https://en.xen.wiki/index.php?action=history&feed=atom&title=Seminaiadmic_chords 2026-06-10T23:02:42Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Seminaiadmic_chords&diff=212582&oldid=prev 2025-10-10T07:59:57Z

<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 07:59, 10 October 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" 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>'''Seminaiadmic chords''' are [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]].</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>'''Seminaiadmic chords''' are [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]].</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>Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.</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>Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.</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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">14-7</del>/4 with steps of 17/14<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>8/7, 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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–7</ins>/4 with steps of 17/14<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-13</del>/<del style="font-weight: bold; text-decoration: none;">9-7</del>/4 with steps of 13/9<del style="font-weight: bold; text-decoration: none;">-</del>17/14<del style="font-weight: bold; text-decoration: none;">-</del>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;">1–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–7</ins>/4 with steps of 13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/14<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/14 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>28/17, 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;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/14 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>28/17, 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;">13-17</del>/14 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/14 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>28/17;</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;">1-14</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>18/17<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>18/17<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;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">17-8</del>/7 with steps of 18/17<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;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">17–8</ins>/7 with steps of 18/17<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 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 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;">16-17</del>/<del style="font-weight: bold; text-decoration: none;">14-7</del>/4 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>8/7<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–7</ins>/4 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<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" 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>18/17<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>18/17<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"></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;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">14-7</del>/4 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>8/7, 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;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–7</ins>/4 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-13</del>/<del style="font-weight: bold; text-decoration: none;">9-14</del>/<del style="font-weight: bold; text-decoration: none;">9-7</del>/4 with steps of 13/9<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>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;">1–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–14</ins>/<ins style="font-weight: bold; text-decoration: none;">9–7</ins>/4 with steps of 13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">14-18</del>/13 with steps of 9/8<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>13/9, 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;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–18</ins>/13 with steps of 9/8<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>13/9, 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;">1-8</del>/<del style="font-weight: bold; text-decoration: none;">7-16</del>/<del style="font-weight: bold; text-decoration: none;">13-18</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>9/8<del style="font-weight: bold; text-decoration: none;">-</del>13/9;</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;">13–18</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>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9;</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;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">14-9</del>/7 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/9, 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;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–9</ins>/7 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/9, 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;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">17-8</del>/<del style="font-weight: bold; text-decoration: none;">7-9</del>/7 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/9;</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;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">17–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–9</ins>/7 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/9;</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;">16-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/14 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>28/17, 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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/14 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>28/17, 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>/14 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<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;">1–14</ins>/<ins style="font-weight: bold; text-decoration: none;">13–8</ins>/<ins style="font-weight: bold; text-decoration: none;">7–17</ins>/14 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<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" 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;">7-18</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>17/14<del style="font-weight: bold; text-decoration: none;">-</del>13/9, 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;">7–18</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/14<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9, 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;">14-9</del>/<del style="font-weight: bold; text-decoration: none;">7-18</del>/13 with steps of 17/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9;</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;">14–9</ins>/<ins style="font-weight: bold; text-decoration: none;">7–18</ins>/13 with steps of 17/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9;</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;">7-28</del>/17 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>17/14, 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;">7–28</ins>/17 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/14, 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;">1-13</del>/<del style="font-weight: bold; text-decoration: none;">9-26</del>/<del style="font-weight: bold; text-decoration: none;">17-28</del>/17 with steps of 13/9<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>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>* <ins style="font-weight: bold; text-decoration: none;">1–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–26</ins>/<ins style="font-weight: bold; text-decoration: none;">17–28</ins>/17 with steps of 13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/14.