::shakes head:: Where to start.
There was a well-temperament craze as part of the early music movement of the 1980s and 1990s that led to a bunch of performances and recordings being made with pianos, harpsichords, and organs tuned to mean-tone temperament. Many if not most performance-grade synths and stage pianos have a setting to do it in software. My S90es does. I don't think I've ever used it.
The main problem with fretted instruments is that the effective vibrating length of the string is going to vary depending on the diameter of the string and whether it's wound or solid. On an acoustic guitar, a properly cut bridge will adjust for this, for the most part, and on an electric, a properly adjusted bridge will compensate for it. The adjustment will be exact only for one position on the fingerboard, and most technicians will cut the bridge to compromise in a way that favors the open strings and 1st through 7th frets that most people use for chords. Maybe for a 7 stringer for a metalhead where most of the playing is done further up the neck the optimization would be done a little differently.
The temperament differences aren't as great and any system that is other than equal tone is only going be optimized for one key. Well I can think of a few bands that play everything in the same key but usually they aren't the ones with a level of musicianship where tunnig is taken all that seriously.
Anyone who really cares about tuning that much really should take up violin, viola, or cello, and play in a string quartet, because that's the only ensemble that can, reliably, get it right. Well, except maybe for a really good a capella vocal group.
We now return to your regularly scheduled discussion of Fourier transforms and modified sine waves.