23-limit: Difference between revisions
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{{Prime limit navigation|23}} | {{Prime limit navigation|23}} | ||
The '''23-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 23. The prime 23 is significant as being the start of a record prime gap ending at 29, the previous record prime gap being the one corresponding to the [[7-limit]]. Thus, it is arguably a potential ideal stopping point for [[prime limit]]s due to it corresponding to the full [[27-odd-limit]] and thus corresponding to mode 14 of the [[harmonic series]], which is to say that all of the first 28 [[harmonic]]s are in the 23-limit. | The '''23-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 23. It is the 9th [[prime limit]] and is thus a superset of the [[19-limit]] and a subset of the [[29-limit]]. The prime 23 is significant as being the start of a record prime gap ending at 29, the previous record prime gap being the one corresponding to the [[7-limit]]. Thus, it is arguably a potential ideal stopping point for [[prime limit]]s due to it corresponding to the full [[27-odd-limit]] and thus corresponding to mode 14 of the [[harmonic series]], which is to say that all of the first 28 [[harmonic]]s are in the 23-limit. | ||
== Edo approximations == | == Edo approximations == | ||
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== See also == | == See also == | ||
* [[23-odd-limit]] | * [[23-odd-limit]] | ||
[[Category:23-limit| ]] <!-- main article --> | [[Category:23-limit| ]] <!-- main article --> | ||