Constrained tuning/Analytical solution to constrained Euclidean tunings: Difference between revisions
→CEE tuning: I don't think these are ever gonna be solved, so I'm gonna discuss them as plain observations |
Sintel bot (talk | contribs) Fix <math> environments for MathJax v4 (align->aligned, etc.) |
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| Line 43: | Line 43: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
VP_{\rm C} &= V \\ | VP_{\rm C} &= V \\ | ||
P_{\rm C}M &= O | P_{\rm C}M &= O | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 90: | Line 90: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
V_X &= VX \\ | V_X &= VX \\ | ||
(M_I)_X &= X^+ M_I | (M_I)_X &= X^+ M_I | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 143: | Line 143: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
V_S &= VS \\ | V_S &= VS \\ | ||
(M_I)_S &= S^{-1}M_I | (M_I)_S &= S^{-1}M_I | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 156: | Line 156: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
V_X &= VX \\ | V_X &= VX \\ | ||
(M_I)_X &= X^+ M_I | (M_I)_X &= X^+ M_I | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 171: | Line 171: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
V_{XS} &= VXS \\ | V_{XS} &= VXS \\ | ||
(M_I)_{XS} &= (XS)^+ M_I | (M_I)_{XS} &= (XS)^+ M_I | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 197: | Line 197: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
P &= V^+V \\ | P &= V^+V \\ | ||
&= \frac{1}{446} | &= \frac{1}{446} | ||
| Line 206: | Line 206: | ||
-61 & -38 & 92 & 413 | -61 & -38 & 92 & 413 | ||
\end{bmatrix} | \end{bmatrix} | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 216: | Line 216: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
P_{\rm M} &= V_{\rm M}^+V_{\rm M} \\ | P_{\rm M} &= V_{\rm M}^+V_{\rm M} \\ | ||
&= \frac{1}{117} | &= \frac{1}{117} | ||
| Line 224: | Line 224: | ||
10 & 40 & 100 | 10 & 40 & 100 | ||
\end{bmatrix} | \end{bmatrix} | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||
| Line 254: | Line 254: | ||
<math>\displaystyle | <math>\displaystyle | ||
\begin{ | \begin{aligned} | ||
T_{\rm C} &= JP_{\rm C} \\ | T_{\rm C} &= JP_{\rm C} \\ | ||
&= \langle \begin{matrix} 1200 & 1896.8843 & 2787.5374 & 3368.8435 \end{matrix} ] | &= \langle \begin{matrix} 1200 & 1896.8843 & 2787.5374 & 3368.8435 \end{matrix} ] | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||