47edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 240945805 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 288886171 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-12-31 01:36:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288886171</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">=<span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span>= | <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">=<span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span>= | ||
**//47-EDO//** divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N subgroups|2*47 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[Chromatic pairs#Baldy|baldy]] and [[Chromatic pairs#Silver|silver]] temperaments and relatives.</pre></div> | **//47-EDO//** divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N subgroups|2*47 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[Chromatic pairs#Baldy|baldy]] and [[Chromatic pairs#Silver|silver]] temperaments and relatives. | ||
==Intervals of 47edo== | |||
||~ Degrees of 47edo ||~ Cents Value || | |||
|| 0 || 0 || | |||
|| 1 || 25.532 || | |||
|| 2 || 51.064 || | |||
|| 3 || 76.596 || | |||
|| 4 || 102.128 || | |||
|| 5 || 127.66 || | |||
|| 6 || 153.191 || | |||
|| 7 || 178.723 || | |||
|| 8 || 204.255 || | |||
|| 9 || 229.787 || | |||
|| 10 || 255.319 || | |||
|| 11 || 280.851 || | |||
|| 12 || 306.383 || | |||
|| 13 || 331.915 || | |||
|| 14 || 357.447 || | |||
|| 15 || 382.979 || | |||
|| 16 || 408.511 || | |||
|| 17 || 434.043 || | |||
|| 18 || 459.574 || | |||
|| 19 || 485.106 || | |||
|| 20 || 510.638 || | |||
|| 21 || 536.17 || | |||
|| 22 || 561.702 || | |||
|| 23 || 587.234 || | |||
|| 24 || 612.766 || | |||
|| 25 || 638.298 || | |||
|| 26 || 663.83 || | |||
|| 27 || 689.362 || | |||
|| 28 || 714.894 || | |||
|| 29 || 740.426 || | |||
|| 30 || 765.957 || | |||
|| 31 || 791.489 || | |||
|| 32 || 817.021 || | |||
|| 33 || 842.553 || | |||
|| 34 || 868.085 || | |||
|| 35 || 893.617 || | |||
|| 36 || 919.149 || | |||
|| 37 || 944.681 || | |||
|| 38 || 970.213 || | |||
|| 39 || 995.745 || | |||
|| 40 || 1021.277 || | |||
|| 41 || 1046.809 || | |||
|| 42 || 1072.34 || | |||
|| 43 || 1097.872 || | |||
|| 44 || 1123.404 || | |||
|| 45 || 1148.936 || | |||
|| 46 || 1174.468 ||</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>47edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x47 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span></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>47edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x47 tone Equal Temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #616161; font-size: 99%;">47 tone Equal Temperament</span></h1> | ||
<br /> | <br /> | ||
<strong><em>47-EDO</em></strong> divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*47 subgroup</a> of the <a class="wiki_link" href="/23-limit">23-limit</a>, on which it tempers out the same commas as <a class="wiki_link" href="/94edo">94edo</a>. It provides a good tuning for <a class="wiki_link" href="/Chromatic%20pairs#Baldy">baldy</a> and <a class="wiki_link" href="/Chromatic%20pairs#Silver">silver</a> temperaments and relatives.</body></html></pre></div> | <strong><em>47-EDO</em></strong> divides the octave into 47 equal parts of 25.5319 cents each. It has a fifth which is 12.5933 cents flat, unless you use the alternative fifth which is 12.9386 cents sharp. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*47 subgroup</a> of the <a class="wiki_link" href="/23-limit">23-limit</a>, on which it tempers out the same commas as <a class="wiki_link" href="/94edo">94edo</a>. It provides a good tuning for <a class="wiki_link" href="/Chromatic%20pairs#Baldy">baldy</a> and <a class="wiki_link" href="/Chromatic%20pairs#Silver">silver</a> temperaments and relatives.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x47 tone Equal Temperament-Intervals of 47edo"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals of 47edo</h2> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Degrees of 47edo<br /> | |||
</th> | |||
<th>Cents Value<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>25.532<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>51.064<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>76.596<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>102.128<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>127.66<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>153.191<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>178.723<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>204.255<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>229.787<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>255.319<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>280.851<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>306.383<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>331.915<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>357.447<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>382.979<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>408.511<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>434.043<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>459.574<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>485.106<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>510.638<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>536.17<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>561.702<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>587.234<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>612.766<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>638.298<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26<br /> | |||
</td> | |||
<td>663.83<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>27<br /> | |||
</td> | |||
<td>689.362<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28<br /> | |||
</td> | |||
<td>714.894<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29<br /> | |||
</td> | |||
<td>740.426<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>30<br /> | |||
</td> | |||
<td>765.957<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>31<br /> | |||
</td> | |||
<td>791.489<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>32<br /> | |||
</td> | |||
<td>817.021<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>33<br /> | |||
</td> | |||
<td>842.553<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>34<br /> | |||
</td> | |||
<td>868.085<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>35<br /> | |||
</td> | |||
<td>893.617<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36<br /> | |||
</td> | |||
<td>919.149<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37<br /> | |||
</td> | |||
<td>944.681<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38<br /> | |||
</td> | |||
<td>970.213<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>39<br /> | |||
</td> | |||
<td>995.745<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>40<br /> | |||
</td> | |||
<td>1021.277<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>41<br /> | |||
</td> | |||
<td>1046.809<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>42<br /> | |||
</td> | |||
<td>1072.34<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>43<br /> | |||
</td> | |||
<td>1097.872<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>44<br /> | |||
</td> | |||
<td>1123.404<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>45<br /> | |||
</td> | |||
<td>1148.936<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>46<br /> | |||
</td> | |||
<td>1174.468<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||