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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | ''104edo'' divides the octave into 104 parts of size 11.54 cents each. It has two different equally viable 5-limit [[val|val]]s, and both are useful. The flat major third val, <104 165 241|, tempers out 3125/3072, and supports [[Magic_family|magic temperament]]. The sharp major third val, <104 165 242|, tempers out 2048/2025 and supports [[Diaschismic_family|diaschismic temperament]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-14 17:06:24 UTC</tt>.<br>
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| : The original revision id was <tt>599442450</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>
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| <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">//104edo// divides the octave into 104 parts of size 11.54 cents each. It has two different equally viable 5-limit [[val]]s, and both are useful. The flat major third val, <104 165 241|, tempers out 3125/3072, and supports [[Magic family|magic temperament]]. The sharp major third val, <104 165 242|, tempers out 2048/2025 and supports [[Diaschismic family|diaschismic temperament]].
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|
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|
| 104edo with the flat third is especially notable as an excellent tuning for [[Magic family|magic temperament]], providing the [[optimal patent val]] for 11-limit magic and the 13-limit magic extension [[Magic family#Magic-13-limit-Necromancy|necromancy]]. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out 225/224, 245/243 and 875/864; and in the 11-limit, 100/99, 896/891, 385/384 and 540/539. It provides an excellent tuning also for the rank three temperaments pairing 100/99 with 225/224 (apollo temperament), 245/243 or 875/864, or the rank four temperament tempering out 100/99, for which it gives the [[optimal patent val]]. | | 104edo with the flat third is especially notable as an excellent tuning for [[Magic_family|magic temperament]], providing the [[Optimal_patent_val|optimal patent val]] for 11-limit magic and the 13-limit magic extension [[Magic_family#Magic-13-limit-Necromancy|necromancy]]. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out 225/224, 245/243 and 875/864; and in the 11-limit, 100/99, 896/891, 385/384 and 540/539. It provides an excellent tuning also for the rank three temperaments pairing 100/99 with 225/224 (apollo temperament), 245/243 or 875/864, or the rank four temperament tempering out 100/99, for which it gives the [[Optimal_patent_val|optimal patent val]]. |
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| 104 with the sharp third is excellent for 11, 13, or 17 limit diaschismic. It tempers out 2048/2025 in the 5-limit, 126/125 and 5120/5103 in the 7-limit, 176/175 and 896/891 in the 11-limit, 196/195 and 364/363 in the 13-limit and 136/135 and 256/255 in the 17-limit. | | 104 with the sharp third is excellent for 11, 13, or 17 limit diaschismic. It tempers out 2048/2025 in the 5-limit, 126/125 and 5120/5103 in the 7-limit, 176/175 and 896/891 in the 11-limit, 196/195 and 364/363 in the 13-limit and 136/135 and 256/255 in the 17-limit. |
| Line 14: |
