29-limit: Difference between revisions

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The '''29-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 29. It is the 10th [[prime limit]] and is ~~thus~~ a superset of the [[23-limit]] and a subset of the [[31-limit]]. The prime 29 is notable as being the prime that ends a record prime gap starting at 23. Thus, the 29-limit is in some sense analogous to the [[11-limit]] as both include the prime ending a record prime gap.

The '''29-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 29. It is the 10th [[prime limit]] and is a superset of the [[23-limit]] and a subset of the [[31-limit]]. The prime 29 is notable as being the prime that ends a record prime gap starting at 23. Thus, the 29-limit is in some sense analogous to the [[11-limit]] as both include the prime ending a record prime gap.

The 29-limit is a rank-10 system, and can be modeled in a 9-dimensional lattice, with the primes 3 to 29 represented by each dimension. The prime 2 does not appear in the typical 29-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a tenth dimension is needed.

These things are contained by the 29-limit, but not the 23-limit:

* The [[29-odd-limit]];

* Mode 15 of the harmonic or subharmonic series.

== Edo approximations ==

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; [[Randy Wells]]

* [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021)

~~== See also ==~~

* [[29-odd-limit]]

[[Category:29-limit| ]]

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 {{Prime limit navigation|29}}
-The '''29-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 29. It is the 10th [[prime limit]] and is thus a superset of the [[23-limit]] and a subset of the [[31-limit]]. The prime 29 is notable as being the prime that ends a record prime gap starting at 23. Thus, the 29-limit is in some sense analogous to the [[11-limit]] as both include the prime ending a record prime gap.
+The '''29-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 29. It is the 10th [[prime limit]] and is a superset of the [[23-limit]] and a subset of the [[31-limit]]. The prime 29 is notable as being the prime that ends a record prime gap starting at 23. Thus, the 29-limit is in some sense analogous to the [[11-limit]] as both include the prime ending a record prime gap.
+The 29-limit is a rank-10 system, and can be modeled in a 9-dimensional lattice, with the primes 3 to 29 represented by each dimension. The prime 2 does not appear in the typical 29-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, a tenth dimension is needed.
+These things are contained by the 29-limit, but not the 23-limit:
+* The [[29-odd-limit]];
+* Mode 15 of the harmonic or subharmonic series.
 == Edo approximations ==
@@ Line 8: / Line 14: @@
 ; [[Randy Wells]]
 * [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021)
-== See also ==
-* [[29-odd-limit]]
 [[Category:29-limit| ]] <!-- main article -->