208edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The ''208 equal division'' divides the [[Octave|octave]] into 208 equal parts of size 5.769 [[cent|cent]]s each. It tempers out 15625/15552, the kleisma, and is the [[Optimal_patent_val|optimal patent val]] for the kleismic temperament [[Kleismic_family|metakleismic]], and 7, 11 and 13 limit rank three [[Tolermic_family|tolerant]] temperament. It is also the optimal patent val for the rank four [[11-limit|11-limit]] temperament tempering out 896/891, the pentacircle temperament. Other commas it tempers out include 2200/2187 in the 11-limit and 325/324, 352/351, 364/363 and 625/624 in the 13-limit.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-16 12:13:55 UTC</tt>.<br>
: The original revision id was <tt>477814578</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>
<h4>Original Wikitext content:</h4>
<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 //208 equal division// divides the [[octave]] into 208 equal parts of size 5.769 [[cent]]s each. It tempers out 15625/15552, the kleisma, and is the [[optimal patent val]] for the kleismic temperament [[Kleismic family|metakleismic]], and 7, 11 and 13 limit rank three [[Tolermic family|tolerant]] temperament. It is also the optimal patent val for the rank four [[11-limit]] temperament tempering out 896/891, the pentacircle temperament. Other commas it tempers out include 2200/2187 in the 11-limit and 325/324, 352/351, 364/363 and 625/624 in the 13-limit.


