13-limit
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- This revision was by author Andrew_Heathwaite and made on 2011-05-26 17:01:50 UTC.
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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>