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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:xenwolf|xenwolf]] and made on <tt>2016-12-29 14:47:57 UTC</tt>.<br>
| |
| : The original revision id was <tt>602898192</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>
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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">**103edo** is the [[equal division of the octave]] into 103 steps of size 11.6505 [[cent]]s each. It is a good [[Gamelismic clan|miracle]] tuning, especially for the [[7-limit|7-]] and [[13-limi|13-]] limits and [[Gamelismic clan|benediction]] and [[Gamelismic clan|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] 78732/78125 in the [[5-limit]]; 225/224, 1029/1024 and 2401/2400 in the 7-limit; 243/242, 441/440 and 540/539 in the [[11-limit]]; 351/350 and 847/845 in the 13-limit. In the 13-limit it provides the optimal patent val for [[Marvel family#Marvel|marvel temperament]] as well as [[Gamelismic clan#Miracle|benediction]] and [[Gamelismic clan#Hemisecordite|hemisecordite]].
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| 103edo is the 27th [[prime numbers|prime]] edo. | | == Theory == |
| ===13-limit temperaments===
| | In 103edo, all intervals within the [[17-odd-limit]] are [[consistent]], with the sole exception of [[9/8]] and its octave complement [[16/9]], which barely miss (relative error 50.2%). Its closest [[zeta peak index]], [[596zpi]], [[stretched and compressed tuning|stretches the octave]] by +0.739 cents. This expansion is uniquely consistent within the 15-integer-limit. |
| || Degree || cents || temperament ||
| |
| || 1 || 11.650 || Marvel and Benediction ||
| |
| || 2 || 23.301 || Hemisecordite ||
| |
| || 3 || 34.951 || Marvel and Benediction, Hemisecordite ||
| |
| || 4 || 46.602 || Marvel and Benediction ||
| |
| || 5 || 58.252 || Hemisecordite ||
| |
| || 6 || 69.903 || Marvel and Benediction ||
| |
| || 7 || 81.553 || Marvel and Benediction, Hemisecordite ||
| |
| || 8 || 93.204 || Hemisecordite ||
| |
| || 9 || 104.854 || Marvel and Benediction ||
| |
| || 10 || 116.505 || Marvel and Benediction, Hemisecordite ||
| |
| || 11 || 128.155 || Marvel and Benediction ||
| |
| || 12 || 139.806 || Hemisecordite ||
| |
| || 13 || 151.456 || Marvel and Benediction, Hemisecordite ||
| |
| || 14 || 163.107 || Marvel and Benediction ||
| |
| || 15 || 174.757 || Hemisecordite ||
| |
| || 16 || 186.408 || Marvel and Benediction ||
| |
| || 17 || 198.058 || Marvel and Benediction, Hemisecordite ||
| |
| || 18 || 209.708 || Hemisecordite ||
| |
| || 19 || 221.359 || Marvel and Benediction ||
| |
| || 20 || 233.010 || Marvel and Benediction, Hemisecordite ||
| |
| || 21 || 244.660 || Marvel and Benediction ||
| |
| || 22 || 256.311 || Hemisecordite ||
| |
| || 23 || 267.961 || Marvel and Benediction, Hemisecordite ||
| |
| || 24 || 279.712 || Marvel and Benediction ||
| |
| || 25 || 291.262 || Hemisecordite ||
| |
| || 26 || 303.013 || Marvel and Benediction ||
| |
| || 27 || 314.563 || Marvel and Benediction, Hemisecordite ||
| |
| || 28 || 326.214 || Hemisecordite ||
| |
| || 29 || 337.864 || Marvel and Benediction ||
| |
| || 30 || 349.615 || Marvel and Benediction, Hemisecordite ||
| |
| || 31 || 361.165 || Marvel and Benediction ||
| |
| || 32 || 372.816 || Hemisecordite ||
| |
| || 33 || 384.466 || Marvel and Benediction, Hemisecordite ||
| |
| || 34 || 396.117 || Marvel and Benediction ||
| |
| || 35 || 407.767 || Hemisecordite ||
| |
| || 36 || 419.4175 || Marvel and Benediction ||
| |
| || 37 || 431.068 || Marvel and Benediction, Hemisecordite ||
| |
| || 38 || 442.708 || Hemisecordite ||
| |
| || 39 || 454.369 || Marvel and Benediction ||
| |
| || 40 || 466.019 || Marvel and Benediction, Hemisecordite ||
| |
| || 41 || 477.670 || Marvel and Benediction ||
| |
| || 42 || 489.320 || Hemisecordite ||
| |
| || 43 || 500.971 || Marvel and Benediction, Hemisecordite ||
| |
| || 44 || 512.621 || Marvel and Benediction ||
| |
| || 45 || 524.272 || Hemisecordite ||
| |
| || 46 || 535.922 || Marvel and Benediction ||
| |
| || 47 || 547.573 || Marevel and Benediction, Hemisecordite ||
| |
| || 48 || 559.223 || Hemisecordite ||
| |
| || 49 || 570.874 || Marvel and Benediction ||
| |
| || 50 || 582.524 || Marvel and Benediction, Hemisecordite ||
| |
| || 52 || 605.825 || Marvel and Benediction, Hemisecordite ||