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| 104 is also notable as a no-fives system; on 2.3.7.11.13, it tempers out 352/351, 364/363, 896/891, 2197/2187, 16807/16731, 20449/20412, 21632/21609, 26411/26364 and 10648/10647. It is the optimal patent val for the 17&87 2.3.7.11.13 subgroup temperament tempering out 352/351, 364/363 and 2197/2187, which has a 13/9 generator, three of which give a 3. | | 104 is also notable as a no-fives system; on 2.3.7.11.13, it tempers out 352/351, 364/363, 896/891, 2197/2187, 16807/16731, 20449/20412, 21632/21609, 26411/26364 and 10648/10647. It is the optimal patent val for the 17&87 2.3.7.11.13 subgroup temperament tempering out 352/351, 364/363 and 2197/2187, which has a 13/9 generator, three of which give a 3. |
|
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|
| **17-limit Regular Temperaments**
| | '''17-limit Regular Temperaments''' |
| ||~ Degree ||~ Cents ||
| |
| || **2** || **23.08** ||
| |
| || 3 || 34.615 ||
| |
| || 4 || 46.15 ||
| |
| || **5** || **57.69** ||
| |
| || **7** || **80.77** ||
| |
| || 8 || 92.31 ||
| |
| || 9 || 103.85 ||
| |
| || 10 || 115.385 ||
| |
| || 11 || 126.92 ||
| |
| || 12 || 138.46 ||
| |
| || **13** || **150** ||
| |
| || 14 || 161.54 ||
| |
| || 15 || 173.08 ||
| |
| || 16 || 184.615 ||
| |
| || 17 || 196.15 ||
| |
| || **18** || **207.69** ||
| |
| || **20** || **230.77** ||
| |
| || 21 || 242.31 ||
| |
| || 22 || 253.85 ||
| |
| || **23** || **265.385** ||
| |
| || **25** || **288.46** ||
| |
| || 26 || 300 ||
| |
| || 27 || 311.54 ||
| |
| || 28 || 323.08 ||
| |
| || 29 || 334.615 ||
| |
| || **30** || **346.15** ||
| |
| || 31 || 357.69 ||
| |
| || 32 || 369.23 ||
| |
| || 33 || 380.77 ||
| |
| || 34 || 392.31 ||
| |
| || 35 || 403.85 ||
| |
| || 36 || 415.385 ||
| |
| || 38 || 438.46 ||
| |
| || 39 || 450 ||
| |
| || 40 || 461.54 ||
| |
| || **41** || **473.08** ||
| |
| || **43** || **496.15** ||
| |
| || **45** || **519.23** ||
| |
| || 46 || 530.77 ||
| |
| || 47 || 542.31 ||
| |
| || **48** || **553.85** ||
| |
| || 50 || 576.92 ||
| |
| || 51 || 588.45 ||
| |
| || 52 || 600 ||
| |
| || 53 || 611.54 ||
| |
| || **54** || **623.08** ||
| |
| || 56 || 646.15 ||
| |
| || 57 || 657.69 ||
| |
| || 58 || 669.23 ||
| |
| || 59 || 680.77 ||
| |
| || **61** || **703.85** ||
| |
| || 63 || 726.92 ||
| |
| || 64 || 738.46 ||
| |
| || 65 || 750 ||
| |
| || **66** || **761.54** ||
| |
| || 67 || 773.08 ||
| |
| || **68** || **784.615** ||
| |
| || 69 || 796.15 ||
| |
| || 70 || 807.69 ||
| |
| || 71 || 819.23 ||
| |
| || 72 || 830.77 ||
| |
| || 73 || 842.31 ||
| |
| || **74** || **853.85** ||
| |
| || 75 || 865.385 ||
| |
| || 76 || 876.92 ||
| |
| || 77 || 888.46 ||
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| || 78 || 900 ||
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| || 79 || 911.54 ||
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| || **81** || **934.615** ||
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| || 82 || 946.15 ||
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| || 83 || 957.69 ||
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| || **84** || **969.23** ||
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| || 86 || 992.31 ||
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| || 87 || 1003.85 ||
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| || 88 || 1015.385 ||
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| || 89 || 1026.92 ||
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| || 90 || 1038.46 ||
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| || **91** || **1050** ||
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| || 92 || 1061.54 ||
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| || 93 || 1073.08 ||
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| || 95 || 1096.15 ||
