a tuning-math guitar question

Here's a tuning-math question I'm not quite sure of...

What's the math behind the notes that sound when you pick behind a
fretted note (in other words between the fretted note and the nut)?

thanks,

--Dan Stearns

> What's the math behind the notes that sound when you pick behind a
> fretted note (in other words between the fretted note and the nut)?

Oh! If you ignore stretching from fretting, stiffness, on a guitar with
miniscule frets inlaid for equal temperament where

l_s is length from bridge to nut (scale length?)
n is number of frets per octave
x is fret number (0 is nut)
l(x) is length from bridge to fret

l(x)=l/(2*(x/n))

the fret behind x is [x-1] and its distance from the bridge is

l(x-1)=l/(2^((x-1)/n)

so its distance from the nut should be

l-l/(2^((x-1)/n)

I got to play with this 6-string instrument called a hamatar. This was
like two electric guitars joined at the nut, but which used a blank fret
space between usually where there was a capo. It was meant for two
handed hammering, I lost the capo and played so both sides used whatever
pair of frets I fingered between.

Clark