| |
| || 53 || 617.476 || Marvel and Benediction, Hemisecordite ||
| |
| || 54 || 629.126 || Marvel and Benediction ||
| |
| || 55 || 640.777 || Hemisecordite ||
| |
| || 56 || 652.427 || Marvel and Benediction, Hemisecordite ||
| |
| || 57 || 664.078 || Marvel and Benediction ||
| |
| || 58 || 675.728 || Hemisecordite ||
| |
| || 59 || 687.379 || Marvel and Benediction ||
| |
| || 60 || 699.029 || Marvel and Benediction, Hemisecordite ||
| |
| || 61 || 710.677 || Hemisecordite ||
| |
| || 62 || 722.330 || Marvel and Benediction ||
| |
| || 63 || 733.981 || Marvel and Benediction, Hemisecordite ||
| |
| || 64 || 745.631 || Marvel and Benediction ||
| |
| || 65 || 757.282 || Hemisecordite ||
| |
| || 66 || 768.932 || Marvel and Benediction, Hemisecordite ||
| |
| || 67 || 780.583 || Marvel and Benediction ||
| |
| || 68 || 792.233 || Hemisecordite ||
| |
| || 69 || 803.883 || Marvel and Benediction ||
| |
| || 70 || 815.534 || Marvel and Benediction, Hemisecordite ||
| |
| || 71 || 827.185 || Hemisecordite ||
| |
| || 72 || 838.835 || Marvel and Benediction ||
| |
| || 73 || 850.385 || Marvel and Benediction. Hemisecordite ||
| |
| || 74 || 862.156 || Marvel and Benediction ||
| |
| || 75 || 873.786 || Hemisecordite ||
| |
| || 76 || 885.537 || Marvel and Benediction, Hemisecordite ||
| |
| || 77 || 896.987 || Marvel and Benediction ||
| |
| || 78 || 908.638 || Hemisecordite ||
| |
| || 79 || 920.388 || Marvel and Benediction, Hemisecordite ||
| |
| || 80 || 932.039 || Marvel and Benediction ||
| |
| || 81 || 943.689 || Hemisecordite ||
| |
| || 82 || 955.34 || Marvel and Benediction ||
| |
| || 83 || 966.99 || Marvel and Benediction, Hemisecordite ||
| |
| || 84 || 978.641 || Marvel and Benediction ||
| |
| || 85 || 990.291 || Hemisecordite ||
| |
| || 86 || 1001.942 || Marvel and Benediction, Hemisecordite ||
| |
| || 87 || 1013.592 || Marvel and Benediction ||
| |
| || 88 || 1025.243 || Hemisecordite ||
| |
| || 89 || 1036.893 || Marvel and Benediction ||
| |
| || 90 || 1048.544 || Marvel and Benediction, Hemisecordite ||
| |
| || 91 || 1060.194 || Hemisecordite ||
| |
| || 92 || 1071.845 || Marvel and Benediction ||
| |
| || 93 || 1083.495 || Marvel and Benediction, Hemisecordite ||
| |
| || 94 || 1095.146 || Marvel and Benediction ||
| |
| || 95 || 1106.796 || Hemisecordite ||
| |
| || 96 || 1118.447 || Marvel and Benediction, Hemisecordite ||
| |
| || 97 || 1130.097 || Marvel and Benediction ||
| |
| || 98 || 1141.748 || Hemisecordite || | |
| || 99 || 1153.398 || Marvel and Benediction ||
| |
| || 100 || 1165.0485 || Marvel and Benediction, Hemisecordite ||
| |
| || 101 || 1176.609 || Hemisecordite ||
| |
| || 102 || 1188.3495 || Marvel and Benediction ||</pre></div>
| |
| <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>103edo</title></head><body><strong>103edo</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into 103 steps of size 11.6505 <a class="wiki_link" href="/cent">cent</a>s each. It is a good <a class="wiki_link" href="/Gamelismic%20clan">miracle</a> tuning, especially for the <a class="wiki_link" href="/7-limit">7-</a> and <a class="wiki_link" href="/13-limi">13-</a> limits and <a class="wiki_link" href="/Gamelismic%20clan">benediction</a> and <a class="wiki_link" href="/Gamelismic%20clan">hemisecordite</a>, two of the <a class="wiki_link" href="/13-limit">13-limit</a> extensions of miracle. It <a class="wiki_link" href="/tempering%20out">tempers out</a> 78732/78125 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 225/224, 1029/1024 and 2401/2400 in the 7-limit; 243/242, 441/440 and 540/539 in the <a class="wiki_link" href="/11-limit">11-limit</a>; 351/350 and 847/845 in the 13-limit. In the 13-limit it provides the optimal patent val for <a class="wiki_link" href="/Marvel%20family#Marvel">marvel temperament</a> as well as <a class="wiki_link" href="/Gamelismic%20clan#Miracle">benediction</a> and <a class="wiki_link" href="/Gamelismic%20clan#Hemisecordite">hemisecordite</a>.<br />
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| <br />
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| 103edo is the 27th <a class="wiki_link" href="/prime%20numbers">prime</a> edo.<br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--13-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->13-limit temperaments</h3>
