46edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 240945749 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 246103413 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-15 17:55:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>246103413</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> | ||
| Line 20: | Line 20: | ||
=46edo srutis= | =46edo srutis= | ||
[[Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music. | [[Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music. | ||
=Linear temperaments= | |||
|| Periods | |||
per octave || Generator || Cents || Temperaments || | |||
|| 1 || 1\46 || 26.087 || || | |||
|| || 3\46 || 78.261 || || | |||
|| || 5\46 || 130.435 || || | |||
|| || 7 || 182.609 || || | |||
|| || 9 || 234.783 || || | |||
|| || 11 || 286.957 || || | |||
|| || 13 || 339.13 || || | |||
|| || 15 || 391.304 || || | |||
|| || 17 || 443.478 || || | |||
|| || 19 || 495.652 || || | |||
|| || 21 || 547.826 || || | |||
|| 2 || 1 || 26.087 || || | |||
|| || 2 || 52.174 || || | |||
|| || 3 || 78.261 || || | |||
|| || 4 || 104.348 || || | |||
|| || 5 || 130.435 || || | |||
|| || 6 || 156.522 || || | |||
|| || 7 || 182.609 || || | |||
|| || 8 || 208.696 || || | |||
|| || 9 || 234.783 || || | |||
|| || 10 || 260.87 || || | |||
|| || 11 || 286.957 || || | |||
|| 23 || 1 || 26.087 || || | |||
=Intervals= | =Intervals= | ||
| Line 92: | Line 119: | ||
[[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] The central portion is in [[27edo]], the rest in 46edo.</pre></div> | [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]] [[http://www.archive.org/download/MusicForYourEars/musicfor.mp3|play]] The central portion is in [[27edo]], the rest in 46edo.</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>46edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>46edo</title></head><body><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#x46 tone equal temperament">46 tone equal temperament</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#x46edo srutis">46edo srutis</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Approximation to Mode 8 of the Harmonic Series">Approximation to Mode 8 of the Harmonic Series</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:22 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span></h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x46 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #300094; font-family: 'Times New Roman',Times,serif; font-size: 113%;">46 tone equal temperament</span></h1> | ||
| Line 107: | Line 134: | ||
<a class="wiki_link" href="/Magic22%20as%20srutis#shrutar22assrutis">Shrutar22 as srutis</a> describes a possible use of 46edo for <a class="wiki_link" href="/Indian">Indian</a> music.<br /> | <a class="wiki_link" href="/Magic22%20as%20srutis#shrutar22assrutis">Shrutar22 as srutis</a> describes a possible use of 46edo for <a class="wiki_link" href="/Indian">Indian</a> music.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Linear temperaments</h1> | ||
<table class="wiki_table"> | |||
<tr> | |||
<td>Periods<br /> | |||
per octave<br /> | |||
</td> | |||
<td>Generator<br /> | |||
</td> | |||
<td>Cents<br /> | |||
</td> | |||
<td>Temperaments<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>1\46<br /> | |||
</td> | |||
<td>26.087<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>3\46<br /> | |||
</td> | |||
<td>78.261<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>5\46<br /> | |||
</td> | |||
<td>130.435<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td>182.609<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td>234.783<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
<td>286.957<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
<td>339.13<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>15<br /> | |||
</td> | |||
<td>391.304<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
<td>443.478<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
<td>495.652<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>21<br /> | |||
</td> | |||
<td>547.826<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>26.087<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td>52.174<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td>78.261<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td>104.348<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td>130.435<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td>156.522<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td>182.609<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td>208.696<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td>234.783<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td>260.87<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
<td>286.957<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>26.087<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1> | |||
| Line 396: | Line 671: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:8 -->Approximation to Mode 8 of the Harmonic Series</h1> | ||
<br /> | <br /> | ||
46edo represents <a class="wiki_link" href="/overtone">overtone</a>s 8 through 16 (written as <a class="wiki_link" href="/JI">JI</a> ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.<br /> | 46edo represents <a class="wiki_link" href="/overtone">overtone</a>s 8 through 16 (written as <a class="wiki_link" href="/JI">JI</a> ratios 8:9:10:11:12:13:14:15:16) with degrees 0, 8, 15, 21, 27, 32, 37, 42, 46. In steps-in-between, that's 8, 7, 6, 6, 5, 5, 5, 4.<br /> | ||
| Line 406: | Line 681: | ||
4\46edo (104.35¢) stands in for <a class="wiki_link" href="/16_15">16:15</a> (111.73¢).<br /> | 4\46edo (104.35¢) stands in for <a class="wiki_link" href="/16_15">16:15</a> (111.73¢).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->Scales</h1> | ||
<ul><li><a class="wiki_link" href="/plum">plum</a></li><li><a class="wiki_link" href="/sensi5">sensi5</a></li><li><a class="wiki_link" href="/sensi8">sensi8</a></li><li><a class="wiki_link" href="/sensi11">sensi11</a></li><li><a class="wiki_link" href="/sensi19">sensi19</a></li></ul><br /> | <ul><li><a class="wiki_link" href="/plum">plum</a></li><li><a class="wiki_link" href="/sensi5">sensi5</a></li><li><a class="wiki_link" href="/sensi8">sensi8</a></li><li><a class="wiki_link" href="/sensi11">sensi11</a></li><li><a class="wiki_link" href="/sensi19">sensi19</a></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:12 -->Music</h1> | ||
by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> | by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow">Chromosounds</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3" rel="nofollow">play</a><br /> | <a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow">Chromosounds</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3" rel="nofollow">play</a><br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> The central portion is in <a class="wiki_link" href="/27edo">27edo</a>, the rest in 46edo.</body></html></pre></div> | <a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a> <a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow">play</a> The central portion is in <a class="wiki_link" href="/27edo">27edo</a>, the rest in 46edo.</body></html></pre></div> | ||