29-limit: Difference between revisions

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29-limit is the 10th prime ~~just~~ limit ~~where~~ 29 is the ~~highest~~ prime ~~division~~ for ~~each interval~~.

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 ==

[[282edo]] is the smallest edo that is [[consistent]] to the [[29-odd-limit]]. [[1323edo]] is the smallest edo that is [[distinctly consistent]] to the 29-odd-limit. Intervals [[29/16]] and [[32/29]] are very accurately approximated by [[7edo]] (1\7 for 32/29, 6\7 for 29/16).

== Music ==

; [[Randy Wells]]

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

[[Category:29-limit| ]]

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--limit is the 10th prime just limit where 29 is the highest prime division for each interval.
+{{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 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 ==
+[[282edo]] is the smallest edo that is [[consistent]] to the [[29-odd-limit]]. [[1323edo]] is the smallest edo that is [[distinctly consistent]] to the 29-odd-limit. Intervals [[29/16]] and [[32/29]] are very accurately approximated by [[7edo]] (1\7 for 32/29, 6\7 for 29/16).
+== Music ==
+; [[Randy Wells]]
+* [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021)
+{{stub}}
+[[Category:29-limit| ]] <!-- main article -->