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	<id>https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=Timbral_tuning</id>
	<title>Timbral tuning - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=Timbral_tuning"/>
	<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;action=history"/>
	<updated>2026-07-10T14:37:00Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=105000&amp;oldid=prev</id>
		<title>Fredg999 category edits: Categories</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=105000&amp;oldid=prev"/>
		<updated>2023-03-08T02:31:56Z</updated>

		<summary type="html">&lt;p&gt;Categories&lt;/p&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 02:31, 8 March 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-l8&quot;&gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&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;&amp;lt;ul&amp;gt;&amp;lt;li&amp;gt;[https://www.youtube.com/watch?v=xcSod-sj2CE The Hyperpiano] by Kevin Hobby and Bill Sethares&amp;lt;/li&amp;gt;&amp;lt;li&amp;gt;[[kai-metalbar-nonoct|A non-octave &amp;quot;tonality diamond&amp;quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/li&amp;gt;&amp;lt;/ul&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;ul&amp;gt;&amp;lt;li&amp;gt;[https://www.youtube.com/watch?v=xcSod-sj2CE The Hyperpiano] by Kevin Hobby and Bill Sethares&amp;lt;/li&amp;gt;&amp;lt;li&amp;gt;[[kai-metalbar-nonoct|A non-octave &amp;quot;tonality diamond&amp;quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/li&amp;gt;&amp;lt;/ul&amp;gt;&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;&lt;/ins&gt;&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;[[Category:Tuning]]&lt;/ins&gt;&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;[[Category:Timbre]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Fredg999 category edits</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=98696&amp;oldid=prev</id>
		<title>Kaiveran: Kaiveran moved page Generalized overtone tuning to Timbral tuning: As per Bullet51 on Discord</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=98696&amp;oldid=prev"/>
		<updated>2022-10-29T21:06:45Z</updated>

		<summary type="html">&lt;p&gt;Kaiveran moved page &lt;a href=&quot;/w/Generalized_overtone_tuning&quot; class=&quot;mw-redirect&quot; title=&quot;Generalized overtone tuning&quot;&gt;Generalized overtone tuning&lt;/a&gt; to &lt;a href=&quot;/w/Timbral_tuning&quot; title=&quot;Timbral tuning&quot;&gt;Timbral tuning&lt;/a&gt;: As per Bullet51 on Discord&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 21:06, 29 October 2022&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;[In need &lt;/del&gt;of a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;better name &lt;/del&gt;perhaps]&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;A possibility largely neglected until very recently due to a variety &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;factors, &#039;&#039;&#039;timbral tuning&#039;&#039;&#039; is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;system that takes into account the actual &quot;real-world&quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and &lt;/ins&gt;perhaps &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[Just_intonation|just]&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while timbral tuning can also embrace inharmonic sounds of any stripe.&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; 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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;takes into account the actual &lt;/del&gt;&quot;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;real&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;world&lt;/del&gt;&quot; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;overtone spectrum of any instrument or voice, be it real or virtual&lt;/del&gt;, and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;basis for &lt;/del&gt;tuning&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. This differs from [[Just_intonation|just]] or rational intonation, &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;while generalized overtone &lt;/del&gt;tuning &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can also embrace inharmonic sounds &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;any stripe. An important pioneer in this field is [[Bill_Sethares|Bill Sethares]]&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;(Note &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;what exactly &lt;/ins&gt;&quot;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;close&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;enough&lt;/ins&gt;&quot; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;means is debatable&lt;/ins&gt;, and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one could make the argument that &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;subtle form of timbral &lt;/ins&gt;tuning &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;arises &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;several instruments which display inharmonicity&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;such as the stretched &lt;/ins&gt;tuning of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a piano or the balancing act across a guitar&#039;s neck&lt;/ins&gt;.&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;&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and flat gongs. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and flat gongs. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;. An important pioneer in this field is [[Bill Sethares]]&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;&amp;#039;&amp;#039;&amp;#039;Works and Examples and Things&amp;#039;&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;&amp;#039;Works and Examples and Things&amp;#039;&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;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;ul&amp;gt;&amp;lt;li&amp;gt;[https://www.youtube.com/watch?v=xcSod-sj2CE The Hyperpiano] by Kevin Hobby and Bill Sethares&amp;lt;/li&amp;gt;&amp;lt;li&amp;gt;[[kai-metalbar-nonoct|A non-octave &amp;quot;tonality diamond&amp;quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/li&amp;gt;&amp;lt;/ul&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;ul&amp;gt;&amp;lt;li&amp;gt;[https://www.youtube.com/watch?v=xcSod-sj2CE The Hyperpiano] by Kevin Hobby and Bill Sethares&amp;lt;/li&amp;gt;&amp;lt;li&amp;gt;[[kai-metalbar-nonoct|A non-octave &amp;quot;tonality diamond&amp;quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/li&amp;gt;&amp;lt;/ul&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Kaiveran</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=98690&amp;oldid=prev</id>
		<title>Kaiveran: Kaiveran moved page Generalized overtone tuning to Timbral tuning: As per Bullet51 on Discord</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=98690&amp;oldid=prev"/>
		<updated>2022-10-29T21:01:30Z</updated>

		<summary type="html">&lt;p&gt;Kaiveran moved page &lt;a href=&quot;/w/Generalized_overtone_tuning&quot; class=&quot;mw-redirect&quot; title=&quot;Generalized overtone tuning&quot;&gt;Generalized overtone tuning&lt;/a&gt; to &lt;a href=&quot;/w/Timbral_tuning&quot; title=&quot;Timbral tuning&quot;&gt;Timbral tuning&lt;/a&gt;: As per Bullet51 on Discord&lt;/p&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 21:01, 29 October 2022&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;en&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Kaiveran</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=1980&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=Timbral_tuning&amp;diff=1980&amp;oldid=prev"/>
