https://en.xen.wiki/index.php?action=history&feed=atom&title=Ed8%2F3_and_beyond 2026-07-01T11:59:36Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=206124&oldid=prev 2025-08-02T00:05:09Z

<p>Todo</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 00:05, 2 August 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Line 16:</td> <td colspan="2" class="diff-lineno">Line 16:</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>[[Category:Nonoctave]]</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:Nonoctave]]</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;">{{todo|improve synopsis}}</ins></div></td></tr> </table>

BudjarnLambeth https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=112428&oldid=prev 2023-05-07T06:53:40Z

<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 06:53, 7 May 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>Equal divisions of [[8/3]] and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that <del style="font-weight: bold; text-decoration: none;">''</del>it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done<del style="font-weight: bold; text-decoration: none;">''</del>. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of [[8/3]] and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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>*[[Ed8/3|Equal divisions of 8/3]]</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>*[[Ed8/3|Equal divisions of 8/3]]</div></td></tr> </table>

CompactStar https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=112427&oldid=prev 2023-05-07T06:53:22Z

<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 06:53, 7 May 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>Equal divisions of [[8/3]] and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that &#039;&#039;it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done&#039;&#039;. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of [[8/3]] and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that &#039;&#039;it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done&#039;&#039;. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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>*[[Ed8/3|Equal divisions of <del style="font-weight: bold; text-decoration: none;">the </del>8/3]]</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>*[[Ed8/3|Equal divisions of 8/3]]</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;"><div>*[[Ed20/7|Equal divisions of 20/7]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Ed20/7|Equal divisions of 20/7]]</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[[Edt|Equal divisions of the tritave]]</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>*[[Edt|Equal divisions of the tritave]]</div></td></tr> </table>

CompactStar https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=112426&oldid=prev 2023-05-07T06:53:18Z

<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 06:53, 7 May 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>Equal divisions of <del style="font-weight: bold; text-decoration: none;">elevenths (e. g. </del>8/3<del style="font-weight: bold; text-decoration: none;">) </del>and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of <ins style="font-weight: bold; text-decoration: none;">[[</ins>8/3<ins style="font-weight: bold; text-decoration: none;">]] </ins>and beyond can be conceived of as to use one interval of these as an [[equivalence]], or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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;">EdXI</del>|Equal divisions of <del style="font-weight: bold; text-decoration: none;">elevenths (e. g. </del>8/3<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>*[[<ins style="font-weight: bold; text-decoration: none;">Ed8/3</ins>|Equal divisions of <ins style="font-weight: bold; text-decoration: none;">the </ins>8/3]]</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;">EdXII</del>|Equal divisions of <del style="font-weight: bold; text-decoration: none;">twelfths (e. g. 3/1 and </del>20/7<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>*[[<ins style="font-weight: bold; text-decoration: none;">Ed20/7</ins>|Equal divisions of 20/7]]</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">*</del>*[[Edt|Equal divisions of the tritave]]</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>*[[Edt|Equal divisions of the tritave]]</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;">EdXIII</del>|Equal <del style="font-weight: bold; text-decoration: none;">divisions </del>of <del style="font-weight: bold; text-decoration: none;">thirteenths (e. g. </del>10/3<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>*[[<ins style="font-weight: bold; text-decoration: none;">Ed10/3</ins>|Equal <ins style="font-weight: bold; text-decoration: none;">division </ins>of 10/3]]</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;">EdXIV</del>|Equal <del style="font-weight: bold; text-decoration: none;">divisions </del>of <del style="font-weight: bold; text-decoration: none;">fourteenths (e. g. </del>7/2<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>*[[<ins style="font-weight: bold; text-decoration: none;">Ed7/2</ins>|Equal <ins style="font-weight: bold; text-decoration: none;">division </ins>of 7/2<ins style="font-weight: bold; text-decoration: none;">]]</ins></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;">*[[Ed4|Equal division of the double octave</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>*[[Ed5|Equal divisions of the fifth harmonic]]</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>*[[Ed5|Equal divisions of the fifth harmonic]]</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>*[[Ed6|Equal divisions of the sixth harmonic]]</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>*[[Ed6|Equal divisions of the sixth harmonic]]</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12">Line 12:</td> <td colspan="2" class="diff-lineno">Line 13:</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>*[[Ed11|Equal divisions of the eleventh harmonic]]</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>*[[Ed11|Equal divisions of the eleventh harmonic]]</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>*[[Ed12|Equal divisions of the twelfth harmonic]]</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>*[[Ed12|Equal divisions of the twelfth harmonic]]</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>*[[Equal divisions of the thirteenth harmonic]]</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;">Ed13|</ins>Equal divisions of the thirteenth harmonic]]</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>[[Category:Nonoctave]]</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:Nonoctave]]</div></td></tr> </table>