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| || 96 || 1107.69 ||
| |
| || **97** || **1119.23** ||
| |
| || 99 || 1142.31 ||
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| || **100** || **1153.85** ||
| |
| || 101 || 1165.385 ||
| |
| || **102** || **1176.92** ||</pre></div>
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| <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>104edo</title></head><body><em>104edo</em> divides the octave into 104 parts of size 11.54 cents each. It has two different equally viable 5-limit <a class="wiki_link" href="/val">val</a>s, and both are useful. The flat major third val, &lt;104 165 241|, tempers out 3125/3072, and supports <a class="wiki_link" href="/Magic%20family">magic temperament</a>. The sharp major third val, &lt;104 165 242|, tempers out 2048/2025 and supports <a class="wiki_link" href="/Diaschismic%20family">diaschismic temperament</a>.<br />
| |
| <br />
| |
| 104edo with the flat third is especially notable as an excellent tuning for <a class="wiki_link" href="/Magic%20family">magic temperament</a>, providing the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit magic and the 13-limit magic extension <a class="wiki_link" href="/Magic%20family#Magic-13-limit-Necromancy">necromancy</a>. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out 225/224, 245/243 and 875/864; and in the 11-limit, 100/99, 896/891, 385/384 and 540/539. It provides an excellent tuning also for the rank three temperaments pairing 100/99 with 225/224 (apollo temperament), 245/243 or 875/864, or the rank four temperament tempering out 100/99, for which it gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>.<br />
| |
| <br />
| |
| 104 with the sharp third is excellent for 11, 13, or 17 limit diaschismic. It tempers out 2048/2025 in the 5-limit, 126/125 and 5120/5103 in the 7-limit, 176/175 and 896/891 in the 11-limit, 196/195 and 364/363 in the 13-limit and 136/135 and 256/255 in the 17-limit.<br />
| |
| <br />
| |
| 104 is also notable as a no-fives system; on 2.3.7.11.13, it tempers out 352/351, 364/363, 896/891, 2197/2187, 16807/16731, 20449/20412, 21632/21609, 26411/26364 and 10648/10647. It is the optimal patent val for the 17&amp;87 2.3.7.11.13 subgroup temperament tempering out 352/351, 364/363 and 2197/2187, which has a 13/9 generator, three of which give a 3.<br />
| |
| <br />
| |
| <strong>17-limit Regular Temperaments</strong><br />
| |
|
| |
|
| | | {| class="wikitable" |
| <table class="wiki_table">
| | |- |
| <tr>
| | ! | Degree |
| <th>Degree<br />
| | ! | Cents |
| </th>
| | |- |
| <th>Cents<br />
| | | | '''2''' |
| </th>
| | | | '''23.08''' |
| </tr>
| | |- |
| <tr>
| | | | 3 |
| <td><strong>2</strong><br />
| | | | 34.615 |
| </td>
| | |- |
| <td><strong>23.08</strong><br />
| | | | 4 |
| </td>
| | | | 46.15 |
| </tr>
| | |- |
| <tr>
| | | | '''5''' |
| <td>3<br />
| | | | '''57.69''' |
| </td>
| | |- |
| <td>34.615<br />
| | | | '''7''' |
| </td>
| | | | '''80.77''' |
| </tr>
| | |- |
| <tr>
| | | | 8 |
| <td>4<br />
| | | | 92.31 |
| </td>
| | |- |
| <td>46.15<br />
| | | | 9 |
| </td>
| | | | 103.85 |
| </tr>
| | |- |
| <tr>
| | | | 10 |
| <td><strong>5</strong><br />
| | | | 115.385 |
| </td>
| | |- |
| <td><strong>57.69</strong><br />
| | | | 11 |
| </td>
| | | | 126.92 |
| </tr>
| | |- |
| <tr>
| | | | 12 |
| <td><strong>7</strong><br />
| | | | 138.46 |
| </td>
| | |- |
| <td><strong>80.77</strong><br />
| | | | '''13''' |
| </td>
| | | | '''150''' |
| </tr>
| | |- |
| <tr>
| | | | 14 |
| <td>8<br />
