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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2012-08-28 02:43:18 UTC</tt>.<br>
| |
| : The original revision id was <tt>360370070</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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>
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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>=
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| **//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.
| | == Theory == |
| | 47edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths, as both fall between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. The fifth closest to [[3/2]] is 12.593-cent flat, unless you use the alternative fifth which is 12.939-cent sharp, similar to [[35edo]]. The soft diatonic scale generated from its flat fifth is so soft, with {{nowrap|L:s {{=}} 7:6}}, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. The hard diatonic scale generated from its sharp fifth is extremely hard, with {{nowrap|L:s {{=}} 9:1}}. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp. |
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| |
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| 47edo is the 15th [[prime numbers|prime]] edo, beforing [[43edo]] and following [[53edo]]. | | 47edo is one of the most difficult diatonic edos to notate in [[native fifth notation|native fifths]], because no other diatonic edo's fifth is as extreme. |
|
| |
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| ==Intervals of 47edo== | | === Odd harmonics === |
| | {{Harmonics in equal|47}} |
|
| |
|
| ||~ Degrees of 47edo ||~ Cents Value ||
| | 47edo 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 [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament. |
| || 0 || 0 ||
| |
| || 1 || 25.5319 ||
| |
| || 2 || 51.0638 ||
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| || 3 || 76.5957 ||
| |
| || 4 || 102.1277 ||
| |
| || 5 || 127.6596 ||
| |
| || 6 || 153.1915 ||
| |
| || 7 || 178.7234 ||
| |
| || 8 || 204.2553 ||
| |
| || 9 || 229.7872 ||
| |
| || 10 || 255.3191 ||
| |
| || 11 || 280.8511 ||
| |
| || 12 || 306.383 ||
| |
| || 13 || 331.9149 ||
| |
| || 14 || 357.4468 ||
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| || 15 || 382.9787 ||
| |
| || 16 || 408.5106 ||
| |
| || 17 || 434.0426 ||
| |
| || 18 || 459.5745 ||
| |
| || 19 || 485.1064 ||
| |
| || 20 || 510.6383 ||
| |
| || 21 || 536.1702 ||
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| || 22 || 561.7021 ||
| |
| || 23 || 587.234 ||
| |
| || 24 || 612.766 ||
| |
| || 25 || 638.2979 ||
| |
| || 26 || 663.8298 ||
| |
| || 27 || 689.3617 ||
| |
| || 28 || 714.8936 ||
| |
| || 29 || 740.4255 ||
| |
| || 30 || 765.9574 ||
| |
| || 31 || 791.4894 ||
| |
| || 32 || 817.0213 ||
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| || 33 || 842.5532 ||
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| || 34 || 868.0851 ||
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| || 35 || 893.617 ||
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| || 36 || 919.1489 ||
| |
| || 37 || 944.6809 ||
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| || 38 || 970.2128 ||
| |
| || 39 || 995.7447 ||
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| || 40 || 1021.2766 ||
| |
| || 41 || 1046.8085 ||
| |
| || 42 || 1072.3404 ||
| |
| || 43 || 1097.8723 ||
| |
| || 44 || 1123.4043 ||
| |
| || 45 || 1148.9362 ||
| |
| || 46 || 1174.4681 ||</pre></div>
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| <h4>Original HTML content:</h4>
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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>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>
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| <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.<br />
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| <br />
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| 47edo is the 15th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, beforing <a class="wiki_link" href="/43edo">43edo</a> and following <a class="wiki_link" href="/53edo">53edo</a>.<br />
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| <br />
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| <!-- 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>
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| <br />
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| | 47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one. |
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| |
|
| <table class="wiki_table">
| | === Subsets and supersets === |
| <tr>
