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 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~~.

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 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 a substantial increment in its harmonic contents. Specifically, these things are contained by the 23-limit, but not the 19-limit:

* The [[23-odd-limit|23-]], [[25-odd-limit|25-]], and [[27-odd-limit]];

* Mode 12, 13, and 14 of the harmonic or subharmonic series.

== Edo approximation ==

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; {{W|Noah Dean DaSilva Jordan}}

* [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ Gracias a Dios] (2023) for solo jarana (series 23/22, 23/21....23/12)

~~== See also ==~~

* [[23-odd-limit]]

[[Category:23-limit| ]]

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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 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.
+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 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 a substantial increment in its harmonic contents. Specifically, these things are contained by the 23-limit, but not the 19-limit:
+* The [[23-odd-limit|23-]], [[25-odd-limit|25-]], and [[27-odd-limit]];
+* Mode 12, 13, and 14 of the harmonic or subharmonic series.
 == Edo approximation ==
@@ Line 182: / Line 186: @@
 ; {{W|Noah Dean DaSilva Jordan}}
 * [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ Gracias a Dios] (2023) for solo jarana (series 23/22, 23/21....23/12)
-== See also ==
-* [[23-odd-limit]]
 [[Category:23-limit| ]] <!-- main article -->