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Yep. Just keep thinking on it and you'll get it.

For a given string, frequency is determined by vibrating length and string tension. The nut position has no effect on fret-to-saddle distance or tension (although you may be tempted to alter the tension yourself by retuning the open string to a specific frequency).

Here's a picture to hopefully help explain how moving the nut is equivalent to moving board and saddle together, and doesn't change the vibrating length of fretted notes. Only the 12th fret is shown, but all the others would move with it. The pale lines are just for visual reference of what has and hasn't moved. The distances are in pixels.

This is the last post I'll make on this topic. It really isn't interesting anymore.
I'll get out my condescension piercing light saber and reply one last time.
If position of the nut makes no difference after the open string is fretted then try this:
Tune your 1st harmonic to be perfect with your twelfth fret when fretted. Now add 1/4" to the end of your fingerboard without changing location of frets or saddle.
Re-tune fretted 12th fret to exactly the same pitch as before. 12 to saddle distance is the same but the tension will be different due to the added length. Should be easy to match the fretted pitch to pre-lengthening fretted pitch.
Check where the first harmonic falls on the open string.
It certainly won't line up with the 12th fret.
All the fret positions will be sharp.

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Sorry. I'm trying to be helpful, but apparently failing at it. And your example sounds right, so we may be arguing over nothing at this point. The harmonic will indeed no longer match, but that's because it's played on the open string. And the frets will indeed be sharp, but only in relation to the open string. They'll all be the same absolute pitch as before. Which means only the open string was affected by the change.

No discussion of compensated nuts should go without reference to the source:

http://www.mimf.com/nutcomp/

"Re-tune fretted 12th fret to exactly the same pitch as before. 12 to saddle distance is the same but the tension will be different due to the added length."

This is where you are mistaken. The tension will be the same if the distance is the same and the pitch is the same. There is no "added length", the end of the string "cut off" by the fret doesn't affect the speaking length of the string.

This was an interesting read. I could not imagine sending an instrument out looking like that though. Do you do this on your guitars?


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I did this for a Martin that had a really poor intonation on the bass E string. To get the string in tune would require moving the saddle back almost a 1/4" from the existing saddle slot! I have never seen anything like this. And it wasn't a bad string. Compensating the nut took care of it.

Trevor Gore compensates both the saddle and nuts. Yes, it looks a bit weird, but it really works.