closely related to [[68edo]], but the [[patent val]]s differ on the [[mapping]] for 13. Using this val, it is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[121/120]], [[176/175]], [[245/243]], and [[1375/1372]]. It tempers out [[169/168]] and [[847/845]] in the 13-limit; [[136/135]], [[154/153]], [[256/255]], [[561/560]], and [[1089/1088]] in the 17-limit; [[190/189]], [[343/342]], [[361/360]], 363/361, and [[400/399]] in the 19-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 136e val, it tempers out 2560/2541 in the 11-limit; 169/168, [[352/351]], 832/825, [[1001/1000]], and [[1716/1715]] in the 13-limit. Using the 136ef val, it tempers out [[196/195]], [[325/324]], [[364/363]], [[512/507]], and [[625/624]] 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 136e val, it tempers out 2560/2541 in the 11-limit; <ins style="font-weight: bold; text-decoration: none;">[[</ins>169/168<ins style="font-weight: bold; text-decoration: none;">]]</ins>, [[352/351]], <ins style="font-weight: bold; text-decoration: none;">[[</ins>832/825<ins style="font-weight: bold; text-decoration: none;">]]</ins>, [[1001/1000]], and [[1716/1715]] in the 13-limit. Using the 136ef val, it tempers out [[196/195]], [[325/324]], [[364/363]], [[512/507]], and [[625/624]] 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>Using the 136b val, it tempers out [[81/80]], [[99/98]], [[126/125]], and 136410197/134217728 in the 11-limit; [[847/845]], 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit [[meantone]] tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics].  </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 136b val, it tempers out [[81/80]], [[99/98]], [[126/125]], and 136410197/134217728 in the 11-limit; [[847/845]], 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit [[meantone]] tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics].  </div></td></tr> </table>

Fredg999 https://en.xen.wiki/index.php?title=136edo&diff=145028&oldid=prev 2024-05-26T11:04:02Z

<p>+subsets and supersets</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 11:04, 26 May 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">Line 12:</td> <td colspan="2" class="diff-lineno">Line 12:</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|136}}</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|136}}</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 136 factors into {{factorization|136}}, 136edo has subset edos {{EDOs| 2, 4, 8, 17, 34, and 68 }}.</ins></div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=136edo&diff=145027&oldid=prev 2024-05-26T11:02:51Z

