https://en.xen.wiki/index.php?action=history&feed=atom&title=Quadrantonismic_chords 2026-06-10T05:25:34Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Quadrantonismic_chords&diff=218482&oldid=prev 2025-12-03T08:20:50Z

<p>Cleanup</p> <a href="https://en.xen.wiki/index.php?title=Quadrantonismic_chords&amp;diff=218482&amp;oldid=122142">Show changes</a>

FloraC https://en.xen.wiki/index.php?title=Quadrantonismic_chords&diff=122142&oldid=prev 2023-08-16T05:02:26Z

<p>Now it&#039;s clear this is pattern 2 (thanks to Xenllium); readability improvement</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 05:02, 16 August 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Quadrantonismic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the quadrantonisma, [[1156/1155]].  </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;Quadrantonismic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the quadrantonisma, [[1156/1155]].  </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;">There </del>are <del style="font-weight: bold; text-decoration: none;">six triads, fifteen tetrads and six pentads as no-thirteen </del>[[subgroup]] 17-odd-limit <del style="font-weight: bold; text-decoration: none;">essentially tempered chords</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;">Quadrantonismic chords </ins>are <ins style="font-weight: bold; text-decoration: none;">of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.7.11.17 </ins>[[subgroup]] <ins style="font-weight: bold; text-decoration: none;">[[</ins>17-odd-limit<ins style="font-weight: bold; text-decoration: none;">]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures</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>For triads, there are three pairs of chords in inverse relationship:</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>For triads, there are three pairs of chords in inverse relationship:</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>* 1-17/11-7/4 with steps 17/11-17/15-8/7 and its inverse 1-17/15-7/4 with steps 17/15-17/11-8/7;</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>* 1-17/11-7/4 with steps 17/11-17/15-8/7 and its inverse</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>* 1-17/11-15/8 with steps 17/11-17/14-16/15 and its inverse 1-17/14-15/8 with steps 17/14-17/11-15/8;</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>1-17/15-7/4 with steps 17/15-17/11-8/7;</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>* 1-17/14-11/8 with steps 17/14-17/15-16/11 and its inverse 1-17/15-11/8 with steps 17/15-17/14-16/11.</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>* 1-17/11-15/8 with steps 17/11-17/14-16/15 and its inverse</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>1-17/14-15/8 with steps 17/14-17/11-15/8;</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>* 1-17/14-11/8 with steps 17/14-17/15-16/11 and its inverse</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>1-17/15-11/8 with steps 17/15-17/14-16/11.</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>For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are</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>For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14">Line 14:</td> <td colspan="2" class="diff-lineno">Line 17:</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>The inversely related pairs of chords are</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>The inversely related pairs of chords are</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>* 1-17/11-7/4-15/8 with steps 17/11-17/15-15/14-16/15 and its inverse 1-17/11-28/17-30/17 with steps 17/11-16/15-15/14-17/15;</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>* 1-17/11-7/4-15/8 with steps 17/11-17/15-15/14-16/15 and its inverse</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>* 1-17/15-11/8-7/4 with steps 17/15-17/14-14/11-8/7 and its inverse 1-17/14-11/8-11/7 with steps 