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The one being recommended is '267-PROSYSTEM.pal'; NTSC on left, PAL on right.
Why? Technically the phase shift of the 7800 is ~25.7; actually, 25.714 according to the math here https://sites.google.com/site/atari7800wiki/rgb (Thank you Eric Ball). The reality though is most (all?) 7800 systems fluctuate the phase shift higher as the system 'warms up'; additionally there is a variable resistor which also impacts the ultimate end results. The color references affected the most - and consequently most noticeable - are values E$ and F$.
At the 25.7 setting colors 1$ and F$ match near exact. To the naked eye they in fact look exact. According to the books this would be proper having a 180 degree color-burst resulting. However, no system - even a new one I obtained within the last year - stays at that level. There is a deviation from it, resulting in the shift going higher than 25.7 degrees. The question is how much greater do we go?
Simply stated, color F$ more realistically ends up between the hue of Color 1$ and 2$; darker than 1$, but lighter than 2$.
If we set the phase two degrees higher (27.7) we end up with colors E$ and F$ as a near exact match of colors 1$ and 2$. Some systems, including one of my own, phases this much and even higher (~28.7) over several hours (To the point where E$ and F$ fall in between 2$ and 3$ in hue - and most other values have shifted a complete row less (I.E. $8 looks like a $7, $7 looks like a 6$, etc.); but now that is swinging the pendulum too far in the other direction.
So, if 25.7 is technically accurate, but hardly, (if ever) the reality, and 27.7 brings too much of a phase shift to the palette, then a happy medium would be 26.7.
Setting the phase to 26.7 we obtain a color F$ that is in between the hues of color 1$ and 2$. MESS, in fact, has F$ documented (Thank you Dan Boris) as a 'light orange' range, whereas 1$ is a 'gold' range and 2$ is a 'orange' range. Additionally, we obtain light browns from 1$, while now having darker browns set under F$.
Looking at color E$ under the 26.7 setting, it falls right as a 'pea soup', the 'Linda Blair special', puke-ish green throughout; placing it in between a green and a brown color. Going back to 25.7 causes E$ to become a stronger green on the lower end, swinging the pendulum to 27.7 makes E$ a brown color. The happy medium and often noted intension is for the E$ range to fall between a green and a brown, and it does exactly that at 26.7.
The extensive work done in brightness, contrast, saturation with the literally hundreds of palettes created and viewed across half dozen displays, along with the input of the community, has helped achieved a nicely saturated and bright palette setting from the base values. The is easily adjusted and open to interpretation of course, so if you want something more/less saturated, brighter, etc...Just ask.
Additionally, the "BASE" palettes are being included for those who perhaps just want the base values and or like to self-adjust saturation, brightness, contrast, etc. BASE palettes are highlighted below (NTSC left, PAL right):
Opposite to the GCCFINAL palettes, we are not looking to factor in a wide range of television tints or pot adjustments. This palette presumes a properly calibrated/pot adjusted 7800 and a television which falls within a neutral tint setting - and expects similar from the monitor it is being displayed upon.
It's almost a certainty that programming color choices were made on systems with a variety of phase settings as well. For instance, some games like Choplifter and Midnight Mutants look better with a higher (27.7) phase shift, but others like Pole Position II and Joust look better with a lower (25.7) one.
Again, the one being recommended is '267-PROSYSTEM.pal'. Honestly though, a 'perfect Fuji' (Enable the BIOS) demands '257-PROSYSTEM' - and it is the technically accurate ideal, if not actually experienced (Or at least not for a long duration of time); regardless, good thing it's included along with ‘277-PROSYSTEM’.