Talk:Tenney–Euclidean tuning: Difference between revisions
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The article says, "Just as TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, TE tuning minimizes the maximum TE-weighted (L2) error of any interval." But shouldn't it be "damage", not "error"? As far as I understand it, there would be no way to minimize the maximum error of any interval under a tuning, because you could always find a more complex interval with more error; minimaxing only makes sense for damage, which scales proportionally with the complexity of the interval. Or am I misunderstanding these concepts? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:50, 28 July 2021 (UTC) | The article says, "Just as TOP tuning minimizes the maximum Tenney-weighted (L1) error of any interval, TE tuning minimizes the maximum TE-weighted (L2) error of any interval." But shouldn't it be "damage", not "error"? As far as I understand it, there would be no way to minimize the maximum error of any interval under a tuning, because you could always find a more complex interval with more error; minimaxing only makes sense for damage, which scales proportionally with the complexity of the interval. Or am I misunderstanding these concepts? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:50, 28 July 2021 (UTC) | ||
: Ah, I think I see. "Damage" may be a bit of an outdated term. It's what Paul Erlich uses in his Middle Path paper. But it means error weighted (divided) by the Tenney height, which is equivalent to the L1 norm, and so "Tenney-weighted (L1) error" is the same thing as damage. And "TE-weighted (L2) error" means error weighted by the TE height, which is equivalent to the L2 norm, so it's similar to damage. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:04, 28 July 2021 (UTC) | |||