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|
| <table class="wiki_table">
| | 103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]], and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]], and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite. |
| <tr>
| |
| <td>Degree<br />
| |
| </td>
| |
| <td>cents<br />
| |
| </td>
| |
| <td>temperament<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>11.650<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>23.301<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>34.951<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>46.602<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>58.252<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>69.903<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td>81.553<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td>93.204<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td>104.854<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>116.505<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>128.155<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>139.806<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>151.456<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td>163.107<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15<br />
| |
| </td>
| |
| <td>174.757<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16<br />
| |
| </td>
| |
| <td>186.408<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17<br />
| |
| </td>
| |
| <td>198.058<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18<br />
| |
| </td>
| |
| <td>209.708<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19<br />
| |
| </td>
| |
| <td>221.359<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>20<br />
| |
| </td>
| |
| <td>233.010<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>21<br />
| |
| </td>
| |
| <td>244.660<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22<br />
| |
| </td>
| |
| <td>256.311<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23<br />
| |
| </td>
| |
| <td>267.961<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>24<br />
| |
| </td>
| |
| <td>279.712<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>25<br />
| |
| </td>
| |
| <td>291.262<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>26<br />
| |
| </td>
| |
| <td>303.013<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>27<br />
| |
| </td>
| |
| <td>314.563<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>28<br />
| |
| </td>
| |
| <td>326.214<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29<br />
| |
| </td>
| |
| <td>337.864<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td>349.615<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td>361.165<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>372.816<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>384.466<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>396.117<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td>407.767<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>419.4175<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td>431.068<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td>442.708<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>454.369<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>466.019<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>477.670<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>489.320<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>500.971<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>512.621<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>524.272<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>535.922<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>547.573<br />
| |
| </td>
| |
| <td>Marevel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>559.223<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>570.874<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>582.524<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>605.825<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>617.476<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>629.126<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>640.777<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>652.427<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>664.078<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58<br />
