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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">75 tone equal temperament</span>= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:bootmii|bootmii]] and made on <tt>2016-12-22 19:22:12 UTC</tt>.<br>
| |
| : The original revision id was <tt>602769034</tt>.<br>
| |
| : The revision comment was: <tt>Y'all need to explain what 12&51 temperament is.</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>
| |
| <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: #000080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">75 tone equal temperament</span>=
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| 75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot family|tetracot temperament]]. It provides the optimal patent val for <span class="wiki_link">[[M&N temperaments|12&51]]</span>[[M&N temperaments| temperament]] in the 7-limit and the [[M&N temperaments|31&75 temperament]] in the 13-limit. | | 75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for [[Tetracot_family|tetracot temperament]]. It provides the optimal patent val for <span style="">[[M&N_temperaments|12&51]]</span>[[M&N_temperaments| temperament]] in the 7-limit and the [[M&N_temperaments|31&75 temperament]] in the 13-limit. |
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| ===Intervals=== | | ===Intervals=== |
| || **Step** || **Size in Cents** ||
| |
| || 0 || 0 ||
| |
| || 1 || 16 ||
| |
| || 2 || 32 ||
| |
| || 3 || 48 ||
| |
| || 4 || 64 ||
| |
| || 5 || 80 ||
| |
| || 6 || 96 ||
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| || 7 || 112 ||
| |
| || 8 || 128 ||
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| || 9 || 144 ||
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| || 10 || 160 ||
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| || 11 || 176 ||
| |
| || 12 || 192 ||
| |
| || 13 || 208 ||
| |
| || 14 || 224 ||
| |
| || 15 || 240 ||
| |
| || 16 || 256 ||
| |
| || 17 || 272 ||
| |
| || 18 || 288 ||
| |
| || 19 || 304 ||
| |
| || 20 || 320 ||
| |
| || 21 || 336 ||
| |
| || 22 || 352 ||
| |
| || 23 || 368 ||
| |
| || 24 || 384 ||
| |
| || 25 || 400 ||
| |
| || 26 || 416 ||
| |
| || 27 || 432 ||
| |
| || 28 || 448 ||
| |
| || 29 || 464 ||
| |
| || 30 || 480 ||
| |
| || 31 || 496 ||
| |
| || 32 || 512 ||
| |
| || 33 || 528 ||
| |
| || 34 || 544 ||
| |
| || 35 || 560 ||
| |
| || 36 || 576 ||
| |
| || 37 || 592 ||
| |
| || 38 || 608 ||
| |
| || 39 || 624 ||
| |
| || 40 || 640 ||
| |
| || 41 || 656 ||
| |
| || 42 || 672 ||
| |
| || 43 || 688 ||
| |
| || 44 || 704 ||
| |
| || 45 || 720 ||
| |
| || 46 || 736 ||
| |
| || 47 || 752 ||
| |
| || 48 || 768 ||
| |
| || 49 || 784 ||
| |
| || 50 || 800 ||
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| || 51 || 816 ||
| |
| || 52 || 832 ||
| |
| || 53 || 848 ||
| |
| || 54 || 864 ||
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| || 55 || 880 ||
| |
| || 56 || 896 ||
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| || 57 || 912 ||
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| || 58 || 928 ||
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| || 59 || 944 ||
| |
| || 60 || 960 ||
| |
| || 61 || 976 ||
| |
| || 62 || 992 ||
| |
| || 63 || 1008 ||
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| || 64 || 1024 ||
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| || 65 || 1040 ||
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| || 66 || 1056 ||
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| || 67 || 1072 ||
