Golden meantone: Difference between revisions
Wikispaces>genewardsmith **Imported revision 468775292 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 479295880 - 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: | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2013-12-24 18:24:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>479295880</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> | ||
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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 the Fibonacci series 1 1 2 3 5 8 13 21... you get the following approximations: | 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, 2 -> [[12edo]] | |||
2, 3 -> [[19edo]] | |||
3, 5 -> [[31edo]] | |||
5, 8 -> [[50edo]] | |||
8, 13 -> [[81edo]] | |||
13, 21 -> [[131edo]] | 13, 21 -> [[131edo]] | ||
== Evaluation == | ==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.// | 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 == | ==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> | [[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. | ||
==Additional reading== | |||
[[@http://www.tonalsoft.com/enc/g/golden.aspx|Golden meantone - Tonalsoft encyclopedia]]</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 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 /> | <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 /> | ||
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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 the Fibonacci series 1 1 2 3 5 8 13 21... you get the following approximations:<br /> | 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, 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 /> | |||
8, 13 -&gt; <a class="wiki_link" href="/81edo">81edo</a><br /> | |||
13, 21 -&gt; <a class="wiki_link" href="/131edo">131edo</a><br /> | 13, 21 -&gt; <a class="wiki_link" href="/131edo">131edo</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc1"><a name="x-Evaluation"></a><!-- ws:end:WikiTextHeadingRule:5 --> Evaluation </h2> | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc1"><a name="x-Evaluation"></a><!-- ws:end:WikiTextHeadingRule:5 -->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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc2"><a name="x-Listening"></a><!-- ws:end:WikiTextHeadingRule:7 -->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.<br /> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc3"><a name="x-Additional reading"></a><!-- ws:end:WikiTextHeadingRule:9 -->Additional reading</h2> | ||
<br /> | |||
<a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/g/golden.aspx" rel="nofollow" target="_blank">Golden meantone - Tonalsoft encyclopedia</a></body></html></pre></div> | |||