"Considering this, my appreciation for the ad hoc fret leveling jobs done by some of the most respected repair people has increased dramatically. This led to some heavy geometric analysis (PDFs below), and also some interesting pragmatic conclusions. This suggested that guitar string profiles set by luthiers more typically follow a surface that is not strictly conical. However Mottolo found that in practice, measured guitar saddle radii rarely matched this calculated optimal expectation, despite playing well at low actions. Thus, on a typical neck, for example a strat with typical E-E spacings at the nut and bridge on a 25.5" scale with 9.5" radius (ie radius at the point where the strings leave the nut), one calculates an expected string radius at the bridge of ~14" (!). Luthier L.Mottola presents Hartstein's formula for calculating the radius at the bridge of the diverging - and therefore obligatory conical - profile of the strings between nut and bridge. And it's a rabbit hole the more you do look into it. That seems to be the best practical conclusion.
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