		<updated>2018-07-17T00:00:00Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&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;[In need of a better name perhaps]&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:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-11-28 01:31:24 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;622564417&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;[In need of a better name perhaps]&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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &quot;real-world&quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;xenharmonic/Just intonation&lt;/del&gt;|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &quot;real-world&quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Just_intonation&lt;/ins&gt;|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Bill_Sethares|&lt;/ins&gt;Bill Sethares]].&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 resources of these kinds of tunings are theoretically as rich as those of JI. In practice, resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and flat gongs. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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 resources of these kinds of tunings are theoretically as rich as those of JI. In practice, resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and flat gongs. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;**&lt;/del&gt;Works and Examples and Things&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&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;Works and Examples and Things&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;&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;* [&lt;/del&gt;[https://www.youtube.com/watch?v=xcSod-sj2CE&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;|&lt;/del&gt;The Hyperpiano&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&lt;/del&gt;] by Kevin Hobby and Bill Sethares&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;/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;* &lt;/del&gt;[[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;xenharmonic/&lt;/del&gt;kai-metalbar-nonoct|A non-octave &quot;tonality diamond&quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;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;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ul&amp;gt;&amp;lt;li&amp;gt;&lt;/ins&gt;[https://www.youtube.com/watch?v=xcSod-sj2CE The Hyperpiano] by Kevin Hobby and Bill Sethares&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/li&amp;gt;&amp;lt;li&amp;gt;&lt;/ins&gt;[[kai-metalbar-nonoct|A non-octave &quot;tonality diamond&quot;]] based on the spectrum of a metal bar free to vibrate at both ends&amp;lt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;li&lt;/ins&gt;&amp;gt;&amp;lt;/ul&amp;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;h4&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Original HTML content:&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/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;width: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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;http://xenharmonic.wikispaces.com/Just%20intonation&quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/Bill%20Sethares&quot;&amp;amp;gt;Bill Sethares&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and flat gongs. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;&amp;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&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;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://www.youtube.com/watch?v=xcSod-sj2CE&quot; rel=&quot;nofollow&quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;http://xenharmonic.wikispaces.com/kai-metalbar-nonoct&quot;&amp;amp;gt;A non-octave &amp;amp;amp;quot;tonality diamond&amp;amp;amp;quot;&amp;amp;lt;/a&amp;amp;gt; based on the spectrum of a metal bar free to vibrate at both ends&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;&lt;/del&gt;/ul&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;gt;&amp;amp;lt;/body&amp;amp;gt;&amp;amp;lt;/html&amp;amp;gt;&amp;lt;/pre&amp;gt;&amp;lt;/div&lt;/del&gt;&amp;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=Timbral_tuning&amp;diff=16514&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 622564417 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16514&amp;oldid=prev"/>
		<updated>2017-11-28T01:31:24Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 622564417 - Original comment: **&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 01:31, 28 November 2017&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;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&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;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;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;: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;04&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12 20&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;23&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;06 &lt;/del&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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 revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;11&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;28 01&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;31&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;24 &lt;/ins&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;610762773&lt;/del&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;622564417&lt;/ins&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;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;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;/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 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;/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-l10&quot;&gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, snare drums &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the like&lt;/del&gt;. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and &lt;/ins&gt;it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;flat gongs&lt;/ins&gt;. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;**Works and Examples and Things**&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;**Works and Examples and Things**&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-l20&quot;&gt;Line 20:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 20:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, snare drums &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the like&lt;/del&gt;. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;resources are limited by the number of identifiable overtones in the source timbre (plus the accuracy of their measure or definition), and &lt;/ins&gt;it may not prove fruitful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;flat gongs&lt;/ins&gt;. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;amp;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;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://www.youtube.com/watch?v=xcSod-sj2CE&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/kai-metalbar-nonoct&amp;quot;&amp;amp;gt;A non-octave &amp;amp;amp;quot;tonality diamond&amp;amp;amp;quot;&amp;amp;lt;/a&amp;amp;gt; based on the spectrum of a metal bar free to vibrate at both ends&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&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;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://www.youtube.com/watch?v=xcSod-sj2CE&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/kai-metalbar-nonoct&amp;quot;&amp;amp;gt;A non-octave &amp;amp;amp;quot;tonality diamond&amp;amp;amp;quot;&amp;amp;lt;/a&amp;amp;gt; based on the spectrum of a metal bar free to vibrate at both ends&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;kai.lugheidh</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16515&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 610762773 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16515&amp;oldid=prev"/>
