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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The 13-prime-limit refers to a constraint on selecting just intonation intervals such that the highest [[prime_numbers|prime number]] in all ratios is 13. Thus, [[40/39|40/39]] would be allowable, since 40 is 2*2*2*5 and 39 is 3*13, but 34/33 would not be allowable, since 34 is 2*17, and [[17-limit|17]] is a prime number higher than 13. An interval doesn't need to contain a 13 to be considered within the 13-limit. For instance, [[3/2|3/2]] is considered part of the 13-limit, since the primes 2 and 3 are smaller than 13. Also, an interval with a 13 in it is not necessarily within the 13-limit. [[23/13|23/13]] is not within the 13-limit, since [[23-limit|23]] is a prime number higher than 13).
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-09-17 04:50:23 UTC</tt>.<br>
: The original revision id was <tt>592460348</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">The 13-prime-limit refers to a constraint on selecting just intonation intervals such that the highest [[prime numbers|prime number]] in all ratios is 13. Thus, [[40_39|40/39]] would be allowable, since 40 is 2*2*2*5 and 39 is 3*13, but 34/33 would not be allowable, since 34 is 2*17, and [[17-limit|17]] is a prime number higher than 13. An interval doesn't need to contain a 13 to be considered within the 13-limit. For instance, [[3_2|3/2]] is considered part of the 13-limit, since the primes 2 and 3 are smaller than 13. Also, an interval with a 13 in it is not necessarily within the 13-limit. [[23_13|23/13]] is not within the 13-limit, since [[23-limit|23]] is a prime number higher than 13).


The 13-prime-limit can be modeled in a 5-dimensional lattice, with the primes 3, 5, 7, 11, and 13 represented by each dimension. The prime 2 does not appear in the typical 13-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a sixth dimension is need.
The 13-prime-limit can be modeled in a 5-dimensional lattice, with the primes 3, 5, 7, 11, and 13 represented by each dimension. The prime 2 does not appear in the typical 13-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a sixth dimension is need.


[[Edo]]s good for 13-limit are 1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 16, 17, 19, 20, 22, 24, 26, 31, 37, 46, 50, 53, 63, 77, 84, 87, 130, 140, 161, 183, 207, 217, 224, 270, 494, 851, 1075, 1282, 1578, 2159, 2190, 2684, 3265, 3535, 4573, 5004, 5585, 6079, 8269, 8539, 13854, 14124, 16808, 20203, 22887, 28742, 32007, 37011, 50434, 50928, 51629, 54624, 56202, 59467, 64471, 65052, ... .
[[EDO|Edo]]s good for 13-limit are 1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 16, 17, 19, 20, 22, 24, 26, 31, 37, 46, 50, 53, 63, 77, 84, 87, 130, 140, 161, 183, 207, 217, 224, 270, 494, 851, 1075, 1282, 1578, 2159, 2190, 2684, 3265, 3535, 4573, 5004, 5585, 6079, 8269, 8539, 13854, 14124, 16808, 20203, 22887, 28742, 32007, 37011, 50434, 50928, 51629, 54624, 56202, 59467, 64471, 65052, ... .
 
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=Music=  
=Music=
[[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Venusian Cataclysms]] [[http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.mp3|play]] by [[Dave Hill]]
[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Venusian Cataclysms] [http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.mp3 play] by [[Dave_Hill|Dave Hill]]
[[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm|Chord Progression on the Harmonic Overtone Series]] [[http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3|play]] by Dave Hill
 
[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Chord Progression on the Harmonic Overtone Series] [http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play] by Dave Hill


=See also=  
=See also=
[[Harmonic limit]]</pre></div>
[[Harmonic_Limit|Harmonic limit]]     [[Category:13-limit]]
<h4>Original HTML content:</h4>
[[Category:limit]]
<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;13-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 13-prime-limit refers to a constraint on selecting just intonation intervals such that the highest &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime number&lt;/a&gt; in all ratios is 13. Thus, &lt;a class="wiki_link" href="/40_39"&gt;40/39&lt;/a&gt; would be allowable, since 40 is 2*2*2*5 and 39 is 3*13, but 34/33 would not be allowable, since 34 is 2*17, and &lt;a class="wiki_link" href="/17-limit"&gt;17&lt;/a&gt; is a prime number higher than 13. An interval doesn't need to contain a 13 to be considered within the 13-limit. For instance, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; is considered part of the 13-limit, since the primes 2 and 3 are smaller than 13. Also, an interval with a 13 in it is not necessarily within the 13-limit. &lt;a class="wiki_link" href="/23_13"&gt;23/13&lt;/a&gt; is not within the 13-limit, since &lt;a class="wiki_link" href="/23-limit"&gt;23&lt;/a&gt; is a prime number higher than 13).&lt;br /&gt;
[[Category:listen]]
&lt;br /&gt;
[[Category:prime_limit]]
The 13-prime-limit can be modeled in a 5-dimensional lattice, with the primes 3, 5, 7, 11, and 13 represented by each dimension. The prime 2 does not appear in the typical 13-limit lattice because octave equivalence is presumed. If octave equivalence is not presumed, a sixth dimension is need.&lt;br /&gt;
[[Category:rank_6]]
&lt;br /&gt;
&lt;a class="wiki_link" href="/Edo"&gt;Edo&lt;/a&gt;s good for 13-limit are 1, 2, 3, 4, 5, 6, 7, 9, 10, 15, 16, 17, 19, 20, 22, 24, 26, 31, 37, 46, 50, 53, 63, 77, 84, 87, 130, 140, 161, 183, 207, 217, 224, 270, 494, 851, 1075, 1282, 1578, 2159, 2190, 2684, 3265, 3535, 4573, 5004, 5585, 6079, 8269, 8539, 13854, 14124, 16808, 20203, 22887, 28742, 32007, 37011, 50434, 50928, 51629, 54624, 56202, 59467, 64471, 65052, ... .&lt;br /&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="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;
&lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow"&gt;Venusian Cataclysms&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Dave%20Hill"&gt;Dave Hill&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow"&gt;Chord Progression on the Harmonic Overtone Series&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Dave Hill&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;See also&lt;/h1&gt;
&lt;a class="wiki_link" href="/Harmonic%20limit"&gt;Harmonic limit&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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