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 Golden Ratio (sqrt(5)+1)/2 (who does it in <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.
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<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:29: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:29 -->] written in German.<br /> <br /> The system is based on the paradigm that the relation between whole and half tone intervals should be the Golden Ratio <br /> <br /> (sqrt(5)+1)/2 (who does it in <math> ?)<br /> <br /> Thus some edo systems - the 12-step too - could be considered as approximations to this ideal.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Construction"></a><!-- ws:end:WikiTextHeadingRule:0 --> 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:2:<h2> --><h2 id="toc1"><a name="x-Listening"></a><!-- ws:end:WikiTextHeadingRule:2 --> 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>