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. 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 == For an acoustic example have a look [[Warped canon]] - Kornerup himself had no chance to do so
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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.<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 /> For an acoustic example have a look <a class="wiki_link" href="/Warped%20canon">Warped canon</a> - Kornerup himself had no chance to do so</body></html>