Talk:Tenney–Euclidean tuning: Difference between revisions
→Crazy math theory's dominating the article: new section |
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It's a least square problem of the following linear equations: | It's a least square problem of the following linear equations: | ||
<math> | <math>(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. | 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 ( | This is an overdetermined system saying that the sum of (MW)<sup>T</sup><sub>''ij''</sub> steps of generator '''g'''<sub>''j''</sub> for all ''j'' equals the corresponding interval (W'''p''')<sub>''i''</sub>. | ||
'''How to solve it?''' | '''How to solve it?''' | ||
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The only thing that matters is to identify the problem as a least square problem. The rest is nothing but manual labor. | 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. | I'm gonna try improving the readability of this article by adding my thoughts and probably clear it up. | ||
[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:52, 24 June 2020 (UTC) | |||