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Comment by baddox | Hacker News Reader

That's solving a different problem, which is intonation (having every fret on every string in tune on the entire neck). But it still just provides intonation for a single temperament, like equal temperament.

More info here: http://www.truetemperament.com/site/index.php?go=4#A1

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Right, I'm aware. Maybe I misread the last line of the grandparent, but I assumed that was exactly the problem being referred to -- the vagaries of details like string width and action height mean that even an instrument nominally designed with equal temperament in mind requires per-key adjustments to sound in tune by the standards of equal temperament.

There is no per-key adjustment in equal temperament. Equal temperament assigns an exact pitch (frequency) to each note, regardless of what key, chord, or interval the note is in. These weird frets are intended to make each note on the guitar play the exact pitch that is assigned to it by equal temperament, because normal straight frets cannot do that.

Yes, that's a basic fact that I'm well aware of. To hopefully express what I'm saying more clearly: Assume your open strings on a guitar are tuned perfectly in the standard way: the A string is 110 Hz, the low E string is 110 * 2^-5/12 Hz, the D string is 110 * 2^5/12 Hz, and so forth. This will allow you to play an in-tune E minor chord on the open strings, but other chords will not be in tune (again, with reference to the equally-tempered pitch space) to the same degree because of the fact that the strings have different densities and widths. You could imagine accounting for this by tuning the strings such that some other chord was in tune, but then your original E minor chord would no longer be in tune. Thus my point that even though the guitar's design is predicated on equal temperament, it still requires per-key adjustments to be in tune for an arbitrary chord, unless you're using one of the guitars I linked to above.

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