45edt: Difference between revisions
Wikispaces>genewardsmith **Imported revision 250635956 - Original comment: ** |
Wikispaces>guest **Imported revision 332550746 - 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: | : This revision was by author [[User:guest|guest]] and made on <tt>2012-05-09 12:42:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>332550746</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> | ||
<h4>Original Wikitext content:</h4> | <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 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth [[The Riemann Zeta Function and Tuning#Removing | <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 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth [[The Riemann Zeta Function and Tuning#Removing%20primes|no-twos zeta peak edt]]. | ||
=<span style="font-size: 1.4em;">Intervals of 45edt</span>= | |||
|| Degrees || Cents || Approximate Ratios || | |||
|| 0 || 0 || <span style="color: #660000;"><span style="color: #660000;">[[xenharmonic/1_1|1/1]]</span></span> || | |||
|| 1 || 42.266 || || | |||
|| 2 || 84.531 || || | |||
|| 3 || 126.797 || [[xenharmonic/14_13|14/13]], [[xenharmonic/15_14|15/14]], [[xenharmonic/16_15|16/15]], 29/27 || | |||
|| 4 || 169.063 || || | |||
|| 5 || 211.328 || 9/8 || | |||
|| 6 || 253.594 || [[xenharmonic/15_13|15/13]] || | |||
|| 7 || 295.860 || || | |||
|| 8 || 338.125 || || | |||
|| 9 || 380.391 || <span style="color: #660000;">[[xenharmonic/5_4|5/4]]</span> || | |||
|| 10 || 422.657 || || | |||
|| 11 || 464.922 || 13/10 || | |||
|| 12 || 507.188 || [[xenharmonic/4_3|4/3]] || | |||
|| 13 || 549.454 || || | |||
|| 14 || 591.719 || 7/5 || | |||
|| 15 || 633.985 || [[xenharmonic/13_9|13/9]] || | |||
|| 16 || 676.251 || || | |||
|| 17 || 718.516 || || | |||
|| 18 || 760.782 || <span style="color: #660000;"><span style="color: #660000;">[[xenharmonic/14_9|14/9]]</span></span> || | |||
|| 19 || 803.048 || 8/5 || | |||
|| 20 || 845.313 || || | |||
|| 21 || 887.579 || [[xenharmonic/5_3|5/3]] || | |||
|| 22 || 929.845 || 12/7 || | |||
|| 23 || 972.110 || 7/4 || | |||
|| 24 || 1014.376 || [[xenharmonic/9_5|9/5]] || | |||
|| 25 || 1056.642 || || | |||
|| 26 || 1098.907 || 17/9 || | |||
|| 27 || 1141.173 || <span style="color: #660000;"><span style="color: #660000;">[[xenharmonic/27_14|27/14]]</span></span> || | |||
|| 28 || 1183.439 || || | |||
|| 29 || 1225.704 || || | |||
|| 30 || 1267.970 || <span style="color: #660000;">[[xenharmonic/27_13|27/13]]</span> || | |||
|| 31 || 1310.236 || || | |||
|| 32 || 1352.501 || || | |||
|| 33 || 1394.767 || <span style="color: #660000;">[[xenharmonic/9_4|9/4]]</span> ([[xenharmonic/9_8|9/8]] plus an octave) || | |||
|| 34 || 1437.033 || 16/7 || | |||
|| 35 || 1479.298 || || | |||
|| 36 || 1521.564 || <span style="color: #660000;">[[xenharmonic/12_5|12/5]]</span> (<span style="color: #660000;">[[xenharmonic/6_5|6/5]]</span> plus an octave) || | |||
|| 37 || 1563.830 || || | |||
|| 38 || 1606.095 || || | |||
|| 39 || 1648.361 || <span style="color: #660000;">[[xenharmonic/13_5|13/5]]</span> ([[xenharmonic/13_10|13/10]] plus an octave) || | |||
|| 40 || 1690.627 || 8/3 || | |||
|| 41 || 1732.892 || || | |||
|| 42 || 1775.158 || <span style="color: #660000;">[[xenharmonic/14_5|14/5]]</span> ([[xenharmonic/7_5|7/5]] plus an octave) || | |||
|| 43 || 1817.424 || 20/7 || | |||
|| 44 || 1859.689 || || | |||
|| 45 || 1901.955 || <span style="color: #660000;">[[xenharmonic/3_1|3/1]]</span> ||</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>45edt</title></head><body>The 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing | <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>45edt</title></head><body>The 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit. It is the tenth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes">no-twos zeta peak edt</a>.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Intervals of 45edt"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="font-size: 1.4em;">Intervals of 45edt</span></h1> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Degrees<br /> | |||
</td> | |||
<td>Cents<br /> | |||
</td> | |||
<td>Approximate Ratios<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
<td><span style="color: #660000;"><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/1_1">1/1</a></span></span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>42.266<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>84.531<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>126.797<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_13">14/13</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/15_14">15/14</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/16_15">16/15</a>, 29/27<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>169.063<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>211.328<br /> | |||
</td> | |||
<td>9/8<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>253.594<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/15_13">15/13</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>295.860<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>338.125<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>380.391<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5_4">5/4</a></span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>422.657<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>464.922<br /> | |||
</td> | |||
<td>13/10<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>507.188<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/4_3">4/3</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>549.454<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>591.719<br /> | |||
</td> | |||
<td>7/5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>633.985<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_9">13/9</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>676.251<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>718.516<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>760.782<br /> | |||
</td> | |||
<td><span style="color: #660000;"><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_9">14/9</a></span></span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>803.048<br /> | |||
</td> | |||
<td>8/5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>845.313<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>887.579<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/5_3">5/3</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>929.845<br /> | |||
</td> | |||
<td>12/7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>972.110<br /> | |||
</td> | |||
<td>7/4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>1014.376<br /> | |||
</td> | |||
<td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_5">9/5</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>1056.642<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>1098.907<br /> | |||
</td> | |||
<td>17/9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>1141.173<br /> | |||
</td> | |||
<td><span style="color: #660000;"><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/27_14">27/14</a></span></span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>1183.439<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>1225.704<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>1267.970<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/27_13">27/13</a></span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31<br /> | |||
</td> | |||
<td>1310.236<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32<br /> | |||
</td> | |||
<td>1352.501<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33<br /> | |||
</td> | |||
<td>1394.767<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_4">9/4</a></span> (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/9_8">9/8</a> plus an octave)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>34<br /> | |||
</td> | |||
<td>1437.033<br /> | |||
</td> | |||
<td>16/7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35<br /> | |||
</td> | |||
<td>1479.298<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36<br /> | |||
</td> | |||
<td>1521.564<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/12_5">12/5</a></span> (<span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/6_5">6/5</a></span> plus an octave)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37<br /> | |||
</td> | |||
<td>1563.830<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38<br /> | |||
</td> | |||
<td>1606.095<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>39<br /> | |||
</td> | |||
<td>1648.361<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_5">13/5</a></span> (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/13_10">13/10</a> plus an octave)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>40<br /> | |||
</td> | |||
<td>1690.627<br /> | |||
</td> | |||
<td>8/3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41<br /> | |||
</td> | |||
<td>1732.892<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>42<br /> | |||
</td> | |||
<td>1775.158<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/14_5">14/5</a></span> (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_5">7/5</a> plus an octave)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43<br /> | |||
</td> | |||
<td>1817.424<br /> | |||
</td> | |||
<td>20/7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>44<br /> | |||
</td> | |||
<td>1859.689<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>45<br /> | |||
</td> | |||
<td>1901.955<br /> | |||
</td> | |||
<td><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/3_1">3/1</a></span><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||