The correct name of the tuning I'm referring to is "Extended 1/6 syntonic comma meantone".
People might automatically think that this is an unnecessary complication - however the following brief article from which I have copied a paragraph - should help to dismiss that idea..
In music with a restricted range of keys -- Renaissance, early Classical, folk, rock-n-roll, R'n'B, country, gospel... -- there is no reason to accept the sub-optimal distribution of the syntonic comma which ET offers. On the guitar it is easy to experiment with tuning the fourths a couple of cents wider, and there are many recordings of harpsichords and organs with 1/4-comma, 1/5-comma, 1/6-comma (etc.) meantone tuning. You might wonder what happens musically when you meet the wolf note - a very flat Ab or a very sharp D#, for example. If the music was intended to be played in meantone, these notes will be used in such a way that they don't disrupt the piece and can actually add to its expressive range. I did read somewhere that the pianos in a famous Nashville studio were tuned in an unequal temperament, simply because they were always being used to play the same three chords. Now you know why.
The reference to guitar tuning here is interesting. I'm curious to know if this is similar to the process being used by the Peterson guitar sweetner. (though Peterson does not publish the details)
I have found out that in practise 1/6 comma meantone is used with a fixed A base, however when the opportunity arises it seems best to base it on the root. It's interesting discussing this with real music experts because outside of Peterson circles the idea of allowing the A to float according to the root seems to be very alien to them. Regardless of this I cannot fault the Peterson logic - though I'm not sure what base Peterson would choose with this particular form of scale.