11-limit: Difference between revisions

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The //11-limit// consists of all [[JustIntonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14_11|14/11]], [[11_8|11/8]], [[27_22|27/22]] and [[99_98|99/98]]. The 11 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 11. Reduced to an octave, these are the ratios 1/1, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, 11/9, 5/4, 14/11, 9/7, 4/3, 11/8, 7/5, 10/7, 16/11, 3/2, 14/9, 11/7, 8/5, 18/11, 5/3, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 2/1. In an 11-limit system, all the ratios of the 11 odd-limit can be treated as potential consonances.

||ratio||harmonic solfege||
|| 12/11 || fu-sol ||
|| 11/10 || mi-fu ||
|| 10/9 || re-mi ||
|| 9/8 || do-re ||
|| 8/7 || ta-do ||
|| 7/6 || sol-ta ||
|| 6/5 || mi-sol, ti-re ||
|| 11/9 || re-fu ||
|| 5/4 || do-mi ||
|| 14/11 || fu-ta ||
|| 9/7 || ta-re ||
|| 4/3 || do-fa ||
|| 11/8 || do-fu ||
|| 7/5 || mi-ta ||
|| 10/7 || ta-mi ||
|| 16/11 || fu-do ||
|| 3/2 || do-sol ||
|| 14/9 || re-ta ||
|| 11/7 || ta-fu ||
|| 8/5 || mi-do ||
|| 18/11 || fu-re ||
|| 5/3 || sol-mi ||
|| 12/7 || ta-sol ||
|| 7/4 || do-ta ||
|| 16/9 || re-do ||
|| 9/5 || mi-re ||
|| 20/11 || fu-mi ||
|| 11/6 || sol-fu ||
|| 2/1 || do-do ||

While the [[7-limit]] introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of [[12edo]], the 11-limit introduces neutral intervals, [[superfourth]]s and [[subfifth]]s, which fall in between major, minor and perfect [[interval category|interval categories]] and thus demand new distinctions. It is thus inescapably xenharmonic.

Relative to their size, [[edo]]s which do (relatively) well in supporting 11-limit intervals are: [[12edo]], [[15edo]], [[22edo]], [[31edo]], [[41edo]], [[46edo]], [[58edo]], [[72edo]], [[118edo]], [[130edo]] and [[152edo]].

[[image:11-limit_compare.png]]

==Intervals== 
Some of the simplest intervals of 11 include:

|| Interval || Cents Value ||
|| [[12_11|12/11]] || 150.637 ||
|| [[11_10|11/10]] || 165.004 ||
|| [[11_9|11/9]] || 347.408 ||
|| [[14_11|14/11]] || 417.508 ||
|| [[15_11|15/11]] || 536.951 ||
|| [[11_8|11/8]] || 551.318 ||
|| [[16_11|16/11]] || 648.682 ||
|| [[22_15|22/15]] || 663.049 ||
|| [[11_7|11/7]] || 782.492 ||
|| [[18_11|18/11]] || 852.592 ||
|| [[20_11|20/11]] || 1034.996 ||
|| [[11_6|11/6]] || 1049.363 ||
See: [[Gallery of Just Intervals]]

=Music= 
[[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Study #3]] ////[[http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3|play]]//// by [[Dave Hill]]
[[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Brief 11-ratio composition]] ////[[http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3|play]]//// by Dave Hill
////[[http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3|11 Limit Piano]]//// by [[Chris Vaisvil]]
[[https://soundcloud.com/andrew_heathwaite/11-limit-singtervals|11-limit singtervals]] by [[Andrew Heathwaite]]

=See also= 
[[Harmonic Limit]]
[[media type="custom" key="12438854"]]

Original HTML content:

<html><head><title>11-limit</title></head><body>The <em>11-limit</em> consists of all <a class="wiki_link" href="/JustIntonation">justly tuned</a> intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are <a class="wiki_link" href="/14_11">14/11</a>, <a class="wiki_link" href="/11_8">11/8</a>, <a class="wiki_link" href="/27_22">27/22</a> and <a class="wiki_link" href="/99_98">99/98</a>. The 11 odd-limit consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 11. Reduced to an octave, these are the ratios 1/1, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, 11/9, 5/4, 14/11, 9/7, 4/3, 11/8, 7/5, 10/7, 16/11, 3/2, 14/9, 11/7, 8/5, 18/11, 5/3, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 2/1. In an 11-limit system, all the ratios of the 11 odd-limit can be treated as potential consonances.<br />
<br />