		<updated>2017-04-12T20:23:06Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 610762773 - Original comment: **&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 20:23, 12 April 2017&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;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&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;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;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;: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;03&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17 00&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;30&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;07 &lt;/del&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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 revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;04&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12 20&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;23&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;06 &lt;/ins&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608990879&lt;/del&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;610762773&lt;/ins&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;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;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;/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 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;/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-l10&quot;&gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;very useful &lt;/del&gt;for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fruitful &lt;/ins&gt;for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;**Works and Examples and Things**&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;**Works and Examples and Things**&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;* [[https://www.youtube.com/watch?v=xcSod-sj2CE|The Hyperpiano]] by Kevin Hobby and Bill Sethares&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;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;* [[https://www.youtube.com/watch?v=xcSod-sj2CE|The Hyperpiano]] by Kevin Hobby and Bill Sethares&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;* [[xenharmonic/kai-metalbar-nonoct|A non-octave &quot;tonality diamond&quot;]] based on the spectrum of a metal bar free to vibrate at both ends&lt;/ins&gt;&amp;lt;/pre&amp;gt;&amp;lt;/div&amp;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;lt;h4&amp;gt;Original HTML content:&amp;lt;/h4&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;h4&amp;gt;Original HTML content:&amp;lt;/h4&amp;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;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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&amp;amp;lt;br /&amp;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;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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&amp;amp;lt;br /&amp;amp;gt;&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-l19&quot;&gt;Line 19:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 20:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessarily limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;very useful &lt;/del&gt;for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fruitful &lt;/ins&gt;for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;amp;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;&amp;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://www.youtube.com/watch?v=xcSod-sj2CE&quot; rel=&quot;nofollow&quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&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;&amp;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&quot;wiki_link_ext&quot; href=&quot;https://www.youtube.com/watch?v=xcSod-sj2CE&quot; rel=&quot;nofollow&quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;http://xenharmonic.wikispaces.com/kai-metalbar-nonoct&quot;&amp;amp;gt;A non-octave &amp;amp;amp;quot;tonality diamond&amp;amp;amp;quot;&amp;amp;lt;/a&amp;amp;gt; based on the spectrum of a metal bar free to vibrate at both ends&lt;/ins&gt;&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;kai.lugheidh</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16516&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 608990879 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16516&amp;oldid=prev"/>
		<updated>2017-03-17T00:30:07Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 608990879 - Original comment: **&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 00:30, 17 March 2017&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;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&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;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;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;: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;16 19&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;02 &lt;/del&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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 revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;17 00&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;30&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;07 &lt;/ins&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608982615&lt;/del&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608990879&lt;/ins&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;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;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;/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 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;/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-l8&quot;&gt;Line 8:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 8:&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;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;[In need of a better name perhaps]&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;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;[In need of a better name perhaps]&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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &quot;real-world&quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;necessary &lt;/del&gt;limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &quot;real-world&quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;necessarily &lt;/ins&gt;limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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 resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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 resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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-l17&quot;&gt;Line 17:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 17:&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;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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&amp;amp;lt;br /&amp;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;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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;http://xenharmonic.wikispaces.com/Just%20intonation&quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;necessary &lt;/del&gt;limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/Bill%20Sethares&quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;http://xenharmonic.wikispaces.com/Just%20intonation&quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;necessarily &lt;/ins&gt;limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&quot;wiki_link&quot; href=&quot;/Bill%20Sethares&quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;kai.lugheidh</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16517&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 608982615 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16517&amp;oldid=prev"/>
		<updated>2017-03-16T19:12:02Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 608982615 - Original comment: **&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;
