34edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 315451336 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 315490454 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-03-28 12:46:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>315490454</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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<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">=<span style="color: #991785; font-family: 'Times New Roman',Times,serif; font-size: 113%;">34 tone equal temperament</span>= | <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">=<span style="color: #991785; font-family: 'Times New Roman',Times,serif; font-size: 113%;">34 tone equal temperament</span>= | ||
//**34edo**// divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two [[17edo]]'s and the half-octave tritone of 600 cents. | //**34edo**// divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two [[17edo]]'s and the half-octave tritone of 600 cents. | ||
===Approximations to Just Intonation=== | ===Approximations to Just Intonation=== | ||
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//Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]]) | //Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]]) | ||
===34edo and phi=== | |||
As a Fibonacci number, 34edo contains a fraction of an octave which is close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates [[MOSScales|Moment of Symmetry]] scales with near-phi relationships between the step sizes. As a 2.3.5.13 temperament, the 21\34 generator is an approximate 20/13, and the temperament tempers out 512/507 and 140625/140608. From the tempering of 512/507, two 16/13 neutral thirds are an approximate 3/2, defining an essentially tempered neutral triad with a sharp rather than a flat fifth. | |||
===Linear temperaments=== | ===Linear temperaments=== | ||
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<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>34edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x34 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #991785; font-family: 'Times New Roman',Times,serif; font-size: 113%;">34 tone equal temperament</span></h1> | <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>34edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x34 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #991785; font-family: 'Times New Roman',Times,serif; font-size: 113%;">34 tone equal temperament</span></h1> | ||
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<em><strong>34edo</strong></em> divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two <a class="wiki_link" href="/17edo">17edo</a>'s and the half-octave tritone of 600 cents. | <em><strong>34edo</strong></em> divides the octave into 34 equal steps of approximately 35.29412 cents. 34edo contains two <a class="wiki_link" href="/17edo">17edo</a>'s and the half-octave tritone of 600 cents. <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x34 tone equal temperament--Approximations to Just Intonation"></a><!-- ws:end:WikiTextHeadingRule:2 -->Approximations to Just Intonation</h3> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x34 tone equal temperament--Approximations to Just Intonation"></a><!-- ws:end:WikiTextHeadingRule:2 -->Approximations to Just Intonation</h3> | ||
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<em>Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.</em> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow">Wikipedia</a>)<br /> | <em>Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.</em> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow">Wikipedia</a>)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x34 tone equal temperament--Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x34 tone equal temperament--34edo and phi"></a><!-- ws:end:WikiTextHeadingRule:4 -->34edo and phi</h3> | ||
As a Fibonacci number, 34edo contains a fraction of an octave which is close approximation to the irrational interval phi -- 21 degrees of 34edo, approximately 741.2 cents. Repeated iterations of this interval generates <a class="wiki_link" href="/MOSScales">Moment of Symmetry</a> scales with near-phi relationships between the step sizes. As a 2.3.5.13 temperament, the 21\34 generator is an approximate 20/13, and the temperament tempers out 512/507 and 140625/140608. From the tempering of 512/507, two 16/13 neutral thirds are an approximate 3/2, defining an essentially tempered neutral triad with a sharp rather than a flat fifth.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x34 tone equal temperament--Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Linear temperaments</h3> | |||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x34 tone equal temperament--Intervals:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals:</h3> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x34 tone equal temperament-Listen"></a><!-- ws:end:WikiTextHeadingRule:10 -->Listen</h2> | ||
<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li></ul>Drums Bass and 34-tone guitar<br /> | <ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Ascension_105" rel="nofollow" target="_blank">Ascension</a></li></ul>Drums Bass and 34-tone guitar<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x34 tone equal temperament-Links"></a><!-- ws:end:WikiTextHeadingRule:12 -->Links</h2> | ||
<ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="/Larry%20Hanson">Larry Hanson</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://www.microstick.net/34guitararticle.htm" rel="nofollow">34 Equal Guitar</a> by <a class="wiki_link" href="/Larry%20Hanson">Larry Hanson</a></li></ul></body></html></pre></div> | ||