https://en.xen.wiki/index.php?action=history&feed=atom&title=1-3-5-9_by_64%2F45_bihexany 2026-06-06T00:52:39Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=1-3-5-9_by_64/45_bihexany&diff=214696&oldid=prev 2025-10-26T18:32:19Z

<p>Create Page.</p> <p><b>New page</b></p><div>[[File:1-3-5-9_by_64-45_Bihexany.png|thumb|Circle diagram.]] A [[5-limit]] [[bihexany]] that is one of the simplest ways of detempering 12edo into a just intonation scale. This creates a scale of 1 16/15 9/8 32/27 5/4 4/3 64/45 3/2 8/5 5/3 16/9 15/8 2/1, with steps of 16/15 135/128 256/243 135/128 16/15 16/15 135/128 16/15 25/24 16/15 135/128 16/15. Initially, it might seem that using the inversion [[45/32]] as an offset interval would be simpler, and the two would ultimately create the same scale. However, this way around the ratios cancel out, making this mode more consonant overall. (The other way around would produce a most complex interval of 675/512.) The overall complexity of the ratios is still slightly greater than the [[1-3-5-9 by 7/5 bihexany]], but it makes up for this by having less severe wolf fifths, with 9 perfect ones, 2 flat by a [[syntonic comma]] and one sharp by a [[diaschisma]].<br /> <br /> &lt;pre&gt;<br /> ! 1-3-5-9_by_64/45_Hexany.scl<br /> !<br /> 1 3 5 9 by 64/45 2-combination Hexany<br /> 12<br /> !<br /> 111.731<br /> 203.910<br /> 294.134<br /> 386.313<br /> 498.044<br /> 609.776<br /> 701.955<br /> 813.686<br /> 884.358<br /> 996.089<br /> 1088.268<br /> &lt;/pre&gt;<br /> <br /> [[Category:Hexanies]]<br /> [[Category:12-tone scales]]<br /> [[Category:Pages with Scala files]]</div>

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