BOP tuning: Difference between revisions
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It so happens that we can use the same recipe to define a closely related tuning that instead minimizes the max <math>1/(nd)^s</math> weighting on all rationals, where s is a free parameter > 1. We will call this the "BOP" tuning for [[Benedetti height|Benedetti Optimal]]. | It so happens that we can use the same recipe to define a closely related tuning that instead minimizes the max <math>1/(nd)^s</math> weighting on all rationals, where s is a free parameter > 1. We will call this the "BOP" tuning for [[Benedetti height|Benedetti Optimal]]. | ||
Similarly to TOP, we will show that this is easily obtained by minimizing the max <math>1/p^s</math> weighting on just the primes. | Similarly to TOP, we will show that this is easily obtained by minimizing the max <math>1/p^s</math> weighting on just the primes, which means it is also optimal using the [[Wilson tuning]]. | ||
For now, we show that this result holds for all full-limits, | For now, we show that this result holds for all full-limits, though it can be extended to arbitrary subgroups. | ||
= Proof of Benedetti-Optimality On All Rationals = | = Proof of Benedetti-Optimality On All Rationals = | ||