| | 47edo is the 15th [[prime edo]], following [[43edo]] and preceding [[53edo]], so it does not contain any nontrivial subset edos, though it contains [[47ed4]]. [[94edo]], which doubles it, corrects its approximations of harmonics 3 and 11 to near-just qualities. |
| <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>25.5319<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>51.0638<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>76.5957<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>102.1277<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>127.6596<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>153.1915<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>178.7234<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
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| </td>
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| <td>204.2553<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>229.7872<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
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| </td>
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| <td>255.3191<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>11<br />
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| </td>
| |
| <td>280.8511<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>12<br />
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| </td>
| |
| <td>306.383<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>13<br />
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| </td>
| |
| <td>331.9149<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>357.4468<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
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| </td>
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| <td>382.9787<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>408.5106<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>17<br />
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| </td>
| |
| <td>434.0426<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>18<br />
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| </td>
| |
| <td>459.5745<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
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| <td>485.1064<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>510.6383<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>536.1702<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>561.7021<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>587.234<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>612.766<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>25<br />
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| </td>
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| <td>638.2979<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>663.8298<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>689.3617<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>28<br />
| |
| </td>
| |
| <td>714.8936<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>740.4255<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
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| <td>765.9574<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
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| <td>791.4894<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>32<br />
| |
| </td>
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| <td>817.0213<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>33<br />
| |
| </td>
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| <td>842.5532<br />
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| </td>
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| </tr>
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| <tr>
| |
| <td>34<br />
| |
| </td>
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| <td>868.0851<br />
| |
| </td>
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| </tr>
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| <tr>
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| <td>35<br />
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| </td>
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| <td>893.617<br />
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| </td>
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| </tr>
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| <tr>
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| <td>36<br />
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| </td>
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| <td>919.1489<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
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| <td>944.6809<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>38<br />
