Das Goldene Tonsystem: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>~~2010~~-09-~~20 03~~:11:15 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-11-13 10:11:35 UTC</tt>.<br>

: The original revision id was <tt>~~163861541~~</tt>.<br>

: The original revision id was <tt>468693558</tt>.<br>

: The revision comment was: <tt></tt><br>

: The revision comment was: <tt>moved content to Golden Meantone</tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

<h4>Original Wikitext content:</h4>

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als Fundament der Theoretischen Akustik

is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935.

is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935, that describes [[Golden Meantone]].

~~The system is based on the paradigm that the relation between whole and half tone intervals should be the [[http://en.wikipedia.org/wiki/Golden_ratio|Golden Ratio]]~~

</pre></div>

~~[[math]]~~

~~\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,~~

~~[[math]]~~

~~Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.~~

~~== Construction ==~~

~~If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13 21... you get the following approximations:~~

~~1, 1 -> [[7edo]]~~

~~1, 2 -> [[12edo]]~~

~~2, 3 -> [[19edo]]~~

~~3, 5 -> [[31edo]]~~

~~5, 8 -> [[50edo]]~~

~~8, 13 -> [[81edo]]~~

~~13, 21 -> [[131edo]]~~

~~== Evaluation ==~~

Graham Breed [[http://x31eq.com/meantone.htm|writes]]: //I think of this as the standard melodic meantone because the all these ratios are the same. It has the mellow sound of 1/4 comma, but does still have a character of its own. Some algorithms make this almost exactly the optimum 5-limit tuning. It's fairly good as a 7-limit tuning as well. Almost the optimum (according to me) for diminished sevenths. I toyed with this as a guitar tuning, but rejected it because 4:6:9 chords aren't quite good enough. That is, the poor fifth leads to a sludgy major ninth.//

~~== Listening ==~~

~~[[http://www.io.com/~hmiller/midi/canon-golden.mid|An acoustic experience]] - Kornerup himself had no chance to have it - is contained in the [[Warped canon]] collection.~~</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Das Goldene Tonsystem</title></head><body><strong><a class="wiki_link_ext" href="http://d-nb.info/361092458" rel="nofollow">Das Goldene Tonsystem</a></strong><br />

als Fundament der Theoretischen Akustik<br />

<br />

is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935~~.<br />~~

is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935, that describes <a class="wiki_link" href="/Golden%20Meantone">Golden Meantone</a>.</body></html></pre></div>

~~<br />~~

~~The system is based on the paradigm~~ that ~~the relation between whole and half tone intervals should be the~~ <a class="~~wiki_link_ext~~" href="~~http:~~/~~/en.wikipedia.org/wiki/Golden_ratio" rel="nofollow">~~Golden ~~Ratio</a><br />~~

~~<br />~~

~~<!-- ws:start:WikiTextMathRule:0:~~

~~[[math]]&lt;br/&gt;~~

~~\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,&lt;br/&gt;[[math]]~~

~~--><script type="math/tex">\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,</script><br />~~

~~<br />~~

~~Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.<br />~~

~~<br />~~

~~<h2 id="toc0"><a name="x-Construction"></a> Construction </h2>~~

~~If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13 21... you get the following approximations:<br />~~

~~1, 1 -&gt; <a class="wiki_link" href="/7edo">7edo</a><br />~~

~~1, 2 -&gt; <a class="wiki_link" href="/12edo">12edo</a><br />~~

~~2, 3 -&gt; <a class="wiki_link" href="/19edo">19edo</a><br />~~

~~3, 5 -&gt; <a class="wiki_link" href="/31edo">31edo</a><br />~~

~~5, 8 -&gt; <a class="wiki_link" href="/50edo">50edo</a><br />~~

~~8, 13 -&gt; <a class="wiki_link" href="/81edo">81edo</a><br />~~

~~13, 21 -&gt; <a class="wiki_link" href="/131edo">131edo</a><br />~~

~~<br />~~

~~<h2 id="toc1"><a name="x-Evaluation"></a> Evaluation </h2>~~

~~<br />~~

Graham Breed <a class="wiki_link_ext" href="http://x31eq.com/meantone.htm" rel="nofollow">writes</a>: <em>I think of this as the standard melodic meantone because the all these ratios are the same. It has the mellow sound of 1/4 comma, but does still have a character of its own. Some algorithms make this almost exactly the optimum 5-limit tuning. It's fairly good as a 7-limit tuning as well. Almost the optimum (according to me) for diminished sevenths. I toyed with this as a guitar tuning, but rejected it because 4:6:9 chords aren't quite good enough. That is, the poor fifth leads to a sludgy major ninth.</em><br />

