23-limit: Difference between revisions

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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.

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 the [[14afdo|14th]] mode [[Overtone scale|of the harmonic series]], which is to say that all of the first 28 [[harmonic]]s are in the 23-limit.

== Edo approximations ==

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 {{Prime limit navigation|23}}
-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.
+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 the [[14afdo|14th]] mode [[Overtone scale|of the harmonic series]], which is to say that all of the first 28 [[harmonic]]s are in the 23-limit.
 == Edo approximations ==