Talk:Tenney–Euclidean tuning: Difference between revisions
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Some notes on Frobenius tuning |
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: 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 "Damage" may be a bit of an outdated term.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) | : 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 "Damage" may be a bit of an outdated term.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) | ||
== "Frobenius" tuning == | |||
Frobenius tuning has nothing to do with the Frobenius norm. It's simply the unweighted Euclidean norm. I propose renaming it to simply that: "unweighted Euclidean tuning". | |||
The article also says: | |||
: This leads to a different tuning, the Frobenius tuning, which is perfectly functional but has less theoretical justification than TE tuning. | |||
What theoretical justifications? This is ironic since the next paragraph proceeds to list several theoretical advantages of this tuning. | |||
Not weighting the primes leads to -on average- errors that are the same across primes. It is the Tenney-Euclidean tuning that is biased towards lower primes and not the opposite. This is not a problem at all but the article is in no way clear on this. (In fact, even unweighted norms usually result in temperaments with a slight bias towards low primes, simply because the way temperaments are usually constructed (e.g. stacking edo maps) already has this bias (and especially wrt octaves)) | |||
-[[User:Sintel|Sintel]] ([[User talk:Sintel|talk]]) 19:37, 18 December 2021 (UTC) | |||