208 = 16 * 13, and has divisors 2, 4, 8, 16, 13, 26, 52, 104.
208 = 16 * 13, and has divisors 2, 4, 8, 16, 13, 26, 52, 104.
Line 12: Line 5:
=13-limit transversal=
=13-limit transversal=
[196/195, 100/99, 91/90, 64/63, 55/54, 49/48, 40/39, 77/75, 36/35, 28/27, 80/77, 25/24, 245/234, 22/21, 21/20, 81/77, 35/33, 52/49, 16/15, 77/72, 15/14, 14/13, 250/231, 13/12, 49/45, 12/11, 35/32, 100/91, 11/10, 54/49, 10/9, 49/44, 39/35, 28/25, 55/49, 9/8, 147/130, 25/22, 91/80, 8/7, 55/48, 147/128, 15/13, 196/169, 64/55, 7/6, 90/77, 75/64, 147/125, 13/11, 77/65, 25/21, 105/88, 117/98, 6/5, 77/64, 40/33, 63/52, 128/105, 11/9, 49/40, 16/13, 154/125, 26/21, 56/45, 96/77, 5/4, 49/39, 44/35, 63/50, 80/63, 14/11, 125/98, 32/25, 77/60, 9/7, 35/27, 100/77, 13/10, 64/49, 55/42, 21/16, 120/91, 33/25, 65/49, 4/3, 147/110, 75/56, 35/26, 66/49, 27/20, 49/36, 15/11, 175/128, 48/35, 11/8, 135/98, 18/13, 245/176, 39/28, 7/5, 108/77, 45/32, 147/104, 64/45, 77/54, 10/7, 56/39, 351/245, 13/9, 196/135, 16/11, 35/24, 143/98, 22/15, 72/49, 40/27, 49/33, 52/35, 112/75, 220/147, 3/2, 98/65, 50/33, 91/60, 32/21, 55/36, 49/32, 20/13, 77/50, 54/35, 14/9, 120/77, 25/16, 196/125, 11/7, 63/40, 100/63, 35/22, 78/49, 8/5, 77/48, 45/28, 21/13, 125/77, 13/8, 49/30, 18/11, 105/64, 104/63, 33/20, 81/49, 5/3, 147/88, 117/70, 42/25, 130/77, 22/13, 245/144, 75/44, 77/45, 12/7, 55/32, 169/98, 26/15, 256/147, 96/55, 7/4, 135/77, 44/25, 260/147, 16/9, 98/55, 25/14, 70/39, 88/49, 9/5, 49/27, 20/11, 91/50, 64/35, 11/6, 90/49, 24/13, 231/125, 13/7, 28/15, 144/77, 15/8, 49/26, 66/35, 91/48, 40/21, 21/11, 245/128, 25/13, 77/40, 27/14, 35/18, 150/77, 39/20, 49/25, 55/28, 63/32, 125/63, 99/50, 195/98, 2]
[196/195, 100/99, 91/90, 64/63, 55/54, 49/48, 40/39, 77/75, 36/35, 28/27, 80/77, 25/24, 245/234, 22/21, 21/20, 81/77, 35/33, 52/49, 16/15, 77/72, 15/14, 14/13, 250/231, 13/12, 49/45, 12/11, 35/32, 100/91, 11/10, 54/49, 10/9, 49/44, 39/35, 28/25, 55/49, 9/8, 147/130, 25/22, 91/80, 8/7, 55/48, 147/128, 15/13, 196/169, 64/55, 7/6, 90/77, 75/64, 147/125, 13/11, 77/65, 25/21, 105/88, 117/98, 6/5, 77/64, 40/33, 63/52, 128/105, 11/9, 49/40, 16/13, 154/125, 26/21, 56/45, 96/77, 5/4, 49/39, 44/35, 63/50, 80/63, 14/11, 125/98, 32/25, 77/60, 9/7, 35/27, 100/77, 13/10, 64/49, 55/42, 21/16, 120/91, 33/25, 65/49, 4/3, 147/110, 75/56, 35/26, 66/49, 27/20, 49/36, 15/11, 175/128, 48/35, 11/8, 135/98, 18/13, 245/176, 39/28, 7/5, 108/77, 45/32, 147/104, 64/45, 77/54, 10/7, 56/39, 351/245, 13/9, 196/135, 16/11, 35/24, 143/98, 22/15, 72/49, 40/27, 49/33, 52/35, 112/75, 220/147, 3/2, 98/65, 50/33, 91/60, 32/21, 55/36, 49/32, 20/13, 77/50, 54/35, 14/9, 120/77, 25/16, 196/125, 11/7, 63/40, 100/63, 35/22, 78/49, 8/5, 77/48, 45/28, 21/13, 125/77, 13/8, 49/30, 18/11, 105/64, 104/63, 33/20, 81/49, 5/3, 147/88, 117/70, 42/25, 130/77, 22/13, 245/144, 75/44, 77/45, 12/7, 55/32, 169/98, 26/15, 256/147, 96/55, 7/4, 135/77, 44/25, 260/147, 16/9, 98/55, 25/14, 70/39, 88/49, 9/5, 49/27, 20/11, 91/50, 64/35, 11/6, 90/49, 24/13, 231/125, 13/7, 28/15, 144/77, 15/8, 49/26, 66/35, 91/48, 40/21, 21/11, 245/128, 25/13, 77/40, 27/14, 35/18, 150/77, 39/20, 49/25, 55/28, 63/32, 125/63, 99/50, 195/98, 2]
</pre></div>
[[Category:11-limit]]
<h4>Original HTML content:</h4>
[[Category:13-limit]]
<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;208edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;208 equal division&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 208 equal parts of size 5.769 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. It tempers out 15625/15552, the kleisma, and is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the kleismic temperament &lt;a class="wiki_link" href="/Kleismic%20family"&gt;metakleismic&lt;/a&gt;, and 7, 11 and 13 limit rank three &lt;a class="wiki_link" href="/Tolermic%20family"&gt;tolerant&lt;/a&gt; temperament. It is also the optimal patent val for the rank four &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; temperament tempering out 896/891, the pentacircle temperament. Other commas it tempers out include 2200/2187 in the 11-limit and 325/324, 352/351, 364/363 and 625/624 in the 13-limit.&lt;br /&gt;
[[Category:7-limit]]
&lt;br /&gt;
[[Category:edo]]
208 = 16 * 13, and has divisors 2, 4, 8, 16, 13, 26, 52, 104.&lt;br /&gt;
[[Category:theory]]
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x13-limit transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;13-limit transversal&lt;/h1&gt;
[196/195, 100/99, 91/90, 64/63, 55/54, 49/48, 40/39, 77/75, 36/35, 28/27, 80/77, 25/24, 245/234, 22/21, 21/20, 81/77, 35/33, 52/49, 16/15, 77/72, 15/14, 14/13, 250/231, 13/12, 49/45, 12/11, 35/32, 100/91, 11/10, 54/49, 10/9, 49/44, 39/35, 28/25, 55/49, 9/8, 147/130, 25/22, 91/80, 8/7, 55/48, 147/128, 15/13, 196/169, 64/55, 7/6, 90/77, 75/64, 147/125, 13/11, 77/65, 25/21, 105/88, 117/98, 6/5, 77/64, 40/33, 63/52, 128/105, 11/9, 49/40, 16/13, 154/125, 26/21, 56/45, 96/77, 5/4, 49/39, 44/35, 63/50, 80/63, 14/11, 125/98, 32/25, 77/60, 9/7, 35/27, 100/77, 13/10, 64/49, 55/42, 21/16, 120/91, 33/25, 65/49, 4/3, 147/110, 75/56, 35/26, 66/49, 27/20, 49/36, 15/11, 175/128, 48/35, 11/8, 135/98, 18/13, 245/176, 39/28, 7/5, 108/77, 45/32, 147/104, 64/45, 77/54, 10/7, 56/39, 351/245, 13/9, 196/135, 16/11, 35/24, 143/98, 22/15, 72/49, 40/27, 49/33, 52/35, 112/75, 220/147, 3/2, 98/65, 50/33, 91/60, 32/21, 55/36, 49/32, 20/13, 77/50, 54/35, 14/9, 120/77, 25/16, 196/125, 11/7, 63/40, 100/63, 35/22, 78/49, 8/5, 77/48, 45/28, 21/13, 125/77, 13/8, 49/30, 18/11, 105/64, 104/63, 33/20, 81/49, 5/3, 147/88, 117/70, 42/25, 130/77, 22/13, 245/144, 75/44, 77/45, 12/7, 55/32, 169/98, 26/15, 256/147, 96/55, 7/4, 135/77, 44/25, 260/147, 16/9, 98/55, 25/14, 70/39, 88/49, 9/5, 49/27, 20/11, 91/50, 64/35, 11/6, 90/49, 24/13, 231/125, 13/7, 28/15, 144/77, 15/8, 49/26, 66/35, 91/48, 40/21, 21/11, 245/128, 25/13, 77/40, 27/14, 35/18, 150/77, 39/20, 49/25, 55/28, 63/32, 125/63, 99/50, 195/98, 2]&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The 208 equal division divides the octave into 208 equal parts of size 5.769 cents each. It tempers out 15625/15552, the kleisma, and is the optimal patent val for the kleismic temperament metakleismic, and 7, 11 and 13 limit rank three tolerant temperament. It is also the optimal patent val for the rank four 11-limit temperament tempering out 896/891, the pentacircle temperament. Other commas it tempers out include 2200/2187 in the 11-limit and 325/324, 352/351, 364/363 and 625/624 in the 13-limit.

