46edo: Difference between revisions

Revision as of 17:54, 4 March 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author Andrew_Heathwaite and made on 2011-03-04 17:54:32 UTC.

The original revision id was 207480856.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=<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 cents, an interval close in size to 66/65, the interval from 13/11 to 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 overtones 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 (203.91¢).
7\46edo (182.61¢) stands in for 10:9 (182.40¢).
6\46edo (156.52¢) stands in for 11:10 (165.00¢) and 12:11 (150.64¢).
5\46edo (130.43¢) stands in for 13:12 (138.57¢), 14:13 (128.30¢) and 15:14 (119.44¢).
4\46edo (104.35¢) stands in for 16:15 (111.73¢).

==Music== 
by [[Gene Ward Smith]]
* [[http://www.archive.org/details/Chromosounds|Chromosounds]]
* [[http://www.archive.org/details/MusicForYourEars|Music For Your Ears]]

Original HTML content:

<html><head><title>46edo</title></head><body><!-- 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>
 <br />
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 cents, an interval close in size to 66/65, the interval from 13/11 to 6/5.<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. Rank two temperaments it supports include sensi, valentine, shrutar, rodan, leapday and unidec. The 11-limit <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 13-limit, 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 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.<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;h2&gt; --><h2 id="toc1"><a name="x46 tone equal temperament-46edo srutis"></a><!-- ws:end:WikiTextHeadingRule:2 -->46edo srutis</h2>
 <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;h2&gt; --><h2 id="toc2"><a name="x46 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
 

<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;h2&gt; --><h2 id="toc3"><a name="x46 tone equal temperament-Approximation to Mode 8 of the Harmonic Series"></a><!-- ws:end:WikiTextHeadingRule:6 -->Approximation to Mode 8 of the Harmonic Series</h2>
 <br />
46edo represents overtones 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.<br />
<br />
8\46edo (208.70¢) stands in for frequency ratio 9:8 (203.91¢).<br />
7\46edo (182.61¢) stands in for 10:9 (182.40¢).<br />
6\46edo (156.52¢) stands in for 11:10 (165.00¢) and 12:11 (150.64¢).<br />
5\46edo (130.43¢) stands in for 13:12 (138.57¢), 14:13 (128.30¢) and 15:14 (119.44¢).<br />
4\46edo (104.35¢) stands in for 16:15 (111.73¢).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x46 tone equal temperament-Music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Music</h2>
 by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br />
<ul><li><a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow">Chromosounds</a></li><li><a class="wiki_link_ext" href="http://www.archive.org/details/MusicForYourEars" rel="nofollow">Music For Your Ears</a></li></ul></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>2011-02-11 16:10:29 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-03-04 17:54:32 UTC</tt>.<br>
-: The original revision id was <tt>201021338</tt>.<br>
+: The original revision id was <tt>207480856</tt>.<br>
-: The revision comment was: <tt>link to composer</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>
@@ Line 68: / Line 68: @@
 || 45 || 1173.91 ||
+==Approximation to Mode 8 of the Harmonic Series==
+edo represents overtones 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.
+\46edo (208.70¢) stands in for frequency ratio 9:8 (203.91¢).
+\46edo (182.61¢) stands in for 10:9 (182.40¢).
+\46edo (156.52¢) stands in for 11:10 (165.00¢) and 12:11 (150.64¢).
+\46edo (130.43¢) stands in for 13:12 (138.57¢), 14:13 (128.30¢) and 15:14 (119.44¢).
+\46edo (104.35¢) stands in for 16:15 (111.73¢).
 ==Music==
@@ Line 376: / Line 385: @@
 &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;br /&gt;
+edo represents overtones 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.&lt;br /&gt;
+&lt;br /&gt;
+\46edo (208.70¢) stands in for frequency ratio 9:8 (203.91¢).&lt;br /&gt;
+\46edo (182.61¢) stands in for 10:9 (182.40¢).&lt;br /&gt;
+\46edo (156.52¢) stands in for 11:10 (165.00¢) and 12:11 (150.64¢).&lt;br /&gt;
+\46edo (130.43¢) stands in for 13:12 (138.57¢), 14:13 (128.30¢) and 15:14 (119.44¢).&lt;br /&gt;
+\46edo (104.35¢) stands in for 16:15 (111.73¢).&lt;br /&gt;
 &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-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Music&lt;/h2&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;
   by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/details/Chromosounds" rel="nofollow"&gt;Chromosounds&lt;/a&gt;&lt;/li&gt;&lt;li&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;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

46edo: Difference between revisions

Revision as of 17:54, 4 March 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

Navigation menu

Search