17/14-17/15-8/7-14/11;</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>1-17/11-28/17-30/17 with steps 17/11-16/15-15/14-17/15;</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>* 1-17/14-11/8-15/8 with steps 17/14-17/15-15/11-16/15 and its inverse 1-17/15-11/8-22/15 with steps 17/15-17/14-16/15-15/11;</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>* 1-17/15-11/8-7/4 with steps 17/15-17/14-14/11-8/7 and its inverse</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>* 1-17/16-17/15-7/4 with steps 17/16-16/15-17/11-8/7 and its inverse 1-17/11-28/17-7/4 with steps 17/11-16/15-17/16-8/7;</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>1-17/14-11/8-11/7 with steps 17/14-17/15-8/7-14/11;</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>* 1-17/15-22/17-11/8 with steps 17/15-8/7-17/16-16/11 and its inverse 1-17/16-17/14-11/8 with steps 17/16-8/7-17/15-16/11;</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>* 1-17/14-11/8-15/8 with steps 17/14-17/15-15/11-16/15 and its inverse</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>* 1-17/14-22/17-11/8 with steps 17/14-16/15-17/16-16/11 and its inverse 1-17/16-17/15-11/8 with steps 17/16-16/15-17/14-16/11.</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>1-17/15-11/8-22/15 with steps 17/15-17/14-16/15-15/11;</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>* 1-17/16-17/15-7/4 with steps 17/16-16/15-17/11-8/7 and its inverse</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>1-17/11-28/17-7/4 with steps 17/11-16/15-17/16-8/7;</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>* 1-17/15-22/17-11/8 with steps 17/15-8/7-17/16-16/11 and its inverse</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>1-17/16-17/14-11/8 with steps 17/16-8/7-17/15-16/11;</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>* 1-17/14-22/17-11/8 with steps 17/14-16/15-17/16-16/11 and its inverse</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>1-17/16-17/15-11/8 with steps 17/16-16/15-17/14-16/11.</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>For pentads, there are three pairs of chords in inverse relationship:</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>For pentads, there are three pairs of chords in inverse relationship:</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>* 1-17/15-17/14-22/17-11/8 with steps 17/15-15/14-16/15-17/16-16/11 and its inverse 1-17/16-17/15-17/14-11/8 with steps 17/16-16/15-15/14-17/15-16/11;</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>* 1-17/15-17/14-22/17-11/8 with steps 17/15-15/14-16/15-17/16-16/11 and its inverse</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>* 1-17/16-17/14-11/8-15/8 with steps 17/16-8/7-17/15-15/11-16/15 and its inverse 1-17/15-22/17-11/8-22/15 with steps 17/15-8/7-17/16-16/15-15/11;</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>1-17/16-17/15-17/14-11/8 with steps 17/16-16/15-15/14-17/15-16/11;</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>* 1-17/16-17/15-11/8-7/4 with steps 17/16-16/15-17/14-14/11-8/7 and its inverse 1-17/14-22/17-11/8-11/7 with steps 17/14-16/15-17/16-8/7-14/11.</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>* 1-17/16-17/14-11/8-15/8 with steps 17/16-8/7-17/15-15/11-16/15 and its inverse</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>1-17/15-22/17-11/8-22/15 with steps 17/15-8/7-17/16-16/15-15/11;</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>* 1-17/16-17/15-11/8-7/4 with steps 17/16-16/15-17/14-14/11-8/7 and its inverse</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>1-17/14-22/17-11/8-11/7 with steps 17/14-16/15-17/16-8/7-14/11.