29-limit: Difference between revisions

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'''29-limit''' 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.

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

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.

~~== See also ==~~

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

* [[Harmonic limit]]

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

* [[29-odd-limit]]

* Mode 15 of the harmonic or subharmonic series.

[[~~Category:~~29-limit]]

== Edo approximations ==

[[~~Category:Limit~~]]

[[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).

[~~[Category~~:~~Prime limit]~~]

[[Category:~~Rank 10~~]]

== Music ==

; [[Randy Wells]]

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

[[Category:29-limit| ]]

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-'''29-limit''' 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.
+{{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.
-[[282edo|282EDO]] is the smallest EDO that is consistent to the 29-odd-limit. Intervals [[29/16]] and [[32/29]] are very accurately approximated by [[7edo|7EDO]] (1\7 for 32/29, 6\7 for 29/16).
+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.
-== See also ==
+These things are contained by the 29-limit, but not the 23-limit:
-* [[Harmonic limit]]
+* The [[29-odd-limit]];
-* [[29-odd-limit]]
+* Mode 15 of the harmonic or subharmonic series.
-[[Category:29-limit]]
+== Edo approximations ==
-[[Category:Limit]]
+[[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).
-[[Category:Prime limit]]
-[[Category:Rank 10]]
+== Music ==
+; [[Randy Wells]]
+* [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021)
+{{stub}}
+[[Category:29-limit| ]] <!-- main article -->