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| </td>
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| <td>970.2128<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
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| <td>995.7447<br />
| |
| </td>
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| </tr>
| |
| <tr>
| |
| <td>40<br />
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| </td>
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| <td>1021.2766<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>41<br />
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| </td>
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| <td>1046.8085<br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>42<br />
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| </td>
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| <td>1072.3404<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>1097.8723<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>1123.4043<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>1148.9362<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>1174.4681<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | == Intervals == |
| | {| class="wikitable center-all right-2" |
| | |- |
| | ! [[Degree|#]] |
| | ! [[Cent]]s |
| | ! colspan="2" | Relative notation |
| | ! Absolute notation |
| | |- |
| | | 0 |
| | | 0.0 |
| | | perfect unison |
| | | P1 |
| | | D |
| | |- |
| | | 1 |
| | | 25.5 |
| | | aug 1sn |
| | | A1 |
| | | D# |
| | |- |
| | | 2 |
| | | 51.1 |
| | | double-aug 1sn |
| | | AA1 |
| | | Dx |
| | |- |
| | | 3 |
| | | 76.6 |
| | | triple-aug 1sn, triple-dim 2nd |
| | | A<sup>3</sup>1, d<sup>3</sup>2 |
| | | D#<sup>3</sup>, Eb<sup>4</sup> |
| | |- |
| | | 4 |
| | | 102.1 |
| | | double-dim 2nd |
| | | dd2 |
| | | Eb<sup>3</sup> |
| | |- |
| | | 5 |
| | | 127.7 |
| | | dim 2nd |
| | | d2 |
| | | Ebb |
| | |- |
| | | 6 |
| | | 153.2 |
| | | minor 2nd |
| | | m2 |
| | | Eb |
| | |- |
| | | 7 |
| | | 178.7 |
| | | major 2nd |
| | | M2 |
| | | E |
| | |- |
| | | 8 |
| | | 204.3 |
| | | aug 2nd |
| | | A2 |
| | | E# |
| | |- |
| | | 9 |
| | | 229.8 |
| | | double-aug 2nd |
| | | AA2 |
| | | Ex |
| | |- |
| | | 10 |
| | | 255.3 |
| | | triple-aug 2nd, triple-dim 3rd |
| | | A<sup>3</sup>2, d<sup>3</sup>3 |
| | | E#<sup>3</sup>, Fb<sup>3</sup> |
| | |- |
| | | 11 |
| | | 280.9 |
| | | double-dim 3rd |
| | | dd3 |
| | | Fbb |
| | |- |
| | | 12 |
| | | 306.4 |
| | | dim 3rd |
| | | d3 |
| | | Fb |
| | |- |
| | | 13 |
| | | 331.9 |
| | | minor 3rd |
| | | m3 |
| | | F |
| | |- |
| | | 14 |
| | | 357.4 |
| | | major 3rd |
| | | M3 |
| | | F# |
| | |- |
| | | 15 |
| | | 383.0 |
| | | aug 3rd |
| | | A3 |
| | | Fx |
| | |- |
| | | 16 |
| | | 408.5 |
| | | double-aug 3rd |
| | | AA3 |
| | | F#<sup>3</sup> |
| | |- |
| | | 17 |
| | | 434.0 |
| | | triple-aug 3rd, triple-dim 4th |
| | | A<sup>3</sup>3, d<sup>3</sup>4 |
| | | F#<sup>4</sup>, Gb<sup>3</sup> |
| | |- |
| | | 18 |
| | | 459.6 |
| | | double-dim 4th |
| | | dd4 |
| | | Gbb |
| | |- |
| | | 19 |
| | | 485.1 |
| | | dim 4th |
| | | d4 |
| | | Gb |
| | |- |
| | | 20 |
| | | 510.6 |
| | | perfect 4th |
| | | P4 |
| | | G |
| | |- |
| | | 21 |
| | | 536.2 |
| | | aug 4th |
| | | A4 |
| | | G# |
| | |- |
| | | 22 |
| | | 561.7 |
| | | double-aug 4th |
| | | AA4 |
| | | Gx |
| | |- |
| | | 23 |
| | | 587.2 |
| | | triple-aug 4th |
| | | A<sup>3</sup>4 |
| | | G#<sup>3</sup> |
| | |- |
| | | 24 |
| | | 612.8 |
| | | triple-dim 5th |
| | | d<sup>3</sup>5 |
| | | Ab<sup>3</sup> |
| | |- |
| | | 25 |
| | | 638.3 |
| | | double-dim 5th |
| | | dd5 |
| | | Abb |
| | |- |
| | | 26 |
| | | 663.8 |
| | | dim 5th |
| | | d5 |
| | | Ab |
| | |- |
| | | 27 |
| | | 689.4 |
| | | perfect 5th |
| | | P5 |
| | | A |
| | |- |
| | | 28 |
| | | 714.9 |
| | | aug 5th |
| | | A5 |
| | | A# |
| | |- |
| | | 29 |
| | | 740.4 |
| | | double-aug 5th |
| | | AA5 |
| | | Ax |
| | |- |
| | | 30 |
| | | 766.0 |
| | | triple-aug 5th, triple-dim 6th |
| | | A<sup>3</sup>5, d<sup>3</sup>6 |
| | | A#<sup>3</sup>, Bb<sup>4</sup> |
| | |- |
| | | 31 |
| | | 791.5 |
| | | double-dim 6th |
| | | dd6 |
| | | Bb<sup>3</sup> |
| | |- |
| | | 32 |
| | | 817.0 |
| | | dim 6th |
| | | d6 |
| | | Bbb |
| | |- |
| | | 33 |
| | | 842.6 |
| | | minor 6th |
| | | m6 |
| | | Bb |
| | |- |
| | | 34 |
| | | 868.1 |
| | | major 6th |
| | | M6 |
| | | B |
| | |- |
| | | 35 |
| | | 893.6 |
| | | aug 6th |
| | | A6 |
| | | B# |
| | |- |
| | | 36 |
| | | 919.1 |
| | | double-aug 6th |
| | | AA6 |
| | | Bx |
| | |- |
| | | 37 |
| | | 944.7 |
| | | triple-aug 6th, triple-dim 7th |
| | | A<sup>3</sup>6, d<sup>3</sup>7 |
| | | B#<sup>3</sup>, Cb<sup>3</sup> |
| | |- |
| | | 38 |
| | | 970.2 |
| | | double-dim 7th |
| | | dd7 |
| | | Cbb |
| | |- |