| |
| </td>
| |
| <td>675.728<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>59<br />
| |
| </td>
| |
| <td>687.379<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>60<br />
| |
| </td>
| |
| <td>699.029<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>61<br />
| |
| </td>
| |
| <td>710.677<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>62<br />
| |
| </td>
| |
| <td>722.330<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>63<br />
| |
| </td>
| |
| <td>733.981<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64<br />
| |
| </td>
| |
| <td>745.631<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>65<br />
| |
| </td>
| |
| <td>757.282<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>66<br />
| |
| </td>
| |
| <td>768.932<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>67<br />
| |
| </td>
| |
| <td>780.583<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>68<br />
| |
| </td>
| |
| <td>792.233<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>69<br />
| |
| </td>
| |
| <td>803.883<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>70<br />
| |
| </td>
| |
| <td>815.534<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>71<br />
| |
| </td>
| |
| <td>827.185<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>72<br />
| |
| </td>
| |
| <td>838.835<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>73<br />
| |
| </td>
| |
| <td>850.385<br />
| |
| </td>
| |
| <td>Marvel and Benediction. Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>74<br />
| |
| </td>
| |
| <td>862.156<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>75<br />
| |
| </td>
| |
| <td>873.786<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>76<br />
| |
| </td>
| |
| <td>885.537<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>77<br />
| |
| </td>
| |
| <td>896.987<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>78<br />
| |
| </td>
| |
| <td>908.638<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>79<br />
| |
| </td>
| |
| <td>920.388<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>80<br />
| |
| </td>
| |
| <td>932.039<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>81<br />
| |
| </td>
| |
| <td>943.689<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>82<br />
| |
| </td>
| |
| <td>955.34<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>83<br />
| |
| </td>
| |
| <td>966.99<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>84<br />
| |
| </td>
| |
| <td>978.641<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>85<br />
| |
| </td>
| |
| <td>990.291<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>86<br />
| |
| </td>
| |
| <td>1001.942<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>87<br />
| |
| </td>
| |
| <td>1013.592<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>88<br />
| |
| </td>
| |
| <td>1025.243<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>89<br />
| |
| </td>
| |
| <td>1036.893<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>90<br />
| |
| </td>
| |
| <td>1048.544<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>91<br />
| |
| </td>
| |
| <td>1060.194<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>92<br />
| |
| </td>
| |
| <td>1071.845<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>93<br />
| |
| </td>
| |
| <td>1083.495<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>94<br />
| |
| </td>
| |
| <td>1095.146<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>95<br />
| |
| </td>
| |
| <td>1106.796<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>96<br />
| |
| </td>
| |
| <td>1118.447<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>97<br />
| |
| </td>
| |
| <td>1130.097<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>98<br />
| |
| </td>
| |
| <td>1141.748<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>99<br />
| |
| </td>
| |
| <td>1153.398<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>100<br />
| |
| </td>
| |
| <td>1165.0485<br />
| |
| </td>
| |
| <td>Marvel and Benediction, Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>101<br />
| |
| </td>
| |
| <td>1176.609<br />
| |
| </td>
| |
| <td>Hemisecordite<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>102<br />
| |
| </td>
| |
| <td>1188.3495<br />
| |
| </td>
| |
