Das Goldene Tonsystem
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**Das Goldene Tonsystem** als Fundament der Theoretischen Akustik
...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 [[http://en.wikipedia.org/wiki/Golden_ratio|Golden Ratio]]
[[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... you get the following approximations:
1, 1 -> [[7edo]]
1, 2 -> [[12edo]]
2, 3 -> [[19edo]]
3, 5 -> [[31edo]]
5, 8 -> [[50edo]]
== 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.Original HTML content:
<html><head><title>Das Goldene Tonsystem</title></head><body><strong>Das Goldene Tonsystem</strong> als Fundament der Theoretischen Akustik<br />
<br />
...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 />
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]]<br/>
\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,<br/>[[math]]
--><script type="math/tex">\varphi = \frac 1 2 (\sqrt{5}+1) \approx 1.61803\,39887\ldots\,</script><!-- ws:end:WikiTextMathRule:0 --><br />
<br />
Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:<h2> --><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 />
1, 1 -> <a class="wiki_link" href="/7edo">7edo</a><br />
1, 2 -> <a class="wiki_link" href="/12edo">12edo</a><br />
2, 3 -> <a class="wiki_link" href="/19edo">19edo</a><br />
3, 5 -> <a class="wiki_link" href="/31edo">31edo</a><br />
5, 8 -> <a class="wiki_link" href="/50edo">50edo</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:<h2> --><h2 id="toc1"><a name="x-Listening"></a><!-- ws:end:WikiTextHeadingRule:3 --> 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>