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	<id>https://en.xen.wiki/index.php?action=history&amp;feed=atom&amp;title=User%3AContribution%2FLogarithmic_constants_VS_acoustic_constants_%28opinion_piece_article%29</id>
	<title>User:Contribution/Logarithmic constants VS acoustic constants (opinion piece article) - Revision history</title>
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	<updated>2026-07-03T20:56:01Z</updated>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=User:Contribution/Logarithmic_constants_VS_acoustic_constants_(opinion_piece_article)&amp;diff=104975&amp;oldid=prev</id>
		<title>Contribution at 20:41, 7 March 2023</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=User:Contribution/Logarithmic_constants_VS_acoustic_constants_(opinion_piece_article)&amp;diff=104975&amp;oldid=prev"/>
		<updated>2023-03-07T20:41:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&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 20:41, 7 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-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Logarithmic constants are fake intervals ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;When we are hearing logarithmic phi, we are in fact hearing the number 2**(phi) = 3.070&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;When we are hearing logarithmic phi, we are in fact hearing the number 2**(phi) = 3.070&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 colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l12&quot;&gt;Line 12:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 13:&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;Acoustic constants are the only real musical ones.&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;Acoustic constants are the only real musical ones.&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;== Metallic MOS ==&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;That being said, logarithmic phi has interesting musical applications as [[Metallic MOS]], and in particular the fractal-like possibilities of self-similar subdivision of musical scales.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Contribution</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=User:Contribution/Logarithmic_constants_VS_acoustic_constants_(opinion_piece_article)&amp;diff=104972&amp;oldid=prev</id>
		<title>Contribution: Created page with &quot;When we are hearing logarithmic phi, we are in fact hearing the number 2**(phi) = 3.070  Same thing for logarithmic pi, the number that comes to our ears is 2**(pi) = 8.825  W...&quot;</title>
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		<updated>2023-03-07T19:47:15Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;When we are hearing logarithmic phi, we are in fact hearing the number 2**(phi) = 3.070  Same thing for logarithmic pi, the number that comes to our ears is 2**(pi) = 8.825  W...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;When we are hearing logarithmic phi, we are in fact hearing the number 2**(phi) = 3.070&lt;br /&gt;
&lt;br /&gt;
Same thing for logarithmic pi, the number that comes to our ears is 2**(pi) = 8.825&lt;br /&gt;
&lt;br /&gt;
While these intervals can still be used in a way or another as useful tones in a piece of music, they don&amp;#039;t correspond to anything.&lt;br /&gt;
&lt;br /&gt;
Moreover, music is fundamentally the art of numbers made audible. This is something that was already known in antiquity. That&amp;#039;s why I believe that what is completely outside the &amp;quot;grid of numbers&amp;quot; and the &amp;quot;harmonic grids&amp;quot; that emerge from it does not truly correspond to what music is fundamentally nor to the actual functioning of hearing (for this reason, I believe that most of what was composed in the Second Viennese School does not truly correspond to what music is deeply about, although it is interesting to analyse intellectually).&lt;br /&gt;
&lt;br /&gt;
This is why I say that logarithmic phi and logarithmic pi are not musical.&lt;br /&gt;
&lt;br /&gt;
When it comes to acoustic constants, we are truly hearing the mathematical constants phi = 1.6180 and pi = 3.1416&lt;br /&gt;
&lt;br /&gt;
Acoustic constants are the only real musical ones.&lt;/div&gt;</summary>
		<author><name>Contribution</name></author>
	</entry>
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