Talk:Normal forms: Difference between revisions

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:::::::::::::::::: Thank you. I did a little more work on it this morning based on random things that popped in my head last night. The main thing being that there were some inaccuracies re: canonical form (defactoring removes rows of zeros, so the third step to do so again after HNF was pointless). Also, I thought it was better to separate the issue re: converting intervals between ratio and vector format from discussions of the normal forms, since the format they're written in is independent from the different normal forms. Again, let me know if there's any problem with it and feel free to further adjust yourself. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:17, 4 October 2021 (UTC)

== IRREF ==

The footnote criticizes IRREF for making enfactored mappings. But I originally proposed IRREF for the comma list, not the mapping. I agree that IRREF mappings are a horrible idea! From my last edit of this page: "For a monzo list, it has the advantage of limiting the appearance of the N highest primes to only one comma each (where N is the codimension), isolating each prime's effect on the pergen, but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion." I think IRREF is valuable as a sort of secondary comma list. It would be nice if x31eq listed the IRREF comma list as well as the usual one, so that one could see all the various restrictions at a glance. It also helps compare two different temperaments to see what they have in common. For example consider (81/80 36/35) and (2048/2025 64/63), two comma lists defined by ascending prime limit, least odd limit and no enfactoring. Their IRREF forms are (81/80 64/63) and (2048/2025 64/63). The IRREFs show that they have 64/63 in common. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:55, 13 October 2021 (UTC)

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 :::::::::::::::::: Thank you. I did a little more work on it this morning based on random things that popped in my head last night. The main thing being that there were some inaccuracies re: canonical form (defactoring removes rows of zeros, so the third step to do so again after HNF was pointless). Also, I thought it was better to separate the issue re: converting intervals between ratio and vector format from discussions of the normal forms, since the format they're written in is independent from the different normal forms. Again, let me know if there's any problem with it and feel free to further adjust yourself. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:17, 4 October 2021 (UTC)
+== IRREF ==
+The footnote criticizes IRREF for making enfactored mappings. But I originally proposed IRREF for the comma list, not the mapping. I agree that IRREF mappings are a horrible idea! From my last edit of this page: "For a monzo list, it has the advantage of limiting the appearance of the N highest primes to only one comma each (where N is the codimension), isolating each prime's effect on the pergen, but has the disadvantage that the commas tend to have high odd limits, and the comma list may have torsion." I think IRREF is valuable as a sort of secondary comma list. It would be nice if x31eq listed the IRREF comma list as well as the usual one, so that one could see all the various restrictions at a glance. It also helps compare two different temperaments to see what they have in common. For example consider (81/80 36/35) and (2048/2025 64/63), two comma lists defined by ascending prime limit, least odd limit and no enfactoring. Their IRREF forms are (81/80 64/63) and (2048/2025 64/63). The IRREFs show that they have 64/63 in common. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 22:55, 13 October 2021 (UTC)