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	<id>https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=Hydra</id>
	<title>Hydra - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=Hydra"/>
	<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Hydra&amp;action=history"/>
	<updated>2026-06-27T04:23:51Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Hydra&amp;diff=124493&amp;oldid=prev</id>
		<title>FloraC: Style</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Hydra&amp;diff=124493&amp;oldid=prev"/>
		<updated>2023-09-20T11:03:46Z</updated>

		<summary type="html">&lt;p&gt;Style&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;col class=&quot;diff-content&quot; /&gt;
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				&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 11:03, 20 September 2023&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 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;&amp;#039;Hydra&amp;#039;&amp;#039;&amp;#039; is a 9-note subset of [[17edo|17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&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;&amp;#039;Hydra&amp;#039;&amp;#039;&amp;#039; is a 9-note subset of [[17edo|17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Hydra was originally envisioned as the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://en.wikipedia.org/wiki/Union_&lt;/del&gt;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set_theory&lt;/del&gt;) union&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] &lt;/del&gt;of the [[5L 2s|diatonic]] [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;MOS&lt;/del&gt;]] and the [[Mohajira|rast]] [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;MODMOS&lt;/del&gt;]] in [[17edo]]. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Screamapillar|&lt;/del&gt;screamapillar]]), and therefore can do everything those scales can, and more.&lt;/div&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;Hydra was originally envisioned as the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{w|Union &lt;/ins&gt;(&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set theory&lt;/ins&gt;)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/ins&gt;union&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}} &lt;/ins&gt;of the [[5L 2s|diatonic]] [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mos&lt;/ins&gt;]] and the [[Mohajira|rast]] [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;modmos&lt;/ins&gt;]] in [[17edo]]. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[screamapillar]]), and therefore can do everything those scales can, and more.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &quot;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://en.wikipedia.org/wiki/The_Magical_Number_Seven&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;_Plus_or_Minus_Two &lt;/del&gt;seven plus or minus two&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;&quot; range.&lt;/div&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;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &quot;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{w|The Magical Number Seven&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Plus or Minus Two|&lt;/ins&gt;seven plus or minus two&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}}&lt;/ins&gt;&quot; range.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an [[MOS]]&lt;/del&gt;, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://en.wikipedia.org/wiki/Moment_&lt;/del&gt;(mathematics) moments&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;, where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2edo|&lt;/del&gt;2edo]].&lt;/div&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;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a mos&lt;/ins&gt;, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{w|Moment &lt;/ins&gt;(mathematics)&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/ins&gt;moments&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}}&lt;/ins&gt;, where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[2edo]].&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, &lt;/del&gt;with more than 7 pitches) scales are those that have a highly uneven, rather than maximally even or &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;MOS&lt;/del&gt;-like structures.&lt;/div&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;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i.e. with more than 7 pitches) scales are those that have a highly uneven, rather than maximally even or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mos&lt;/ins&gt;-like structures.&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;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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are analogues of hydra in other edos, too, obtained by fusing that edo&#039;s version of diatonic with its version of the rast &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;MODMOS&lt;/del&gt;. The [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;31edo|&lt;/del&gt;31edo]] version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[https://en.wikipedia.org/wiki/&lt;/del&gt;Xiangliu Xiangliu&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;. Both of these scales have four different step sizes, whereas hydra only has three.&lt;/div&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;There are analogues of hydra in other edos, too, obtained by fusing that edo&#039;s version of diatonic with its version of the rast &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;modmos&lt;/ins&gt;. The [[31edo]] version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{w|&lt;/ins&gt;Xiangliu&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/ins&gt;Xiangliu&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;}}&lt;/ins&gt;. Both of these scales have four different step sizes, whereas hydra only has three.&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;/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;[[Category:17edo]]&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;[[Category:17edo]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>FloraC</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Hydra&amp;diff=124471&amp;oldid=prev</id>
		<title>Sintel: add internal links</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Hydra&amp;diff=124471&amp;oldid=prev"/>
		<updated>2023-09-19T21:59:20Z</updated>

