3L 7s: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 565459111 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 598697682 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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> | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-07 12:17:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>598697682</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">=3L+7s "Fair Mosh" (Modi | <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">=3L+7s "Fair Mosh" (Modi Sephiratorum)= | ||
= = | = = | ||
Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0). | Fair Mosh is found in [[Magic|magic]] (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0). | ||
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi | This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum. Temperament using phi directly approximates the higher Fibonacci harmonics best. | ||
If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and so on. This ends at s=0 which gives multiples of [[3edo]]. | If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and so on. This ends at s=0 which gives multiples of [[3edo]]. | ||
| Line 35: | Line 35: | ||
|| 3\10 || || || || || || 360 || 120 || 120 ||= || | || 3\10 || || || || || || 360 || 120 || 120 ||= || | ||
|| 28\93 || || || || || || 361.290 || 129.032 || 116.129 ||= || | || 28\93 || || || || || || 361.290 || 129.032 || 116.129 ||= || | ||
|| 25\83 || || || || || || 361.446 || 130.1205 || 115.663 ||= || | || 25\83 || || || || || || 361.446 || [[tel:130.1205|130.1205]] || 115.663 ||= || | ||
|| 22\73 || || || || || || 361.644 || 131.507 || 115.0685 ||= || | || 22\73 || || || || || || 361.644 || 131.507 || [[tel:115.0685|115.0685]] ||= || | ||
|| 19\63 || || || || || || 361.905 || 133.333 || 114.286 ||= || | || 19\63 || || || || || || 361.905 || 133.333 || 114.286 ||= || | ||
|| 16\53 || || || || || || 362.264 || 135.849 || 113.2075 ||= || | || 16\53 || || || || || || 362.264 || 135.849 || [[tel:113.2075|113.2075]] ||= || | ||
|| 13\43 || || || || || || 362.791 || 139.535 || 111.628 ||= || | || 13\43 || || || || || || 362.791 || 139.535 || 111.628 ||= || | ||
|| 10\33 || || || || || || 363.636 || 145.455 || 109.091 ||= || | || 10\33 || || || || || || 363.636 || 145.455 || 109.091 ||= || | ||
| Line 50: | Line 50: | ||
|| || || || || 199\652 || || 366.258 || 163.804 || 101.227 || | || || || || || 199\652 || || 366.258 || 163.804 || 101.227 || | ||
|| || || || 76\249 || || || 366.265 || 163.855 || 101.205 ||= || | || || || || 76\249 || || || 366.265 || 163.855 || 101.205 ||= || | ||
|| || || 29\95 || || || || 366.316 || 164.2105 || 101.053 ||= || | || || || 29\95 || || || || 366.316 || [[tel:164.2105|164.2105]] || 101.053 ||= || | ||
|| || 11\36 || || || || || 366.667 || 166.667 || 100 ||= || | || || 11\36 || || || || || 366.667 || 166.667 || 100 ||= || | ||
|| || || || || || || 367.203 || 170.419 || 98.392 || || | || || || || || || || 367.203 || 170.419 || 98.392 || || | ||
| Line 62: | Line 62: | ||
|| || || || || 157\505 || || 373.069 || 211.485 || 80.792 || || | || || || || || 157\505 || || 373.069 || 211.485 || 80.792 || || | ||
|| || || || || || 411\1322 || 373.071 || 211.498 || 80.787 || || | || || || || || || 411\1322 || 373.071 || 211.498 || 80.787 || || | ||
|| || || || || 254\817 || || 373.072 || 211.5055 || 80.783 || || | || || || || || 254\817 || || 373.072 || [[tel:211.5055|211.5055]] || 80.783 || || | ||
|| || || || 97\312 || || || 373.077 || 211.5385 || 80.769 || || | || || || || 97\312 || || || 373.077 || [[tel:211.5385|211.5385]] || 80.769 || || | ||
|| || || 37\119 || || || || 373.109 || 211.765 || 80.672 || || | || || || 37\119 || || || || 373.109 || 211.765 || 80.672 || || | ||
|| || 14\45 || || || || || 373.333 || 213.333 || 80 ||= || | || || 14\45 || || || || || 373.333 || 213.333 || 80 ||= || | ||
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etc.</pre></div> | etc.</pre></div> | ||
<h4>Original HTML content:</h4> | <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>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L+7s &quot;Fair Mosh&quot; (Modi | <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>3L 7s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x3L+7s &quot;Fair Mosh&quot; (Modi Sephiratorum)"></a><!-- ws:end:WikiTextHeadingRule:0 -->3L+7s &quot;Fair Mosh&quot; (Modi Sephiratorum)</h1> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><!-- ws:end:WikiTextHeadingRule:2 --> </h1> | ||
Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0).<br /> | Fair Mosh is found in <a class="wiki_link" href="/Magic">magic</a> (chains of the 5th harmonic). It occupies the spectrum from 10edo (L=s) to 3edo (s=0).<br /> | ||
<br /> | <br /> | ||
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi | This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (L=3 s=2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.<br /> | ||
<br /> | <br /> | ||
If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall <a class="wiki_link" href="/13edo">13edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, and so on. This ends at s=0 which gives multiples of <a class="wiki_link" href="/3edo">3edo</a>.<br /> | If L=s, ie. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 5/4 and 13/8. In this category fall <a class="wiki_link" href="/13edo">13edo</a>, <a class="wiki_link" href="/16edo">16edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, and so on. This ends at s=0 which gives multiples of <a class="wiki_link" href="/3edo">3edo</a>.<br /> | ||
| Line 209: | Line 209: | ||
<td>361.446<br /> | <td>361.446<br /> | ||
</td> | </td> | ||
<td>130.1205<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/130.1205">130.1205</a><br /> | ||
</td> | </td> | ||
<td>115.663<br /> | <td>115.663<br /> | ||
| Line 233: | Line 233: | ||
<td>131.507<br /> | <td>131.507<br /> | ||
</td> | </td> | ||
<td>115.0685<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/115.0685">115.0685</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 277: | Line 277: | ||
<td>135.849<br /> | <td>135.849<br /> | ||
</td> | </td> | ||
<td>113.2075<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/113.2075">113.2075</a><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 537: | Line 537: | ||
<td>366.316<br /> | <td>366.316<br /> | ||
</td> | </td> | ||
<td>164.2105<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/164.2105">164.2105</a><br /> | ||
</td> | </td> | ||
<td>101.053<br /> | <td>101.053<br /> | ||
| Line 780: | Line 780: | ||
<td>373.072<br /> | <td>373.072<br /> | ||
</td> | </td> | ||
<td>211.5055<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/211.5055">211.5055</a><br /> | ||
</td> | </td> | ||
<td>80.783<br /> | <td>80.783<br /> | ||
| Line 802: | Line 802: | ||
<td>373.077<br /> | <td>373.077<br /> | ||
</td> | </td> | ||
<td>211.5385<br /> | <td><a class="wiki_link" href="http://tel.wikispaces.com/211.5385">211.5385</a><br /> | ||
</td> | </td> | ||
<td>80.769<br /> | <td>80.769<br /> | ||