31920edo: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-23 01:30:08 UTC</tt>.<br>

: The original revision id was <tt>510766294</tt>.<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;white-space: pre-wrap ! important" class="old-revision-html">The 31920 division divides the octave into 31920 equal parts of 0.03759 cents each, making a cent equal to exactly 26.6 steps of 31920edo. It is distinctly consistent through the 41 limit, and is an atomic temperament, tempering out the Kirnberger atom, |161 -84 -12&gt;. It is a very "smooth" number, with many divisors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920. These facts make it a good candidate for an [[interval size measure]], and one step of it may be called an "imp", so that the cent is 26.6 imps, and a 12edo semitone is 2660 imps. A single step of 15edo is 2128 imps, of 19edo 1680 imps, of 84edo 380 imps, of 140edo 228 imps, of 152edo 210 imps, of 190edo 168 imps, and of 665edo 48 imps.</pre></div>

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;31920edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 31920 division divides the octave into 31920 equal parts of 0.03759 cents each, making a cent equal to exactly 26.6 steps of 31920edo. It is distinctly consistent through the 41 limit, and is an atomic temperament, tempering out the Kirnberger atom, |161 -84 -12&amp;gt;. It is a very &amp;quot;smooth&amp;quot; number, with many divisors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 19, 20, 21, 24, 28, 30, 35, 38, 40, 42, 48, 56, 57, 60, 70, 76, 80, 84, 95, 105, 112, 114, 120, 133, 140, 152, 168, 190, 210, 228, 240, 266, 280, 285, 304, 336, 380, 399, 420, 456, 532, 560, 570, 665, 760, 798, 840, 912, 1064, 1140, 1330, 1520, 1596, 1680, 1995, 2128, 2280, 2660, 3192, 3990, 4560, 5320, 6384, 7980, 10640, 15960, 31920. These facts make it a good candidate for an &lt;a class="wiki_link" href="/interval%20size%20measure"&gt;interval size measure&lt;/a&gt;, and one step of it may be called an &amp;quot;imp&amp;quot;, so that the cent is 26.6 imps, and a 12edo semitone is 2660 imps. A single step of 15edo is 2128 imps, of 19edo 1680 imps, of 84edo 380 imps, of 140edo 228 imps, of 152edo 210 imps, of 190edo 168 imps, and of 665edo 48 imps.&lt;/body&gt;&lt;/html&gt;</pre></div>