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	<id>https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=1-3-5-9-81_dekany</id>
	<title>1-3-5-9-81 dekany - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=1-3-5-9-81_dekany"/>
	<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;action=history"/>
	<updated>2026-07-03T19:41:19Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.43.6</generator>
	<entry>
		<id>https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=212007&amp;oldid=prev</id>
		<title>Yourmusic Productions: Add circle diagram.</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=212007&amp;oldid=prev"/>
		<updated>2025-10-05T08:20:18Z</updated>

		<summary type="html">&lt;p&gt;Add circle diagram.&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 08:20, 5 October 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[File:1-3-5-9-81_Dekany.png|thumb|Circle diagram.]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;A [[5-limit]] [[Dekany]] comprised of four simple numbers and one more complex one. This creates a scale of 1 135/128 9/8 5/4 81/64 3/2 5/3 27/16 15/18 243/128, with steps of 135/128 16/15 10/9 81/80 32/27 10/9 81/80 10/9 81/80 256/243. This creates a near-diatonic scale that instead of tempering out the syntonic comma, emphasises it, with three of the notes having [[3-limit]] and 5-limit variants that you can use to either create or evade dissonance. Since it lacks any kind of fourth, most diatonic music does not translate directly to it, but there are still many major and minor chords available, each with multiple variants that mean it should be possible to compose songs that would sound pleasing to listeners unfamiliar with microtonality rather than simply ambient pieces using this tuning.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;A [[5-limit]] [[Dekany]] comprised of four simple numbers and one more complex one. This creates a scale of 1 135/128 9/8 5/4 81/64 3/2 5/3 27/16 15/18 243/128, with steps of 135/128 16/15 10/9 81/80 32/27 10/9 81/80 10/9 81/80 256/243. This creates a near-diatonic scale that instead of tempering out the syntonic comma, emphasises it, with three of the notes having [[3-limit]] and 5-limit variants that you can use to either create or evade dissonance. Since it lacks any kind of fourth, most diatonic music does not translate directly to it, but there are still many major and minor chords available, each with multiple variants that mean it should be possible to compose songs that would sound pleasing to listeners unfamiliar with microtonality rather than simply ambient pieces using this tuning.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;pre&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;pre&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yourmusic Productions</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=208693&amp;oldid=prev</id>
		<title>Yourmusic Productions: Add music.</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=208693&amp;oldid=prev"/>
		<updated>2025-08-28T19:08:36Z</updated>

		<summary type="html">&lt;p&gt;Add music.&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;en&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:08, 28 August 2025&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l22&quot;&gt;Line 22:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 22:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;== Music ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;== Music ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;; [[Marcus Hobbs]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;; [[Marcus Hobbs]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &#039;&#039;[https://soundcloud.com/marcus_satellite/20180417-aks1-demo-dekany-1-3-5-9-81-00 20180417 Aks1 Demo Dekany 1 3 5 9 81 00]&#039;&#039;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;* &amp;#039;&amp;#039;[https://soundcloud.com/marcus_satellite/20180418-aks1-demo-dekany-1 20180418 Aks1 Demo Dekany 1 3 5 9 81 01]&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;* &amp;#039;&amp;#039;[https://soundcloud.com/marcus_satellite/20180418-aks1-demo-dekany-1 20180418 Aks1 Demo Dekany 1 3 5 9 81 01]&amp;#039;&amp;#039;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Yourmusic Productions</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=208690&amp;oldid=prev</id>
		<title>Yourmusic Productions: Create Page.</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=1-3-5-9-81_dekany&amp;diff=208690&amp;oldid=prev"/>
		<updated>2025-08-28T18:53:27Z</updated>

		<summary type="html">&lt;p&gt;Create Page.&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;A [[5-limit]] [[Dekany]] comprised of four simple numbers and one more complex one. This creates a scale of 1 135/128 9/8 5/4 81/64 3/2 5/3 27/16 15/18 243/128, with steps of 135/128 16/15 10/9 81/80 32/27 10/9 81/80 10/9 81/80 256/243. This creates a near-diatonic scale that instead of tempering out the syntonic comma, emphasises it, with three of the notes having [[3-limit]] and 5-limit variants that you can use to either create or evade dissonance. Since it lacks any kind of fourth, most diatonic music does not translate directly to it, but there are still many major and minor chords available, each with multiple variants that mean it should be possible to compose songs that would sound pleasing to listeners unfamiliar with microtonality rather than simply ambient pieces using this tuning.&lt;br /&gt;
&amp;lt;pre&amp;gt;&lt;br /&gt;
! 1-3-5-9-81_Dekany.scl&lt;br /&gt;
!&lt;br /&gt;
1 3 5 9 81 2-combination Dekany&lt;br /&gt;
10&lt;br /&gt;
!&lt;br /&gt;
135/128&lt;br /&gt;
9/8&lt;br /&gt;
5/4&lt;br /&gt;
81/64&lt;br /&gt;
3/2&lt;br /&gt;
5/3&lt;br /&gt;
27/16&lt;br /&gt;
15/8&lt;br /&gt;
243/128&lt;br /&gt;
2/1&lt;br /&gt;
&amp;lt;/pre&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Suggested keyboard mapping: C Db D Eb E G Ab A Bd B C. Note that this keeps the 3-limit intervals on the white notes and the 5-limit ones on the black notes, which makes navigation more intuitive. If you want to fill in the blank notes to expand it to a full 12 note scale, putting 4/3 on the F and 45/32 on the F# makes most sense.&lt;br /&gt;
&lt;br /&gt;
== Music ==&lt;br /&gt;
; [[Marcus Hobbs]]&lt;br /&gt;
* &amp;#039;&amp;#039;[https://soundcloud.com/marcus_satellite/20180418-aks1-demo-dekany-1 20180418 Aks1 Demo Dekany 1 3 5 9 81 01]&amp;#039;&amp;#039;&lt;br /&gt;
&lt;br /&gt;
[[Category:Dekanies]]&lt;br /&gt;
[[Category:10-tone scales]]&lt;br /&gt;
[[Category:Pages with Scala files]]&lt;/div&gt;</summary>
		<author><name>Yourmusic Productions</name></author>
	</entry>
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