| | | | 161.54 |
| </td>
| | |- |
| <td>92.31<br />
| | | | 15 |
| </td>
| | | | 173.08 |
| </tr>
| | |- |
| <tr>
| | | | 16 |
| <td>9<br />
| | | | 184.615 |
| </td>
| | |- |
| <td>103.85<br />
| | | | 17 |
| </td>
| | | | 196.15 |
| </tr>
| | |- |
| <tr>
| | | | '''18''' |
| <td>10<br />
| | | | '''207.69''' |
| </td>
| | |- |
| <td>115.385<br />
| | | | '''20''' |
| </td>
| | | | '''230.77''' |
| </tr>
| | |- |
| <tr>
| | | | 21 |
| <td>11<br />
| | | | 242.31 |
| </td>
| | |- |
| <td>126.92<br />
| | | | 22 |
| </td>
| | | | 253.85 |
| </tr>
| | |- |
| <tr>
| | | | '''23''' |
| <td>12<br />
| | | | '''265.385''' |
| </td>
| | |- |
| <td>138.46<br />
| | | | '''25''' |
| </td>
| | | | '''288.46''' |
| </tr>
| | |- |
| <tr>
| | | | 26 |
| <td><strong>13</strong><br />
| | | | 300 |
| </td>
| | |- |
| <td><strong>150</strong><br />
| | | | 27 |
| </td>
| | | | 311.54 |
| </tr>
| | |- |
| <tr>
| | | | 28 |
| <td>14<br />
| | | | 323.08 |
| </td>
| | |- |
| <td>161.54<br />
| | | | 29 |
| </td>
| | | | 334.615 |
| </tr>
| | |- |
| <tr>
| | | | '''30''' |
| <td>15<br />
| | | | '''346.15''' |
| </td>
| | |- |
| <td>173.08<br />
| | | | 31 |
| </td>
| | | | 357.69 |
| </tr>
| | |- |
| <tr>
| | | | 32 |
| <td>16<br />
| | | | 369.23 |
| </td>
| | |- |
| <td>184.615<br />
| | | | 33 |
| </td>
| | | | 380.77 |
| </tr>
| | |- |
| <tr>
| | | | 34 |
| <td>17<br />
| | | | 392.31 |
| </td>
| | |- |
| <td>196.15<br />
| | | | 35 |
| </td>
| | | | 403.85 |
| </tr>
| | |- |
| <tr>
| | | | 36 |
| <td><strong>18</strong><br />
| | | | 415.385 |
| </td>
| | |- |
| <td><strong>207.69</strong><br />
| | | | 38 |
| </td>
| | | | 438.46 |
| </tr>
| | |- |
| <tr>
| | | | 39 |
| <td><strong>20</strong><br />
| | | | 450 |
| </td>
| | |- |
| <td><strong>230.77</strong><br />
| | | | 40 |
| </td>
| | | | 461.54 |
| </tr>
| | |- |
| <tr>
| | | | '''41''' |
| <td>21<br />
| | | | '''473.08''' |
| </td>
| | |- |
| <td>242.31<br />
| | | | '''43''' |
| </td>
| | | | '''496.15''' |
| </tr>
| | |- |
| <tr>
| | | | '''45''' |
| <td>22<br />
| | | | '''519.23''' |
| </td>
| | |- |
| <td>253.85<br />
| | | | 46 |
| </td>
| | | | 530.77 |
| </tr>
| | |- |
| <tr>
| | | | 47 |
| <td><strong>23</strong><br />
| | | | 542.31 |
| </td>
| | |- |
| <td><strong>265.385</strong><br />
| | | | '''48''' |
| </td>
| | | | '''553.85''' |
| </tr>
| | |- |
| <tr>
| | | | 50 |
| <td><strong>25</strong><br />
| | | | 576.92 |
| </td>
| | |- |
| <td><strong>288.46</strong><br />
| | | | 51 |
| </td>
| | | | 588.45 |
| </tr>
| | |- |
| <tr>
| | | | 52 |
| <td>26<br />
| | | | 600 |
| </td>
| | |- |
| <td>300<br />
| | | | 53 |
| </td>
| | | | 611.54 |
| </tr>
| | |- |
| <tr>
| | | | '''54''' |
| <td>27<br />
| | | | '''623.08''' |
| </td>
| | |- |
| <td>311.54<br />
| | | | 56 |
| </td>
| | | | 646.15 |
| </tr>
| | |- |
| <tr>
| | | | 57 |
| <td>28<br />
| | | | 657.69 |
| </td>
| | |- |
| <td>323.08<br />
| | | | 58 |
| </td>
| | | | 669.23 |
| </tr>
| | |- |
| <tr>
| | | | 59 |
| <td>29<br />
| | | | 680.77 |
| </td>
| | |- |
| <td>334.615<br />
| | | | '''61''' |
| </td>
| | | | '''703.85''' |
| </tr>
| | |- |
| <tr>
| | | | 63 |
| <td><strong>30</strong><br />
| | | | 726.92 |
| </td>
| | |- |
| <td><strong>346.15</strong><br />
| | | | 64 |
| </td>
| | | | 738.46 |
| </tr>
| | |- |
| <tr>
| | | | 65 |
| <td>31<br />
| | | | 750 |
| </td>
| | |- |
| <td>357.69<br />
| | | | '''66''' |
| </td>
| | | | '''761.54''' |
| </tr>
| | |- |
| <tr>
| | | | 67 |
| <td>32<br />
| | | | 773.08 |
| </td>
| | |- |
| <td>369.23<br />
| | | | '''68''' |
