23-limit: Difference between revisions
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In 23-limit [[ | In 23-limit [[just intonation]], all ratios contain no prime factors 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 limits 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 harmonics are in the 23-limit. | ||
Ratios of 23 in the 23-odd limit include: | Ratios of 23 in the 23-odd limit include: | ||
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[[94edo]] is the first [[EDO]] to be consistent in the [[23-odd-limit]]. The smallest EDO where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent. | [[94edo]] is the first [[EDO]] to be consistent in the [[23-odd-limit]]. The smallest EDO where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent. | ||
See | == See also == | ||
[[Category:23-limit]] | * [[Harmonic limit]] | ||
[[Category:limit | * [[23-odd-limit]] | ||
[[Category:23-limit| ]] <!-- main article --> | |||
[[Category:Prime limit]] | |||