208 = 16 * 13, and has divisors 2, 4, 8, 16, 13, 26, 52, 104.

13-limit transversal

[196/195, 100/99, 91/90, 64/63, 55/54, 49/48, 40/39, 77/75, 36/35, 28/27, 80/77, 25/24, 245/234, 22/21, 21/20, 81/77, 35/33, 52/49, 16/15, 77/72, 15/14, 14/13, 250/231, 13/12, 49/45, 12/11, 35/32, 100/91, 11/10, 54/49, 10/9, 49/44, 39/35, 28/25, 55/49, 9/8, 147/130, 25/22, 91/80, 8/7, 55/48, 147/128, 15/13, 196/169, 64/55, 7/6, 90/77, 75/64, 147/125, 13/11, 77/65, 25/21, 105/88, 117/98, 6/5, 77/64, 40/33, 63/52, 128/105, 11/9, 49/40, 16/13, 154/125, 26/21, 56/45, 96/77, 5/4, 49/39, 44/35, 63/50, 80/63, 14/11, 125/98, 32/25, 77/60, 9/7, 35/27, 100/77, 13/10, 64/49, 55/42, 21/16, 120/91, 33/25, 65/49, 4/3, 147/110, 75/56, 35/26, 66/49, 27/20, 49/36, 15/11, 175/128, 48/35, 11/8, 135/98, 18/13, 245/176, 39/28, 7/5, 108/77, 45/32, 147/104, 64/45, 77/54, 10/7, 56/39, 351/245, 13/9, 196/135, 16/11, 35/24, 143/98, 22/15, 72/49, 40/27, 49/33, 52/35, 112/75, 220/147, 3/2, 98/65, 50/33, 91/60, 32/21, 55/36, 49/32, 20/13, 77/50, 54/35, 14/9, 120/77, 25/16, 196/125, 11/7, 63/40, 100/63, 35/22, 78/49, 8/5, 77/48, 45/28, 21/13, 125/77, 13/8, 49/30, 18/11, 105/64, 104/63, 33/20, 81/49, 5/3, 147/88, 117/70, 42/25, 130/77, 22/13, 245/144, 75/44, 77/45, 12/7, 55/32, 169/98, 26/15, 256/147, 96/55, 7/4, 135/77, 44/25, 260/147, 16/9, 98/55, 25/14, 70/39, 88/49, 9/5, 49/27, 20/11, 91/50, 64/35, 11/6, 90/49, 24/13, 231/125, 13/7, 28/15, 144/77, 15/8, 49/26, 66/35, 91/48, 40/21, 21/11, 245/128, 25/13, 77/40, 27/14, 35/18, 150/77, 39/20, 49/25, 55/28, 63/32, 125/63, 99/50, 195/98, 2]

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