</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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">14-7</del>/4 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>8/7, 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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–7</ins>/4 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>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>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">16-17</del>/<del style="font-weight: bold; text-decoration: none;">14-7</del>/<del style="font-weight: bold; text-decoration: none;">4-17</del>/9 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>8/7<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17;</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;">16–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–7</ins>/<ins style="font-weight: bold; text-decoration: none;">4–17</ins>/9 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>8/7<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17;</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;">1-14</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>18/17, 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;">13–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17, 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;">13-17</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>13/9;</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;">13–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/<ins style="font-weight: bold; text-decoration: none;">13–18</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9;</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;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">14-9</del>/<del style="font-weight: bold; text-decoration: none;">7-18</del>/13 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9, 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;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–9</ins>/<ins style="font-weight: bold; text-decoration: none;">7–18</ins>/13 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9, 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;">7-16</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/13 with steps of 14/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>14/13<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>13/9.</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;">13–18</ins>/13 with steps of 14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>14/13<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9.</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 seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}.</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 seminaiadmic chords include {{Optimal ET sequence| 10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}.</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=Seminaiadmic_chords&diff=127900&oldid=prev 2023-11-26T03:46:00Z

<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 03:46, 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" 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>'''Seminaiadmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]].  </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>'''Seminaiadmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]].</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>Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.  </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>Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.</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 three pairs of chords in inverse relationship:</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 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>* 1-17/14-7/4 with steps of 17/14-13/9-8/7 and its inverse 1-13/9-7/4 with steps of 13/9-17/14-8/7;</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>* 1-17/14-7/4 with steps of 17/14-13/9-8/7<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>* 1-9/8-17/14 with steps of 9/8-14/13-28/17 and its inverse 1-14/13-17/14 with steps of 14/13-9/8-28/17;</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;">* </ins>1-13/9-7/4 with steps of 13/9-17/14-8/7;</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>* 1-14/13-8/7 with steps of 14/13-18/17-7/4 and its inverse 1-18/17-8/7 with steps of 18/17-14/13-7/4.</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>* 1-9/8-17/14 with steps of 9/8-14/13-28/17<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>1-14/13-17/14 with steps of 14/13-9/8-28/17;</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>* 1-14/13-8/7 with steps of 14/13-18/17-7/4<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>1-18/17-8/7 with steps of 18/17-14/13-7/4.</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 three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are<del style="font-weight: bold; text-decoration: none;">:</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>For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are  </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>* 1-17/16-17/14-7/4 with steps of 17/16-8/7-13/9-8/7;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 1-17/16-17/14-7/4 with steps of 17/16-8/7-13/9-8/7;</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>* 1-14/13-17/14-17/13 with steps of 14/13-9/8-14/13-26/17;</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>* 1-14/13-17/14-17/13 with steps of 14/13-9/8-14/13-26/17;</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;"><div>* 1-14/13-8/7-16/13 with steps of 14/13-18/17-14/13-13/8.</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>* 1-14/13-8/7-16/13 with steps of 14/13-18/17-14/13-13/8.