https://en.xen.wiki/index.php?action=history&feed=atom&title=3-5-15-19_by_9%2F8_bihexany 2026-06-06T05:31:29Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=3-5-15-19_by_9/8_bihexany&diff=217716&oldid=prev 2025-11-25T22:43:28Z

<p>Linking.</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 22:43, 25 November 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>[[File:3-5-15-19_by_9-8_Bihexany.png|thumb|Circle diagram.]] A [[19-limit]] [[bihexany]]. This creates a scale of 1 171/160 9/8 19/16 5/4 171/128 45/32 3/2 19/12 27/16 57/32 19/10 2/1, with steps of 171/160 20/19 19/18 20/19 171/160 20/19 16/15 19/18 81/76 19/18 16/15 20/19. Since the <del style="font-weight: bold; text-decoration: none;">basic </del>hexany maps neatly to the augmented scale, this degree of offset works well to provide a just 12 note scale that fits a regular keyboard unambiguously with many consonant chords. 6 notes have perfect 3/2's above them, a 7th has a 256/171 fifth that is indistinguishable from just to most ears, <del style="font-weight: bold; text-decoration: none;">3 have </del>flat <del style="font-weight: bold; text-decoration: none;">wolf fifths </del>and 2 <del style="font-weight: bold; text-decoration: none;">have sharp wolf fifths</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>[[File:3-5-15-19_by_9-8_Bihexany.png|thumb|Circle diagram.]] A [[19-limit]] [[bihexany]]. This creates a scale of 1 171/160 9/8 19/16 5/4 171/128 45/32 3/2 19/12 27/16 57/32 19/10 2/1, with steps of 171/160 20/19 19/18 20/19 171/160 20/19 16/15 19/18 81/76 19/18 16/15 20/19. Since the <ins style="font-weight: bold; text-decoration: none;">[[3-5-15-19 </ins>hexany<ins style="font-weight: bold; text-decoration: none;">|base hexany]] </ins>maps neatly to the augmented scale, this degree of offset works well to provide a just 12 note scale that fits a regular keyboard unambiguously with many consonant chords. 6 notes have perfect 3/2's above them, a 7th has a 256/171 fifth that is indistinguishable from just to most ears, <ins style="font-weight: bold; text-decoration: none;">2 are sharp and 1 is </ins>flat <ins style="font-weight: bold; text-decoration: none;">by [[76/75]], </ins>and 2 <ins style="font-weight: bold; text-decoration: none;">are flat by a [[syntonic comma]], creating obvious wolves if used to create 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;"><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>&lt;pre&gt;</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>&lt;pre&gt;</div></td></tr> </table>

Yourmusic Productions https://en.xen.wiki/index.php?title=3-5-15-19_by_9/8_bihexany&diff=212333&oldid=prev 2025-10-08T09:19:46Z

<p>Create Page.</p> <p><b>New page</b></p><div>[[File:3-5-15-19_by_9-8_Bihexany.png|thumb|Circle diagram.]] A [[19-limit]] [[bihexany]]. This creates a scale of 1 171/160 9/8 19/16 5/4 171/128 45/32 3/2 19/12 27/16 57/32 19/10 2/1, with steps of 171/160 20/19 19/18 20/19 171/160 20/19 16/15 19/18 81/76 19/18 16/15 20/19. Since the basic hexany maps neatly to the augmented scale, this degree of offset works well to provide a just 12 note scale that fits a regular keyboard unambiguously with many consonant chords. 6 notes have perfect 3/2&#039;s above them, a 7th has a 256/171 fifth that is indistinguishable from just to most ears, 3 have flat wolf fifths and 2 have sharp wolf fifths.<br /> <br /> &lt;pre&gt;<br /> ! 3-5-15-19_by_9/8_Bihexany.scl<br /> !<br /> 3 5 15 19 2-combination Hexany<br /> 12<br /> !<br /> 115.109<br /> 203.910<br /> 297.513<br /> 386.313<br /> 501.423<br /> 590.223<br /> 701.955<br /> 795.558<br /> 905.865<br /> 999.468<br /> 1111.199<br /> 1200<br /> &lt;/pre&gt;<br /> <br /> <br /> [[Category:Hexanies]]<br /> [[Category:12-tone scales]]<br /> [[Category:Pages with Scala files]]</div>

Yourmusic Productions