<table class="wiki_table">
    <tr>
        <td>ratio<br />
</td>
        <td>harmonic solfege<br />
</td>
    </tr>
    <tr>
        <td>12/11<br />
</td>
        <td>fu-sol<br />
</td>
    </tr>
    <tr>
        <td>11/10<br />
</td>
        <td>mi-fu<br />
</td>
    </tr>
    <tr>
        <td>10/9<br />
</td>
        <td>re-mi<br />
</td>
    </tr>
    <tr>
        <td>9/8<br />
</td>
        <td>do-re<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>ta-do<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>sol-ta<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>mi-sol, ti-re<br />
</td>
    </tr>
    <tr>
        <td>11/9<br />
</td>
        <td>re-fu<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>do-mi<br />
</td>
    </tr>
    <tr>
        <td>14/11<br />
</td>
        <td>fu-ta<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>ta-re<br />
</td>
    </tr>
    <tr>
        <td>4/3<br />
</td>
        <td>do-fa<br />
</td>
    </tr>
    <tr>
        <td>11/8<br />
</td>
        <td>do-fu<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>mi-ta<br />
</td>
    </tr>
    <tr>
        <td>10/7<br />
</td>
        <td>ta-mi<br />
</td>
    </tr>
    <tr>
        <td>16/11<br />
</td>
        <td>fu-do<br />
</td>
    </tr>
    <tr>
        <td>3/2<br />
</td>
        <td>do-sol<br />
</td>
    </tr>
    <tr>
        <td>14/9<br />
</td>
        <td>re-ta<br />
</td>
    </tr>
    <tr>
        <td>11/7<br />
</td>
        <td>ta-fu<br />
</td>
    </tr>
    <tr>
        <td>8/5<br />
</td>
        <td>mi-do<br />
</td>
    </tr>
    <tr>
        <td>18/11<br />
</td>
        <td>fu-re<br />
</td>
    </tr>
    <tr>
        <td>5/3<br />
</td>
        <td>sol-mi<br />
</td>
    </tr>
    <tr>
        <td>12/7<br />
</td>
        <td>ta-sol<br />
</td>
    </tr>
    <tr>
        <td>7/4<br />
</td>
        <td>do-ta<br />
</td>
    </tr>
    <tr>
        <td>16/9<br />
</td>
        <td>re-do<br />
</td>
    </tr>
    <tr>
        <td>9/5<br />
</td>
        <td>mi-re<br />
</td>
    </tr>
    <tr>
        <td>20/11<br />
</td>
        <td>fu-mi<br />
</td>
    </tr>
    <tr>
        <td>11/6<br />
</td>
        <td>sol-fu<br />
</td>
    </tr>
    <tr>
        <td>2/1<br />
</td>
        <td>do-do<br />
</td>
    </tr>
</table>

<br />
While the <a class="wiki_link" href="/7-limit">7-limit</a> introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of <a class="wiki_link" href="/12edo">12edo</a>, the 11-limit introduces neutral intervals, <a class="wiki_link" href="/superfourth">superfourth</a>s and <a class="wiki_link" href="/subfifth">subfifth</a>s, which fall in between major, minor and perfect <a class="wiki_link" href="/interval%20category">interval categories</a> and thus demand new distinctions. It is thus inescapably xenharmonic.<br />
<br />
Relative to their size, <a class="wiki_link" href="/edo">edo</a>s which do (relatively) well in supporting 11-limit intervals are: <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/118edo">118edo</a>, <a class="wiki_link" href="/130edo">130edo</a> and <a class="wiki_link" href="/152edo">152edo</a>.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:269:&lt;img src=&quot;/file/view/11-limit_compare.png/354832066/11-limit_compare.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/11-limit_compare.png/354832066/11-limit_compare.png" alt="11-limit_compare.png" title="11-limit_compare.png" /><!-- ws:end:WikiTextLocalImageRule:269 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:1:&lt;h2&gt; --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:1 -->Intervals</h2>
 Some of the simplest intervals of 11 include:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>Interval<br />
</td>
        <td>Cents Value<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/12_11">12/11</a><br />
</td>
        <td>150.637<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_10">11/10</a><br />
</td>
        <td>165.004<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_9">11/9</a><br />
</td>
        <td>347.408<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/14_11">14/11</a><br />
</td>
        <td>417.508<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_11">15/11</a><br />
</td>
        <td>536.951<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_8">11/8</a><br />
</td>
        <td>551.318<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/16_11">16/11</a><br />
</td>
        <td>648.682<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/22_15">22/15</a><br />
</td>
        <td>663.049<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_7">11/7</a><br />
</td>
        <td>782.492<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/18_11">18/11</a><br />
</td>
        <td>852.592<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/20_11">20/11</a><br />
</td>
        <td>1034.996<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_6">11/6</a><br />
</td>
        <td>1049.363<br />
</td>
    </tr>
</table>

See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:3 -->Music</h1>
 <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow">Study #3</a> <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Dave%20Hill">Dave Hill</a><br />
<a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow">Brief 11-ratio composition</a> <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3" rel="nofollow">play</a> by Dave Hill<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3" rel="nofollow">11 Limit Piano</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<a class="wiki_link_ext" href="https://soundcloud.com/andrew_heathwaite/11-limit-singtervals" rel="nofollow">11-limit singtervals</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:5 -->See also</h1>
 <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a><br />
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/12438854?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;12438854&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js">
</script><!-- ws:end:WikiTextMediaRule:0 --></body></html>

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 <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:xenjacob|xenjacob]] and made on <tt>2012-07-25 23:47:57 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2013-10-17 03:32:33 UTC</tt>.<br>
-: The original revision id was <tt>354855404</tt>.<br>
+: The original revision id was <tt>460616054</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>another listening example found</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 67: / Line 67: @@
 [[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Brief 11-ratio composition]] ////[[http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3|play]]//// by Dave Hill
 ////[[http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3|11 Limit Piano]]//// by [[Chris Vaisvil]]
+[[https://soundcloud.com/andrew_heathwaite/11-limit-singtervals|11-limit singtervals]] by [[Andrew Heathwaite]]
 =See also=
@@ Line 358: / Line 359: @@
 &lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow"&gt;Brief 11-ratio composition&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Dave Hill&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3" rel="nofollow"&gt;11 Limit Piano&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="https://soundcloud.com/andrew_heathwaite/11-limit-singtervals" rel="nofollow"&gt;11-limit singtervals&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;See also&lt;/h1&gt;

11-limit: Difference between revisions

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