		<summary type="html">&lt;p&gt;add internal links&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&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 21:59, 19 September 2023&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 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;&amp;#039;Hydra&amp;#039;&amp;#039;&amp;#039; is a 9-note subset of [[17edo|17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&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;&amp;#039;Hydra&amp;#039;&amp;#039;&amp;#039; is a 9-note subset of [[17edo|17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Hydra was originally envisioned as the [https://en.wikipedia.org/wiki/Union_(set_theory) union] of the diatonic MOS and the [[Mohajira|rast]] MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[Screamapillar|screamapillar]]), and therefore can do everything those scales can, and more.&lt;/div&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;Hydra was originally envisioned as the [https://en.wikipedia.org/wiki/Union_(set_theory) union] of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[5L 2s|&lt;/ins&gt;diatonic&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] [[&lt;/ins&gt;MOS&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;and the [[Mohajira|rast]] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;MODMOS&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]] &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[&lt;/ins&gt;17edo&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[Screamapillar|screamapillar]]), and therefore can do everything those scales can, and more.&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;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;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &amp;quot;[https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two seven plus or minus two]&amp;quot; range.&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;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &amp;quot;[https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two seven plus or minus two]&amp;quot; range.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a &lt;/del&gt;MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using [https://en.wikipedia.org/wiki/Moment_(mathematics) moments], where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[2edo|2edo]].&lt;/div&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;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an [[&lt;/ins&gt;MOS&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using [https://en.wikipedia.org/wiki/Moment_(mathematics) moments], where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[2edo|2edo]].&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or fractal-like&lt;/del&gt;, rather than maximally even or MOS-like&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, structure&lt;/del&gt;.&lt;/div&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;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven, rather than maximally even or MOS-like &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;structures&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;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;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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Sintel</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Hydra&amp;diff=2182&amp;oldid=prev</id>
		<title>Wikispaces&gt;FREEZE at 00:00, 17 July 2018</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Hydra&amp;diff=2182&amp;oldid=prev"/>
		<updated>2018-07-17T00:00:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&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 00:00, 17 July 2018&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 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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;gt;&lt;/del&gt;&lt;/div&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;&#039;&lt;/ins&gt;Hydra&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039; &lt;/ins&gt;is a 9-note subset of [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17edo|&lt;/ins&gt;17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on &amp;lt;tt&amp;gt;2016-04-06 19:02:22 UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: The original revision id was &amp;lt;tt&amp;gt;579346205&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.&amp;lt;br&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;h4&amp;gt;Original Wikitext content:&amp;lt;/h4&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;div style=&quot;width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em&quot;&amp;gt;&amp;lt;pre style=&quot;margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important&quot; class=&quot;old-revision-html&quot;&amp;gt;**&lt;/del&gt;Hydra&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;** &lt;/del&gt;is a 9-note subset of [[17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Hydra was originally envisioned as the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[&lt;/del&gt;[https://en.wikipedia.org/wiki/Union_(set_theory)&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/del&gt;union&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;] of the diatonic MOS and the [[Mohajira|rast]] MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[screamapillar]]), and therefore can do everything those scales can, and more.&lt;/div&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;Hydra was originally envisioned as the [https://en.wikipedia.org/wiki/Union_(set_theory) union] of the diatonic MOS and the [[Mohajira|rast]] MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Screamapillar|&lt;/ins&gt;screamapillar]]), and therefore can do everything those scales can, and more.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &quot;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[&lt;/del&gt;[https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/del&gt;seven plus or minus two&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;]&quot; range.&lt;/div&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;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &quot;[https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two seven plus or minus two]&quot; range.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not a MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[&lt;/del&gt;[https://en.wikipedia.org/wiki/Moment_(mathematics)&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/del&gt;moments&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;], where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[2edo]].