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'''''Compensated nuts''''' are nuts that vary the point at which the string leaves the nut for each string. Thus, if your bridge saddles are all set to the same spot, you would still have different string lengths for open strings. This applies the true temperament concept above to only the nut. So it can help for open position chords to sound in-tune regardless of which chord shape you use; but beyond open position, there are no benefits.
→True Temperament Fretting Systems and Compensated Nuts
=== True Temperament Fretting Systems and Compensated Nuts ===
The [http://www.truetemperament.com/ '''''True Temperament Fretting System'''''] uses "squiggly" frets, so that each string will have a slightly different length for each fret (ignoring different bridge saddle adjustments). The makers of this system claim that string pitch is incorrectly simplified as a linear equation using string diameter and length - there is more advanced physics going on, and this system compensates for that.
The big mistake is that people assume this is a just intonation, designed for a specific key. No, this is still equal temperament - it is just a supposed improvement to intonate better towards an ideal equal temperament than traditional straight fretting. However, they do provide a few variations that move more towards just intonation for a few keys.
I would really like to play one of these guitars to see if the supposed benefits are clearly noticeable as well as if there is any trade-off on playability - it seems like bends might feel a bit weird, and there's a possibility some chords will be harder to finger. I am also curious about maintenance - I do not know if the frets can be crowned using traditional methods.
=== Just-Intonated and Special Instruments ===