CompactStar https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=112423&oldid=prev 2023-05-07T06:50:36Z

<p>CompactStar moved page <a href="/index.php?title=EdXI_and_beyond&amp;action=edit&amp;redlink=1" class="new" title="EdXI and beyond (page does not exist)">EdXI and beyond</a> to <a href="/w/Ed8/3_and_beyond" title="Ed8/3 and beyond">Ed8/3 and beyond</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 06:50, 7 May 2023</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

CompactStar https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=86022&oldid=prev 2022-02-14T13:08:00Z

<p>+category,+link</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 13:08, 14 February 2022</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>Equal divisions of elevenths (e. g. 8/3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of elevenths (e. g. 8/3) and beyond can be conceived of as to use one interval of these as an <ins style="font-weight: bold; text-decoration: none;">[[</ins>equivalence<ins style="font-weight: bold; text-decoration: none;">]]</ins>, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1946 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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>*[[EdXI|Equal divisions of elevenths (e. g. 8/3)]]</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>*[[EdXI|Equal divisions of elevenths (e. g. 8/3)]]</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td> <td colspan="2" class="diff-lineno">Line 13:</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>*[[Ed12|Equal divisions of the twelfth harmonic]]</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>*[[Ed12|Equal divisions of the twelfth harmonic]]</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>*[[Equal divisions of the thirteenth harmonic]]</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 divisions of the thirteenth harmonic]]</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></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;">[[Category:Nonoctave]]</ins></div></td></tr> </table>

Dummy index https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=41161&oldid=prev 2019-03-25T13:22:10Z

<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 13:22, 25 March 2019</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11">Line 11:</td> <td colspan="2" class="diff-lineno">Line 11:</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>*[[Ed10|Equal divisions of the tenth harmonic]]</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>*[[Ed10|Equal divisions of the tenth harmonic]]</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>*[[Ed11|Equal divisions of the eleventh harmonic]]</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>*[[Ed11|Equal divisions of the eleventh harmonic]]</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;">*[[Ed12|Equal divisions of the twelfth harmonic]]</ins></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;">*[[Equal divisions of the thirteenth harmonic]]</ins></div></td></tr> </table>

Moremajorthanmajor https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=41160&oldid=prev 2019-03-25T13:17:48Z

<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 13:17, 25 March 2019</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>Equal divisions of elevenths (e. g. 8/3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as <del style="font-weight: bold; text-decoration: none;">1947 </del>cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of elevenths (e. g. 8/3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as <ins style="font-weight: bold; text-decoration: none;">1946 </ins>cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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>*[[EdXI|Equal divisions of elevenths (e. g. 8/3)]]</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>*[[EdXI|Equal divisions of elevenths (e. g. 8/3)]]</div></td></tr> </table>

Moremajorthanmajor https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=39865&oldid=prev 2019-01-30T07:10:51Z

