Editing Riemann zeta function (section)

===Musical tuning===
In the theory of [[musical tuning]]s, the zeta function can be used to find [[Equal temperament|equal divisions of the octave]] (EDOs) that closely approximate the intervals of the [[Harmonic series (music)|harmonic series]]. For increasing values of <math>t \in \mathbb{R}</math>, the value of

:<math>\left\vert \zeta \left( \frac{1}{2} + \frac{2\pi{i}}{\ln{(2)}}t \right) \right\vert</math>

peaks near integers that correspond to such EDOs.<ref>{{cite web|url=https://oeis.org/A117536 |title=Nearest integer to locations of increasingly large peaks of abs(zeta(0.5 + i*2*Pi/log(2)*t)) for increasing real t |author=Gene Ward Smith |website=The On-Line Encyclopedia of Integer Sequences |access-date=2022-03-04}}</ref> Examples include popular choices such as 12, 19, and 53.<ref>{{cite book|title=Tuning, Timbre, Spectrum, Scale |author=William A. Sethares |date=2005 |edition=2nd |publisher=Springer-Verlag London |page=74 |quote=...there are many different ways to evaluate the goodness, reasonableness, fitness, or quality of a scale...Under some measures, 12-tet is the winner, under others 19-tet appears best, 53-tet often appears among the victors...}}</ref>