29-limit: Difference between revisions
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{{Prime limit navigation|29}} | {{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 | 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 == | == Edo approximations == | ||
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; [[Randy Wells]] | ; [[Randy Wells]] | ||
* [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021) | * [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021) | ||
[[Category:29-limit| ]] <!-- main article --> | [[Category:29-limit| ]] <!-- main article --> | ||
Revision as of 15:39, 17 December 2024
The 29-limit consists of just intonation intervals whose ratios contain no prime factors 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
- Cloud Aliens (2021)