Well, this isn't entirely un-processed, as I use commercial mayonnaise (although, come to think of it, now that I'm getting eggs from a nearby farm, I could make my own mayo safely). It is well known that I use only Hellman's, and that I never, ever touch the "lite" or low-fat or whatever it is variety. Of course, all cooks suit themselves and those who will dine on their creations, so suit yourself!
I started making tartar sauce when a jar of the commercial stuff that I had in the fridge looked pretty iffy--it was rather old and not very appetizing. Now I just make a small quantity whenever we have fish; I no longer have ancient jars of it to wonder about or toss out. It's fast, simple, and can be varied in numerous small ways if you like. Usually I use home-made dill relish (I can it during cucumber season) instead of the chopped pickle, but last night I had neither relish nor dill pickles, so I simply chopped up some dilled green beans (canned last summer). They worked fine--Jim didn't know they were beans until I told him.
This is the quantity I make for the two of us. Sometimes I have a tablespoon or two to throw out, but it's better than throwing away half-full jars. If I know we'll be having fish again within the week, I'll make a little extra and keep it refrigerated.
1/2 cup mayonnaise (I don't actually measure, just eyeball it)
1 T. or more, to taste, dill relish or chopped dill pickle
1 T. minced or grated onion
1 T. parsley, minced (opt.)
1/2 T. capers (opt.)
1/2 T. lemon juice, or to taste
1/8 tsp. salt, or to taste
Just mix the ingredients together. I sometimes put some dried dill in, especially if I'm too rushed or lazy to deal with the parsley. Chopped stuffed green olives also make a good addition.