Talk:Height: Difference between revisions

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: Could you provide some materials on what it is? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:49, 31 December 2022 (UTC)

: The gradus suavitatis is indeed a proper height function. It might be worth adding because of its historical significance. Not sure about the other ones, though a lot of those (tenney, te_norm, weil, wilson) are already described as height functions on the wiki. – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:43, 25 April 2025 (UTC)

== Counterexample ==

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– [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:41, 25 April 2025 (UTC)

: Agreed. The [[Complexity]] page will also require an update, as it literally states that the complexity of an interval is called "height", whereas this counterexample shows that heights are a subset of interval complexity measures. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:45, 25 April 2025 (UTC)

:: Actually, I'm not really sure if we should be talking about height functions at all, since those properties aren't really used anywhere! The only place heights actuall show up is in the proof for Dirichlet (logflat) badness, where it's actually a height on temperaments, not intervals! And then the actual height functions we do end up using are actually just norms on some vector space. – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 11:19, 26 April 2025 (UTC)

::: I'd love to do away with heights and stick to complexities. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 02:38, 30 April 2025 (UTC)

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 : Could you provide some materials on what it is? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:49, 31 December 2022 (UTC)
+: The gradus suavitatis is indeed a proper height function. It might be worth adding because of its historical significance. Not sure about the other ones, though a lot of those (tenney, te_norm, weil, wilson) are already described as height functions on the wiki. – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:43, 25 April 2025 (UTC)
 == Counterexample ==
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 – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 13:41, 25 April 2025 (UTC)
+: Agreed. The [[Complexity]] page will also require an update, as it literally states that the complexity of an interval is called "height", whereas this counterexample shows that heights are a subset of interval complexity measures. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 20:45, 25 April 2025 (UTC)
+:: Actually, I'm not really sure if we should be talking about height functions at all, since those properties aren't really used anywhere! The only place heights actuall show up is in the proof for Dirichlet (logflat) badness, where it's actually a height on temperaments, not intervals! And then the actual height functions we do end up using are actually just norms on some vector space. – [[User:Sintel|Sintel🎏]] ([[User_talk:Sintel|talk]]) 11:19, 26 April 2025 (UTC)
+::: I'd love to do away with heights and stick to complexities. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 02:38, 30 April 2025 (UTC)