Barleywine
The Sun is in the exaltation of Jupiter (Cancer) and Jupiter in Sagittarius a Fire sign, and the Day triplicity ruler of Fire is the Sun. So that gives a mutual reception and we should not treat the Sun as being Peregrine.
Is this an extrapolation of the idea of "essential dignity by exaltation"? Technically, wouldn't Jupiter have to be in Aries, the sign of the Sun's exaltation? But I can see the sense of using triplicity "by extension," I just couldn't get that idea out of the table of dignities. Perhaps I need better source material.
Again using your chart, Saturn is in the Terms (and Face) of Jupiter and Jupiter is in the Terms (and Face) of Saturn. So Saturn has a mutual reception and is not Peregrine.
This makes sense too, but I also couldn't get it out of the table. Is it described in detail somewhere?
However it's not clear to what extent traditional astrologers put weight on mutual receptions by minor dignities (Terms and Face) by Lilly's time. Certainly Morin did not put any weight on the minor dignities at all. So at best these type of mutual receptions might just cancel out being Peregrine but add no real dignity. I think it's a matter of testing to see if you end up giving too much weight or too little to essential dignities using mutual receptions by Terms and Face.
I can see where it would add enough dignity to erase being peregrine since, as you point out, the whole idea of weighting is to get a general idea of relative planetary strength. Anything that improves their mutual relationship would seem to be worth counting to some degree. Perhaps, given no other more potent dignity between the two, this more minor one would assume greater importance. They are also in trine by triplicity, although not partile. Jupiter would seem to have the upper hand, though, since it's in its sign of rulership and Saturn is in its detriment.
There's one further point on mutual receptions. If the two planets are essentially debilitated does this suddenly transform them into being essentially strong - for example I have Sun in Libra, the exaltation of Saturn and Saturn in Leo the rulership of the Sun. But Sun in Libra is in Fall (-4) and Saturn in Leo is in Detriment (-5) So how do I score the mutual reception. Do I treat both planets as now essentially strong or does it simply show two weak planets trying to do their best for each other? I don't think I can count the two as now very strong but I don't count them as being in Detriment and Fall. Perhaps treating them as having 0 essential dignity might be the best approach and then add on their accidental dignities for an overall score. But I have seen writers suddenly bumping up the dignities to being very strong and treating Saturn as though it were in exaltation and the Sun as though it were in Rulership.
I think it's the "blending" involved that makes this such an interesting subject for me. How much of one key quality (exaltation or rulership) is sufficient to cancel out an abundance of the other type (detriment or fall)? When both types are strong, it would seem to be best to take the essential dignity level to zero as you suggest and then tweak from there by observing the operation of any accidental dignities. That would make them peregrine. right? And all that entails regarding "learning opportunities" should be readily observable in the way the planetary functions are experienced.
The Moon is oriental, having passed it's opposition to the Sun (but only by a few degrees). The reason why the situation for the Moon is the opposite of the three superior planets is because the Moon is faster than the Sun but they are slower. So when the Moon is past the New Moon, stage it is further on in the zodiac than the Sun and moving away from it. When the three superiors are ahead of the Sun in the zodiac it's moving towards them.
I'm still struggling with Lilly on this one. He says ". . . orientality is nothing but to rise before the Sun and occidentality is to set after him, or to be seen above the horizon after the Sun is set." In the case of my Moon being just past the full phase, it would still be below the eastern horizon when the Sun sets in the west, seeming to make it occidental by this definition. Lilly also says "The Moon is oriental of the Sun from the time of her conjunction to the opposition, and occidental from the opposition to the conjunction." This would seem to reinforce the above, since the Moon is past the opposition and moving toward the next conjunction. Is he guilty of "bad science" here, or am I just reading him wrong?
For a freebie, Morinus is outstanding. I use it quite a bit, even though I have Solar Fire on my computer. You can also add and edit Arabic Parts. When you get to Primary Directions it becomes invaluable.
Planetary strength is identified by the author as still being on his "to do" list.