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| || 68 || 1088 ||
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| || 69 || 1104 ||
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| || 70 || 1120 ||
| |
| || 71 || 1136 ||
| |
| || 72 || 1152 ||
| |
| || 73 || 1168 ||
| |
| || 74 || 1184 ||</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>75edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x75 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 113%;">75 tone equal temperament</span></h1>
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| <br />
| |
| 75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for <a class="wiki_link" href="/Tetracot%20family">tetracot temperament</a>. It provides the optimal patent val for <span class="wiki_link"><a class="wiki_link" href="/M%26N%20temperaments">12&amp;51</a></span><a class="wiki_link" href="/M%26N%20temperaments"> temperament</a> in the 7-limit and the <a class="wiki_link" href="/M%26N%20temperaments">31&amp;75 temperament</a> in the 13-limit.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x75 tone equal temperament--Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h3>
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|
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|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td><strong>Step</strong><br />
| | | | '''Step''' |
| </td>
| | | | '''Size in Cents''' |
| <td><strong>Size in Cents</strong><br />
| | |- |
| </td>
| | | | 0 |
| </tr>
| | | | 0 |
| <tr>
| | |- |
| <td>0<br />
| | | | 1 |
| </td>
| | | | 16 |
| <td>0<br />
| | |- |
| </td>
| | | | 2 |
| </tr>
| | | | 32 |
| <tr>
| | |- |
| <td>1<br />
| | | | 3 |
| </td>
| | | | 48 |
| <td>16<br />
| | |- |
| </td>
| | | | 4 |
| </tr>
| | | | 64 |
| <tr>
| | |- |
| <td>2<br />
| | | | 5 |
| </td>
| | | | 80 |
| <td>32<br />
| | |- |
| </td>
| | | | 6 |
| </tr>
| | | | 96 |
| <tr>
| | |- |
| <td>3<br />
| | | | 7 |
| </td>
| | | | 112 |
| <td>48<br />
| | |- |
| </td>
| | | | 8 |
| </tr>
| | | | 128 |
| <tr>
| | |- |
| <td>4<br />
| | | | 9 |
| </td>
| | | | 144 |
| <td>64<br />
| | |- |
| </td>
| | | | 10 |
| </tr>
| | | | 160 |
| <tr>
| | |- |
| <td>5<br />
| | | | 11 |
| </td>
| | | | 176 |
| <td>80<br />
| | |- |
| </td>
| | | | 12 |
| </tr>
| | | | 192 |
| <tr>
| | |- |
| <td>6<br />
| | | | 13 |
| </td>
| | | | 208 |
| <td>96<br />
| | |- |
| </td>
| | | | 14 |
| </tr>
| | | | 224 |
| <tr>
| | |- |
| <td>7<br />
| | | | 15 |
| </td>
| | | | 240 |
| <td>112<br />
| | |- |
| </td>
| | | | 16 |
| </tr>
| | | | 256 |
| <tr>
| | |- |
| <td>8<br />
| | | | 17 |
| </td>
| | | | 272 |
| <td>128<br />
| | |- |
| </td>
| | | | 18 |
| </tr>
| | | | 288 |
| <tr>
| | |- |
| <td>9<br />
| | | | 19 |
| </td>
| | | | 304 |
| <td>144<br />
| | |- |
| </td>
| | | | 20 |
| </tr>
| | | | 320 |
| <tr>
| | |- |
| <td>10<br />
| | | | 21 |
| </td>
| | | | 336 |
| <td>160<br />
| | |- |
| </td>
| | | | 22 |
| </tr>
| | | | 352 |
| <tr>
| | |- |
| <td>11<br />
| | | | 23 |
| </td>
| | | | 368 |
| <td>176<br />
| | |- |
| </td>
| | | | 24 |
| </tr>
| | | | 384 |
| <tr>
| | |- |
| <td>12<br />
| | | | 25 |
| </td>
| | | | 400 |
| <td>192<br />
| | |- |
| </td>
| | | | 26 |
| </tr>
| | | | 416 |
| <tr>
| | |- |
| <td>13<br />
| | | | 27 |
| </td>
| | | | 432 |
| <td>208<br />
| | |- |
| </td>
| | | | 28 |
| </tr>
| | | | 448 |
| <tr>
| | |- |
| <td>14<br />
| | | | 29 |
| </td>
| | | | 464 |
| <td>224<br />
| | |- |
| </td>
| | | | 30 |
| </tr>
| | | | 480 |
| <tr>
| | |- |
| <td>15<br />
| | | | 31 |