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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 19:12, 16 March 2017&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;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&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;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;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;: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-16 19:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;07&lt;/del&gt;:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;05 &lt;/del&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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 revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-16 19:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;12&lt;/ins&gt;:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;02 &lt;/ins&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608982469&lt;/del&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608982615&lt;/ins&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;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;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;/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 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;/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-l10&quot;&gt;Line 10:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 10:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&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;The resources of these kinds of tunings are theoretically as rich &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and complex &lt;/del&gt;as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&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;**Works and Examples and Things**&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;**Works and Examples and Things**&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-l19&quot;&gt;Line 19:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 19:&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 possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;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;A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&amp;amp;lt;/a&amp;amp;gt;.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and complex &lt;/del&gt;as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;The resources of these kinds of tunings are theoretically as rich as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;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;amp;lt;br /&amp;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;amp;lt;br /&amp;amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;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;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;amp;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;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://www.youtube.com/watch?v=xcSod-sj2CE&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&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;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://www.youtube.com/watch?v=xcSod-sj2CE&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;kai.lugheidh</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16518&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 608982469 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16518&amp;oldid=prev"/>
		<updated>2017-03-16T19:07:05Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 608982469 - Original comment: **&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 19:07, 16 March 2017&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;lt;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&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;h2&amp;gt;IMPORTED REVISION FROM WIKISPACES&amp;lt;/h2&amp;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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&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;This is an imported revision from Wikispaces. The revision metadata is included below for reference:&amp;lt;br&amp;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;: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-16 19:07:&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;04 &lt;/del&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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 revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-16 19:07:&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;05 &lt;/ins&gt;UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608982465&lt;/del&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The original revision id was &amp;lt;tt&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;608982469&lt;/ins&gt;&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&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;: The revision comment was: &amp;lt;tt&amp;gt;&amp;lt;/tt&amp;gt;&amp;lt;br&amp;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;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;/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 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;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Wikispaces&gt;kai.lugheidh</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16519&amp;oldid=prev</id>
		<title>Wikispaces&gt;kai.lugheidh: **Imported revision 608982465 - Original comment: **</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Timbral_tuning&amp;diff=16519&amp;oldid=prev"/>
		<updated>2017-03-16T19:07:04Z</updated>

		<summary type="html">&lt;p&gt;**Imported revision 608982465 - 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:kai.lugheidh|kai.lugheidh]] and made on &amp;lt;tt&amp;gt;2017-03-16 19:07:04 UTC&amp;lt;/tt&amp;gt;.&amp;lt;br&amp;gt;&lt;br /&gt;
: The original revision id was &amp;lt;tt&amp;gt;608982465&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;[In need of a better name perhaps]&lt;br /&gt;
&lt;br /&gt;
A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;quot;real-world&amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from [[xenharmonic/Just intonation|just]] or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is [[Bill Sethares]].&lt;br /&gt;
&lt;br /&gt;
The resources of these kinds of tunings are theoretically as rich and complex as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&lt;br /&gt;
&lt;br /&gt;
**Works and Examples and Things**&lt;br /&gt;
* [[https://www.youtube.com/watch?v=xcSod-sj2CE|The Hyperpiano]] by Kevin Hobby and Bill Sethares&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;Generalized overtone tuning&amp;amp;lt;/title&amp;amp;gt;&amp;amp;lt;/head&amp;amp;gt;&amp;amp;lt;body&amp;amp;gt;[In need of a better name perhaps]&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
A possibility largely neglected until very recently due to a variety of factors, generalized overtone tuning is a system that takes into account the actual &amp;amp;amp;quot;real-world&amp;amp;amp;quot; overtone spectrum of any instrument or voice, be it real or virtual, and uses intervals between these overtones (and perhaps their multiples, quotients, inverses, etc) as a basis for tuning. This differs from &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;http://xenharmonic.wikispaces.com/Just%20intonation&amp;quot;&amp;amp;gt;just&amp;amp;lt;/a&amp;amp;gt; or rational intonation, in that JI only accepts integer relations and thus necessary limits its purview to harmonic (or close-enough) timbres, while generalized overtone tuning can also embrace inharmonic sounds of any stripe. An important pioneer in this field is &amp;amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Bill%20Sethares&amp;quot;&amp;amp;gt;Bill Sethares&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;
The resources of these kinds of tunings are theoretically as rich and complex as those of JI. In practice, it may not prove very useful for very noisy or dense timbres that fail to give an impression of definite pitch, such as cymbals, snare drums and the like. Nevertheless, it may be far too early to make any definite judgements about so young a field, and it is undoubtedly ripe for exploration.&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;strong&amp;amp;gt;Works and Examples and Things&amp;amp;lt;/strong&amp;amp;gt;&amp;amp;lt;br /&amp;amp;gt;&lt;br /&gt;
&amp;amp;lt;ul&amp;amp;gt;&amp;amp;lt;li&amp;amp;gt;&amp;amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;https://www.youtube.com/watch?v=xcSod-sj2CE&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;amp;gt;The Hyperpiano&amp;amp;lt;/a&amp;amp;gt; by Kevin Hobby and Bill Sethares&amp;amp;lt;/li&amp;amp;gt;&amp;amp;lt;/ul&amp;amp;gt;&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;kai.lugheidh</name></author>
	</entry>
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