https://en.xen.wiki/index.php?action=history&feed=atom&title=Heptacircle_chords 2026-06-27T18:00:01Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Heptacircle_chords&diff=218651&oldid=prev 2025-12-06T09:18:42Z

<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 09:18, 6 December 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>'''Heptacircle chords''' are [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord|essentially tempered chords]] tempered by the heptacircle comma, [[2431/2430]].</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>'''Heptacircle chords''' are [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord|essentially tempered chords]] tempered by the heptacircle comma, [[2431/2430]].</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>Heptacircle chords are of [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[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>Heptacircle chords are of [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/13 with steps of 11/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/13 with steps of 11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<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;">1-13</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/11 with steps of 13/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>11/9;</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;">1–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/11 with steps of 13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9;</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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-13</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>18/13, 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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–13</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>18/13, 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;">17-13</del>/9 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/11<del style="font-weight: bold; text-decoration: none;">-</del>18/13;</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;">17–13</ins>/9 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/13;</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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-11</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>18/11, 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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–11</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>18/11, and its inverse  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">17-11</del>/9 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/13<del style="font-weight: bold; text-decoration: none;">-</del>18/11.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">17–11</ins>/9 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/11.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are  </div></td></tr> <tr><td class="diff-marker" data-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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/<del style="font-weight: bold; text-decoration: none;">13-22</del>/13 with steps of 11/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>13/11;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–22</ins>/13 with steps of 11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>13/11;</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-13</del>/<del style="font-weight: bold; text-decoration: none;">9-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>17/13<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-11</del>/<del style="font-weight: bold; text-decoration: none;">9-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>17/11<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17.</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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 11/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>15/11<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;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>11/9<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-5</del>/<del style="font-weight: bold; text-decoration: none;">3-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–5</ins>/<ins style="font-weight: bold; text-decoration: none;">3–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<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;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">15-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>15/11<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;">15–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<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;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 18/13<del style="font-weight: bold; text-decoration: none;">-</del>13/11<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 18/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/11<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-15</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>13/11<del style="font-weight: bold; text-decoration: none;">-</del>18/13<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>6/5<del style="font-weight: bold; text-decoration: none;">-</del>15/11<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>6/5<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>6/5<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>6/5<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">15-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-5</del>/<del style="font-weight: bold; text-decoration: none;">3-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>13/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–5</ins>/<ins style="font-weight: bold; text-decoration: none;">3–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<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;">1-13</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 13/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>13/9<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>13/9<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For pentads, there are 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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-15</del>/<del style="font-weight: bold; text-decoration: none;">11-5</del>/<del style="font-weight: bold; text-decoration: