13-limit: Difference between revisions

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The '''13-limit''' or 13-prime-limit consists of [[just intonation]] [[interval]]s such that the highest [[prime factor]] in all [[ratio]]s is 13. Thus, [[40/39]] would be within the 13-limit, since 40 is {{nowrap|2 × 2 × 2 × 5}} and 39 is {{nowrap|3 × 13}}, but [[34/33]] would not, since 34 is {{nowrap|2 × 17}}, and [[17-limit|17]] is a prime number higher than 13. The 13-limit is the 6th [[prime limit]] and is a superset of the [[11-limit]] and a subset of the [[17-limit]].

The '''13-limit''' (AKA ''yazalatha'' in [[color notation]]) or 13-prime-limit consists of [[just intonation]] [[interval]]s such that the highest [[prime factor]] in all [[ratio]]s is 13. Thus, [[40/39]] would be within the 13-limit, since 40 is {{nowrap|2 × 2 × 2 × 5}} and 39 is {{nowrap|3 × 13}}, but [[34/33]] would not, since 34 is {{nowrap|2 × 17}}, and [[17-limit|17]] is a prime number higher than 13. The 13-limit is the 6th [[prime limit]] and is a superset of the [[11-limit]] and a subset of the [[17-limit]].

The 13-limit is a [[rank and codimension|rank-6]] system, and can be modeled in a 5-dimensional [[lattice]], with the primes [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] represented by each dimension. The prime [[2/1|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 needed.

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 {{Prime limit navigation|13}}
-The '''13-limit''' or 13-prime-limit consists of [[just intonation]] [[interval]]s such that the highest [[prime factor]] in all [[ratio]]s is 13. Thus, [[40/39]] would be within the 13-limit, since 40 is {{nowrap|2 × 2 × 2 × 5}} and 39 is {{nowrap|3 × 13}}, but [[34/33]] would not, since 34 is {{nowrap|2 × 17}}, and [[17-limit|17]] is a prime number higher than 13. The 13-limit is the 6th [[prime limit]] and is a superset of the [[11-limit]] and a subset of the [[17-limit]].
+The '''13-limit''' (AKA ''yazalatha'' in [[color notation]]) or 13-prime-limit consists of [[just intonation]] [[interval]]s such that the highest [[prime factor]] in all [[ratio]]s is 13. Thus, [[40/39]] would be within the 13-limit, since 40 is {{nowrap|2 × 2 × 2 × 5}} and 39 is {{nowrap|3 × 13}}, but [[34/33]] would not, since 34 is {{nowrap|2 × 17}}, and [[17-limit|17]] is a prime number higher than 13. The 13-limit is the 6th [[prime limit]] and is a superset of the [[11-limit]] and a subset of the [[17-limit]].
 The 13-limit is a [[rank and codimension|rank-6]] system, and can be modeled in a 5-dimensional [[lattice]], with the primes [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]] represented by each dimension. The prime [[2/1|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 needed.