29-limit: Difference between revisions
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{{Prime limit navigation|29}} | {{Prime limit navigation|29}} | ||
'''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 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. | ||
[[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 | == 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). | |||
== See also == | == See also == | ||
* [[29-odd-limit]] | * [[29-odd-limit]] | ||
[[Category:29-limit| ]] <!-- main article --> | [[Category:29-limit| ]] <!-- main article --> | ||
Revision as of 10:49, 29 September 2023
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 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.
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).