none;">3-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>13/11<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–5</ins>/<ins style="font-weight: bold; text-decoration: none;">3–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>13/11<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<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;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">15-18</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>13/11<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">15–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>13/11<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-13</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–13</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/<del style="font-weight: bold; text-decoration: none;">13-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/11<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/<ins style="font-weight: bold; text-decoration: none;">13–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">13-11</del>/<del style="font-weight: bold; text-decoration: none;">9-18</del>/<del style="font-weight: bold; text-decoration: none;">13-17</del>/9 with steps of 15/13<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>15/11<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">13–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–18</ins>/<ins style="font-weight: bold; text-decoration: none;">13–17</ins>/9 with steps of 15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>15/11<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/<del style="font-weight: bold; text-decoration: none;">11-18</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 15/11<del style="font-weight: bold; text-decoration: none;">-</del>17/15<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/13<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/<ins style="font-weight: bold; text-decoration: none;">11–18</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 15/11<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/13<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17.</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 heptacircle chords include {{Optimal ET sequence|24, 34, 53, 58, 72, 87, 94, 111, 159, 183, 217, 270, 277, 311, 494, 581, 605, 677 and 764 }}.</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 heptacircle chords include {{Optimal ET sequence| 24, 34, 53, 58, 72, 87, 94, 111, 159, 183, 217, 270, 277, 311, 494, 581, 605, 677 and 764 }}.</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=Heptacircle_chords&diff=127905&oldid=prev 2023-11-26T04:44:43Z

<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 04:44, 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>'''Heptacircle chords''' are [[Dyadic chord|essentially tempered <del style="font-weight: bold; text-decoration: none;">dyadic </del>chords]] tempered by the heptacircle comma, [[2431/2430]].  </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>'''Heptacircle chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the heptacircle comma, [[2431/2430]].</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>Heptacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[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>Heptacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[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>* 1-11/9-18/13 with steps of 11/9-17/15-13/9 and its inverse 1-13/9-18/11 with steps of 13/9-17/15-11/9;</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>* 1-11/9-18/13 with steps of 11/9-17/15-13/9<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>* 1-15/11-13/9 with steps of 15/11-18/17-18/13 and its inverse 1-18/17-13/9 with steps of 18/17-15/11-18/13;</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>1-13/9-18/11 with steps of 13/9-17/15-11/9;</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>* 1-15/13-11/9 with steps of 15/13-18/17-18/11 and its inverse 1-18/17-11/9 with steps of 18/17-15/13-18/11.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/11-13/9 with steps of 15/11-18/17-18/13<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>1-18/17-13/9 with steps of 18/17-15/11-18/13;</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>* 1-15/13-11/9 with steps of 15/13-18/17-18/11<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>1-18/17-11/9 with steps of 18/17-15/13-18/11.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-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>* 1-11/9-18/13-22/13 with steps of 11/9-17/15-11/9-13/11;</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>* 1-11/9-18/13-22/13 with steps of 11/9-17/15-11/9-13/11;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/11-13/9-17/9 with steps of 15/11-18/17-17/13-18/17;</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>* 1-15/11-13/9-17/9 with steps of 15/11-18/17-17/13-18/17;</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>* 1-15/13-11/9-17/9 with steps of 15/13-18/17-17/11-18/17.</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>* 1-15/13-11/9-17/9 with steps of 15/13-18/17-17/11-18/17.</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<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>* 1-11/9-18/13-17/9 with steps of 11/9-17/15-15/11-18/17 and its inverse 1-15/11-17/11-17/9 with steps of 15/11-17/15-11/9-18/17;</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>* 1-11/9-18/13-17/9 with steps of 11/9-17/15-15/11-18/17<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>* 1-15/11-5/3-17/9 with steps of 15/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-17/9 with steps of 17/15-11/9-15/11-18/17;</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;">* </ins>1-15/11-17/11-17/9 with steps of 15/11-17/15-11/9-18/17;</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>* 1-18/13-18/11-17/9 with steps of 18/13-13/11-15/13-18/17 and its inverse 1-15/13-15/11-17/9 with steps of 15/13-13/11-18/13-18/17;</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>* 1-15/11-5/3-17/9 with steps of 15/11-11/9-17/15-18/17<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>* 1-15/13-18/13-17/9 with steps of 15/13-6/5-15/11-18/17 and its inverse 1-15/11-18/11-17/9 with steps of 15/11-6/5-15/13-18/17;</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><ins style="font-weight: bold; text-decoration: none;">* </ins>1-17/15-18/13-17/9 with steps of 17/15-11/9-15/11-18/17;</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>* 1-17/15-18/11-17/9 with steps of 17/15-13/9-15/13-18/17 and its inverse 1-15/13-5/3-17/9 with steps of 15/13-13/9-17/15-18/17;</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>* 1-18/13-18/11-17/9 with steps of 18/13-13/11-15/13-18/17<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>* 1-13/9-18/11-17/9 with steps of 13/9-17/15-15/13-18/17 and its inverse 1-15/13-17/13-17/9 with steps of 15/13-17/15-13/9-18/17.