Diamond tradeoff: Difference between revisions
Cmloegcmluin (talk | contribs) |
ArrowHead294 (talk | contribs) m Writing \frac without brackets in LaTeX is bad practice. |
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(MU)^{-1} \\ | (MU)^{-1} \\ | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
1 & \ | 1 & \frac{1}{2} \\ | ||
0 & \ | 0 & \frac{1}{4} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} | ||
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(MU)^{-1} \\ | (MU)^{-1} \\ | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
1 & \ | 1 & \frac{1}{2} \\ | ||
0 & \ | 0 & \frac{1}{4} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} | ||
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1 & 0 \\ | 1 & 0 \\ | ||
0 & 0 \\ | 0 & 0 \\ | ||
0 & \ | 0 & \frac{1}{4} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} | ||
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This tells us our generator is { | This tells us our generator is <math>\monzo{0 & 0 & \frac{1}{4}}</math>, or 5<sup>{{frac|1|4}}</sup>. In cents, that's {{nowrap|1200 × log<sub>2</sub>(5<sup>{{frac|1|4}}</sup>) ≈ 696.578{{c}}}}. | ||
==== Third diamond extrema ==== | ==== Third diamond extrema ==== | ||
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(MU)^{-1} \\ | (MU)^{-1} \\ | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
1 & \ | 1 & \frac{2}{3} \\ | ||
0 & -\ | 0 & -\frac{1}{3} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} | ||
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(MU)^{-1} \\ | (MU)^{-1} \\ | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
1 & \ | 1 & \frac{2}{3} \\ | ||
0 & -\ | 0 & -\frac{1}{3} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} | ||
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G \\ | G \\ | ||
\left[ \begin{array} {rrr} | \left[ \begin{array} {rrr} | ||
1 & \ | 1 & \frac{1}{3} \\ | ||
0 & -\ | 0 & -\frac{1}{3} \\ | ||
0 & \ | 0 & \frac{1}{3} \\ | ||
\end{array} \right] | \end{array} \right] | ||
\end{array} | \end{array} |