34edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 596940418 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 597692694 - Original comment: removed tel links** |
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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:xenwolf|xenwolf]] and made on <tt>2016-11-01 18:31:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597692694</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>removed tel links</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> | ||
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=34edo and phi= | =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 [[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 | 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. Yes. But, to be clear the harmonic ratio of phi is ~ 833 cents, and the equal divisions of octave approximating this interval closely are 13edo and [[36edo]]. | ||
=Rank two temperaments= | =Rank two temperaments= | ||
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=Commas= | =Commas= | ||
34-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < | 34-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < 34 54 79 95 118 126 |.) | ||
||= **Comma** ||= **Monzo** ||= **Value (Cents)** ||= **Names** || | ||= **Comma** ||= **Monzo** ||= **Value (Cents)** ||= **Names** || | ||
||= 134217728/129140163 || | 27 -17 > ||> 66.765 ||= 17-comma || | ||= 134217728/129140163 || | 27 -17 > ||> 66.765 ||= 17-comma || | ||
||= 20000/19683 || | 5 -9 4 > ||> 27.660 ||= Minimal Diesis, Tetracot Comma || | ||= 20000/19683 || | 5 -9 4 > ||> 27.660 ||= Minimal Diesis, Tetracot Comma || | ||
||= 2048/2025 || | 11 -4 -2 > ||> 19.553 ||= Diaschisma || | ||= 2048/2025 || | 11 -4 -2 > ||> 19.553 ||= Diaschisma || | ||
||= | ||= 393216/390625 || | 17 1 -8 > ||> 11.445 ||= Würschmidt comma || | ||
||= 15625/15552 || | -6 -5 6 > ||> 8.1073 ||= Kleisma, Semicomma Majeur || | ||= 15625/15552 || | -6 -5 6 > ||> 8.1073 ||= Kleisma, Semicomma Majeur || | ||
||= | ||= 1212717/1210381 || | 23 6 -14 > ||> 3.338 ||= Vishnuzma, Semisuper || | ||
||= 1029/1000 || | -3 1 -3 3 > ||> 49.492 ||= Keega || | ||= 1029/1000 || | -3 1 -3 3 > ||> 49.492 ||= Keega || | ||
||= [[50_49|50/49]] || | 1 0 2 -2 > ||> 34.976 ||= Fifty forty-nine || | ||= [[50_49|50/49]] || | 1 0 2 -2 > ||> 34.976 ||= Fifty forty-nine || | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x34edo and phi"></a><!-- ws:end:WikiTextHeadingRule:2 -->34edo and phi</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x34edo and phi"></a><!-- ws:end:WikiTextHeadingRule:2 -->34edo and phi</h1> | ||
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 | 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. Yes. But, to be clear the harmonic ratio of phi is ~ 833 cents, and the equal divisions of octave approximating this interval closely are 13edo and <a class="wiki_link" href="/36edo">36edo</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank two temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank two temperaments</h1> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1> | ||
34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt | 34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; 34 54 79 95 118 126 |.)<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">393216/390625<br /> | ||
</td> | </td> | ||
<td>| 17 1 -8 &gt;<br /> | <td>| 17 1 -8 &gt;<br /> | ||
| Line 1,143: | Line 1,143: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1212717/1210381<br /> | ||
</td> | </td> | ||
<td>| 23 6 -14 &gt;<br /> | <td>| 23 6 -14 &gt;<br /> | ||