<p>Cleanup; group the vals by similarity; -redundant 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 11:02, 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><del style="font-weight: bold; text-decoration: none;">It </del>is closely related to [[68edo]], but the patent <del style="font-weight: bold; text-decoration: none;">vals </del>differ on the mapping for 13.  </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;">136edo </ins>is closely related to [[68edo]], but the <ins style="font-weight: bold; text-decoration: none;">[[</ins>patent <ins style="font-weight: bold; text-decoration: none;">val]]s </ins>differ on the <ins style="font-weight: bold; text-decoration: none;">[[</ins>mapping<ins style="font-weight: bold; text-decoration: none;">]] </ins>for 13<ins style="font-weight: bold; text-decoration: none;">. Using this val, it is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[121/120]], [[176/175]], [[245/243]], and [[1375/1372]]. It tempers out [[169/168]] and [[847/845]] in the 13-limit; [[136/135]], [[154/153]], [[256/255]], [[561/560]], and [[1089/1088]] in the 17-limit; [[190/189]], [[343/342]], [[361/360]], 363/361, and [[400/399]] in the 19-limit</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 is </del>[[<del style="font-weight: bold; text-decoration: none;">contorted</del>]] in the <del style="font-weight: bold; text-decoration: none;">11</del>-limit, <del style="font-weight: bold; text-decoration: none;">tempering </del>out <del style="font-weight: bold; text-decoration: none;">121</del>/<del style="font-weight: bold; text-decoration: none;">120</del>, <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;">245</del>/<del style="font-weight: bold; text-decoration: none;">243</del>, and <del style="font-weight: bold; text-decoration: none;">1375</del>/<del style="font-weight: bold; text-decoration: none;">1372</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;">Using the 136e val, it tempers out 2560/2541 in the 11-limit; 169/168, [[352/351]], 832/825, [[1001/1000]], and </ins>[[<ins style="font-weight: bold; text-decoration: none;">1716/1715</ins>]] in the <ins style="font-weight: bold; text-decoration: none;">13</ins>-limit<ins style="font-weight: bold; text-decoration: none;">. Using the 136ef val</ins>, <ins style="font-weight: bold; text-decoration: none;">it tempers </ins>out <ins style="font-weight: bold; text-decoration: none;">[[196</ins>/<ins style="font-weight: bold; text-decoration: none;">195]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[325</ins>/<ins style="font-weight: bold; text-decoration: none;">324]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[364</ins>/<ins style="font-weight: bold; text-decoration: none;">363]], [[512/507]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[625</ins>/<ins style="font-weight: bold; text-decoration: none;">624]] in the 13-limit</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;">patent </del>val, it tempers out <del style="font-weight: bold; text-decoration: none;">169</del>/<del style="font-weight: bold; text-decoration: none;">168 </del>and <del style="font-weight: bold; text-decoration: none;">847</del>/<del style="font-weight: bold; text-decoration: none;">845 </del>in the <del style="font-weight: bold; text-decoration: none;">13</del>-limit; <del style="font-weight: bold; text-decoration: none;">136</del>/<del style="font-weight: bold; text-decoration: none;">135</del>, <del style="font-weight: bold; text-decoration: none;">154</del>/<del style="font-weight: bold; text-decoration: none;">153</del>, <del style="font-weight: bold; text-decoration: none;">256</del>/<del style="font-weight: bold; text-decoration: none;">255</del>, <del style="font-weight: bold; text-decoration: none;">561</del>/<del style="font-weight: bold; text-decoration: none;">560</del>, and <del style="font-weight: bold; text-decoration: none;">1089</del>/<del style="font-weight: bold; text-decoration: none;">1088 </del>in the <del style="font-weight: bold; text-decoration: none;">17</del>-limit<del style="font-weight: bold; text-decoration: none;">; 190</del>/<del style="font-weight: bold; text-decoration: none;">189, 343</del>/<del style="font-weight: bold; text-decoration: none;">342, 361</del>/<del style="font-weight: bold; text-decoration: none;">360, 363</del>/<del style="font-weight: bold; text-decoration: none;">361, and 400</del>/<del style="font-weight: bold; text-decoration: none;">399 in the 19</del>-<del style="font-weight: bold; text-decoration: none;">limit</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;">136b </ins>val, it tempers out <ins style="font-weight: bold; text-decoration: none;">[[81</ins>/<ins style="font-weight: bold; text-decoration: none;">80]], [[99/98]], [[126/125]], </ins>and <ins style="font-weight: bold; text-decoration: none;">136410197</ins>/<ins style="font-weight: bold; text-decoration: none;">134217728 </ins>in the <ins style="font-weight: bold; text-decoration: none;">11</ins>-limit; <ins style="font-weight: bold; text-decoration: none;">[[847</ins>/<ins style="font-weight: bold; text-decoration: none;">845]]</ins>, <ins style="font-weight: bold; text-decoration: none;">2704</ins>/<ins style="font-weight: bold; text-decoration: none;">2695</ins>, <ins style="font-weight: bold; text-decoration: none;">3042</ins>/<ins style="font-weight: bold; text-decoration: none;">3025</ins>, <ins style="font-weight: bold; text-decoration: none;">5445</ins>/<ins style="font-weight: bold; text-decoration: none;">5408</ins>, and <ins style="font-weight: bold; text-decoration: none;">15379</ins>/<ins style="font-weight: bold; text-decoration: none;">15360 </ins>in the <ins style="font-weight: bold; text-decoration: none;">13-limit, making it close to optimal as an 11</ins>-limit <ins style="font-weight: bold; text-decoration: none;">[[meantone]] tuning [http:</ins>//<ins style="font-weight: bold; text-decoration: none;">www.tonalsoft.com</ins>/<ins style="font-weight: bold; text-decoration: none;">enc</ins>/<ins style="font-weight: bold; text-decoration: none;">m</ins>/<ins style="font-weight: bold; text-decoration: none;">meantone</ins>-<ins style="font-weight: bold; text-decoration: none;">error.aspx | by some metrics]</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;">136b </del>val, it tempers out <del style="font-weight: bold; text-decoration: none;">81</del>/<del style="font-weight: bold; text-decoration: none;">80</del>, <del style="font-weight: bold; text-decoration: none;">99</del>/<del style="font-weight: bold; text-decoration: none;">98</del>, <del style="font-weight: bold; text-decoration: none;">126</del>/<del style="font-weight: bold; text-decoration: none;">125</del>, and <del style="font-weight: bold; text-decoration: none;">136410197</del>/<del style="font-weight: bold; text-decoration: none;">134217728 </del>in the 11-limit; 847/845, <del style="font-weight: bold; text-decoration: none;">2704</del>/<del style="font-weight: bold; text-decoration: none;">2695</del>, <del style="font-weight: bold; text-decoration: none;">3042</del>/<del style="font-weight: bold; text-decoration: none;">3025, 5445/5408</del>, and <del style="font-weight: bold; text-decoration: none;">15379</del>/<del style="font-weight: bold; text-decoration: none;">15360 </del>in the 13-limit<del style="font-weight: bold; text-decoration: none;">, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]</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;">136bcd </ins>val, it tempers out <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;">[[1375</ins>/<ins style="font-weight: bold; text-decoration: none;">1372]]</ins>, <ins style="font-weight: bold; text-decoration: none;">2079</ins>/<ins style="font-weight: bold; text-decoration: none;">2048</ins>, and <ins style="font-weight: bold; text-decoration: none;">[[3125</ins>/<ins style="font-weight: bold; text-decoration: none;">3072]] </ins>in the 11-limit; <ins style="font-weight: bold; text-decoration: none;">[[105/104]], </ins>847/845, <ins style="font-weight: bold; text-decoration: none;">[[1188</ins>/<ins style="font-weight: bold; text-decoration: none;">1183]]</ins>, <ins style="font-weight: bold; text-decoration: none;">[[1287</ins>/<ins style="font-weight: bold; text-decoration: none;">1280]]</ins>, and <ins style="font-weight: bold; text-decoration: none;">6561</ins>/<ins style="font-weight: bold; text-decoration: none;">6500 </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><del style="font-weight: bold; text-decoration: none;">Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. </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;">= Odd harmonics =</ins>==</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> </div></td><td colspan="2" class="diff-side-added"></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 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 in the 13-limit.</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">Harmonics</del>==</div></td><td colspan="2" class="diff-side-added"></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|136}}</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|136}}</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;"></del></div></td><td colspan="2" class="diff-side-added"></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=136edo&diff=133395&oldid=prev 2024-01-29T01:38:40Z