| </td>
| | | | 496 |
| <td>240<br />
| | |- |
| </td>
| | | | 32 |
| </tr>
| | | | 512 |
| <tr>
| | |- |
| <td>16<br />
| | | | 33 |
| </td>
| | | | 528 |
| <td>256<br />
| | |- |
| </td>
| | | | 34 |
| </tr>
| | | | 544 |
| <tr>
| | |- |
| <td>17<br />
| | | | 35 |
| </td>
| | | | 560 |
| <td>272<br />
| | |- |
| </td>
| | | | 36 |
| </tr>
| | | | 576 |
| <tr>
| | |- |
| <td>18<br />
| | | | 37 |
| </td>
| | | | 592 |
| <td>288<br />
| | |- |
| </td>
| | | | 38 |
| </tr>
| | | | 608 |
| <tr>
| | |- |
| <td>19<br />
| | | | 39 |
| </td>
| | | | 624 |
| <td>304<br />
| | |- |
| </td>
| | | | 40 |
| </tr>
| | | | 640 |
| <tr>
| | |- |
| <td>20<br />
| | | | 41 |
| </td>
| | | | 656 |
| <td>320<br />
| | |- |
| </td>
| | | | 42 |
| </tr>
| | | | 672 |
| <tr>
| | |- |
| <td>21<br />
| | | | 43 |
| </td>
| | | | 688 |
| <td>336<br />
| | |- |
| </td>
| | | | 44 |
| </tr>
| | | | 704 |
| <tr>
| | |- |
| <td>22<br />
| | | | 45 |
| </td>
| | | | 720 |
| <td>352<br />
| | |- |
| </td>
| | | | 46 |
| </tr>
| | | | 736 |
| <tr>
| | |- |
| <td>23<br />
| | | | 47 |
| </td>
| | | | 752 |
| <td>368<br />
| | |- |
| </td>
| | | | 48 |
| </tr>
| | | | 768 |
| <tr>
| | |- |
| <td>24<br />
| | | | 49 |
| </td>
| | | | 784 |
| <td>384<br />
| | |- |
| </td>
| | | | 50 |
| </tr>
| | | | 800 |
| <tr>
| | |- |
| <td>25<br />
| | | | 51 |
| </td>
| | | | 816 |
| <td>400<br />
| | |- |
| </td>
| | | | 52 |
| </tr>
| | | | 832 |
| <tr>
| | |- |
| <td>26<br />
| | | | 53 |
| </td>
| | | | 848 |
| <td>416<br />
| | |- |
| </td>
| | | | 54 |
| </tr>
| | | | 864 |
| <tr>
| | |- |
| <td>27<br />
| | | | 55 |
| </td>
| | | | 880 |
| <td>432<br />
| | |- |
| </td>
| | | | 56 |
| </tr>
| | | | 896 |
| <tr>
| | |- |
| <td>28<br />
| | | | 57 |
| </td>
| | | | 912 |
| <td>448<br />
| | |- |
| </td>
| | | | 58 |
| </tr>
| | | | 928 |
| <tr>
| | |- |
| <td>29<br />
| | | | 59 |
| </td>
| | | | 944 |
| <td>464<br />
| | |- |
| </td>
| | | | 60 |
| </tr>
| | | | 960 |
| <tr>
| | |- |
| <td>30<br />
| | | | 61 |
| </td>
| | | | 976 |
| <td>480<br />
| | |- |
| </td>
| | | | 62 |
| </tr>
| | | | 992 |
| <tr>
| | |- |
| <td>31<br />
| | | | 63 |
| </td>
| | | | 1008 |
| <td>496<br />
| | |- |
| </td>
| | | | 64 |
| </tr>
| | | | 1024 |
| <tr>
| | |- |
| <td>32<br />
| | | | 65 |
| </td>
| | | | 1040 |
| <td>512<br />
| | |- |
| </td>
| | | | 66 |
| </tr>
| | | | 1056 |
| <tr>
| | |- |
| <td>33<br />
| | | | 67 |
| </td>
| | | | 1072 |
| <td>528<br />
| | |- |
| </td>
| | | | 68 |
| </tr>
| | | | 1088 |
| <tr>
| | |- |
| <td>34<br />
| | | | 69 |
| </td>
| | | | 1104 |
| <td>544<br />
| | |- |
| </td>
| | | | 70 |
| </tr>
| | | | 1120 |
| <tr>
| | |- |
| <td>35<br />
| | | | 71 |
| </td>
| | | | 1136 |
| <td>560<br />
| | |- |
| </td>
| | | | 72 |
| </tr>
| | | | 1152 |
| <tr>
| | |- |
| <td>36<br />
| | | | 73 |
| </td>
| | | | 1168 |
| <td>576<br />
| | |- |
| </td>
| | | | 74 |
| </tr>
| | | | 1184 |
| <tr>
| | |} |
| <td>37<br />
| |
| </td>
| |
| <td>592<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td>608<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>624<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>640<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>656<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>672<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>688<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>704<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>720<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>736<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