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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =21 Equal Divisions of the Tritave= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-20 10:26:34 UTC</tt>.<br>
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| : The original revision id was <tt>592857626</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>
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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">=21 Equal Divisions of the Tritave=
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|
| || Degrees || Cents || Approximate Ratio || | | {| class="wikitable" |
| || 0 || 0 || [[1_1|1/1]] || | | |- |
| || 1 || 90.569 || [[21_20|21/20]], [[135_128|135/128]] || | | | | Degrees |
| || 2 || 181.139 || [[10_9|10/9]] || | | | | Cents |
| || 3 || 271.708 || [[7_6|7/6]] || | | | | Approximate Ratio |
| || 4 || 362.277 || [[16_13|16/13]] || | | |- |
| || 5 || 452.846 || [[13_10|13/10]] || | | | | 0 |
| || 6 || 543.416 || [[15_11|15/11]], [[11_8|11/8]] || | | | | 0 |
| || 7 || 633.985 || [[13_9|13/9]] || | | | | [[1/1|1/1]] |
| || 8 || 724.554 || 35/23 || | | |- |
| || 9 || 815.124 || [[8_5|8/5]] || | | | | 1 |
| || 10 || 905.693 || 27/16 || | | | | 90.569 |
| || 11 || 996.262 || 16/9 || | | | | [[21/20|21/20]], [[135/128|135/128]] |
| || 12 || 1086.831 || [[15_8|15/8]] || | | |- |
| || 13 || 1177.401 || 69/35 || | | | | 2 |
| || 14 || 1267.970 || 27/13 || | | | | 181.139 |
| || 15 || 1358.539 || 11/5 ([[11_10|11/10]] plus an octave), 24/11 (12/11 plus an octave) || | | | | [[10/9|10/9]] |
| || 16 || 1449.109 || 30/13 ([[15_13|15/13]] plus an octave) || | | |- |
| || 17 || 1539.678 || 39/16 || | | | | 3 |
| || 18 || 1630.247 || 18/7 ([[9_7|9/7]] plus an octave) || | | | | 271.708 |
| || 19 || 1720.816 || 27/10 || | | | | [[7/6|7/6]] |
| || 20 || 1811.386 || 20/7, 128/45 || | | |- |
| || 21 || 1901.955 || 3/1 || | | | | 4 |
| | | | 362.277 |
| | | | [[16/13|16/13]] |
| | |- |
| | | | 5 |
| | | | 452.846 |
| | | | [[13/10|13/10]] |
| | |- |
| | | | 6 |
| | | | 543.416 |
| | | | [[15/11|15/11]], [[11/8|11/8]] |
| | |- |
| | | | 7 |
| | | | 633.985 |
| | | | [[13/9|13/9]] |
| | |- |
| | | | 8 |
| | | | 724.554 |
| | | | 35/23 |
| | |- |
| | | | 9 |
| | | | 815.124 |
| | | | [[8/5|8/5]] |
| | |- |
| | | | 10 |
| | | | 905.693 |
| | | | 27/16 |
| | |- |
| | | | 11 |
| | | | 996.262 |
| | | | 16/9 |
| | |- |
| | | | 12 |
| | | | 1086.831 |
| | | | [[15/8|15/8]] |
| | |- |
| | | | 13 |
| | | | 1177.401 |
| | | | 69/35 |
| | |- |
| | | | 14 |
| | | | 1267.970 |
| | | | 27/13 |
| | |- |
| | | | 15 |
| | | | 1358.539 |
| | | | 11/5 ([[11/10|11/10]] plus an octave), 24/11 (12/11 plus an octave) |
| | |- |
| | | | 16 |
| | | | 1449.109 |
| | | | 30/13 ([[15/13|15/13]] plus an octave) |
| | |- |
| | | | 17 |
| | | | 1539.678 |
| | | | 39/16 |
| | |- |
| | | | 18 |
| | | | 1630.247 |
| | | | 18/7 ([[9/7|9/7]] plus an octave) |
| | |- |
| | | | 19 |
| | | | 1720.816 |
| | | | 27/10 |
| | |- |
| | | | 20 |
| | | | 1811.386 |
| | | | 20/7, 128/45 |
| | |- |
| | | | 21 |
| | | | 1901.955 |
| | | | 3/1 |
| | |} |
|
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|
| | | 21edt contains 6 intervals from [[7edt|7edt]] and 2 intervals from [[3edt|3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30... |
| 21edt contains 6 intervals from [[7edt]] and 2 intervals from [[3edt]], meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30... | |
|
| |
|
| 21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL. | | 21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL. |
|
| |
|
| | 21edt also contains a 4L5s MOS similar to [[BP|BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt|3edt]] essentially tempered chord). |
|
| |
|
| 21edt also contains a 4L5s MOS similar to [[BP]], with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the [[3edt]] essentially tempered chord).
| | Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it. |
| | | [[Category:edt]] |
| Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.</pre></div> | | [[Category:tritave]] |
| <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>21edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x21 Equal Divisions of the Tritave"></a><!-- ws:end:WikiTextHeadingRule:0 -->21 Equal Divisions of the Tritave</h1>
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| <br />
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| | |
| <table class="wiki_table">
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| <tr>
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| <td>Degrees<br />
| |
| </td>
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| <td>Cents<br />
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| </td>
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| <td>Approximate Ratio<br />
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| </td>
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| </tr>
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| <tr>
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| <td>0<br />
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| </td>
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| <td>0<br />
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| </td>
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| <td><a class="wiki_link" href="/1_1">1/1</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>1<br />
| |
| </td>
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| <td>90.569<br />
| |
| </td>
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| <td><a class="wiki_link" href="/21_20">21/20</a>, <a class="wiki_link" href="/135_128">135/128</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>2<br />
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| </td>
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| <td>181.139<br />
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| </td>
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| <td><a class="wiki_link" href="/10_9">10/9</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>3<br />
| |
| </td>
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| <td>271.708<br />
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| </td>
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| <td><a class="wiki_link" href="/7_6">7/6</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
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| </td>
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| <td>362.277<br />
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| </td>
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| <td><a class="wiki_link" href="/16_13">16/13</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>452.846<br />
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| </td>
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| <td><a class="wiki_link" href="/13_10">13/10</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>6<br />
| |
| </td>
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| <td>543.416<br />
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| </td>
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| <td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/11_8">11/8</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>633.985<br />
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| </td>
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| <td><a class="wiki_link" href="/13_9">13/9</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
| |
| </td>
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| <td>724.554<br />
| |
| </td>
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| <td>35/23<br />
| |
| </td>
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| </tr>
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| <tr>
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| <td>9<br />
| |
| </td>
| |
| <td>815.124<br />
| |
| </td>
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| <td><a class="wiki_link" href="/8_5">8/5</a><br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
| |
| </td>
| |
| <td>905.693<br />
| |
| </td>
| |
| <td>27/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td>996.262<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td>1086.831<br />
| |
| </td>
| |
| <td><a class="wiki_link" href="/15_8">15/8</a><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>1177.401<br />
| |
| </td>
| |
| <td>69/35<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>14<br />
| |
| </td>
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| <td>1267.970<br />
| |
| </td>
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| <td>27/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>15<br />
| |
| </td>
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| <td>1358.539<br />
| |
| </td>
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| <td>11/5 (<a class="wiki_link" href="/11_10">11/10</a> plus an octave), 24/11 (12/11 plus an octave)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>16<br />
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| </td>
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| <td>1449.109<br />
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| </td>
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| <td>30/13 (<a class="wiki_link" href="/15_13">15/13</a> plus an octave)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>17<br />
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| </td>
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| <td>1539.678<br />
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| </td>
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| <td>39/16<br />
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| </td>
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| </tr>
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| <tr>
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| <td>18<br />
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| </td>
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| <td>1630.247<br />
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| </td>
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| <td>18/7 (<a class="wiki_link" href="/9_7">9/7</a> plus an octave)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>19<br />
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| </td>
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| <td>1720.816<br />
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| </td>
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| <td>27/10<br />
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| </td>
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| </tr>
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| <tr>
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| <td>20<br />
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| </td>
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| <td>1811.386<br />
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| </td>
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| <td>20/7, 128/45<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21<br />
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| </td>
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| <td>1901.955<br />
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| </td>
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| <td>3/1<br />
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| </td>
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| </tr>
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| </table>
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| | |
| <br />
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| <br />
| |
| 21edt contains 6 intervals from <a class="wiki_link" href="/7edt">7edt</a> and 2 intervals from <a class="wiki_link" href="/3edt">3edt</a>, meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...<br />
| |
| <br />
| |
| 21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.<br />
| |
| <br />
| |
| <br />
| |
| 21edt also contains a 4L5s MOS similar to <a class="wiki_link" href="/BP">BP</a>, with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the <a class="wiki_link" href="/3edt">3edt</a> essentially tempered chord).<br />
| |
| <br />
| |
| Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.</body></html></pre></div>
| |
21 Equal Divisions of the Tritave
| Degrees
|
Cents
|
Approximate Ratio
|
| 0
|
0
|
1/1
|
| 1
|
90.569
|
21/20, 135/128
|
| 2
|
181.139
|
10/9
|
| 3
|
271.708
|
7/6
|
| 4
|
362.277
|
16/13
|
| 5
|
452.846
|
13/10
|
| 6
|
543.416
|
15/11, 11/8
|
| 7
|
633.985
|
13/9
|
| 8
|
724.554
|
35/23
|
| 9
|
815.124
|
8/5
|
| 10
|
905.693
|
27/16
|
| 11
|
996.262
|
16/9
|
| 12
|
1086.831
|
15/8
|
| 13
|
1177.401
|
69/35
|
| 14
|
1267.970
|
27/13
|
| 15
|
1358.539
|
11/5 (11/10 plus an octave), 24/11 (12/11 plus an octave)
|
| 16
|
1449.109
|
30/13 (15/13 plus an octave)
|
| 17
|
1539.678
|
39/16
|
| 18
|
1630.247
|
18/7 (9/7 plus an octave)
|
| 19
|
1720.816
|
27/10
|
| 20
|
1811.386
|
20/7, 128/45
|
| 21
|
1901.955
|
3/1
|
21edt contains 6 intervals from 7edt and 2 intervals from 3edt, meaning that it introduces 12 new intervals not available in lower edt's. These new intervals allow for construction of strange chords like 9:10:13:16:22:27:30...
21edt contains a 7L7s MOS similar to Whitewood, which I call Ivory. It has a period of 1/7 of the tritave and the generator is one step. The major scale is LsLsLsLsLsLsLs, and the minor scale is sLsLsLsLsLsLsL.
21edt also contains a 4L5s MOS similar to BP, with a 4:1 ratio of large to small; quite exaggerated from the optimal 2:1. Although the 7/3 is a little off, the 4L+5s BP scale is pretty. However, one of the star scales in 21edt is the 3L+6s (ssLssLssL and modes thereof) which is very harmonically rich, the cornerstone of which is the approximate 9:13:19 chord (which is just the 3edt essentially tempered chord).
Not the best approximations but all within 20 cents: it has 5th (+20c), 7th(-16c), 10th (+2c), 11th (+15c), 13th (-3c), 17th (-14c), 23rd (+6 c), and 37th (-2c) harmonics. For a lower division of the tritave that's quite a constellation! The chord is a little out of tune but it works, you can really sink into it.