I became Feiten certified some years back. I've only applied this to electrics but.....The measurement system (entered into a computer program) seemed very cumbersome to me. (measuring from the first fret to the edge of the nut....) After doing some very simple math, I discovered that for any electric guitar, you just add .030" to the face of the nut. They just make it more complicated than it has to be in order to make it seem like its taking a lot of variables into account. Didn't matter what scale length, fret size, or even string gauge. Well, it was an additional .005" or so for jazz strings......
I called them and complained about the illusion of their "system" but didn't really get anywhere. I started offering customers a .030" brass shim added to their original nut. Takes about 30/45 minutes to do, (if you've precut some brass pieces in bulk) and I charged $75 instead of the $150 BFTS. I tell customers if they don't notice a difference I'll pop it off of there and will give a refund...haven't refunded yet. But I haven't done any in a while as the fad seems to be dying off a bit.
Thing is, the nut compensation system really does work. I was surprised. Open chords especially benefiting from this. Its all about end tension....as someone else already mentioned.
Problem is, if you move the nut closer to the 12th, you have to move the saddle closer to the 12th to intonate. So I use the upper frets (19) to the guitars harmonics to set it. So you actually trade off intonation at the nut for intonation on the upper register. But its a slight amount, and the guitars seem to play better in my opinion. I'm sure I don't understand all of what's going on, but it seems like a step forward.
I should also note, that I don't sell my brass shim as a BFTS operation. Customers ask if I do BFTS, and I tell them no, but I do this and its cheaper and in my opinion, better. And yeah, nut compensation theory has been around forever....I later discovered. I told Fieten to take me off their site and I haven't ordered from there in years, but I'm still on it. Whatever.
Compensation is done at the bridge, for the stretch
down to the top of frets. This stretch increases
as you fret up towards the bridge, but the proportions equals out.
But you also stretch a further amount behind a fret
down towards the fingerboard - an amount being
roughly equal regardless of position on the board.
However, the open string is not stretched that way,
whether a nut or a zero fret, and here lies a difference,
that could only be compensated for at the nut.
How much, depends on gauge, how high the frets
and how hard you sqeeze....
With all due respect to any prefabric nut or a BF system,
I think it must be custom made for satisfaction.
I first put a capo on top of the 1:st fret and check the bridge.
Then I do the nut (no further work at the bridge)
I am much more comfortable with my guitars,
after doing that little extra setup.
Nut compensation (as I understand it) is not done so much for the amount pulled down to the board, but for the tension that is at the string at that point. Say you wiggle the string back and forth at the 12th fret....then you do the same motion at the 1st fret....you have different amounts of resistance. That resistance sharpens the note (when fretted) exponentially as you get closer to the nut. A quick test to observe this would be to tune a guitar up by fretting an open E chord. Then play an open D....the B string will sound sharp.
I'm not proclaiming that this is absolute law.....but its what Fieten explained for the purpose of the shelf nut, and its what I have observed for the most part. Are we saying the same thing? What are you referring to as that when you said "that could only be compensated for at the nut."
Dividing the fretting in
a) down to the top of the fret, and
b) down behind the fret,
the stretch effect from (b) is a bit higher towards the nut,
as you get less tension from (a) before going further to (b)
Wiggling I think compares to (a) which is not that much near the nut.
Trying to compensate for (b) at the other end (bridge),
still leaves you with an unfretted open string.