|
|
| (8 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{DISPLAYTITLE:''Das Goldene Tonsystem''}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | '''''[http://d-nb.info/361092458 Das Goldene Tonsystem 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, that describes [[golden meantone]]. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-01 17:11:24 UTC</tt>.<br>
| |
| : The original revision id was <tt>146329239</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>
| |
| <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">**[[http://d-nb.info/361092458|Das Goldene Tonsystem]]**
| |
| 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.
| | [[Category:Golden meantone]] |
| | | [[Category:Resources]] |
| 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]]
| |
| | |
| == 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 />
| |
| <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><!-- 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:&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 />
| |
| 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 />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="x-Evaluation"></a><!-- ws:end:WikiTextHeadingRule:3 --> 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 />
| |
| <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="x-Listening"></a><!-- ws:end:WikiTextHeadingRule:5 --> 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>
| |