Talk:Tenney–Euclidean tuning: Difference between revisions
Cmloegcmluin (talk | contribs) |
Update to my earlier comment |
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'''What's the problem?''' | '''What's the problem?''' | ||
It's a least | It's a least squares problem of the following linear equations: | ||
<math>( | <math>(AW)^\mathsf{T} \vec{g} = W\vec{p}</math> | ||
where | where A 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 (AW)<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) | ||
[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) | : Update: the page is clear enough now. | ||
: The standard way to write the equation is: | |||
: <math>G(AW) = J_0 W</math> | |||
: The targeted interval list is known as ''JIP'' and is denoted J_0 here. The main difference from my previous comment is that the generator list and the JIP are presented as row vectors. It can be further simplified to | |||
: <math>GV = J</math> | |||
: which is pretty clearly displayed in the article. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 17:39, 16 December 2021 (UTC) | |||
== Damage, not error? == | == Damage, not error? == | ||