https://en.xen.wiki/index.php?action=history&feed=atom&title=6L_3s_%283%2F1-equivalent%29 2026-10-01T13:55:48Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=6L_3s_(3/1-equivalent)&diff=238117&oldid=prev 2026-09-30T12:21:37Z

<p><span class="autocomment">Theory</span></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 12:21, 30 September 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l37">Line 37:</td> <td colspan="2" class="diff-lineno">Line 37:</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>* 13/5</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>* 13/5</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;"><div>* 3/1</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>* 3/1</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>(The intervals with multiple-of-3 denominators gain [[consonance]] in higher [[<del style="font-weight: bold; text-decoration: none;">tritaves</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>(The intervals with multiple-of-3 denominators gain [[consonance]] in higher [[<ins style="font-weight: bold; text-decoration: none;">tritave</ins>]]<ins style="font-weight: bold; text-decoration: none;">s</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>== Intervals ==</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>== Intervals ==</div></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=6L_3s_(3/1-equivalent)&diff=238115&oldid=prev 2026-09-30T11:55:29Z

<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 11:55, 30 September 2026</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50">Line 50:</td> <td colspan="2" class="diff-lineno">Line 50:</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>{{todo|expand}}</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>{{todo|expand}}</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;">26edt</del>]][[Category:<del style="font-weight: bold; text-decoration: none;">32edt</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;">15edt</ins>]][[Category:<ins style="font-weight: bold; text-decoration: none;">39edt</ins>]]</div></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=6L_3s_(3/1-equivalent)&diff=238114&oldid=prev 2026-09-30T11:55:07Z

<p>This one is useful also</p> <p><b>New page</b></p><div>{{Infobox MOS}}<br /> {{MOS intro}} <br /> <br /> == Theory ==<br /> === Modes ===<br /> {{MOS modes}}<br /> <br /> === Temperament interpretations ===<br /> The temperament that joins [[15edt]] and [[39edt]] produces this MOS. Both 15edt and 39edt are no-twos [[zeta]] peaks. [[69edt]], another no-twos zeta peak, also supports this temperament.<br /> <br /> In 15edt it is generated by 2\15 (~253.6¢) and has a [[hardness]] of exactly 2.0. <br /> <br /> In 69edt it is generated by 9\69 (~248.1¢) and has a hardness of exactly 1.8. <br /> <br /> In 39edt (’Triple Bohlen-Pierce’) it is generated by 5\39 (~243.8¢) and has a hardness of about 1.67.<br /> <br /> In 39edt this MOS has the intervals (in [[cent]]s):<br /> * 243.84<br /> * 390.145<br /> * 633.985<br /> * 877.825<br /> * 1024.13<br /> * 1267.97<br /> * 1511.81<br /> * 1658.115<br /> * 1901.955<br /> (And rotations thereof.)<br /> <br /> That roughly approximates this [[13-limit]] JI scale:<br /> * 7/6<br /> * 5/4<br /> * 13/9<br /> * 5/3<br /> * 9/5<br /> * 25/12<br /> * 12/5<br /> * 13/5<br /> * 3/1<br /> (The intervals with multiple-of-3 denominators gain [[consonance]] in higher [[tritaves]].)<br /> <br /> == Intervals ==<br /> {{MOS intervals}}<br /> <br /> === Scale degrees ===<br /> {{MOS mode degrees}}<br /> <br /> == Scale tree ==<br /> {{MOS tuning spectrum}}<br /> <br /> {{todo|expand}}<br /> <br /> [[Category:26edt]][[Category:32edt]]</div>

BudjarnLambeth