| | | 39 |
| | | 995.7 |
| | | dim 7th |
| | | d7 |
| | | Cb |
| | |- |
| | | 40 |
| | | 1021.3 |
| | | minor 7th |
| | | m7 |
| | | C |
| | |- |
| | | 41 |
| | | 1046.8 |
| | | major 7th |
| | | M7 |
| | | C# |
| | |- |
| | | 42 |
| | | 1072.3 |
| | | aug 7th |
| | | A7 |
| | | Cx |
| | |- |
| | | 43 |
| | | 1097.9 |
| | | double-aug 7th |
| | | AA7 |
| | | C#<sup>3</sup> |
| | |- |
| | | 44 |
| | | 1123.4 |
| | | triple-aug 7th, triple-dim 8ve |
| | | A<sup>3</sup>7, d<sup>3</sup>8 |
| | | C#<sup>4</sup>, Db<sup>3</sup> |
| | |- |
| | | 45 |
| | | 1148.9 |
| | | double-dim 8ve |
| | | dd8 |
| | | Dbb |
| | |- |
| | | 46 |
| | | 1174.5 |
| | | dim 8ve |
| | | d8 |
| | | Db |
| | |- |
| | | 47 |
| | | 1200.0 |
| | | perfect 8ve |
| | | P8 |
| | | D |
| | |} |
| | |
| | == Notation == |
| | A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a 7edo-like scale: |
| | |
| | D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D |
| | |
| | D# is next to D. This notation requires triple, quadruple and in some keys, quintuple or more sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#<sup>3</sup> - F#<sup>5</sup> - A#<sup>3</sup> - C# or as Eb<sup>4</sup> - Gbb - Ab<sup>4</sup> - Db<sup>6</sup>. This is an aug-three double-dim-seven chord, written D#<sup>3</sup>(A3)dd7 or Eb<sup>4</sup>(A3)dd7. It could also be called a sharp-three triple-flat-seven chord, written D#<sup>3</sup>(#3)b<sup>3</sup>7 or Eb<sup>4</sup>(#3)b<sup>3</sup>7. |
| | |
| | Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a 5edo-like scale, with two of the notes inflected by a comma-sized edostep: |
| | |
| | D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D |
| | |
| | D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. |
| | |
| | === Ups and downs notation === |
| | Using [[Helmholtz–Ellis]] accidentals and the sharp fifth, 47edo can be notated using [[ups and downs notation|ups and downs]]: |
| | {{Sharpness-sharp8}} |
| | |
| | With the flat fifth, notation is identical to standard notation: |
| | {{Sharpness-sharp1}} |
| | |
| | === Sagittal notation === |
| | ==== Best fifth notation ==== |
| | This notation uses the same sagittal sequence as [[42edo#Second-best fifth notation|42b]]. |
| | |
| | <imagemap> |
| | File:47-EDO_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 300 0 519 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]] |
| | default [[File:47-EDO_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ==== Second-best fifth notation ==== |
| | ===== Evo and Revo flavors ===== |
| | <imagemap> |
| | File:47b_Sagittal.svg |
| | desc none |
| | rect 80 0 280 50 [[Sagittal_notation]] |
| | rect 280 0 440 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | default [[File:47b_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ===== Alternative Evo flavor ===== |
| | <imagemap> |
| | File:47b_Alternative_Evo_Sagittal.svg |
| | desc none |
| | rect 80 0 300 50 [[Sagittal_notation]] |
| | rect 389 0 549 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 389 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | default [[File:47b_Alternative_Evo_Sagittal.svg]] |
| | </imagemap> |
| | |
| | ===== Evo-SZ flavor ===== |
| | <imagemap> |
| | File:47b_Evo-SZ_Sagittal.svg |
| | desc none |
| | rect 80 0 335 50 [[Sagittal_notation]] |
| | rect 335 0 495 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] |
| | rect 20 80 300 106 [[Fractional_3-limit_notation#Bad-fifths_apotome-fraction_notation | apotome-fraction notation]] |
| | default [[File:47b_Evo-SZ_Sagittal.svg]] |
| | </imagemap> |
| | |
| | == Scales == |
| | * [[Negri in zeta-stretched 47edo]] |
| | * Quasi-equal [[equiheptatonic]] (Dorian): 7 6 7 7 7 6 7 |
| | ** Quasi-equiheptatonic minor pentatonic: 13 7 7 13 7 |
| | * Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7 |
| | * Quasi-equal [[equipentatonic]]: 9 10 9 10 9 |
| | * Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]]) |
| | ** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning) |
| | ** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning) |
| | |
| | == Instruments == |
| | === Lumatone === |
| | * [[Lumatone mapping for 47edo]] |
| | |
| | === Skip fretting === |
| | '''Skip fretting system 47 3 11''' is a [[skip-fretting]] system for [[47edo]] where strings are 11\47 and frets are 3\47. This is effectively 15.6666...-edo. All examples of this system on this page are for 5-string bass. |
| | |
| | ; Chords |
| | Neutral-dominant 7th: 1 0 1 2 2 |
| | |
| | == Music == |
| | * [https://youtu.be/_TqaWw7tv_E Improvisation in 47edo (octave-compressed tuning, 7-note subset of Negri[9<nowiki>]</nowiki>)] by [[Budjarn Lambeth]], Jan 2024 |
| | |
| | [[Category:Listen]] |
| | [[Category:Todo:add rank 2 temperaments table]] |