46edo: Difference between revisions

Revision as of 07:37, 22 June 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author hstraub and made on 2011-06-22 07:37:35 UTC.

The original revision id was 238145679.

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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.

Original Wikitext content:

[[toc|flat]]
----

=<span style="color: #300094; font-size: 111%;">46 tone equal temperament</span>= 
The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]].

46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. [[Rank two temperaments]] it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The [[11-limit]] [[Target tunings|minimax]] tuning for [[Starling family|valentine temperament]], (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the [[13-limit]], though others award that distinction to [[41edo]].

The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the [[just fifth]] and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.

46edo can be treated as two [[23edo]]'s separated by an interval of 26.09 cents.

=46edo srutis= 
[[Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.

=Intervals= 
|| degrees of 46edo || cents value ||
|| 0 || 0.00 ||
|| 1 || 26.09 ||
|| 2 || 52.17 ||
|| 3 || 78.26 ||
|| 4 || 104.35 ||
|| 5 || 130.43 ||
|| 6 || 156.52 ||
|| 7 || 182.61 ||
|| 8 || 208.70 ||
|| 9 || 234.78 ||
|| 10 || 260.87 ||
|| 11 || 286.96 ||
|| 12 || 313.04 ||
|| 13 || 339.13 ||
|| 14 || 365.22 ||
|| 15 || 391.30 ||
|| 16 || 417.39 ||
|| 17 || 443.48 ||
|| 18 || 469.57 ||
|| 19 || 495.65 ||
|| 20 || 521.74 ||
|| 21 || 547.83 ||
|| 22 || 573.91 ||
|| 23 || 600.00 ||
|| 24 || 626.09 ||
|| 25 || 652.17 ||
|| 26 || 628.26 ||
|| 27 || 704.35 ||
|| 28 || 730.43 ||
|| 29 || 756.52 ||
|| 30 || 782.61 ||
|| 31 || 808.70 ||
|| 32 || 834.78 ||
|| 33 || 860.87 ||
|| 34 || 886.96 ||
|| 35 || 913.04 ||
|| 36 || 939.13 ||
|| 37 || 965.22 ||
|| 38 || 991.30 ||
|| 39 || 1017.39 ||
|| 40 || 1043.48 ||
|| 41 || 1069.56 ||
|| 42 || 1095.65 ||
|| 43 || 1121.74 ||
|| 44 || 1147.83 ||
|| 45 || 1173.91 ||

=Approximation to Mode 8 of the Harmonic Series= 

46edo represents [[overtone]]s 8 through 16 (written as [[JI]] 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.

8\46edo (208.70¢) stands in for frequency ratio [[9_8|9:8]] (203.91¢).
7\46edo (182.61¢) stands in for [[10_9|10:9]] (182.40¢).
6\46edo (156.52¢) stands in for [[11_10|11:10]] (165.00¢) and [[12_11|12:11]] (150.64¢).
5\46edo (130.43¢) stands in for [[13_12|13:12]] (138.57¢), [[14_13|14:13]] (128.30¢) and [[15_14|15:14]] (119.44¢).
4\46edo (104.35¢) stands in for [[16_15|16:15]] (111.73¢).

=Scales= 
[[sensi5]]
[[sensi8]]
[[sensi11]]
[[sensi19]]

=Music= 
by [[Gene Ward Smith]]
[[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]
[[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.

Original HTML content:

<html><head><title>46edo</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#x46 tone equal temperament">46 tone equal temperament</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#x46edo srutis">46edo srutis</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Approximation to Mode 8 of the Harmonic Series">Approximation to Mode 8 of the Harmonic Series</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: -->
<!-- ws:end:WikiTextTocRule:19 --><hr />
<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-size: 111%;">46 tone equal temperament</span></h1>
 The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 <a class="wiki_link" href="/cent">cent</a>s, an interval close in size to <a class="wiki_link" href="/66_65">66/65</a>, the interval from <a class="wiki_link" href="/13_11">13/11</a> to <a class="wiki_link" href="/6_5">6/5</a>.<br />
<br />
46et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. <a class="wiki_link" href="/Rank%20two%20temperaments">Rank two temperaments</a> it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/Target%20tunings">minimax</a> tuning for <a class="wiki_link" href="/Starling%20family">valentine temperament</a>, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the <a class="wiki_link" href="/13-limit">13-limit</a>, though others award that distinction to <a class="wiki_link" href="/41edo">41edo</a>.<br />
<br />
The fifth of 46 equal is 2.39 cents sharp, which some people (eg, Margo Schulter) prefer, sometimes strongly, over both the <a class="wiki_link" href="/just%20fifth">just fifth</a> and fifths of temperaments with flat fifths, such as meantone. It gives a characteristic bright sound to triads, distinct from the mellowness of a meantone triad.<br />
<br />
46edo can be treated as two <a class="wiki_link" href="/23edo">23edo</a>'s separated by an interval of 26.09 cents.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h1>
 <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 />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1>
 

