The Riemann zeta function and tuning: Difference between revisions
m IlL moved page The Riemann Zeta Function and Tuning to The Riemann Zeta function and tuning |
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Error on harmonics only: <math>|\textbf{Re}[\zeta(\sigma+it)]|</math> | Error on harmonics only: <math>|\textbf{Re}[\zeta(\sigma+it)]|</math> | ||
Note that, although the last four expressions were all monotonic transformations of one another, this one is not - this is the 'real part' of the zeta function, whereas the others were all some simple monotonic function of the 'absolute value' of the zeta function. The results, however, are very similar - in particular, the peaks are approximately to one another, shifted by only a small amount (at least for reasonably-sized EDOs up to a few hundred). | Note that, although the last four expressions were all monotonic transformations of one another, this one is not - this is the 'real part' of the zeta function, whereas the others were all some simple monotonic function of the 'absolute value' of the zeta function. The results, however, are very similar - in particular, the peaks are approximately identical to one another, shifted by only a small amount (at least for reasonably-sized EDOs up to a few hundred). | ||
==Relationship to Harmonic Entropy== | ==Relationship to Harmonic Entropy== | ||