&lt;/div&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;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not a MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using [https://en.wikipedia.org/wiki/Moment_(mathematics) moments], where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2edo|&lt;/ins&gt;2edo]].&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;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;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven or fractal-like, rather than maximally even or MOS-like, structure.&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;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven or fractal-like, rather than maximally even or MOS-like, structure.&lt;/div&gt;&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-l18&quot;&gt;Line 18:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 11:&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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&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;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&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;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;There are analogues of hydra in other edos, too, obtained by fusing that edo&#039;s version of diatonic with its version of the rast MODMOS. The [[31edo]] version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[&lt;/del&gt;[https://en.wikipedia.org/wiki/Xiangliu&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/del&gt;Xiangliu&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;]. Both of these scales have four different step sizes, whereas hydra only has three.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;gt;&lt;/del&gt;&lt;/div&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;There are analogues of hydra in other edos, too, obtained by fusing that edo&#039;s version of diatonic with its version of the rast MODMOS. The [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;31edo|&lt;/ins&gt;31edo]] version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called [https://en.wikipedia.org/wiki/Xiangliu Xiangliu]. Both of these scales have four different step sizes, whereas hydra only has three.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;h4&amp;gt;Original HTML content:&amp;lt;/h4&amp;gt;&lt;/del&gt;&lt;/div&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;[[Category&lt;/ins&gt;:17edo&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;div style=&quot;width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em&quot;&amp;gt;&amp;lt;pre style=&quot;margin:0px;border:none;background:none;word-wrap:break-word;width&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;200%;white-space: pre-wrap ! important&quot; class=&quot;old-revision-html&quot;&amp;gt;&amp;amp;lt;html&amp;amp;gt;&amp;amp;lt;head&amp;amp;gt;&amp;amp;lt;title&amp;amp;gt;Hydra&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;&amp;amp;lt;strong&amp;amp;gt;Hydra&amp;amp;lt;/strong&amp;amp;gt; is a 9-note subset of &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/&lt;/del&gt;17edo&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;&amp;amp;gt;17edo&amp;amp;lt;/a&amp;amp;gt;, having step pattern 3 3 1 1 2 3 2 1 1.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Hydra was originally envisioned as the &amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://en.wikipedia.org/wiki/Union_(set_theory)&quot; rel=&quot;nofollow&quot;&amp;amp;gt;union&amp;amp;lt;/a&amp;amp;gt; of the diatonic MOS and the &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/Mohajira&quot;&amp;amp;gt;rast&amp;amp;lt;/a&amp;amp;gt; MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/&amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/screamapillar&quot;&amp;amp;gt;screamapillar&amp;amp;lt;/a&amp;amp;gt;), and therefore can do everything those scales can, and more.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &amp;amp;amp;quot;&amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two&quot; rel=&quot;nofollow&quot;&amp;amp;gt;seven plus or minus two&amp;amp;lt;/a&amp;amp;gt;&amp;amp;amp;quot; range.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not a MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using &amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://en.wikipedia.org/wiki/Moment_(mathematics)&quot; rel=&quot;nofollow&quot;&amp;amp;gt;moments&amp;amp;lt;/a&amp;amp;gt;, where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/2edo&quot;&amp;amp;gt;2edo&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven or fractal-like, rather than maximally even or MOS-like, structure.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;br /&amp;amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&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: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There are analogues of hydra in other edos, too, obtained by fusing that edo&#039;s version of diatonic with its version of the rast MODMOS. The &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/31edo&quot;&amp;amp;gt;31edo&amp;amp;lt;/a&amp;amp;gt; version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called &amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://en.wikipedia.org/wiki/Xiangliu&quot; rel=&quot;nofollow&quot;&amp;amp;gt;Xiangliu&amp;amp;lt;/a&amp;amp;gt;. Both of these scales have four different step sizes, whereas hydra only has three.&amp;amp;lt;/body&amp;amp;gt;&amp;amp;lt;/html&amp;amp;gt;&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;FREEZE</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Hydra&amp;diff=17626&amp;oldid=prev</id>
		<title>Wikispaces&gt;MasonGreen1: **Imported revision 579346205 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Hydra&amp;diff=17626&amp;oldid=prev"/>
		<updated>2016-04-06T19:02:22Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 579346205 - Original comment: **&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;gt;&lt;br /&gt;
This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;gt;&lt;br /&gt;
: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on &amp;lt;tt&amp;gt;2016-04-06 19:02:22 UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;gt;&lt;br /&gt;
: The original revision id was &amp;lt;tt&amp;gt;579346205&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;gt;&lt;br /&gt;
: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;gt;&lt;br /&gt;
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;lt;h4&amp;gt;Original Wikitext content:&amp;lt;/h4&amp;gt;&lt;br /&gt;