| </td>
| | | | '''784.615''' |
| </tr>
| | |- |
| <tr>
| | | | 69 |
| <td>33<br />
| | | | 796.15 |
| </td>
| | |- |
| <td>380.77<br />
| | | | 70 |
| </td>
| | | | 807.69 |
| </tr>
| | |- |
| <tr>
| | | | 71 |
| <td>34<br />
| | | | 819.23 |
| </td>
| | |- |
| <td>392.31<br />
| | | | 72 |
| </td>
| | | | 830.77 |
| </tr>
| | |- |
| <tr>
| | | | 73 |
| <td>35<br />
| | | | 842.31 |
| </td>
| | |- |
| <td>403.85<br />
| | | | '''74''' |
| </td>
| | | | '''853.85''' |
| </tr>
| | |- |
| <tr>
| | | | 75 |
| <td>36<br />
| | | | 865.385 |
| </td>
| | |- |
| <td>415.385<br />
| | | | 76 |
| </td>
| | | | 876.92 |
| </tr>
| | |- |
| <tr>
| | | | 77 |
| <td>38<br />
| | | | 888.46 |
| </td>
| | |- |
| <td>438.46<br />
| | | | 78 |
| </td>
| | | | 900 |
| </tr>
| | |- |
| <tr>
| | | | 79 |
| <td>39<br />
| | | | 911.54 |
| </td>
| | |- |
| <td>450<br />
| | | | '''81''' |
| </td>
| | | | '''934.615''' |
| </tr>
| | |- |
| <tr>
| | | | 82 |
| <td>40<br />
| | | | 946.15 |
| </td>
| | |- |
| <td>461.54<br />
| | | | 83 |
| </td>
| | | | 957.69 |
| </tr>
| | |- |
| <tr>
| | | | '''84''' |
| <td><strong>41</strong><br />
| | | | '''969.23''' |
| </td>
| | |- |
| <td><strong>473.08</strong><br />
| | | | 86 |
| </td>
| | | | 992.31 |
| </tr>
| | |- |
| <tr>
| | | | 87 |
| <td><strong>43</strong><br />
| | | | 1003.85 |
| </td>
| | |- |
| <td><strong>496.15</strong><br />
| | | | 88 |
| </td>
| | | | 1015.385 |
| </tr>
| | |- |
| <tr>
| | | | 89 |
| <td><strong>45</strong><br />
| | | | 1026.92 |
| </td>
| | |- |
| <td><strong>519.23</strong><br />
| | | | 90 |
| </td>
| | | | 1038.46 |
| </tr>
| | |- |
| <tr>
| | | | '''91''' |
| <td>46<br />
| | | | '''1050''' |
| </td>
| | |- |
| <td>530.77<br />
| | | | 92 |
| </td>
| | | | 1061.54 |
| </tr>
| | |- |
| <tr>
| | | | 93 |
| <td>47<br />
| | | | 1073.08 |
| </td>
| | |- |
| <td>542.31<br />
| | | | 95 |
| </td>
| | | | 1096.15 |
| </tr>
| | |- |
| <tr>
| | | | 96 |
| <td><strong>48</strong><br />
| | | | 1107.69 |
| </td>
| | |- |
| <td><strong>553.85</strong><br />
| | | | '''97''' |
| </td>
| | | | '''1119.23''' |
| </tr>
| | |- |
| <tr>
| | | | 99 |
| <td>50<br />
| | | | 1142.31 |
| </td>
| | |- |
| <td>576.92<br />
| | | | '''100''' |
| </td>
| | | | '''1153.85''' |
| </tr>
| | |- |
| <tr>
| | | | 101 |
| <td>51<br />
| | | | 1165.385 |
| </td>
| | |- |
| <td>588.45<br />
| | | | '''102''' |
| </td>
| | | | '''1176.92''' |
| </tr>
| | |} |
| <tr>
| | [[Category:apollo]] |
| <td>52<br />
| | [[Category:diaschismic]] |
| </td>
| | [[Category:edo]] |
| <td>600<br />
| | [[Category:magic]] |
| </td>
| | [[Category:necromancy]] |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>611.54<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>54</strong><br />
| |
| </td>
| |
| <td><strong>623.08</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>646.15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>657.69<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58<br />
| |
| </td>
| |
| <td>669.23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>59<br />
| |
| </td>
| |
| <td>680.77<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>61</strong><br />
| |
| </td>
| |
| <td><strong>703.85</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>63<br />
| |
| </td>
| |
| <td>726.92<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64<br />
| |
| </td>
| |
| <td>738.46<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>65<br />
| |
| </td>
| |
| <td>750<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>66</strong><br />