<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 07:10, 30 January 2019</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>Equal divisions of elevenths (e. g. 8<del style="font-weight: bold; text-decoration: none;">:</del>3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1947 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of elevenths (e. g. 8<ins style="font-weight: bold; text-decoration: none;">/</ins>3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as 1947 cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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;">&lt;ul&gt;&lt;li&gt;</del>[[EdXI|Equal divisions of elevenths (e. g. 8<del style="font-weight: bold; text-decoration: none;">:</del>3)]]<del style="font-weight: bold; text-decoration: none;">&lt;/li&gt;&lt;li&gt;</del>[[EdXII|Equal divisions of twelfths]]</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>[[EdXI|Equal divisions of elevenths (e. g. 8<ins style="font-weight: bold; text-decoration: none;">/</ins>3)]]</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;">&lt;li&gt;</del>[[<del style="font-weight: bold; text-decoration: none;">edt</del>|Equal divisions of the tritave]]</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>[[EdXII|Equal divisions of twelfths <ins style="font-weight: bold; text-decoration: none;">(e. g. 3/1 and 20/7)</ins>]]</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;">&lt;/li&gt;&lt;/li&gt;&lt;li&gt;</del>[[EdXIII|Equal divisions of thirteenths (e. g. 10/3)]]<del style="font-weight: bold; text-decoration: none;">&lt;/li&gt;&lt;li&gt;</del>[[EdXIV|Equal divisions of fourteenths (e. g. 7/2)]]</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>[[<ins style="font-weight: bold; text-decoration: none;">Edt</ins>|Equal divisions of the tritave]]</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;">&lt;/li&gt;&lt;li&gt;</del>[[<del style="font-weight: bold; text-decoration: none;">ed5</del>|Equal divisions of the fifth harmonic]]</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>[[EdXIII|Equal divisions of thirteenths (e. g. 10/3)]]</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;">&lt;/li&gt;&lt;li&gt;</del>[[<del style="font-weight: bold; text-decoration: none;">ed6</del>|Equal divisions of the sixth harmonic]]<del style="font-weight: bold; text-decoration: none;">&lt;/li&gt;&lt;li&gt;</del>[[<del style="font-weight: bold; text-decoration: none;">ed7</del>|Equal divisions of the seventh harmonic]]<del style="font-weight: bold; text-decoration: none;">&lt;/li&gt;&lt;li&gt;</del>[[Ed10|Equal divisions of the tenth harmonic]]</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>[[EdXIV|Equal divisions of fourteenths (e. g. 7/2)]]</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;">&lt;/li&gt;&lt;li&gt;</del>[[Ed11|Equal divisions of the eleventh harmonic]]</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>[[<ins style="font-weight: bold; text-decoration: none;">Ed5</ins>|Equal divisions of the fifth harmonic]]</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;">&lt;/li&gt;&lt;/ul&gt;</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;">*</ins>[[<ins style="font-weight: bold; text-decoration: none;">Ed6</ins>|Equal divisions of the sixth harmonic]]</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>[[<ins style="font-weight: bold; text-decoration: none;">Ed7</ins>|Equal divisions of the seventh harmonic]]</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>[[Ed10|Equal divisions of the tenth harmonic]]</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>[[Ed11|Equal divisions of the eleventh harmonic]]</div></td></tr> </table>

Xenllium https://en.xen.wiki/index.php?title=Ed8/3_and_beyond&diff=39843&oldid=prev 2019-01-29T22:13:16Z

<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 22:13, 29 January 2019</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>Equal divisions of elevenths (e. g. 8:3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as <del style="font-weight: bold; text-decoration: none;">1923.5 </del>cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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 divisions of elevenths (e. g. 8:3) and beyond can be conceived of as to use one interval of these as an equivalence, or not. However, the utility of such intervals as bases is limited by the fact that ''it is generally difficult for a singer to reach much more than an augmented tenth (in theory as wide as <ins style="font-weight: bold; text-decoration: none;">1947 </ins>cents) above a given note (at least very reliably) without prior training and it is nevertheless not even very dramatic to do it regardless of how reliably it is done''. In particular, the eleventh is slightly complicated to use as a base because it is a suspension of the major third or a compound tritone when it appears in common practice. Even so, a few such wider intervals (they not being powers of rational intervals 1680 cents or narrower) have seen their uses:</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>&lt;ul&gt;&lt;li&gt;[[edt|Equal divisions of the tritave]]&lt;/li&gt;&lt;li&gt;[[ed5|Equal divisions of the fifth harmonic]]&lt;/li&gt;&lt;li&gt;[[ed6|Equal divisions of the sixth harmonic]]&lt;/li&gt;&lt;li&gt;[[ed7|Equal divisions of the seventh harmonic]]&lt;/li&gt;&lt;/ul&gt;</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>&lt;ul&gt;<ins style="font-weight: bold; text-decoration: none;">&lt;li&gt;[[EdXI|Equal divisions of elevenths (e. g. 8:3)]]&lt;/li&gt;&lt;li&gt;[[EdXII|Equal divisions of twelfths]]</ins></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>&lt;li&gt;[[edt|Equal divisions of the tritave]]</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;">&lt;/li&gt;&lt;/li&gt;&lt;li&gt;[[EdXIII|Equal divisions of thirteenths (e. g. 10/3)]]&lt;/li&gt;&lt;li&gt;[[EdXIV|Equal divisions of fourteenths (e. g. 7/2)]]</ins></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>&lt;/li&gt;&lt;li&gt;[[ed5|Equal divisions of the fifth harmonic]]</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>&lt;/li&gt;&lt;li&gt;[[ed6|Equal divisions of the sixth harmonic]]&lt;/li&gt;&lt;li&gt;[[ed7|Equal divisions of the seventh harmonic]]<ins style="font-weight: bold; text-decoration: none;">&lt;/li&gt;&lt;li&gt;[[Ed10|Equal divisions of the tenth harmonic]]</ins></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;">&lt;/li&gt;&lt;li&gt;[[Ed11|Equal divisions of the eleventh harmonic]]</ins></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>&lt;/li&gt;&lt;/ul&gt;</div></td></tr> </table>

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