&amp;lt;div style=&amp;quot;width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em&amp;quot;&amp;gt;&amp;lt;pre style=&amp;quot;margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important&amp;quot; class=&amp;quot;old-revision-html&amp;quot;&amp;gt;**Hydra** is a 9-note subset of [[17edo]], having step pattern 3 3 1 1 2 3 2 1 1.&lt;br /&gt;
&lt;br /&gt;
Hydra was originally envisioned as the [[https://en.wikipedia.org/wiki/Union_(set_theory)|union]] of the diatonic MOS and the [[Mohajira|rast]] MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/[[screamapillar]]), and therefore can do everything those scales can, and more.&lt;br /&gt;
&lt;br /&gt;
As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &amp;quot;[[https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two|seven plus or minus two]]&amp;quot; range.&lt;br /&gt;
&lt;br /&gt;
Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not a MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using [[https://en.wikipedia.org/wiki/Moment_(mathematics)|moments]], where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid [[2edo]].&lt;br /&gt;
&lt;br /&gt;
This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven or fractal-like, rather than maximally even or MOS-like, structure.&lt;br /&gt;
&lt;br /&gt;
The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&lt;br /&gt;
&lt;br /&gt;
There are analogues of hydra in other edos, too, obtained by fusing that edo&amp;#039;s version of diatonic with its version of the rast MODMOS. The [[31edo]] version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called [[https://en.wikipedia.org/wiki/Xiangliu|Xiangliu]]. Both of these scales have four different step sizes, whereas hydra only has three.&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;gt;&lt;br /&gt;
&amp;lt;h4&amp;gt;Original HTML content:&amp;lt;/h4&amp;gt;&lt;br /&gt;
&amp;lt;div style=&amp;quot;width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em&amp;quot;&amp;gt;&amp;lt;pre style=&amp;quot;margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important&amp;quot; class=&amp;quot;old-revision-html&amp;quot;&amp;gt;&amp;amp;lt;html&amp;amp;gt;&amp;amp;lt;head&amp;amp;gt;&amp;amp;lt;title&amp;amp;gt;Hydra&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;&amp;amp;lt;strong&amp;amp;gt;Hydra&amp;amp;lt;/strong&amp;amp;gt; is a 9-note subset of &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/17edo&amp;quot;&amp;amp;gt;17edo&amp;amp;lt;/a&amp;amp;gt;, having step pattern 3 3 1 1 2 3 2 1 1.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
Hydra was originally envisioned as the &amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://en.wikipedia.org/wiki/Union_(set_theory)&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;union&amp;amp;lt;/a&amp;amp;gt; of the diatonic MOS and the &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Mohajira&amp;quot;&amp;amp;gt;rast&amp;amp;lt;/a&amp;amp;gt; MODMOS in 17edo. Since those two scales have five out of seven notes in common, this results in an enneatonic scale. In addition to diatonic and rast, hydra also contains a number of other very useful scales as subsets (such as bayati/&amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/screamapillar&amp;quot;&amp;amp;gt;screamapillar&amp;amp;lt;/a&amp;amp;gt;), and therefore can do everything those scales can, and more.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
As an enneatonic scale, hydra allows for a great deal more variety than heptatonic scales do, but with a relatively manageable number of pitches, and still fits within the &amp;amp;amp;quot;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://en.wikipedia.org/wiki/The_Magical_Number_Seven,_Plus_or_Minus_Two&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;seven plus or minus two&amp;amp;lt;/a&amp;amp;gt;&amp;amp;amp;quot; range.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
Perhaps the most immediately obvious feature of hydra that distinguishes it from more familiar scales is that it is not a MOS, or even close. In fact, the large and small steps tend to cluster together, resulting in a highly uneven scale. This unevenness can be analyzed using &amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://en.wikipedia.org/wiki/Moment_(mathematics)&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;moments&amp;amp;lt;/a&amp;amp;gt;, where the zeroth moment is simply the cardinality of the scale, the first moment is the tendency to form clusters separated by one period, the second moment the tendency to form clusters separated by 1/2 period, etc. As it turns out, hydra minimizes the first moment, but maximizes the second, so its pitches tend to fall near the notes of an overlaid &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/2edo&amp;quot;&amp;amp;gt;2edo&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
This unevenness is not necessarily a bad thing, since it adds more dynamic and contrast to the melody and causes the scale to have a more defined tonality. In fact, it may well be the case that the best-sounding large (i. e., with more than 7 pitches) scales are those that have a highly uneven or fractal-like, rather than maximally even or MOS-like, structure.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
The name hydra is a reference to the nine-headed beast of Greek mythology. Given that this scale was derived by merging together several heptatonic scales into one, the name of a multi-headed beast is particularly fitting.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
There are analogues of hydra in other edos, too, obtained by fusing that edo&amp;#039;s version of diatonic with its version of the rast MODMOS. The &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/31edo&amp;quot;&amp;amp;gt;31edo&amp;amp;lt;/a&amp;amp;gt; version (5 5 3 1 4 5 4 1 3) could be called Nāga; its smallest interval is a diesis, which makes it blatantly microtonal in a way that hydra is not. The 24edo version (4 4 2 1 3 4 3 1 2) could be called &amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://en.wikipedia.org/wiki/Xiangliu&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;Xiangliu&amp;amp;lt;/a&amp;amp;gt;. Both of these scales have four different step sizes, whereas hydra only has three.&amp;amp;lt;/body&amp;amp;gt;&amp;amp;lt;/html&amp;amp;gt;&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;gt;&lt;/div&gt;</summary>
		<author><name>Wikispaces&gt;MasonGreen1</name></author>
	</entry>
</feed>