https://en.xen.wiki/index.php?action=history&feed=atom&title=Fidesmic_chords 2026-06-24T09:00:17Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Fidesmic_chords&diff=218650&oldid=prev 2025-12-06T09:16:38Z

<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 09:16, 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>'''Fidesmic chords''' are [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]].</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>'''Fidesmic chords''' are [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]].</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>Fidesmic chords are of [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.3.5.7.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 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>Fidesmic chords are of [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.3.5.7.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 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 one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">15-9</del>/7 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–9</ins>/7 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>14/9.</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>The inversely related pair of chords is  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The inversely related pair of chords is  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/15 with steps of 15/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>30/17, 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;">14–17</ins>/15 with steps of 15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>30/17, 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;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">17-17</del>/15 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<del style="font-weight: bold; text-decoration: none;">-</del>30/17.</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;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">17–17</ins>/15 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>30/17.</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 tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/<del style="font-weight: bold; text-decoration: none;">15-17</del>/14 with steps of 15/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–17</ins>/14 with steps of 15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<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;">1-18</del>/<del style="font-weight: bold; text-decoration: none;">17-17</del>/<del style="font-weight: bold; text-decoration: none;">15-6</del>/5 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>5/3.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–18</ins>/<ins style="font-weight: bold; text-decoration: none;">17–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–6</ins>/5 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>5/3.</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;">1-17</del>/<del style="font-weight: bold; text-decoration: none;">15-17</del>/<del style="font-weight: bold; text-decoration: none;">14-9</del>/7 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>15/14<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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–9</ins>/7 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<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;">17-17</del>/<del style="font-weight: bold; text-decoration: none;">15-9</del>/7 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<del style="font-weight: bold; text-decoration: none;">-</del>17/15<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;">17–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–9</ins>/7 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>17/15<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;">15-6</del>/<del style="font-weight: bold; text-decoration: none;">5-9</del>/7 with steps of 17/15<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–6</ins>/<ins style="font-weight: bold; text-decoration: none;">5–9</ins>/7 with steps of 17/15<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<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;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/<del style="font-weight: bold; text-decoration: none;">15-9</del>/7 with steps of 15/14<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>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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–9</ins>/7 with steps of 15/14<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>14/9.</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>They can be extended to pentads:  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>They can be extended to pentads:  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-15</del>/<del style="font-weight: bold; text-decoration: none;">14-17</del>/<del style="font-weight: bold; text-decoration: none;">15-17</del>/<del style="font-weight: bold; text-decoration: none;">14-9</del>/7 with steps of 15/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<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;">1–15</ins>/<ins style="font-weight: bold; text-decoration: none;">14–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–17</ins>/<ins style="font-weight: bold; text-decoration: none;">14–9</ins>/7 with steps of 15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<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;">17-17</del>/<del style="font-weight: bold; text-decoration: none;">15-6</del>/<del style="font-weight: bold; text-decoration: none;">5-9</del>/7 with steps of 18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<del style="font-weight: bold; text-decoration: none;">-</del>18/17<del style="font-weight: bold; text-decoration: none;">-</del>15/14<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;">17–17</ins>/<ins style="font-weight: bold; text-decoration: none;">15–6</ins>/<ins style="font-weight: bold; text-decoration: none;">5–9</ins>/7 with steps of 18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17<ins style="font-weight: bold; text-decoration: none;">, </ins>15/14<ins style="font-weight: bold; text-decoration: none;">, </ins>14/9.</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 fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}.</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 fidesmic chords include {{Optimal ET sequence| 10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354 }}.</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=Fidesmic_chords&diff=127902&oldid=prev 2023-11-26T04:23:33Z

