34edo: Difference between revisions
Wikispaces>guest **Imported revision 322565780 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 322721548 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2012-04-19 12:48:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>322721548</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> | ||
| Line 18: | Line 18: | ||
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 [[xenharmonic/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. | 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 [[xenharmonic/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. | ||
=== | ===Rank two temperaments=== | ||
[[xenharmonic/List of 34et rank two temperaments by badness|List of 34et rank two temperaments by badness]] | [[xenharmonic/List of 34et rank two temperaments by badness|List of 34et rank two temperaments by badness]] | ||
||~ Periods | ||~ Periods | ||
| Line 117: | Line 117: | ||
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="http://xenharmonic.wikispaces.com/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 /> | 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="http://xenharmonic.wikispaces.com/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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-- | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x--Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Rank two temperaments</h3> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2034et%20rank%20two%20temperaments%20by%20badness">List of 34et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/List%20of%2034et%20rank%20two%20temperaments%20by%20badness">List of 34et rank two temperaments by badness</a><br /> | ||