13-limit: Difference between revisions
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Wikispaces>xenwolf **Imported revision 215739480 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 232212562 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-05-26 17:01:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>232212562</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">see [[Harmonic limit]]</pre></div> | <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 number in all ratios is 13. Thus, 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 3*17, and 17 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. | |||
see [[Harmonic limit]]</pre></div> | |||
<h4>Original HTML content:</h4> | <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"><html><head><title>13-limit</title></head><body>see <a class="wiki_link" href="/Harmonic%20limit">Harmonic limit</a></body></html></pre></div> | <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"><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 prime number in all ratios is 13. Thus, 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 3*17, and 17 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 /> | |||
see <a class="wiki_link" href="/Harmonic%20limit">Harmonic limit</a></body></html></pre></div> | |||
Revision as of 17:01, 26 May 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 2011-05-26 17:01:50 UTC.
- The original revision id was 232212562.
- 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:
The 13-prime-limit refers to a constraint on selecting just intonation intervals such that the highest prime number in all ratios is 13. Thus, 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 3*17, and 17 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. see [[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 prime number in all ratios is 13. Thus, 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 3*17, and 17 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 /> see <a class="wiki_link" href="/Harmonic%20limit">Harmonic limit</a></body></html>