</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;">* </ins>1-15/13-15/11-17/9 with steps of 15/13-13/11-18/13-18/17;</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>* 1-15/13-18/13-17/9 with steps of 15/13-6/5-15/11-18/17<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>1-15/11-18/11-17/9 with steps of 15/11-6/5-15/13-18/17;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 1-17/15-18/11-17/9 with steps of 17/15-13/9-15/13-18/17<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>1-15/13-5/3-17/9 with steps of 15/13-13/9-17/15-18/17;</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>* 1-13/9-18/11-17/9 with steps of 13/9-17/15-15/13-18/17<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>1-15/13-17/13-17/9 with steps of 15/13-17/15-13/9-18/17.</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>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>* 1-15/13-15/11-5/3-17/9 with steps of 15/13-13/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-18/11-17/9 with steps of 17/15-11/9-13/11-15/13-18/17;</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>* 1-15/13-15/11-5/3-17/9 with steps of 15/13-13/11-11/9-17/15-18/17<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>* 1-15/11-13/9-18/13-17/9 with steps of 15/11-18/17-17/15-15/13-18/17 and its inverse 1-15/13-17/13-18/13-17/9 with steps of 15/13-17/15-18/17-15/11-18/17;</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;">* </ins>1-17/15-18/13-18/11-17/9 with steps of 17/15-11/9-13/11-15/13-18/17;</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>* 1-15/13-11/9-18/13-17/9 with steps of 15/13-18/17-17/15-15/11-18/17 and its inverse 1-15/11-17/11-18/11-17/9 with steps of 15/11-17/15-18/17-15/13-18/17.</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>* 1-15/11-13/9-18/13-17/9 with steps of 15/11-18/17-17/15-15/13-18/17<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>1-15/13-17/13-18/13-17/9 with steps of 15/13-17/15-18/17-15/11-18/17;</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>* 1-15/13-11/9-18/13-17/9 with steps of 15/13-18/17-17/15-15/11-18/17<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>1-15/11-17/11-18/11-17/9 with steps of 15/11-17/15-18/17-15/13-18/17.</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 heptacircle chords include {{Optimal ET sequence|24, 34, 53, 58, 72, 87, 94, 111, 159, 183, 217, 270, 277, 311, 494, 581, 605, 677 and 764 }}.</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 heptacircle chords include {{Optimal ET sequence|24, 34, 53, 58, 72, 87, 94, 111, 159, 183, 217, 270, 277, 311, 494, 581, 605, 677 and 764 }}.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Heptacircle_chords&diff=122638&oldid=prev 2023-08-24T13:39:15Z

<p>Created page with &quot;&#039;&#039;&#039;Heptacircle chords&#039;&#039;&#039; are <a href="/w/Dyadic_chord" title="Dyadic chord">essentially tempered dyadic chords</a> tempered by the heptacircle comma, <a href="/w/2431/2430" title="2431/2430">2431/2430</a>. Heptacircle chords are of Dyadic chord/P...&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Heptacircle chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the heptacircle comma, [[2431/2430]]. <br /> <br /> Heptacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.5.11.13.17 [[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 /> * 1-11/9-18/13 with steps of 11/9-17/15-13/9 and its inverse 1-13/9-18/11 with steps of 13/9-17/15-11/9;<br /> * 1-15/11-13/9 with steps of 15/11-18/17-18/13 and its inverse 1-18/17-13/9 with steps of 18/17-15/11-18/13;<br /> * 1-15/13-11/9 with steps of 15/13-18/17-18/11 and its inverse 1-18/17-11/9 with steps of 18/17-15/13-18/11.<br /> <br /> For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are:<br /> * 1-11/9-18/13-22/13 with steps of 11/9-17/15-11/9-13/11;<br /> * 1-15/11-13/9-17/9 with steps of 15/11-18/17-17/13-18/17;<br /> * 1-15/13-11/9-17/9 with steps of 15/13-18/17-17/11-18/17.<br /> <br /> The inversely related pairs of chords are:<br /> * 1-11/9-18/13-17/9 with steps of 11/9-17/15-15/11-18/17 and its inverse 1-15/11-17/11-17/9 with steps of 15/11-17/15-11/9-18/17;<br /> * 1-15/11-5/3-17/9 with steps of 15/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-17/9 with steps of 17/15-11/9-15/11-18/17;<br /> * 1-18/13-18/11-17/9 with steps of 18/13-13/11-15/13-18/17 and its inverse 1-15/13-15/11-17/9 with steps of 15/13-13/11-18/13-18/17;<br /> * 1-15/13-18/13-17/9 with steps of 15/13-6/5-15/11-18/17 and its inverse 1-15/11-18/11-17/9 with steps of 15/11-6/5-15/13-18/17;<br /> * 1-17/15-18/11-17/9 with steps of 17/15-13/9-15/13-18/17 and its inverse 1-15/13-5/3-17/9 with steps of 15/13-13/9-17/15-18/17;<br /> * 1-13/9-18/11-17/9 with steps of 13/9-17/15-15/13-18/17 and its inverse 1-15/13-17/13-17/9 with steps of 15/13-17/15-13/9-18/17.<br /> <br /> For pentads, there are three pairs of chords in inverse relationship:<br /> * 1-15/13-15/11-5/3-17/9 with steps of 15/13-13/11-11/9-17/15-18/17 and its inverse 1-17/15-18/13-18/11-17/9 with steps of 17/15-11/9-13/11-15/13-18/17;<br /> * 1-15/11-13/9-18/13-17/9 with steps of 15/11-18/17-17/15-15/13-18/17 and its inverse 1-15/13-17/13-18/13-17/9 with steps of 15/13-17/15-18/17-15/11-18/17;<br /> * 1-15/13-11/9-18/13-17/9 with steps of 15/13-18/17-17/15-15/11-18/17 and its inverse 1-15/11-17/11-18/11-17/9 with steps of 15/11-17/15-18/17-15/13-18/17.<br /> <br /> Equal temperaments with heptacircle chords include {{Optimal ET sequence|24, 34, 53, 58, 72, 87, 94, 111, 159, 183, 217, 270, 277, 311, 494, 581, 605, 677 and 764 }}.<br /> <br /> [[Category:17-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Triads]]<br /> [[Category:Tetrads]]<br /> [[Category:Pentads]]<br /> [[Category:Heptacircle]]</div>

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