I believe water PH and hardness tend to be somewhat related in naturally occurring sources of water like ground water, rainwater, and water distilled from the air. However, they aren't necessarily related in water from the tap which is often times conditioned. I have well water with a PH of about 6.5 and a hardness of about 400 ppm (very hard). After running the water through an ion exchange water softener the hardness is reduced by a factor of 40+ to less than 10, while the PH is virtually unchanged. If hardness and PH were directly related, a major change couldn't occur in one without impacting the other. Hence my statement that hardness and PH are not directly related.
I don't know which water characteristics (hardness, PH, TDS, etc.) impact the age related brass tarnishing, or which additives (mild acid, Lemishine, detergents, waxes) might reduce that tarnishing. I suspect there is no one simple answer given the variety in tap water. Perhaps it's easiest just to try a few things that have worked for others who have posted here.
I use only the case cleaning products I posted earlier, with no additional detergents, waxes, etc., along with softened water and have experienced very clean brass and very little age related tarnishing. The use of both hard and softened well water over the years for various tasks has taught me that it is very difficult to completely rinse compounds from something using hard water. Rinsing with hard water seems to always leave a little of the compound and hardness minerals in fabrics or on surfaces.