</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<del style="font-weight: bold; text-decoration: none;">:</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The 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>* 1-9/8-17/14-7/4 with steps of 9/8-14/13-13/9-8/7 and its inverse 1-13/9-14/9-7/4 with steps of 13/9-14/13-9/8-8/7;</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>* 1-9/8-17/14-7/4 with steps of 9/8-14/13-13/9-8/7<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>* 1-9/8-17/14-18/13 with steps of 9/8-14/13-8/7-13/9 and its inverse 1-8/7-16/13-18/13 with steps of 8/7-14/13-9/8-13/9;</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>1-13/9-14/9-7/4 with steps of 13/9-14/13-9/8-8/7;</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>* 1-9/8-17/14-9/7 with steps of 9/8-14/13-18/17-14/9 and its inverse 1-18/17-8/7-9/7 with steps of 18/17-14/13-9/8-14/9;</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>* 1-9/8-17/14-18/13 with steps of 9/8-14/13-8/7-13/9<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>* 1-17/16-9/8-17/14 with steps of 17/16-18/17-14/13-28/17 and its inverse 1-14/13-8/7-17/14 with steps of 14/13-18/17-17/16-28/17;</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><ins style="font-weight: bold; text-decoration: none;">* </ins>1-8/7-16/13-18/13 with steps of 8/7-14/13-9/8-13/9;</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>* 1-14/13-8/7-18/13 with steps of 14/13-18/17-17/14-13/9 and its inverse 1-17/14-9/7-18/13 with steps of 17/14-18/17-14/13-13/9;</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>* 1-9/8-17/14-9/7 with steps of 9/8-14/13-18/17-14/9<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>* 1-14/13-8/7-28/17 with steps of 14/13-18/17-13/9-17/14 and its inverse 1-13/9-26/17-28/17 with steps of 13/9-18/17-14/13-17/14.</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><ins style="font-weight: bold; text-decoration: none;">* </ins>1-18/17-8/7-9/7 with steps of 18/17-14/13-9/8-14/9;</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>* 1-17/16-9/8-17/14 with steps of 17/16-18/17-14/13-28/17<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>1-14/13-8/7-17/14 with steps of 14/13-18/17-17/16-28/17;</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>* 1-14/13-8/7-18/13 with steps of 14/13-18/17-17/14-13/9<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>1-17/14-9/7-18/13 with steps of 17/14-18/17-14/13-13/9;</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>* 1-14/13-8/7-28/17 with steps of 14/13-18/17-13/9-17/14<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>1-13/9-26/17-28/17 with steps of 13/9-18/17-14/13-17/14.</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 pentads, there are three pairs of chords in inverse relationship:</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 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>* 1-17/16-9/8-17/14-7/4 with steps of 17/16-18/17-14/13-13/9-8/7 and its inverse 1-17/16-17/14-7/4-17/9 with steps of 17/16-8/7-13/9-14/13-18/17;</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>* 1-17/16-9/8-17/14-7/4 with steps of 17/16-18/17-14/13-13/9-8/7<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>* 1-14/13-17/14-17/13-17/9 with steps of 14/13-9/8-14/13-13/9-18/17 and its inverse 1-14/13-17/14-17/13-18/13 with steps of 14/13-9/8-14/13-18/17-13/9;</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>1-17/16-17/14-7/4-17/9 with steps of 17/16-8/7-13/9-14/13-18/17;</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>* 1-9/8-17/14-9/7-18/13 with steps of 9/8-14/13-18/17-14/13-13/9 and its inverse 1-14/13-8/7-16/13-18/13 with steps of 14/13-18/17-14/13-9/8-13/9.</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>* 1-14/13-17/14-17/13-17/9 with steps of 14/13-9/8-14/13-13/9-18/17<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>1-14/13-17/14-17/13-18/13 with steps of 14/13-9/8-14/13-18/17-13/9;</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>* 1-9/8-17/14-9/7-18/13 with steps of 9/8-14/13-18/17-14/13-13/9<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>1-14/13-8/7-16/13-18/13 with steps of 14/13-18/17-14/13-9/8-13/9.</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 seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}.</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 seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Seminaiadmic_chords&diff=122528&oldid=prev 2023-08-22T13:49:17Z

<p>Created page with &quot;&#039;&#039;&#039;Seminaiadmic chords&#039;&#039;&#039; are <a href="/w/Dyadic_chord" title="Dyadic chord">essentially tempered dyadic chords</a> tempered by the seminaiadma, <a href="/w/442/441" title="442/441">442/441</a>. Seminaiadmic chords are of Dyadic chord/Pattern...&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Seminaiadmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]]. <br /> <br /> Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures. <br /> <br /> For triads, there are three pairs of chords in inverse relationship:<br /> * 1-17/14-7/4 with steps of 17/14-13/9-8/7 and its inverse 1-13/9-7/4 with steps of 13/9-17/14-8/7;<br /> * 1-9/8-17/14 with steps of 9/8-14/13-28/17 and its inverse 1-14/13-17/14 with steps of 14/13-9/8-28/17;<br /> * 1-14/13-8/7 with steps of 14/13-18/17-7/4 and its inverse 1-18/17-8/7 with steps of 18/17-14/13-7/4.<br /> <br /> For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are:<br /> * 1-17/16-17/14-7/4 with steps of 17/16-8/7-13/9-8/7;<br /> * 1-14/13-17/14-17/13 with steps of 14/13-9/8-14/13-26/17;<br /> * 1-14/13-8/7-16/13 with steps of 14/13-18/17-14/13-13/8.<br /> <br /> The inversely related pairs of chords are:<br /> * 1-9/8-17/14-7/4 with steps of 9/8-14/13-13/9-8/7 and its inverse 1-13/9-14/9-7/4 with steps of 13/9-14/13-9/8-8/7;<br /> * 1-9/8-17/14-18/13 with steps of 9/8-14/13-8/7-13/9 and its inverse 1-8/7-16/13-18/13 with steps of 8/7-14/13-9/8-13/9;<br /> * 1-9/8-17/14-9/7 with steps of 9/8-14/13-18/17-14/9 and its inverse 1-18/17-8/7-9/7 with steps of 18/17-14/13-9/8-14/9;<br /> * 1-17/16-9/8-17/14 with steps of 17/16-18/17-14/13-28/17 and its inverse 1-14/13-8/7-17/14 with steps of 14/13-18/17-17/16-28/17;<br /> * 1-14/13-8/7-18/13 with steps of 14/13-18/17-17/14-13/9 and its inverse 1-17/14-9/7-18/13 with steps of 17/14-18/17-14/13-13/9;<br /> * 1-14/13-8/7-28/17 with steps of 14/13-18/17-13/9-17/14 and its inverse 1-13/9-26/17-28/17 with steps of 13/9-18/17-14/13-17/14.<br /> <br /> For pentads, there are three pairs of chords in inverse relationship:<br /> * 1-17/16-9/8-17/14-7/4 with steps of 17/16-18/17-14/13-13/9-8/7 and its inverse 1-17/16-17/14-7/4-17/9 with steps of 17/16-8/7-13/9-14/13-18/17;<br /> * 1-14/13-17/14-17/13-17/9 with steps of 14/13-9/8-14/13-13/9-18/17 and its inverse 1-14/13-17/14-17/13-18/13 with steps of 14/13-9/8-14/13-18/17-13/9;<br /> * 1-9/8-17/14-9/7-18/13 with steps of 9/8-14/13-18/17-14/13-13/9 and its inverse 1-14/13-8/7-16/13-18/13 with steps of 14/13-18/17-14/13-9/8-13/9.<br /> <br /> Equal temperaments with seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}.<br /> <br /> [[Category:17-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Triads]]<br /> [[Category:Tetrads]]<br /> [[Category:Pentads]]<br /> [[Category:Seminaiadmic]]</div>

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