Buzz Feiten intonation adjustments

John Starrett wrote,

>I have never quite understood why the
>nut should be higher from the first fret than the first fret is from the
>second. With a zero fret, what would the solution to the problem of
>differing pitch bends for different string to fret distances be? Wouldn't
>we need to consider where a player plays on average and just tune the
>bridge appropriately?

Yes. One would not adjust the zero fret. The reason for adjusting the nut is
that is usually quite a bit higher than the frets. The amount of extra
pressure required to press a string down to the first fret is therefore
considerable (try an F minor chord with heavy strings!), and even with
appropriate bridge adjustment giving, say, a perfect octave at the 12th
fret, notes on the first (and to some degree, second and third) fret will
tend to be too sharp.

Although the correct adjustment to the fret placements will be some sort of
complex mathematical function of the nut height, bridge height, and string
tension/stiffness, adjusting the bridge _and_ nut positions, as well as the
open string tuning, gives you three parameters (really, two "interesting"
parameters; the open string tuning is like a constant term) with which to
approximate that function, which is of course better than one parameter
(bridge position only). According to Steve Vai, Buzz Feiten's system
involves a separate nut, bridge, and tuning adjustment for each string.