Harmonic entropy: Difference between revisions

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In all these examples, the left plot is a series of plots of UHE at different N, with the zeta HE being a slightly thicker line in the background. The right plot is the largest N plotted against zeta HE, being almost a perfect line.

Note also that we don't plot the UHE directly, but rather <math>\exp((1-a)UHE)</math>, as described previously. The units have also been converted back to cents. Each HE function has been scaled so that the minimum entropy is 0 and the maximum entropy is 1.

Note also that we don't plot the UHE directly, but rather <math>\exp((1-a)\text{UHE}_a)</math>, as described previously. The units have also been converted back to cents. Each HE function has been scaled so that the minimum entropy is 0 and the maximum entropy is 1.

Lastly, note that, due to our multiplication of UHE by <math>(1-a)</math> above, the UHE would be flipped upside down relative to what we're used to, with higher values corresponding to more concordant intervals. In the pictures below we have flipped it back upside down, for consistency with the earlier pictures.

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 In all these examples, the left plot is a series of plots of UHE at different N, with the zeta HE being a slightly thicker line in the background. The right plot is the largest N plotted against zeta HE, being almost a perfect line.
-Note also that we don't plot the UHE directly, but rather <math>\exp((1-a)UHE)</math>, as described previously. The units have also been converted back to cents. Each HE function has been scaled so that the minimum entropy is 0 and the maximum entropy is 1.
+Note also that we don't plot the UHE directly, but rather <math>\exp((1-a)\text{UHE}_a)</math>, as described previously. The units have also been converted back to cents. Each HE function has been scaled so that the minimum entropy is 0 and the maximum entropy is 1.
 Lastly, note that, due to our multiplication of UHE by <math>(1-a)</math> above, the UHE would be flipped upside down relative to what we're used to, with higher values corresponding to more concordant intervals. In the pictures below we have flipped it back upside down, for consistency with the earlier pictures.