13-limit
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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. [[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. =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|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= [[Harmonic limit]]
Original HTML content:
<html><head><title>13-limit</title></head><body>The 13-prime-limit refers to a constraint on selecting just intonation intervals such that the highest <a class="wiki_link" href="/prime%20numbers">prime number</a> in all ratios is 13. Thus, <a class="wiki_link" href="/40_39">40/39</a> 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 <a class="wiki_link" href="/17-limit">17</a> 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, <a class="wiki_link" href="/3_2">3/2</a> 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. <a class="wiki_link" href="/23_13">23/13</a> is not within the 13-limit, since <a class="wiki_link" href="/23-limit">23</a> is a prime number higher than 13).<br /> <br /> 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.<br /> <br /> <a class="wiki_link" href="/Edo">Edo</a>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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music</h1> <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm" rel="nofollow">Venusian Cataclysms</a> <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.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">Chord Progression on the Harmonic Overtone Series</a> <a class="wiki_link_ext" href="http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3" rel="nofollow">play</a> by Dave Hill<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->See also</h1> <a class="wiki_link" href="/Harmonic%20limit">Harmonic limit</a></body></html>