https://en.xen.wiki/index.php?action=history&feed=atom&title=Twosquare_chords 2026-06-29T22:34:35Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Twosquare_chords&diff=218483&oldid=prev 2025-12-03T08:21:19Z

<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 08:21, 3 December 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">Line 26:</td> <td colspan="2" class="diff-lineno">Line 26:</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 twosquare chords include {{Optimal ET sequence| 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231 }}.</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 twosquare chords include {{Optimal ET sequence| 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231 }}.</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=Twosquare_chords&diff=218481&oldid=prev 2025-12-03T08:13:44Z

<p>Cleanup</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:13, 3 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>'''Twosquare chords''' are [[<del style="font-weight: bold; text-decoration: none;">Dyadic chord|</del>essentially tempered <del style="font-weight: bold; text-decoration: none;">chords</del>]] tempered by the twosquare comma, [[1089/1088]].</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>'''Twosquare chords''' are [[essentially tempered <ins style="font-weight: bold; text-decoration: none;">chord</ins>]]<ins style="font-weight: bold; text-decoration: none;">s </ins>tempered by the twosquare comma, [[1089/1088]].</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>Twosquare chords are of [[<del style="font-weight: bold; text-decoration: none;">Dyadic </del>chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.3.11.17 [[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>Twosquare chords are of [[<ins style="font-weight: bold; text-decoration: none;">dyadic </ins>chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.3.11.17 [[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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/9 with steps of 11/8<del style="font-weight: bold; text-decoration: none;">-</del>11/8<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;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/9 with steps of 11/8<ins style="font-weight: bold; text-decoration: none;">, </ins>11/8<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 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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/11 with steps of 11/8<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17, 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;">8–17</ins>/11 with steps of 11/8<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17, and its inverse  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/11 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>11/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/11 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>11/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17.</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;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/11 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/11 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17;</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;">1-9</del>/<del style="font-weight: bold; text-decoration: none;">8-16</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/11 with steps of 9/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17<del style="font-weight: bold; text-decoration: none;">-</del>17/16<del style="font-weight: bold; text-decoration: none;">-</del>22/17.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–9</ins>/<ins style="font-weight: bold; text-decoration: none;">8–16</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/11 with steps of 9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17.</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;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 11/8<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>11/9<del style="font-weight: bold; text-decoration: none;">-</del>18/17, and its inverse  </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 11/8<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>18/17, and its inverse  </div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del style="font-weight: bold; text-decoration: none;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">9-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/9 with steps of 11/9<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>11/8<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;">1–11</ins>/<ins style="font-weight: bold; text-decoration: none;">9–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/9 with steps of 11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>11/8<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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">8-16</del>/<del style="font-weight: bold; text-decoration: none;">9-17</del>/9 with steps of 11/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17<del style="font-weight: bold; text-decoration: none;">-</del>17/16<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;">8–16</ins>/<ins style="font-weight: bold; text-decoration: none;">9–17</ins>/9 with steps of 11/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<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;">16-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/9 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>22/17<del style="font-weight: bold; text-decoration: none;">-</del>11/8<del style="font-weight: bold; text-decoration: none;">-</del>18/17.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins style="font-weight: bold; text-decoration: none;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/9 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17<ins style="font-weight: bold; text-decoration: none;">, </ins>11/8<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>Then there is an inversely related pair of 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>Then there is an inversely related pair of 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;">1-11</del>/<del style="font-weight: bold; text-decoration: none;">9-11</del>/<del style="font-weight: bold; text-decoration: none;">8-16</del>/<del style="font-weight: bold; text-decoration: none;">9-17</del>/9 with steps of 11/9<del style="font-weight: bold; text-decoration: none;">-</del>9/8<del style="font-weight: bold; text-decoration: none;">-</del>22/17<del style="font-weight: bold; text-decoration: none;">-</del>17/16<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;">9–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–16</ins>/<ins style="font-weight: bold; text-decoration: none;">9–17</ins>/9 with steps of 11/9<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17<ins style="font-weight: bold; text-decoration: none;">, </ins>17/16<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;">16-11</del>/<del style="font-weight: bold; text-decoration: none;">8-17</del>/<del style="font-weight: bold; text-decoration: none;">11-17</del>/9 with steps of 17/16<del style="font-weight: bold; text-decoration: none;">-</del>22/17<del style="font-weight: bold; text-decoration: none;">-</del>9/8<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;">1–17</ins>/<ins style="font-weight: bold; text-decoration: none;">16–11</ins>/<ins style="font-weight: bold; text-decoration: none;">8–17</ins>/<ins style="font-weight: bold; text-decoration: none;">11–17</ins>/9 with steps of 17/16<ins style="font-weight: bold; text-decoration: none;">, </ins>22/17<ins style="font-weight: bold; text-decoration: none;">, </ins>9/8<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"></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 twosquare chords include {{Optimal ET sequence| 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231 }}.</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 twosquare chords include {{Optimal ET sequence| 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231 }}.</div></td></tr> </table>

FloraC https://en.xen.wiki/index.php?title=Twosquare_chords&diff=127898&oldid=prev 2023-11-26T03:16:24Z

<p>Created page with &quot;&#039;&#039;&#039;Twosquare chords&#039;&#039;&#039; are <a href="/w/Dyadic_chord" title="Dyadic chord">essentially tempered chords</a> tempered by the twosquare comma, <a href="/w/1089/1088" title="1089/1088">1089/1088</a>. Twosquare chords are of Dyadic chord/Pattern of esse...&quot;</p> <p><b>New page</b></p><div>&#039;&#039;&#039;Twosquare chords&#039;&#039;&#039; are [[Dyadic chord|essentially tempered chords]] tempered by the twosquare comma, [[1089/1088]].<br /> <br /> Twosquare chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.3.11.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.<br /> <br /> For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is <br /> * 1-11/8-17/9 with steps of 11/8-11/8-18/17.<br /> <br /> The inversely related pair of chords is <br /> * 1-11/8-17/11 with steps of 11/8-9/8-22/17, and its inverse <br /> * 1-9/8-17/11 with steps of 9/8-11/8-22/17.<br /> <br /> For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are <br /> * 1-9/8-11/8-17/11 with steps of 9/8-11/9-9/8-22/17;<br /> * 1-9/8-16/11-17/11 with steps of 9/8-22/17-17/16-22/17.<br /> <br /> The inversely related pairs of chords are <br /> * 1-11/8-17/11-17/9 with steps of 11/8-9/8-11/9-18/17, and its inverse <br /> * 1-11/9-11/8-17/9 with steps of 11/9-9/8-11/8-18/17;<br /> * 1-11/8-16/9-17/9 with steps of 11/8-22/17-17/16-18/17, and its inverse <br /> * 1-17/16-11/8-17/9 with steps of 17/16-22/17-11/8-18/17.<br /> <br /> Then there is an inversely related pair of pentads: <br /> * 1-11/9-11/8-16/9-17/9 with steps of 11/9-9/8-22/17-17/16-18/17, and its inverse <br /> * 1-17/16-11/8-17/11-17/9 with steps of 17/16-22/17-9/8-11/9-18/17.<br /> <br /> Equal temperaments with twosquare chords include {{Optimal ET sequence| 22, 24, 41, 46, 65, 70, 89, 94, 111, 135, 159, 183, 207 and 231 }}.<br /> <br /> [[Category:17-odd-limit]]<br /> [[Category:Essentially tempered chords]]<br /> [[Category:Triads]]<br /> [[Category:Tetrads]]<br /> [[Category:Pentads]]<br /> [[Category:Twosquare]]</div>

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