| |
| </td>
| |
| <td><strong>761.54</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>67<br />
| |
| </td>
| |
| <td>773.08<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>68</strong><br />
| |
| </td>
| |
| <td><strong>784.615</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>69<br />
| |
| </td>
| |
| <td>796.15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>70<br />
| |
| </td>
| |
| <td>807.69<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>71<br />
| |
| </td>
| |
| <td>819.23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>72<br />
| |
| </td>
| |
| <td>830.77<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>73<br />
| |
| </td>
| |
| <td>842.31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>74</strong><br />
| |
| </td>
| |
| <td><strong>853.85</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>75<br />
| |
| </td>
| |
| <td>865.385<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>76<br />
| |
| </td>
| |
| <td>876.92<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>77<br />
| |
| </td>
| |
| <td>888.46<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>78<br />
| |
| </td>
| |
| <td>900<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>79<br />
| |
| </td>
| |
| <td>911.54<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>81</strong><br />
| |
| </td>
| |
| <td><strong>934.615</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>82<br />
| |
| </td>
| |
| <td>946.15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>83<br />
| |
| </td>
| |
| <td>957.69<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>84</strong><br />
| |
| </td>
| |
| <td><strong>969.23</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>86<br />
| |
| </td>
| |
| <td>992.31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>87<br />
| |
| </td>
| |
| <td>1003.85<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>88<br />
| |
| </td>
| |
| <td>1015.385<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>89<br />
| |
| </td>
| |
| <td>1026.92<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>90<br />
| |
| </td>
| |
| <td>1038.46<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>91</strong><br />
| |
| </td>
| |
| <td><strong>1050</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>92<br />
| |
| </td>
| |
| <td>1061.54<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>93<br />
| |
| </td>
| |
| <td>1073.08<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>95<br />
| |
| </td>
| |
| <td>1096.15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>96<br />
| |
| </td>
| |
| <td>1107.69<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>97</strong><br />
| |
| </td>
| |
| <td><strong>1119.23</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>99<br />
| |
| </td>
| |
| <td>1142.31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>100</strong><br />
| |
| </td>
| |
| <td><strong>1153.85</strong><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>101<br />
| |
| </td>
| |
| <td>1165.385<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><strong>102</strong><br />
| |
| </td>
| |
| <td><strong>1176.92</strong><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
104edo divides the octave into 104 parts of size 11.54 cents each. It has two different equally viable 5-limit vals, and both are useful. The flat major third val, <104 165 241|, tempers out 3125/3072, and supports magic temperament. The sharp major third val, <104 165 242|, tempers out 2048/2025 and supports diaschismic temperament.
