Talk:Harmonic limit: Difference between revisions

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== Cleanup of large prime limit pages ==

Many of the pages for large prime limits are stubs. Should all the articles larger than 23-limit be merged into one article named "large prime limits?" --[[User:Hkm|hkm]] ([[User talk:Hkm|talk]]) 22:16, 27 March 2025 (UTC)

: They could even be merged on this page. Instead of the table in the section for individual prime limits, we could have a section for each prime limit, with a quick summary and a link to the main article if it exists, and potentially no section at all if it's not particularly meaningful. The page titles could still redirect to this page though, for convenience. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:36, 28 March 2025 (UTC)

== Complexity and limit ==

The concept of limit seems intrinsically linked to that of complexity. When a limit is applied on the infinite set of JI intervals, a resulting subset is found, and the rule used to find that subset is generally (always?) a rule about the complexity of the intervals. The most common limits are prime limit (complexity defined as the largest prime from the prime factorizaton), the odd limit (the largest odd factor in the fraction) and the integer limit (the largest integer in the fraction). Other limits may also be defined according to other types of complexity. Therefore I believe that this page should first introduce the concept of limit as applied to the complexity of intervals in general, and then introduce the many kinds of limit people use to select musically meaningful subsets of JI intervals. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:43, 27 April 2025 (UTC)

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+== Cleanup of large prime limit pages ==
+Many of the pages for large prime limits are stubs. Should all the articles larger than 23-limit be merged into one article named "large prime limits?" --[[User:Hkm|hkm]] ([[User talk:Hkm|talk]]) 22:16, 27 March 2025 (UTC)
+: They could even be merged on this page. Instead of the table in the section for individual prime limits, we could have a section for each prime limit, with a quick summary and a link to the main article if it exists, and potentially no section at all if it's not particularly meaningful. The page titles could still redirect to this page though, for convenience. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:36, 28 March 2025 (UTC)
+== Complexity and limit ==
+The concept of limit seems intrinsically linked to that of complexity. When a limit is applied on the infinite set of JI intervals, a resulting subset is found, and the rule used to find that subset is generally (always?) a rule about the complexity of the intervals. The most common limits are prime limit (complexity defined as the largest prime from the prime factorizaton), the odd limit (the largest odd factor in the fraction) and the integer limit (the largest integer in the fraction). Other limits may also be defined according to other types of complexity. Therefore I believe that this page should first introduce the concept of limit as applied to the complexity of intervals in general, and then introduce the many kinds of limit people use to select musically meaningful subsets of JI intervals. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:43, 27 April 2025 (UTC)