<table class="wiki_table">
    <tr>
        <td>degrees of 46edo<br />
</td>
        <td>cents value<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0.00<br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>26.09<br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>52.17<br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>78.26<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>104.35<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>130.43<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>156.52<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>182.61<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>208.70<br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>234.78<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>260.87<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>286.96<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>313.04<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>339.13<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>365.22<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>391.30<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>417.39<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>443.48<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>469.57<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>495.65<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>521.74<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>547.83<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>573.91<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>600.00<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>626.09<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>652.17<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>628.26<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>704.35<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>730.43<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>756.52<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>782.61<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>808.70<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>834.78<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>860.87<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>886.96<br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td>913.04<br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td>939.13<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>965.22<br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td>991.30<br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td>1017.39<br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td>1043.48<br />
</td>
    </tr>
    <tr>
        <td>41<br />
</td>
        <td>1069.56<br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td>1095.65<br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td>1121.74<br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td>1147.83<br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td>1173.91<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:6 -->Approximation to Mode 8 of the Harmonic Series</h1>
 <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 />
<br />
8\46edo (208.70¢) stands in for frequency ratio <a class="wiki_link" href="/9_8">9:8</a> (203.91¢).<br />
7\46edo (182.61¢) stands in for <a class="wiki_link" href="/10_9">10:9</a> (182.40¢).<br />
6\46edo (156.52¢) stands in for <a class="wiki_link" href="/11_10">11:10</a> (165.00¢) and <a class="wiki_link" href="/12_11">12:11</a> (150.64¢).<br />
5\46edo (130.43¢) stands in for <a class="wiki_link" href="/13_12">13:12</a> (138.57¢), <a class="wiki_link" href="/14_13">14:13</a> (128.30¢) and <a class="wiki_link" href="/15_14">15:14</a> (119.44¢).<br />
4\46edo (104.35¢) stands in for <a class="wiki_link" href="/16_15">16:15</a> (111.73¢).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->Scales</h1>
 <a class="wiki_link" href="/sensi5">sensi5</a><br />
<a class="wiki_link" href="/sensi8">sensi8</a><br />
<a class="wiki_link" href="/sensi11">sensi11</a><br />
<a class="wiki_link" href="/sensi19">sensi19</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:10 -->Music</h1>
 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/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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-11 12:09:53 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-22 07:37:35 UTC</tt>.<br>
-: The original revision id was <tt>235938894</tt>.<br>
+: The original revision id was <tt>238145679</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>
 <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">=&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;=
+<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">[[toc|flat]]
+----
+=&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;=
 The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the [[octave]] into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 [[cent]]s, an interval close in size to [[66_65|66/65]], the interval from [[13_11|13/11]] to [[6_5|6/5]].
@@ Line 16: / Line 18: @@
 edo can be treated as two [[23edo]]'s separated by an interval of 26.09 cents.
-==46edo srutis==
+=46edo srutis=
 [[Magic22 as srutis#shrutar22assrutis|Shrutar22 as srutis]] describes a possible use of 46edo for [[Indian]] music.
-==Intervals==
+=Intervals=
 || degrees of 46edo || cents value ||
 || 0 || 0.00 ||
@@ Line 68: / Line 70: @@
 || 45 || 1173.91 ||
-==Approximation to Mode 8 of the Harmonic Series==
+=Approximation to Mode 8 of the Harmonic Series=
 edo represents [[overtone]]s 8 through 16 (written as [[JI]] 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.