<p>Edo intro</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 01:38, 29 January 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;">'''136edo''' is the [[</del>EDO<del style="font-weight: bold; text-decoration: none;">|equal division of the octave]] into 136 parts of 8.8235 cents each. </del>It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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;">{{</ins>EDO <ins style="font-weight: bold; text-decoration: none;">intro}}</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> </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 closely related to [[68edo]], but the patent vals differ on the mapping for 13.  </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 [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372.  </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 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-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 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics].  </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 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 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 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 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 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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><ins style="font-weight: bold; text-decoration: none;">==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|136}}</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|136}}</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: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=136edo&diff=96239&oldid=prev 2022-10-04T19:04:47Z

<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 19:04, 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;136edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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>&#039;&#039;&#039;136edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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;"><div>{{Harmonics in equal|136}}</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|136}}</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: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>

Aura https://en.xen.wiki/index.php?title=136edo&diff=93563&oldid=prev 2022-07-25T18:09:32Z

<p>fix link formatting</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 18:09, 25 July 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 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>'''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx| by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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>'''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx | by some metrics]. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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;"><div>{{Harmonics in equal|136}}</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|136}}</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: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>

Yourmusic Productions https://en.xen.wiki/index.php?title=136edo&diff=93562&oldid=prev 2022-07-25T18:06:55Z

<p>Add prime error table, link to Tonalsoft page talking about the edo.</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 18:06, 25 July 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 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>'''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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>'''136edo''' is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit<ins style="font-weight: bold; text-decoration: none;">, making it close to optimal as an 11-limit meantone tuning [http://www.tonalsoft.com/enc/m/meantone-error.aspx| by some metrics]</ins>. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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><ins style="font-weight: bold; text-decoration: none;">{{Harmonics in equal|136}}</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: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>

Yourmusic Productions https://en.xen.wiki/index.php?title=136edo&diff=92946&oldid=prev 2022-07-02T16:34:55Z

<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 16:34, 2 July 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 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;136edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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>&#039;&#039;&#039;136edo&#039;&#039;&#039; is the [[EDO|equal division of the octave]] into 136 parts of 8.8235 cents each. It is closely related to [[68edo]], but the patent vals differ on the mapping for 13. It is [[contorted]] in the 11-limit, tempering out 121/120, 176/175, 245/243, and 1375/1372. Using the patent val, it tempers out 169/168 and 847/845 in the 13-limit; 136/135, 154/153, 256/255, 561/560, and 1089/1088 in the 17-limit; 190/189, 343/342, 361/360, 363/361, and 400/399 in the 19-limit. Using the 136b val, it tempers out 81/80, 99/98, 126/125, and 136410197/134217728 in the 11-limit; 847/845, 2704/2695, 3042/3025, 5445/5408, and 15379/15360 in the 13-limit. Using the 136bcd val, it tempers out 540/539, 1375/1372, 2079/2048, and 3125/3072 in the 11-limit; 105/104, 847/845, 1188/1183, 1287/1280, and 6561/6500 in the 13-limit. Using the 136e val, it tempers out 245/243, 2048/2025, 2401/2400, and 2560/2541 in the 11-limit; 169/168, 352/351, 832/825, 1001/1000, and 1716/1715 in the 13-limit. Using the 136ef val, it tempers out 196/195, 325/324, 364/363, 512/507, and 625/624 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>[[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