</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>If we are willing to go to the 21-odd-limit, There are four additional pairs of triads of inverse relationship:</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>If we are willing to go to the 21-odd-limit, There are four additional pairs of triads of inverse relationship:</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>* 1-5/4-17/11 with steps 5/4-21/17-22/17 and its inverse 1-5/4-34/21 with steps 5/4-22/17-21/17;</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>* 1-5/4-17/11 with steps 5/4-21/17-22/17 and its inverse</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>* 1-21/16-17/11 with steps 21/16-20/17-22/17 and its inverse 1-21/16-17/10 with steps 21/16-22/17-20/17;</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>1-5/4-34/21 with steps 5/4-22/17-21/17;</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>* 1-11/8-17/10 with steps 11/8-21/17-20/17 and its inverse 1-11/8-34/21 with steps 11/8-20/17-21/17;</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>* 1-21/16-17/11 with steps 21/16-20/17-22/17 and its inverse</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>* 1-12/11-30/17 with steps 12/11-34/21-17/15 and its inverse 1-12/11-21/17 with steps 12/11-17/15-34/21.</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>1-21/16-17/10 with steps 21/16-22/17-20/17;</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>* 1-11/8-17/10 with steps 11/8-21/17-20/17 and its inverse</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>1-11/8-34/21 with steps 11/8-20/17-21/17;</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>* 1-12/11-30/17 with steps 12/11-34/21-17/15 and its inverse</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>1-12/11-21/17 with steps 12/11-17/15-34/21.</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>They can be extended to the following palindromic tetrads:</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>They can be extended to the following palindromic tetrads:</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39">Line 39:</td> <td colspan="2" class="diff-lineno">Line 55:</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>As well as the following additional pairs of triads of inverse relationship:</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>As well as the following additional pairs of triads of inverse relationship:</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>* 1-17/14-3/2-30/17 with steps 17/14-21/17-20/17-17/15 and its inverse 1-21/17-3/2-17/10 with steps 21/17-17/14-17/15-20/17;</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>* 1-17/14-3/2-30/17 with steps 17/14-21/17-20/17-17/15 and its inverse</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>* 1-17/14-3/2-15/8 with steps 17/14-21/17-5/4-16/15 and its inverse 1-21/17-3/2-8/5 with steps 21/17-17/14-16/15-5/4;</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>1-21/17-3/2-17/10 with steps 21/17-17/14-17/15-20/17;</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>* 1-21/16-3/2-17/10 with steps 21/16-8/7-17/15-20/17 and its inverse 1-8/7-3/2-30/17 with steps 8/7-21/16-20/17-17/15;</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>* 1-17/14-3/2-15/8 with steps 17/14-21/17-5/4-16/15 and its inverse</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>* 1-17/14-11/8-3/2 with steps 17/14-17/15-12/11-4/3 and its inverse 1-12/11-21/17-3/2 with steps 12/11-17/15-17/14-4/3;</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>1-21/17-3/2-8/5 with steps 21/17-17/14-16/15-5/4;</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>* 1-11/8-3/2-17/10 with steps 11/8-12/11-17/15-20/17 and its inverse 1-12/11-3/2-30/17 with step 12/11-11/8-20/17-17/15;</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>* 1-21/16-3/2-17/10 with steps 21/16-8/7-17/15-20/17 and its inverse</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>* 1-5/4-17/11-7/4 with steps 5/4-21/17-17/15-8/7 and its inverse 1-21/17-17/11-30/17 with steps 21/17-5/4-8/7-17/15;</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>1-8/7-3/2-30/17 with steps 8/7-21/16-20/17-17/15;</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>* 1-21/16-17/11-15/8 with steps 21/16-20/17-17/14-16/15 and its inverse 1-20/17-17/11-28/17 with steps 20/17-21/16-16/15-17/14;</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>* 