Das Goldene Tonsystem: Difference between revisions
Wikispaces>xenwolf **Imported revision 139441103 - Original comment: ** |
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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- | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-01 16:39:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>146322965</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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...is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup. [http://d-nb.info/361092458] written in German. | ...is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup. [http://d-nb.info/361092458] written in German. | ||
The system is based on the paradigm that the relation between whole and half tone intervals should be the Golden Ratio | 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]] | ||
(sqrt | [[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. | Thus some edo systems - the 12-step too - could be considered as approximations to this ideal. | ||
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<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>Das Goldene Tonsystem</strong> als Fundament der Theoretischen Akustik<br /> | <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>Das Goldene Tonsystem</strong> als Fundament der Theoretischen Akustik<br /> | ||
<br /> | <br /> | ||
...is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup. [<!-- ws:start:WikiTextUrlRule: | ...is a book of the danish music theoretician (music reformer and visionary) Thorvald Kornerup. [<!-- ws:start:WikiTextUrlRule:31:http://d-nb.info/361092458 --><a class="wiki_link_ext" href="http://d-nb.info/361092458" rel="nofollow">http://d-nb.info/361092458</a><!-- ws:end:WikiTextUrlRule:31 -->] written in German.<br /> | ||
<br /> | <br /> | ||
The system is based on the paradigm that the relation between whole and half tone intervals should be the Golden Ratio <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 /> | <br /> | ||
(sqrt | <!-- 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><!-- ws:end:WikiTextMathRule:0 --><br /> | |||
<br /> | <br /> | ||
Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.<br /> | Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Construction"></a><!-- ws:end:WikiTextHeadingRule:1 --> Construction </h2> | ||
If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13... you get the following approximations:<br /> | If you use two neighboring numbers from Fibonacci Series 1 1 2 3 5 8 13... you get the following approximations:<br /> | ||
1, 1 -&gt; <a class="wiki_link" href="/7edo">7edo</a><br /> | 1, 1 -&gt; <a class="wiki_link" href="/7edo">7edo</a><br /> | ||
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5, 8 -&gt; <a class="wiki_link" href="/50edo">50edo</a><br /> | 5, 8 -&gt; <a class="wiki_link" href="/50edo">50edo</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x-Listening"></a><!-- ws:end:WikiTextHeadingRule:3 --> Listening </h2> | ||
<br /> | <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> | <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> | ||