Talk:Tenney–Euclidean tuning: Difference between revisions

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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>M^\mathsf{T}W \vec{g} = \vec{p}W</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 (M<sup>T</sup>W)<sub>''ij''</sub> steps of generator '''g'''<sub>''j''</sub> for all ''j'' equals the corresponding interval ('''p'''W)<sub>''i''</sub>.
+'''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.