Talk:Tenney–Euclidean tuning: Difference between revisions
m FloraC moved page Talk:Tenney-Euclidean Tuning to Talk:Tenney-Euclidean tuning: WP:NCCAPS |
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[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:52, 24 June 2020 (UTC) | [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:52, 24 June 2020 (UTC) | ||
== Damage, not error? == | |||
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) | |||
Revision as of 16:50, 28 July 2021
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Crazy math theory's dominating the article
Anybody can read this article in its current shape and learn how to derive the TE tuning, TE generators, etc.? I can't. How I learned it was by coming up with the idea of RMS-error tuning, posting it on reddit and get told that was actually called TE tuning.
That said, TE tuning is an easy problem if you break it down this way.
What's the problem?
It's a least square problem of the following linear equations:
[math]\displaystyle{ (MW)^\mathsf{T} \vec{g} = W\vec{p} }[/math]
where M is the known mapping of the temperament, g the column vector of each generators in cents, p the column vector of targeted intervals in cents, usually prime harmonics, and W the weighting matrix.
This is an overdetermined system saying that the sum of (MW)Tij steps of generator gj for all j equals the corresponding interval (Wp)i.
How to solve it?
The pseudoinverse is a common means to solve least square problems.
We don't need to document what a pseudoinverse is, at least not in so much amount of detail, cuz it's not a concept specific in tuning, and it's well documented on wikipedia. Nor do we need to document why pseudoinverses solve least square problems. Again, that's not a question specific in tuning.
The only thing that matters is to identify the problem as a least square problem. The rest is nothing but manual labor.
I'm gonna try improving the readability of this article by adding my thoughts and probably clear it up.
FloraC (talk) 18:52, 24 June 2020 (UTC)
Damage, not error?
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? --Cmloegcmluin (talk) 16:50, 28 July 2021 (UTC)