https://en.xen.wiki/index.php?action=history&feed=atom&title=94th-octave_temperaments 94th-octave temperaments - Revision history 2026-09-25T01:13:31Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=94th-octave_temperaments&diff=237774&oldid=prev FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| " 2026-09-24T12:33:15Z <p>Text replacement - &quot;Mapping: {{mapping| &quot; to &quot;{{Mapping|legend=0| &quot;</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 12:33, 24 September 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l28">Line 28:</td> <td colspan="2" class="diff-lineno">Line 28:</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>Comma list: 540/539, 4000/3993, 33554432/33480783</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>Comma list: 540/539, 4000/3993, 33554432/33480783</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;">Mapping: </del>{{<del style="font-weight: bold; text-decoration: none;">mapping</del>| 94 149 0 264 107 | 0 0 1 0 1 }}</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;">Mapping|legend=0</ins>| 94 149 0 264 107 | 0 0 1 0 1 }}</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>Optimal tunings:  </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>Optimal tunings:  </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43">Line 43:</td> <td colspan="2" class="diff-lineno">Line 43:</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>Comma list: 540/539, 729/728, 1575/1573, 28672/28561</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>Comma list: 540/539, 729/728, 1575/1573, 28672/28561</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;">Mapping: </del>{{<del style="font-weight: bold; text-decoration: none;">mapping</del>| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}</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;">Mapping|legend=0</ins>| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}</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>Optimal tunings:  </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>Optimal tunings:  </div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l58">Line 58:</td> <td colspan="2" class="diff-lineno">Line 58:</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>Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873</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>Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873</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;">Mapping: </del>{{<del style="font-weight: bold; text-decoration: none;">mapping</del>| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}</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;">Mapping|legend=0</ins>| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}</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>Optimal tunings:  </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>Optimal tunings:  </div></td></tr> </table> FloraC https://en.xen.wiki/index.php?title=94th-octave_temperaments&diff=237192&oldid=prev FloraC: /* Garistearn */ name 2026-09-15T07:56:28Z <p><span class="autocomment">Garistearn: </span> name</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 07:56, 15 September 2026</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;"><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>== Garistearn ==</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>== Garistearn ==</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;">The </del>garistearn temperament (94 &amp; 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].  </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;">Named by [[Xenllium]] in 2021, the </ins>garistearn temperament (94 &amp; 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].  </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>[[Subgroup]]: 2.3.5.7</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>[[Subgroup]]: 2.3.5.7</div></td></tr> </table> FloraC https://en.xen.wiki/index.php?title=94th-octave_temperaments&diff=237181&oldid=prev FloraC: Birth 2026-09-15T07:31:18Z <p>Birth</p> <p><b>New page</b></p><div>{{Technical data page}}<br /> {{Infobox fractional-octave|94}}<br /> [[94edo]] is a &quot;wheel&quot; for some [[fractional-octave temperaments]] because of its excellent [[3/2|perfect fifth]]. <br /> <br /> == Garistearn ==<br /> The garistearn temperament (94 &amp; 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]]. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 118098/117649, 33554432/33480783<br /> <br /> {{Mapping|legend=1| 94 149 0 264 | 0 0 1 0 }}<br /> : mapping generators: ~1029/1024, ~5<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~1029/1024 = 12.7638{{c}}, ~5/4 = 386.7156{{c}} (~5120/5103 = 3.8011{{c}})<br /> : [[error map]]: {{val| -0.201 -0.146 -0.000 +0.822 }}<br /> * [[CWE]]: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.6637{{c}} (~5120/5103 = 3.6850{{c}})<br /> : error map: {{val| 0.000 +0.173 +0.350 +1.387 }}<br /> <br /> {{Optimal ET sequence|legend=1| 94, 188, 282, 658d, 940dd }}<br /> <br /> [[Badness]] (Sintel): 7.77<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 540/539, 4000/3993, 33554432/33480783<br /> <br /> Mapping: {{mapping| 94 149 0 264 107 | 0 0 1 0 1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~1029/1024 = 12.7637{{c}}, ~5/4 = 386.5270{{c}} (~5120/5103 = 3.6174{{c}})<br /> * CWE: ~1029/1024 = 12.7660{{c}}, ~5/4 = 386.4545{{c}} (~5120/5103 = 3.4758{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 94, 188e, 282, 376, 658de }}<br /> <br /> Badness (Sintel): 2.72<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 540/539, 729/728, 1575/1573, 28672/28561<br /> <br /> Mapping: {{mapping| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}<br /> <br /> Optimal tunings: <br /> * WE: ~169/168 = 12.7628{{c}}, ~5/4 = 386.7181{{c}} (~352/351 = 3.8344{{c}})<br /> * CWE: ~169/168 = 12.7660{{c}}, ~5/4 = 386.6570{{c}} (~352/351 = 3.6783{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 94, 188e, 282, 658deff, 940ddeefff }}<br /> <br /> Badness (Sintel): 1.90<br /> <br /> === 17-limit ===<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873<br /> <br /> Mapping: {{mapping| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~169/168 = 12.7628{{c}}, ~5/4 = 386.7471{{c}} (~352/351 = 3.8623{{c}})<br /> * CWE: ~169/168 = 12.7660{{c}}, ~5/4 = 386.6751{{c}} (~352/351 = 3.6963{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 94, 188eg, 282, 658deff, 940ddeefffg }}<br /> <br /> Badness (Sintel): 1.41<br /> <br /> {{Navbox fractional-octave}}<br /> [[Category:94edo]]</div> FloraC