| <td>Marvel and Benediction<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Prime harmonics === |
| | {{Harmonics in equal|103|intervals=prime}} |
| | |
| | === Subsets and supersets === |
| | 103edo is the 27th [[prime edo]], following [[101edo]] and before [[107edo]]. |
| | |
| | == Intervals == |
| | {{Main|Table of 103edo intervals}} |
| | |
| | == Approximation to JI == |
| | === Interval mappings === |
| | {{Q-odd-limit intervals}} |
| | |
| | === Zeta peak index === |
| | {{ZPI |
| | | zpi = 596 |
| | | steps = 102.936629522070 |
| | | step size = 11.6576577800491 |
| | | tempered height = 8.543510 |
| | | pure height = 5.620365 |
| | | integral = 1.340775 |
| | | gap = 18.270998 |
| | | octave = 1200.73875134506 |
| | | consistent = 15 |
| | | distinct = 15 |
| | }} |
| | |
| | == Regular temperament properties == |
| | {| class="wikitable center-4 center-5 center-6" |
| | |- |
| | ! rowspan="2" | [[Subgroup]] |
| | ! rowspan="2" | [[Comma list]] |
| | ! rowspan="2" | [[Mapping]] |
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| | ! colspan="2" | Tuning error |
| | |- |
| | ! [[TE error|Absolute]] (¢) |
| | ! [[TE simple badness|Relative]] (%) |
| | |- |
| | | 2.3 |
| | | {{monzo| -163 103 }} |
| | | {{mapping| 103 166 }} |
| | | +0.923 |
| | | 0.924 |
| | | 7.92 |
| | |- |
| | | 2.3.5 |
| | | 78732/78125, 34171875/33554432 |
| | | {{mapping| 103 166 239 }} |
| | | +0.881 |
| | | 0.757 |
| | | 6.49 |
| | |- |
| | | 2.3.5.7 |
| | | 225/224, 1029/1024, 78732/78125 |
| | | {{mapping| 103 166 239 289 }} |
| | | +0.824 |
| | | 0.663 |
| | | 5.68 |
| | |- |
| | | 2.3.5.7.11 |
| | | 225/224, 243/242, 385/384, 43923/43750 |
| | | {{mapping| 103 166 239 289 356 }} |
| | | +0.876 |
| | | 0.602 |
| | | 5.16 |
| | |- |
| | | 2.3.5.7.11.13 |
| | | 225/224, 243/242, 351/350, 385/384, 847/845 |
| | | {{mapping| 103 166 239 289 356 381 }} |
| | | +0.806 |
| | | 0.571 |
| | | 4.90 |
| | |- |
| | | 2.3.5.7.11.13.17 |
| | | 225/224, 243/242, 273/272, 351/350, 375/374, 847/845 |
| | | {{mapping| 103 166 239 289 356 381 421 }} |
| | | +0.694 |
| | | 0.595 |
| | | 5.10 |
| | |} |
| | |
| | * 103et (103h val) has lower absolute errors than any smaller equal temperaments in the [[13-limit|13-]], [[17-limit|17-]], and [[19-limit]]s, being beaten by [[111edo|111]] in all of them. |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br>ratio* |
| | ! Temperaments |
| | |- |
| | | 1 |
| | | 3\103 |
| | | 34.951 |
| | | 1990656/1953125 |
| | | [[Gammy]] |
| | |- |
| | | 1 |
| | | 5\103 |
| | | 58.252 |
| | | 27/26 |
| | | [[Hemisecordite]] |
| | |- |
| | | 1 |
| | | 9\103 |
| | | 104.854 |
| | | 17/16 |
| | | [[Septendesemi]] |
| | |- |
| | | 1 |
| | | 10\103 |
| | | 116.505 |
| | | 15/14~16/15 |
| | | [[Miracle]] / [[benediction]] |
| | |- |
| | | 1 |
| | | 16\103 |
| | | 186.408 |
| | | 10/9 |
| | | [[Mintone]] |
| | |- |
| | | 1 |
| | | 20\103 |
| | | 233.010 |
| | | 8/7 |
| | | [[Slendric]] |
| | |- |
| | | 1 |
| | | 21\103 |
| | | 244.660 |
| | | 15/13 |
| | | [[Subsemifourth]] |
| | |- |
| | | 1 |
| | | 26\103 |
| | | 303.013 |
| | | 25/21 |
| | | [[Quinmite]] |
| | |- |
| | | 1 |
| | | 31\103 |
| | | 361.165 |
| | | 16/13 |
| | | [[Phicordial]] |
| | |- |
| | | 1 |
| | | 37\103 |
| | | 431.06 |
| | | 77/60 |
| | | [[Lockerbie]] |
| | |- |
| | | 1 |
| | | 38\103 |
| | | 442.708 |
| | | 162/125 |
| | | [[Sensei]] |
| | |- |
| | | 1 |
| | | 39\103 |
| | | 454.369 |
| | | 13/10 |
| | | [[Fibo]] |
| | |- |
| | | 1 |
| | | 40\103 |
| | | 466.019 |
| | | 55/42 |
| | | [[Hemiseptisix]] |
| | |- |
| | | 1 |
| | | 42\103 |
| | | 489.320 |
| | | 65/49 |
| | | [[Catafourth]] |
| | |- |
| | | 1 |
| | | 45\103 |
| | | 524.272 |
| | | 65/48 |
| | | [[Widefourth]] |
| | |- |
| | | 1 |
| | | 47\103 |
| | | 547.573 |
| | | 11/8 |
| | | [[Heinz]] |
| | |- |
| | | 1 |
| | | 48\103 |
| | | 559.223 |
| | | 242/175 |
| | | [[Tritriple]] |
| | |- |
| | | 1 |
| | | 50\103 |
| | | 582.524 |
| | | 7/5 |
| | | [[Neptune]] |
| | |} |
| | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
| | |
| | == Music == |
| | ; [[Francium]] |
| | * "Forest Tribe Dance" from ''Mysteries'' (2023) – [https://open.spotify.com/track/0lPUfgduKoJliGbU3kcow0 Spotify] | [https://francium223.bandcamp.com/track/forest-tribe-dance Bandcamp] | [https://www.youtube.com/watch?v=5pbnmzXAFcM YouTube] |
| | |
| | [[Category:Benediction]] |
| | [[Category:Listen]] |
| | [[Category:Miracle]] |