https://en.xen.wiki/index.php?action=history&feed=atom&title=Horizmic_chords 2026-06-29T00:43:53Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Horizmic_chords&diff=218439&oldid=prev 2025-12-02T08:38:56Z

<p>Cleanup</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:38, 2 December 2025</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>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </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 one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </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;">1-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/13 with steps of 8/7<del style="font-weight: bold; text-decoration: none;">-</del>8/7<del style="font-weight: bold; text-decoration: none;">-</del>26/17.</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;">1–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/13 with steps of 8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17.</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>The inversely related pair of chords is  </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 pair of chords is  </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;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-8</del>/7 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>7/4, and its inverse  </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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–8</ins>/7 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>7/4, 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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-8</del>/7 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>7/4.</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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–8</ins>/7 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>7/4.</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 two palindromic chords and two 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 two palindromic chords and two pairs of chords in inverse relationship. The palindromic 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>* <del style="font-weight: bold; text-decoration: none;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-8</del>/<del style="font-weight: bold; text-decoration: none;">7-16</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/8;</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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–16</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/8;</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;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/14 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>28/17.</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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/14 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>28/17.</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>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>* <del style="font-weight: bold; text-decoration: none;">1-8</del>/<del style="font-weight: bold; text-decoration: none;">7-16</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/13 with steps of 8/7<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>26/17, and its inverse  </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;">1–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–16</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/13 with steps of 8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17, 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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/13 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>8/7<del style="font-weight: bold; text-decoration: none;">-</del>26/17;</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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/13 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17;</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>* <del style="font-weight: bold; text-decoration: none;">1-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/13 with steps of 8/7<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>26/17, and its inverse  </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;">1–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/13 with steps of 8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17, 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>* <del style="font-weight: bold; text-decoration: none;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>8/7<del style="font-weight: bold; text-decoration: none;">-</del>26/17.</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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17.</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>They can be extended to pentads:  </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 pentads:  </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;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-8</del>/<del style="font-weight: bold; text-decoration: none;">7-16</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>26/17, and its inverse  </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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–16</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17, 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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-8</del>/<del style="font-weight: bold; text-decoration: none;">7-17</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/13 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>26/17.</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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/13 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>26/17.</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" 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 horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}.</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 horizmic chords include {{Optimal ET sequence| 10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150 }}.</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:17-odd-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>[[Category:17-odd-limit <ins style="font-weight: bold; text-decoration: none;">chords</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: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 class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 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:Triads]]</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:Triads]]</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=Horizmic_chords&diff=127903&oldid=prev 2023-11-26T04:25:43Z

<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 04:25, 26 November 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;Horizmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the horizma, [[833/832]].</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;Horizmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the horizma, [[833/832]].</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;">three triads, six tetrads and two pentads as </del>2.7.13.17 [[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;">Horizmic chords </ins>are <ins style="font-weight: bold; text-decoration: none;">of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the </ins>2.7.13.17 [[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 3 triads, 6 tetrads and 2 pentads, for a total of 11 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" 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>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is</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>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </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>* 1-8/7-17/13 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 8/7-8/7-26/17.</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>* 1-8/7-17/13 with steps of 8/7-8/7-26/17.</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" 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 inversely related pair of chords is</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 inversely related pair of chords is  </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>* 1-14/13-8/7 with steps of 14/13-17/16-7/4 and its inverse 1-17/16-8/7 with steps of 17/16-14/13-7/4.</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>* 1-14/13-8/7 with steps of 14/13-17/16-7/4<ins style="font-weight: bold; text-decoration: none;">, </ins>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>1-17/16-8/7 with steps of 17/16-14/13-7/4.</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>For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are</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>For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic 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>* 1-14/13-8/7-16/13 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 14/13-17/16-14/13-13/8;</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>* 1-14/13-8/7-16/13 with steps of 14/13-17/16-14/13-13/8;</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>* 1-17/16-8/7-17/14 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 17/16-14/13-17/16-28/17.</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>* 1-17/16-8/7-17/14 with steps of 17/16-14/13-17/16-28/17.</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" 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 inversely related pairs of chords are</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 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>* 1-8/7-16/13-17/13 with steps of 8/7-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/13 with steps of 17/16-14/13-8/7-26/17;</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>* 1-8/7-16/13-17/13 with steps of 8/7-14/13-17/16-26/17<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* 1-8/7-17/14-17/13 with steps of 8/7-17/16-14/13-26/17 and its inverse 1-14/13-8/7-17/13 with steps of 14/13-17/16-8/7-26/17.</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>1-17/16-8/7-17/13 with steps of 17/16-14/13-8/7-26/17;</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>* 1-8/7-17/14-17/13 with steps of 8/7-17/16-14/13-26/17<ins style="font-weight: bold; text-decoration: none;">, </ins>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>1-14/13-8/7-17/13 with steps of 14/13-17/16-8/7-26/17.</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" 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>They can be extended to pentads:</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>They can be extended to pentads:  </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>* 1-14/13-8/7-16/13-17/13 with steps of 14/13-17/16-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/14-17/13 with steps of 17/16-14/13-17/16-14/13-26/17.</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>* 1-14/13-8/7-16/13-17/13 with steps of 14/13-17/16-14/13-17/16-26/17<ins style="font-weight: bold; text-decoration: none;">, </ins>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>1-17/16-8/7-17/14-17/13 with steps of 17/16-14/13-17/16-14/13-26/17.</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>Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}.</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>Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Horizmic_chords&diff=122006&oldid=prev 2023-08-14T11:50:27Z

<p>Created page with &quot;&#039;&#039;&#039;Horizmic chords&#039;&#039;&#039; are <a href="/w/Dyadic_chord" title="Dyadic chord">essentially tempered chords</a> tempered by the horizma, <a href="/w/833/832" title="833/832">833/832</a>. There are three triads, six tetrads and two pentads as 2.7.13.17...&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Horizmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the horizma, [[833/832]].<br /> <br /> There are three triads, six tetrads and two pentads as 2.7.13.17 [[subgroup]] 17-odd-limit essentially tempered chords.<br /> <br /> For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is<br /> * 1-8/7-17/13 chord with steps of 8/7-8/7-26/17.<br /> <br /> The inversely related pair of chords is<br /> * 1-14/13-8/7 with steps of 14/13-17/16-7/4 and its inverse 1-17/16-8/7 with steps of 17/16-14/13-7/4.<br /> <br /> For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are<br /> * 1-14/13-8/7-16/13 chord with steps of 14/13-17/16-14/13-13/8;<br /> * 1-17/16-8/7-17/14 chord with steps of 17/16-14/13-17/16-28/17.<br /> <br /> The inversely related pairs of chords are<br /> * 1-8/7-16/13-17/13 with steps of 8/7-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/13 with steps of 17/16-14/13-8/7-26/17;<br /> * 1-8/7-17/14-17/13 with steps of 8/7-17/16-14/13-26/17 and its inverse 1-14/13-8/7-17/13 with steps of 14/13-17/16-8/7-26/17.<br /> <br /> They can be extended to pentads:<br /> * 1-14/13-8/7-16/13-17/13 with steps of 14/13-17/16-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/14-17/13 with steps of 17/16-14/13-17/16-14/13-26/17.<br /> <br /> Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}.<br /> <br /> [[Category:17-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Triads]]<br /> [[Category:Tetrads]]<br /> [[Category:Pentads]]<br /> [[Category:Horizmic]]</div>

Xenllium