1-17/14-11/8-3/2 with steps 17/14-17/15-12/11-4/3 and its inverse</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>* 1-5/4-21/16-17/11 with steps 5/4-21/20-20/17-22/17 and its inverse 1-20/17-21/17-17/11 with steps 20/17-21/20-5/4-22/17;</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>1-12/11-21/17-3/2 with steps 12/11-17/15-17/14-4/3;</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>* 1-17/14-11/8-17/10 with steps 17/14-17/15-21/17-20/17 and its inverse 1-17/15-11/8-34/21 with steps 17/15-17/14-20/17-21/17;</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>* 1-11/8-3/2-17/10 with steps 11/8-12/11-17/15-20/17 and its inverse</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>* 1-5/4-11/8-34/21 with steps 5/4-11/10-20/17-21/17 and its inverse 1-11/10-11/8-17/10 with steps 11/10-5/4-21/17-20/17;</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>1-12/11-3/2-30/17 with step 12/11-11/8-20/17-17/15;</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>* 1-21/16-11/8-17/10 with steps 21/16-22/21-21/17-20/17 and its inverse 1-22/21-11/8-34/21 with steps 22/21-21/16-20/17-21/17.</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>* 1-5/4-17/11-7/4 with steps 5/4-21/17-17/15-8/7 and its inverse</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>1-21/17-17/11-30/17 with steps 21/17-5/4-8/7-17/15;</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>* 1-21/16-17/11-15/8 with steps 21/16-20/17-17/14-16/15 and its inverse</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>1-20/17-17/11-28/17 with steps 20/17-21/16-16/15-17/14;</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>* 1-5/4-21/16-17/11 with steps 5/4-21/20-20/17-22/17 and its inverse</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>1-20/17-21/17-17/11 with steps 20/17-21/20-5/4-22/17;</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>* 1-17/14-11/8-17/10 with steps 17/14-17/15-21/17-20/17 and its inverse</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>1-17/15-11/8-34/21 with steps 17/15-17/14-20/17-21/17;</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>* 1-5/4-11/8-34/21 with steps 5/4-11/10-20/17-21/17 and its inverse</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>1-11/10-11/8-17/10 with steps 11/10-5/4-21/17-20/17;</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>* 1-21/16-11/8-17/10 with steps 21/16-22/21-21/17-20/17 and its inverse</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>1-22/21-11/8-34/21 with steps 22/21-21/16-20/17-21/17.</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>For pentads, there are</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>For pentads, there are</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>* 1-17/14-3/2-30/17-15/8 with steps 17/14-21/17-20/17-17/16-16/15 and its inverse 1-21/17-3/2-8/5-17/10 with steps 21/17-17/14-16/15-17/16-20/17;</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>* 1-17/14-3/2-30/17-15/8 with steps 17/14-21/17-20/17-17/16-16/15 and its inverse</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>* 1-21/17-21/16-3/2-17/10 with steps 21/17-17/16-8/7-17/15-20/17 and its inverse 1-8/7-17/14-3/2-30/17 with steps 8/7-17/16-21/17-20/17-17/15;</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>1-21/17-3/2-8/5-17/10 with steps 21/17-17/14-16/15-17/16-20/17;</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>* 1-17/14-11/8-3/2-15/8 with steps 17/14-17/15-12/11-5/4-16/15 and its inverse 1-12/11-21/17-3/2-8/5 with steps 12/11-17/15-17/14-16/15-5/4;</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>* 1-21/17-21/16-3/2-17/10 with steps 21/17-17/16-8/7-17/15-20/17 and its inverse</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>* 1-21/16-11/8-3/2-17/10 with steps 21/16-22/21-12/11-17/15-20/17 and its inverse 1-12/11-8/7-3/2-30/17 with steps 12/11-22/21-21/16-20/17-17/15;</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>1-8/7-17/14-3/2-30/17 with steps 8/7-17/16-21/17-20/17-17/15;</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>* 1-17/14-11/8-3/2-17/10 with steps 17/14-17/15-12/11-17/15-20/17 and its inverse 1-12/11-21/17-3/2-30/17 with steps 12/11-17/15-17/14-20/17-17/15.