>752<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>768<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>784<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>800<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td>816<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>832<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>848<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>864<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>880<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>896<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>912<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>58<br />
| |
| </td>
| |
| <td>928<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>59<br />
| |
| </td>
| |
| <td>944<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>60<br />
| |
| </td>
| |
| <td>960<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>61<br />
| |
| </td>
| |
| <td>976<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>62<br />
| |
| </td>
| |
| <td>992<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>63<br />
| |
| </td>
| |
| <td>1008<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>64<br />
| |
| </td>
| |
| <td>1024<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>65<br />
| |
| </td>
| |
| <td>1040<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>66<br />
| |
| </td>
| |
| <td>1056<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>67<br />
| |
| </td>
| |
| <td>1072<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>68<br />
| |
| </td>
| |
| <td>1088<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>69<br />
| |
| </td>
| |
| <td>1104<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>70<br />
| |
| </td>
| |
| <td>1120<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>71<br />
| |
| </td>
| |
| <td>1136<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>72<br />
| |
| </td>
| |
| <td>1152<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>73<br />
| |
| </td>
| |
| <td>1168<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>74<br />
| |
| </td>
| |
| <td>1184<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
75 tone equal temperament
75edo divides the octave into 75 equal parts of exactly 16 cents each. In the 5-limit, it tempers out the tetracot comma, 20000/19683 and the semicomma 2109375/2097152, and provides a good tuning for tetracot temperament. It provides the optimal patent val for 12&51 temperament in the 7-limit and the 31&75 temperament in the 13-limit.
Intervals
| Step
|
Size in Cents
|
| 0
|
0
|
| 1
|
16
|
| 2
|
32
|
| 3
|
48
|
| 4
|
64
|
| 5
|
80
|
| 6
|
96
|
| 7
|
112
|
| 8
|
128
|
| 9
|
144
|
| 10
|
160
|
| 11
|
176
|
| 12
|
192
|
| 13
|
208
|
| 14
|
224
|
| 15
|
240
|
| 16
|
256
|
| 17
|
272
|
| 18
|
288
|
| 19
|
304
|
| 20
|
320
|
| 21
|
336
|
| 22
|
352
|
| 23
|
368
|
| 24
|
384
|
| 25
|
400
|
| 26
|
416
|
| 27
|
432
|
| 28
|
448
|
| 29
|
464
|
| 30
|
480
|
| 31
|
496
|
| 32
|
512
|
| 33
|
528
|
| 34
|
544
|
| 35
|
560
|
| 36
|
576
|
| 37
|
592
|
| 38
|
608
|
| 39
|
624
|
| 40
|
640
|
| 41
|
656
|
| 42
|
672
|
| 43
|
688
|
| 44
|
704
|
| 45
|
720
|
| 46
|
736
|
| 47
|
752
|
| 48
|
768
|
| 49
|
784
|
| 50
|
800
|
| 51
|
816
|
| 52
|
832
|
| 53
|
848
|
| 54
|
864
|
| 55
|
880
|
| 56
|
896
|
| 57
|
912
|
| 58
|
928
|
| 59
|
944
|
| 60
|
960
|
| 61
|
976
|
| 62
|
992
|
| 63
|
1008
|
| 64
|
1024
|
| 65
|
1040
|
| 66
|
1056
|
| 67
|
1072
|
| 68
|
1088
|
| 69
|
1104
|
| 70
|
1120
|
| 71
|
1136
|
| 72
|
1152
|
| 73
|
1168
|
| 74
|
1184
|