104edo with the flat third is especially notable as an excellent tuning for magic temperament, providing the optimal patent val for 11-limit magic and the 13-limit magic extension necromancy. In the 5-limit it tempers out the magic comma, 3125/3072; in the 7-limit, it tempers out 225/224, 245/243 and 875/864; and in the 11-limit, 100/99, 896/891, 385/384 and 540/539. It provides an excellent tuning also for the rank three temperaments pairing 100/99 with 225/224 (apollo temperament), 245/243 or 875/864, or the rank four temperament tempering out 100/99, for which it gives the optimal patent val.
104 with the sharp third is excellent for 11, 13, or 17 limit diaschismic. It tempers out 2048/2025 in the 5-limit, 126/125 and 5120/5103 in the 7-limit, 176/175 and 896/891 in the 11-limit, 196/195 and 364/363 in the 13-limit and 136/135 and 256/255 in the 17-limit.
104 is also notable as a no-fives system; on 2.3.7.11.13, it tempers out 352/351, 364/363, 896/891, 2197/2187, 16807/16731, 20449/20412, 21632/21609, 26411/26364 and 10648/10647. It is the optimal patent val for the 17&87 2.3.7.11.13 subgroup temperament tempering out 352/351, 364/363 and 2197/2187, which has a 13/9 generator, three of which give a 3.
17-limit Regular Temperaments
| Degree
|
Cents
|
| 2
|
23.08
|
| 3
|
34.615
|
| 4
|
46.15
|
| 5
|
57.69
|
| 7
|
80.77
|
| 8
|
92.31
|
| 9
|
103.85
|
| 10
|
115.385
|
| 11
|
126.92
|
| 12
|
138.46
|
| 13
|
150
|
| 14
|
161.54
|
| 15
|
173.08
|
| 16
|
184.615
|
| 17
|
196.15
|
| 18
|
207.69
|
| 20
|
230.77
|
| 21
|
242.31
|
| 22
|
253.85
|
| 23
|
265.385
|
| 25
|
288.46
|
| 26
|
300
|
| 27
|
311.54
|
| 28
|
323.08
|
| 29
|
334.615
|
| 30
|
346.15
|
| 31
|
357.69
|
| 32
|
369.23
|
| 33
|
380.77
|
| 34
|
392.31
|
| 35
|
403.85
|
| 36
|
415.385
|
| 38
|
438.46
|
| 39
|
450
|
| 40
|
461.54
|
| 41
|
473.08
|
| 43
|
496.15
|
| 45
|
519.23
|
| 46
|
530.77
|
| 47
|
542.31
|
| 48
|
553.85
|
| 50
|
576.92
|
| 51
|
588.45
|
| 52
|
600
|
| 53
|
611.54
|
| 54
|
623.08
|
| 56
|
646.15
|
| 57
|
657.69
|
| 58
|
669.23
|
| 59
|
680.77
|
| 61
|
703.85
|
| 63
|
726.92
|
| 64
|
738.46
|
| 65
|
750
|
| 66
|
761.54
|
| 67
|
773.08
|
| 68
|
784.615
|
| 69
|
796.15
|
| 70
|
807.69
|
| 71
|
819.23
|
| 72
|
830.77
|
| 73
|
842.31
|
| 74
|
853.85
|
| 75
|
865.385
|
| 76
|
876.92
|
| 77
|
888.46
|
| 78
|
900
|
| 79
|
911.54
|
| 81
|
934.615
|
| 82
|
946.15
|
| 83
|
957.69
|
| 84
|
969.23
|
| 86
|
992.31
|
| 87
|
1003.85
|
| 88
|
1015.385
|
| 89
|
1026.92
|
| 90
|
1038.46
|
| 91
|
1050
|
| 92
|
1061.54
|
| 93
|
1073.08
|
| 95
|
1096.15
|
| 96
|
1107.69
|
| 97
|
1119.23
|
| 99
|
1142.31
|
| 100
|
1153.85
|
| 101
|
1165.385
|
| 102
|
1176.92
|