Golden meantone: Difference between revisions
Wikispaces>genewardsmith **Imported revision 468774218 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 468775292 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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:genewardsmith|genewardsmith]] and made on <tt>2013-11-13 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-13 13:42:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>468775292</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> | ||
<h4>Original Wikitext content:</h4> | <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">**Golden Meantone** is based on making the relation between whole tone and diatonic semitone intervals be the [[http://en.wikipedia.org/wiki/Golden_ratio|Golden Ratio]] | <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">**Golden Meantone** is based on making the relation between the whole tone and diatonic semitone intervals be the [[http://en.wikipedia.org/wiki/Golden_ratio|Golden Ratio]] | ||
[[math]] | [[math]] | ||
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[[math]] | [[math]] | ||
cents. | cents, approximately 696.214 cents. | ||
Edo systems in a Fibonacci style recurrence beginning with 7 and 12 are successively better approximations to this ideal. | Edo systems in a Fibonacci style recurrence beginning with 7 and 12 are successively better approximations to this ideal. | ||
== Construction == | == Construction == | ||
If you use two neighboring numbers from Fibonacci | If you use two neighboring numbers from the Fibonacci series 1 1 2 3 5 8 13 21... you get the following approximations: | ||
1, 1 -> [[7edo]] | 1, 1 -> [[7edo]] | ||
1, 2 -> [[12edo]] | 1, 2 -> [[12edo]] | ||
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[[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> | [[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> | <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>Golden Meantone</title></head><body><strong>Golden Meantone</strong> is based on making the relation between whole tone and diatonic semitone intervals be the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Golden_ratio" rel="nofollow">Golden Ratio</a><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>Golden Meantone</title></head><body><strong>Golden Meantone</strong> is based on making the relation between the whole tone and diatonic semitone intervals be the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Golden_ratio" rel="nofollow">Golden Ratio</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextMathRule:0: | <!-- ws:start:WikiTextMathRule:0: | ||
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--><script type="math/tex">(9600 - 1200 \varphi) / 11</script><!-- ws:end:WikiTextMathRule:2 --><br /> | --><script type="math/tex">(9600 - 1200 \varphi) / 11</script><!-- ws:end:WikiTextMathRule:2 --><br /> | ||
<br /> | <br /> | ||
cents.<br /> | cents, approximately 696.214 cents.<br /> | ||
<br /> | <br /> | ||
Edo systems in a Fibonacci style recurrence beginning with 7 and 12 are successively better approximations to this ideal.<br /> | Edo systems in a Fibonacci style recurrence beginning with 7 and 12 are successively better approximations to this ideal.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc0"><a name="x-Construction"></a><!-- ws:end:WikiTextHeadingRule:3 --> Construction </h2> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc0"><a name="x-Construction"></a><!-- ws:end:WikiTextHeadingRule:3 --> Construction </h2> | ||
If you use two neighboring numbers from Fibonacci | If you use two neighboring numbers from the Fibonacci series 1 1 2 3 5 8 13 21... 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 /> | ||
1, 2 -&gt; <a class="wiki_link" href="/12edo">12edo</a><br /> | 1, 2 -&gt; <a class="wiki_link" href="/12edo">12edo</a><br /> | ||