@@ Line 78: / Line 80: @@
 \46edo (104.35¢) stands in for [[16_15|16:15]] (111.73¢).
-==Music==
+=Scales=
+[[sensi5]]
+[[sensi8]]
+[[sensi11]]
+[[sensi19]]
+=Music=
 by [[Gene Ward Smith]]
 [[http://www.archive.org/details/Chromosounds|Chromosounds]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3|play]]
-[[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.
+[[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>
-</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;46edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x46 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;46edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#x46 tone equal temperament"&gt;46 tone equal temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#x46edo srutis"&gt;46edo srutis&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Approximation to Mode 8 of the Harmonic Series"&gt;Approximation to Mode 8 of the Harmonic Series&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Scales"&gt;Scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
-  &lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;hr /&gt;
-The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an interval close in size to &lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;, the interval from &lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt; to &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x46 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #300094; font-size: 111%;"&gt;46 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
+  The 46 equal temperament, often abbreviated 46-tET, 46-EDO, or 46-ET, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 46 equally-sized steps. Each step represents a frequency ratio of 26.087 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an interval close in size to &lt;a class="wiki_link" href="/66_65"&gt;66/65&lt;/a&gt;, the interval from &lt;a class="wiki_link" href="/13_11"&gt;13/11&lt;/a&gt; to &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 et tempers out 507/500, 91/90, 686/675, 2048/2025, 121/120, 245/243, 126/125, 169/168, 176/175, 896/891, 196/195, 1029/1024, 5120/5103, 385/384, and 441/440 among other intervals, with varied consequences it would take a very long article to describe. &lt;a class="wiki_link" href="/Rank%20two%20temperaments"&gt;Rank two temperaments&lt;/a&gt; it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/Target%20tunings"&gt;minimax&lt;/a&gt; tuning for &lt;a class="wiki_link" href="/Starling%20family"&gt;valentine temperament&lt;/a&gt;, (11/7)^(1/10), is only 0.01 cents flat of 3/46 octaves. In the opinion of some 46et is the first equal division to deal adequately with the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, though others award that distinction to &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;.&lt;br /&gt;
@@ Line 94: / Line 103: @@
 edo can be treated as two &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;'s separated by an interval of 26.09 cents.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x46 tone equal temperament-46edo srutis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;46edo srutis&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x46edo srutis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;46edo srutis&lt;/h1&gt;
   &lt;a class="wiki_link" href="/Magic22%20as%20srutis#shrutar22assrutis"&gt;Shrutar22 as srutis&lt;/a&gt; describes a possible use of 46edo for &lt;a class="wiki_link" href="/Indian"&gt;Indian&lt;/a&gt; music.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x46 tone equal temperament-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h1&gt;
@@ Line 386: / Line 395: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x46 tone equal temperament-Approximation to Mode 8 of the Harmonic Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Approximation to Mode 8 of the Harmonic Series&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Approximation to Mode 8 of the Harmonic Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Approximation to Mode 8 of the Harmonic Series&lt;/h1&gt;
   &lt;br /&gt;
 edo represents &lt;a class="wiki_link" href="/overtone"&gt;overtone&lt;/a&gt;s 8 through 16 (written as &lt;a class="wiki_link" href="/JI"&gt;JI&lt;/a&gt; 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.&lt;br /&gt;
@@ Line 396: / Line 405: @@
 \46edo (104.35¢) stands in for &lt;a class="wiki_link" href="/16_15"&gt;16:15&lt;/a&gt; (111.73¢).&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x46 tone equal temperament-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Music&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Scales&lt;/h1&gt;
+ &lt;a class="wiki_link" href="/sensi5"&gt;sensi5&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/sensi8"&gt;sensi8&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/sensi11"&gt;sensi11&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/sensi19"&gt;sensi19&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Music&lt;/h1&gt;
   by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow"&gt;Chromosounds&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/chromosounds/GWS-GPO-Jazz-chromosounds.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow"&gt;Music For Your Ears&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/MusicForYourEars/musicfor.mp3" rel="nofollow"&gt;play&lt;/a&gt; The central portion is in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;, the rest in 46edo.&lt;/body&gt;&lt;/html&gt;</pre></div>

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