~~<br />~~

~~<h2 id="toc2"><a name="x-Listening"></a> Listening </h2>~~

~~<br />~~

<a class="wiki_link_ext" href="http://www.io.com/~hmiller/midi/canon-golden.mid" rel="nofollow">An acoustic experience</a> - Kornerup himself had no chance to have it - is contained in the <a class="wiki_link" href="/Warped%~~20canon~~">~~Warped canon~~</a> ~~collection~~.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-20 03:11:15 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-11-13 10:11:35 UTC</tt>.<br>
-: The original revision id was <tt>163861541</tt>.<br>
+: The original revision id was <tt>468693558</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>moved content to Golden Meantone</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 9: / Line 9: @@
 als Fundament der Theoretischen Akustik
-is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935.
+is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935, that describes [[Golden Meantone]].
-The system is based on the paradigm that the relation between whole and half tone intervals should be the [[http://en.wikipedia.org/wiki/Golden_ratio|Golden Ratio]]
+</pre></div>
-[[math]]
-\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,
-[[math]]
-Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.
-== Construction ==
-If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13 21... you get the following approximations:
-, 1 -&gt; [[7edo]]
-, 2 -&gt; [[12edo]]
-, 3 -&gt; [[19edo]]
-, 5 -&gt; [[31edo]]
-, 8 -&gt; [[50edo]]
-, 13 -&gt; [[81edo]]
-, 21 -&gt; [[131edo]]
-== Evaluation ==
-Graham Breed [[http://x31eq.com/meantone.htm|writes]]: //I think of this as the standard melodic meantone because the all these ratios are the same. It has the mellow sound of 1/4 comma, but does still have a character of its own. Some algorithms make this almost exactly the optimum 5-limit tuning. It's fairly good as a 7-limit tuning as well. Almost the optimum (according to me) for diminished sevenths. I toyed with this as a guitar tuning, but rejected it because 4:6:9 chords aren't quite good enough. That is, the poor fifth leads to a sludgy major ninth.//
-== Listening ==
-[[http://www.io.com/~hmiller/midi/canon-golden.mid|An acoustic experience]] - Kornerup himself had no chance to have it - is contained in the [[Warped canon]] collection.</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Das Goldene Tonsystem&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;&lt;a class="wiki_link_ext" href="http://d-nb.info/361092458" rel="nofollow"&gt;Das Goldene Tonsystem&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
 als Fundament der Theoretischen Akustik&lt;br /&gt;
 &lt;br /&gt;
-is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935.&lt;br /&gt;
+is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup, written in German and published in Copenhagen in 1935, that describes &lt;a class="wiki_link" href="/Golden%20Meantone"&gt;Golden Meantone&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
-&lt;br /&gt;
-The system is based on the paradigm that the relation between whole and half tone intervals should be the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Golden_ratio" rel="nofollow"&gt;Golden Ratio&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextMathRule:0:
-[[math]]&amp;lt;br/&amp;gt;
-\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,&amp;lt;br/&amp;gt;[[math]]
- --&gt;&lt;script type="math/tex"&gt;\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&gt;&lt;br /&gt;
-&lt;br /&gt;
-Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Construction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt; Construction &lt;/h2&gt;
-If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13 21... you get the following approximations:&lt;br /&gt;
-, 1 -&amp;gt; &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
-, 2 -&amp;gt; &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
-, 3 -&amp;gt; &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
-, 5 -&amp;gt; &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
-, 8 -&amp;gt; &lt;a class="wiki_link" href="/50edo"&gt;50edo&lt;/a&gt;&lt;br /&gt;
-, 13 -&amp;gt; &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt;&lt;br /&gt;
-, 21 -&amp;gt; &lt;a class="wiki_link" href="/131edo"&gt;131edo&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Evaluation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt; Evaluation &lt;/h2&gt;
-&lt;br /&gt;
-Graham Breed &lt;a class="wiki_link_ext" href="http://x31eq.com/meantone.htm" rel="nofollow"&gt;writes&lt;/a&gt;: &lt;em&gt;I think of this as the standard melodic meantone because the all these ratios are the same. It has the mellow sound of 1/4 comma, but does still have a character of its own. Some algorithms make this almost exactly the optimum 5-limit tuning. It's fairly good as a 7-limit tuning as well. Almost the optimum (according to me) for diminished sevenths. I toyed with this as a guitar tuning, but rejected it because 4:6:9 chords aren't quite good enough. That is, the poor fifth leads to a sludgy major ninth.&lt;/em&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Listening"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt; Listening &lt;/h2&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.io.com/~hmiller/midi/canon-golden.mid" rel="nofollow"&gt;An acoustic experience&lt;/a&gt; - Kornerup himself had no chance to have it - is contained in the &lt;a class="wiki_link" href="/Warped%20canon"&gt;Warped canon&lt;/a&gt; collection.&lt;/body&gt;&lt;/html&gt;</pre></div>