21edo: Difference between revisions
Wikispaces>igliashon **Imported revision 515186756 - Original comment: ** |
Wikispaces>igliashon **Imported revision 515597088 - 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:igliashon|igliashon]] and made on <tt>2014- | : This revision was by author [[User:igliashon|igliashon]] and made on <tt>2014-07-04 14:38:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>515597088</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">=21 equal divisions of the octave= | <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">=21 equal divisions of the octave= | ||
Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other ET <26. | Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other ET <26. | ||
==21-EDO as a temperament:== | ==21-EDO as a temperament:== | ||
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||= Step Pattern ||= Cents ||= Name* || | ||= Step Pattern ||= Cents ||= Name* || | ||
||= 3, 3, 3 ||= 0-171-343-514 ||= Equal diatonic || | ||= 3, 3, 3 ||= 0-171-343-514 ||= Equal diatonic || | ||
||= 4, 3, 2 ||= 0-229-400-514 ||= | ||= 4, 3, 2 ||= 0-229-400-514 ||= Hard diatonic || | ||
||= 4, 4, 1 ||= 0-229-457-514 ||= | ||= 4, 4, 1 ||= 0-229-457-514 ||= Soft diatonic || | ||
||= 5, 3, 1 ||= 0-286-457-514 ||= | ||= 5, 3, 1 ||= 0-286-457-514 ||= Soft chromatic || | ||
||= 5, 2, 2 ||= 0-286-400-514 ||= | ||= 5, 2, 2 ||= 0-286-400-514 ||= Hard chromatic || | ||
||= 6, 2, 1 ||= 0-343-457-514 ||= | ||= 6, 2, 1 ||= 0-343-457-514 ||= Hard enharmonic || | ||
||= 7, 1, 1 ||= 0-400-457-514 ||= | ||= 7, 1, 1 ||= 0-400-457-514 ||= Soft enharmonic || | ||
*these names may not be correct in relating to the ancient Greek tetrachordal genera; please change them if you know better! | *these names may not be correct in relating to the ancient Greek tetrachordal genera; please change them if you know better! | ||
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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>21edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x21 equal divisions of the octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->21 equal divisions of the octave</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>21edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x21 equal divisions of the octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->21 equal divisions of the octave</h1> | ||
<br /> | <br /> | ||
Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or &quot;equi-heptatonic&quot; scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other ET &lt;26. <br /> | Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or &quot;equi-heptatonic&quot; scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other ET &lt;26.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x21 equal divisions of the octave-21-EDO as a temperament:"></a><!-- ws:end:WikiTextHeadingRule:2 -->21-EDO as a temperament:</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x21 equal divisions of the octave-21-EDO as a temperament:"></a><!-- ws:end:WikiTextHeadingRule:2 -->21-EDO as a temperament:</h2> | ||
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<td style="text-align: center;">0-229-400-514<br /> | <td style="text-align: center;">0-229-400-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Hard diatonic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">0-229-457-514<br /> | <td style="text-align: center;">0-229-457-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Soft diatonic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">0-286-457-514<br /> | <td style="text-align: center;">0-286-457-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Soft chromatic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">0-286-400-514<br /> | <td style="text-align: center;">0-286-400-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Hard chromatic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">0-343-457-514<br /> | <td style="text-align: center;">0-343-457-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Hard enharmonic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: center;">0-400-457-514<br /> | <td style="text-align: center;">0-400-457-514<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">Soft enharmonic<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||