On this website, I have urged players to be satisfied and happy with equal temperament (after an instrument has been truly compensated, and plays in tune). Accurate equal temperament allows guitar players to play in good tune, even when playing with other instruments, changing to any key, Using any open or closed chord forms, without re-tuning!
Nevertheless, with slight string bending, accomplished players, especially on electric guitars, can “sweeten” individual notes and chords to natural harmonies in real time, while they are playing.
Many would like to know more about temperaments – and why we don’t use a different scale, so as to produce natural harmonies. (A natural harmony occurs when the frequencies of two notes have a whole number ratio. For example, a note with a frequency of 1/2 of the other (an octave lower), or a note with a frequency of 1/3, 1/4, or 2/5 of the other. Overtones are natural harmonies of the root.)
This stuff is certainly not new! It goes back to Pythagoras, in the 6th century BC, and to the renaissance period, the 14th-17th centuries! Fortunately, there is much excellent information on the subject, so I will simply point you in the right direction. Please enjoy these links:
Wikipedia – Musical Temperament
Seventh String – Note Frequencies
A Just Temperament Guitar Keyboard Rock on!
True Temperament Fretting Systems
True Temperament is not a temperament; it’s a Company that builds guitar replacement necks and fret boards with wiggly shaped frets. Necks start at $795 – that’s unfinished and uninstalled. The frets are curved, with all notes placed according to experimental data. Most of their necks and guitars were set up to play in well temperament, but now they only make use of a Thidell formula one temperament, which they are very proud of! It is a modified equal temperament, and it uses tuning offsets.
Go to their FAQ Page for a good understanding of the products and principles.