<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 04:23, 26 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Fidesmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Fidesmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">There </del>are <del style="font-weight: bold; text-decoration: none;">three triads, six tetrads and two pentads as </del>2.3.5.7.17 [[subgroup]] 17-odd-limit <del style="font-weight: bold; text-decoration: none;">essentially tempered chords</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Fidesmic chords </ins>are <ins style="font-weight: bold; text-decoration: none;">of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the </ins>2.3.5.7.17 [[subgroup]] <ins style="font-weight: bold; text-decoration: none;">[[</ins>17-odd-limit<ins style="font-weight: bold; text-decoration: none;">]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures</ins>.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1-17/15-9/7 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 17/15-17/15-14/9.</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>* 1-17/15-9/7 with steps of 17/15-17/15-14/9.</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>The inversely related pair of chords is</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The inversely related pair of chords is  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/14-17/15 with steps of 15/14-18/17-30/17 and its inverse 1-18/17-17/15 with steps of 18/17-15/14-30/17.</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>* 1-15/14-17/15 with steps of 15/14-18/17-30/17<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>1-18/17-17/15 with steps of 18/17-15/14-30/17.</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 tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/14-17/15-17/14 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 15/14-18/17-15/14-28/17;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/14-17/15-17/14 with steps of 15/14-18/17-15/14-28/17;</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>* 1-18/17-17/15-6/5 <del style="font-weight: bold; text-decoration: none;">chord </del>with steps of 18/17-15/14-18/17-5/3.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* 1-18/17-17/15-6/5 with steps of 18/17-15/14-18/17-5/3.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The inversely related pairs of chords are</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The inversely related pairs of chords are  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9 and its inverse 1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9;</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>* 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9<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>* 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9 and its inverse 1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9.</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;">* </ins>1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9;</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>* 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9<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>1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9.</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>They can be extended to pentads:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>They can be extended to pentads:  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9 and its inverse 1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9.</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>* 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9<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>1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9.</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 fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}.</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 fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}.</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Fidesmic_chords&diff=122010&oldid=prev 2023-08-14T12:48:43Z

<p>Created page with &quot;&#039;&#039;&#039;Fidesmic chords&#039;&#039;&#039; are <a href="/w/Dyadic_chord" title="Dyadic chord">essentially tempered chords</a> tempered by the fidesma, <a href="/w/2025/2023" title="2025/2023">2025/2023</a>. There are three triads, six tetrads and two pentads as 2.3.5.7....&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Fidesmic chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the fidesma, [[2025/2023]].<br /> <br /> There are three triads, six tetrads and two pentads as 2.3.5.7.17 [[subgroup]] 17-odd-limit essentially tempered chords.<br /> <br /> For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is<br /> * 1-17/15-9/7 chord with steps of 17/15-17/15-14/9.<br /> <br /> The inversely related pair of chords is<br /> * 1-15/14-17/15 with steps of 15/14-18/17-30/17 and its inverse 1-18/17-17/15 with steps of 18/17-15/14-30/17.<br /> <br /> For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are<br /> * 1-15/14-17/15-17/14 chord with steps of 15/14-18/17-15/14-28/17;<br /> * 1-18/17-17/15-6/5 chord with steps of 18/17-15/14-18/17-5/3.<br /> <br /> The inversely related pairs of chords are<br /> * 1-17/15-17/14-9/7 with steps of 17/15-15/14-18/17-14/9 and its inverse 1-18/17-17/15-9/7 with steps of 18/17-15/14-17/15-14/9;<br /> * 1-17/15-6/5-9/7 with steps of 17/15-18/17-15/14-14/9 and its inverse 1-15/14-17/15-9/7 with steps of 15/14-18/17-17/15-14/9.<br /> <br /> They can be extended to pentads:<br /> * 1-15/14-17/15-17/14-9/7 with steps of 15/14-18/17-15/14-18/17-14/9 and its inverse 1-18/17-17/15-6/5-9/7 with steps of 18/17-15/14-18/17-15/14-14/9.<br /> <br /> Equal temperaments with fidesmic chords include {{Optimal ET sequence|10, 12, 22, 50, 60, 72, 77, 84, 94, 99, 111, 171, 183, 193, 243, 270, 282 and 354}}.<br /> <br /> [[Category:17-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Triads]]<br /> [[Category:Tetrads]]<br /> [[Category:Pentads]]<br /> [[Category:Fidesmic]]</div>

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