Something I was rather loose with terminology on was the difference between intonation and temperament. When it comes to guitars the two are rather interlinked. Becuse the guitar is a real life mechanical instrument, and yet has a rather rigid idealised design in many ways, the idea of intoning a guitar gets messy.
The nut of a guitar is usually treated as the location of a notional zeroth fret. (Some guitars actually have a nut and a zeroth fret. It is a rare thing however.) Like any real world instrument, you have a disparity with the location of the mechanical endpoint of the string and the physical location of the node of vibration (the witness point). The thicker the string the further in from the nut the witness point is located. Already there is a problem with a guitar, as the nut is a straight line, although the strings vary in thickness. Wound strings have a witness point closer to that of the substrate string. So the nut is already wrong.
When a guitar is played the strings are forced agaist the frets, this leads to a change in tension of the string, partly just to force the string out of a stright line, amd partly the pressure of the finger behind the fret on the string. So the change in tension comes partly in a definable form (from simple geometry of the guitar setup and the string relief) and partly from player’s style (the force a player tends to fret with.) Yet open strings have their frequency defined only by the location of the nut and bridge.
Depending upon your style of guitar the bridge can be of a wide variety of designs. A simple straight piece of material normal to the strings, a straight piece of material placed at a slight slant - and thus providing a first approximation to compensating for the different witness points. A two piece bridge for the wound and unwound strings, both at a slant. which provides better compensation for the witness points. And this goes all the way down to a guitar which provides individual length adjustments for each string. A luthier setting up even a classical guitar will usually file the bridge to change the effective length of each string - although the degree of adjustment is quite narrow.
Adjusting at the bridge is essentially used the to adjust for double the witness point difference, adjusting for the distance for both ends of the string at the bridge end. This is still an unsatifactory set of adjustments. The fret spacing is the same for every string and is derived from a notional string length, not the compensated string length. So the closer you play to the bridge, at least for some strings, the more out of tune.
Also, open strings are played without the additional pressure of fretting the string - and so may be slighty out of tune with the fretted notes. Many luthiers will move the nut very slightly closer to the frets to compensate for this.
So you basically end up with an instrument that is notionally designed to provide equal temperament, but actually is only an approximation. And sometimes not a very good approximation.
Then people start to fiddle.
The thing about a guitar is that it has a set of goemetric qualities that means it is played in a particular manner. One that is significantly different to a piano. For this discussion the most clear one is that the guitar presents the player with more than a single location for most notes. A guitar can span up to 4 octaves (for a 24 fret version) - which is 48 notes. But it has 6 strings, and that same 24 frets yields three times as many discrete frettable notes. On that same 24 fret guitar we can see than in the extreme, the low E is represented in only one place, whilst the high E is represented on every string. On average however, each note is found in about three places. And due to the earlier described mechanical issues, there is essentially no chance at all that those locations actually have the same frequency.
Now we can also note that the strings have discrete roles. The low E string produces either a bassline, or forms the root of many chords. The fifth string, when playing many chords provides the fifth. So, one thought experiement - tune the guitar so that rather than tune the open fifth string to a fourth higher then the sixth, tune it that subtle bit out so that when both are fretted a fifth apart, they are a perfect fifth apart. Power chords, here we come. 
Once you start down this road you can go on forever. A change in bridge position can be used to cause a region of string to have the note intervals be compressed or stretched relative to ET. This may be deemed useful.
We can also note that the guitar favours different key signatures in different ways. One tends not to play chords in the higher fret positions - although they are technically available, the sound isn’t great. You lose the depth of sound when the string is fretted short, and the issues described earlier also push the harmonies out. And so it goes.
So - what does this mean? What one has is a deperately over constrained problem when it comes to getting a guitar in tune. And it is even worse when it comes to harmonies and getting chords to sound reasonable. But you can exploit the nature of the guitar. Offsetting the tuning of some strings away from the technically ideal equal temperment (at least as close as the device can get) allows you to approximate other desirable intonation attributes.
But, what it isn’t (and where the opening comment comes in); this isn’t a temperament. It is an intonation. There is no regular ratio of frequencies in an octave. The ratios from one octave to another will be different, and worse, the same note in the same octave, in different positions on the neck will have different frequencies. The only variables that are available to form this approximate intonation are string diameter, bridge position and string tension. An additional variable that a luthier can bring to the party is nut position. The Buzz Feiten system moves the but. There are other nut variants. Earvanva do a staggered nut that is intended to address the different witness point issue.
Also what there isn’t, is much of a recognised technical understanding of this. Before Buzz Feiten patented his ideas, luthiers had their own personel set of tricks, and experienced ones played with the intonation to suit a player, often simply based upon empirical experience. The Feiten system is still probably the only well codified system. A guitar setup by an experienced luthier can often involve a subset of these ideas. One guy know will set up the intonation to be more consonant at different parts of the neck to suit different styles. Guitar players will also simply find that a particular way of tuning the guitar works better for them than others. Some like to tune with harmonics, some will just use a tuner, others just run down the fretted forths. Some care a lot more than others. Similarly, setting the bridge position. The classic way it to match the frequency when fretted at the 12th fret with the frequency of the second harmonic. But some people find that other rules seems to work better for them. Again, empirical knowledge. But you end up with an intonation that suits the player, and takes the already imperfect approximation the guitar has to ET, to some other intonation, that has some aspects of ET, but also probably some significant variation.
In truth, for 99% of guitar players, no one cares. The guitar is an imperfect approximation to ET, and players learn to avoid those parts of the guitar that sound poor. But the other 1% that do care seem to evolve a set of personal changes to the standard setup that serves them well. What is missing from the world is much of a codification of this.