</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>* 1-17/14-11/8-3/2-15/8 with steps 17/14-17/15-12/11-5/4-16/15 and its inverse</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>1-12/11-21/17-3/2-8/5 with steps 12/11-17/15-17/14-16/15-5/4;</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>* 1-21/16-11/8-3/2-17/10 with steps 21/16-22/21-12/11-17/15-20/17 and its inverse</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>1-12/11-8/7-3/2-30/17 with steps 12/11-22/21-21/16-20/17-17/15;</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>* 1-17/14-11/8-3/2-17/10 with steps 17/14-17/15-12/11-17/15-20/17 and its inverse</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>1-12/11-21/17-3/2-30/17 with steps 12/11-17/15-17/14-20/17-17/15.</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>Equal temperaments with quadrantonismic chords include {{Optimal ET sequence|22, 26, 43, 46, 50, 68, 72, 89, 94, 111, 118, 121, 140, 183, 239, 311, 400, 422 and 494}}.</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>Equal temperaments with quadrantonismic chords include {{Optimal ET sequence| 22, 26, 43, 46, 50, 68, 72, 89, 94, 111, 118, 121, 140, 183, 239, 311, 400, 422 and 494 }}.</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:17-odd-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>[[Category:17-odd-limit]]</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=Quadrantonismic_chords&diff=122051&oldid=prev 2023-08-15T09:32:33Z

<p>Update the article including recategorize and adding supporting ET</p> <a href="https://en.xen.wiki/index.php?title=Quadrantonismic_chords&amp;diff=122051&amp;oldid=114391">Show changes</a>

Xenllium https://en.xen.wiki/index.php?title=Quadrantonismic_chords&diff=114391&oldid=prev 2023-05-23T11:49:52Z

<p>Recategorize</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 11:49, 23 May 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l70">Line 70:</td> <td colspan="2" class="diff-lineno">Line 70:</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:21-odd-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>[[Category:21-odd-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>[[Category:Essentially tempered chords]]</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:Essentially tempered chords]]</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Triads]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Tetrads]]</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Pentads]]</ins></div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Quadrantonismic]]</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:Quadrantonismic]]</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=Quadrantonismic_chords&diff=103645&oldid=prev 2023-02-23T15:53:33Z

<p>Created page with &quot;&#039;&#039;&#039;Quadrantonismic chords&#039;&#039;&#039; are <a href="/w/Essentially_tempered_dyadic_chord" class="mw-redirect" title="Essentially tempered dyadic chord">essentially tempered dyadic chords</a> tempered by the quadrantonisma, <a href="/w/1156/1155" title="1156/1155">1156/1155</a>. Quadrantonismic chords are numerous. There are seven p...&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Quadrantonismic chords&#039;&#039;&#039; are [[essentially tempered dyadic chord]]s tempered by the quadrantonisma, [[1156/1155]]. <br /> <br /> Quadrantonismic chords are numerous. There are seven pairs of quadrantonismic triads of inverse relationship in the no-13 21-odd-limit: <br /> * 1-5/4-17/11 with steps 5/4-21/17-22/17, and its inverse<br /> * 1-5/4-34/21 with steps 5/4-22/17-21/17; <br /> * 1-21/16-17/11 with steps 21/16-20/17-22/17, and its inverse<br /> * 1-21/16-17/10 with steps 21/16-22/17-20/17; <br /> * 1-17/11-7/4 with steps 17/11-17/15-8/7, and its inverse<br /> * 1-17/15-7/4 with steps 17/15-17/11-8/7; <br /> * 1-17/11-15/8 with steps 17/11-17/14-16/15, and its inverse<br /> * 1-17/14-15/8 with steps 17/14-17/11-15/8; <br /> * 1-11/8-17/10 with steps 11/8-21/17-20/17, and its inverse<br /> * 1-11/8-34/21 with steps 11/8-20/17-21/17; <br /> * 1-17/14-11/8 with steps 17/14-17/15-16/11, and its inverse<br /> * 1-17/15-11/8 with steps 17/15-17/14-16/11; <br /> * 1-12/11-30/17 with steps 12/11-34/21-17/15, and its inverse<br /> * 1-12/11-21/17 with steps 12/11-17/15-34/21. <br /> <br /> They can be extended to the following palindromic tetrads: <br /> * 1-5/4-17/11-34/21 with steps 5/4-21/17-22/21-21/17; <br /> * 1-21/16-17/11-17/10 with steps 21/16-20/17-11/10-20/17; <br /> * 1-17/15-17/11-7/4 with steps 17/15-15/11-17/15-7/4; <br /> * 1-17/14-17/11-15/8 with steps 17/14-14/11-17/14-16/15; <br /> * 1-11/8-34/21-17/10 with steps 11/8-20/17-21/20-20/17; <br /> * 1-17/15-17/14-11/8 with steps 17/15-15/14-17/15-16/11; <br /> * 1-12/11-21/17-30/17 with steps 12/11-17/15-10/7-17/15. <br /> <br /> As well as the following inversely related tetrads: <br /> * 1-17/14-3/2-30/17 with steps 17/14-21/17-20/17-17/15, and its inverse<br /> * 1-21/17-3/2-17/10 with steps 21/17-17/14-17/15-20/17; <br /> * 1-17/14-3/2-15/8 with steps 17/14-21/17-5/4-16/15, and its inverse<br /> * 1-21/17-3/2-8/5 with steps 21/17-17/14-16/15-5/4; <br /> * 1-21/16-3/2-17/10 with steps 21/16-8/7-17/15-20/17, and its inverse<br /> * 1-8/7-3/2-30/17 with steps 8/7-21/16-20/17-17/15; <br /> * 1-17/14-11/8-3/2 with steps 17/14-17/15-12/11-4/3, and its inverse<br /> * 1-12/11-21/17-3/2 with steps 12/11-17/15-17/14-4/3; <br /> * 1-11/8-3/2-17/10 with steps 11/8-12/11-17/15-20/17, and its inverse<br /> * 1-12/11-3/2-30/17 with step 12/11-11/8-20/17-17/15; <br /> * 1-5/4-17/11-7/4 with steps 5/4-21/17-17/15-8/7, and its inverse<br /> * 1-21/17-17/11-30/17 with steps 21/17-5/4-8/7-17/15; <br /> * 1-21/16-17/11-15/8 with steps 21/16-20/17-17/14-16/15, and its inverse<br /> * 1-20/17-17/11-28/17 with steps 20/17-21/16-16/15-17/14. <br /> * 1-5/4-21/16-17/11 with steps 5/4-21/20-20/17-22/17, and its inverse<br /> * 1-20/17-21/17-17/11 with steps 20/17-21/20-5/4-22/17; <br /> * 1-17/11-7/4-15/8 with steps 17/11-17/15-15/14-16/15, and its invere<br /> * 1-17/11-28/17-30/17 with steps 17/11-16/15-15/14-17/15; <br /> * 1-17/14-11/8-17/10 with steps 17/14-17/15-21/17-20/17, and its inverse<br /> * 1-17/15-11/8-34/21 with steps 17/15-17/14-20/17-21/17; <br /> * 1-5/4-11/8-34/21 with steps 5/4-11/10-20/17-21/17, and its inverse<br /> * 1-11/10-11/8-17/10 with steps 11/10-5/4-21/17-20/17; <br /> * 1-21/16-11/8-17/10 with steps 21/16-22/21-21/17-20/17 and its inverse<br /> * 1-22/21-11/8-34/21 with steps 22/21-21/16-20/17-21/17; <br /> * 1-17/15-11/8-7/4 with steps 17/15-17/14-14/11-8/7, and its inverse<br /> * 1-17/14-11/8-11/7 with steps 17/14-17/15-8/7-14/11; <br /> * 1-17/14-11/8-15/8 with steps 17/14-17/15-15/11-16/15, and its inverse<br /> * 1-17/15-11/8-22/15 with steps 17/15-17/14-16/15-15/11. <br /> <br /> For pentads, there are<br /> * 1-17/14-3/2-30/17-15/8 with steps 17/14-21/17-20/17-17/16-16/15, and its inverse<br /> * 1-21/17-3/2-8/5-17/10 with steps 21/17-17/14-16/15-17/16-20/17; <br /> * 1-21/17-21/16-3/2-17/10 with steps 21/17-17/16-8/7-17/15-20/17, and its inverse<br /> * 1-8/7-17/14-3/2-30/17 with steps 8/7-17/16-21/17-20/17-17/15; <br /> * 1-17/14-11/8-3/2-15/8 with steps 17/14-17/15-12/11-5/4-16/15, and its inverse<br /> * 1-12/11-21/17-3/2-8/5 with steps 12/11-17/15-17/14-16/15-5/4; <br /> * 1-21/16-11/8-3/2-17/10 with steps 21/16-22/21-12/11-17/15-20/17, and its inverse<br /> * 1-12/11-8/7-3/2-30/17 with steps 12/11-22/21-21/16-20/17-17/15; <br /> * 1-17/14-11/8-3/2-17/10 with steps 17/14-17/15-12/11-17/15-20/17, and its inverse<br /> * 1-12/11-21/17-3/2-30/17 with steps 12/11-17/15-17/14-20/17-17/15. <br /> <br /> [[Category:21-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Quadrantonismic]]</div>

FloraC