In a 10,000 gallon pool, one 8-ounce Tri-Chlor tablet (the 3" kind -- some are 6 or 7 ounces, but I'm using 8 ounces in this example) will lower your pH by 0.1, will add 5.48 ppm Free Chlorine (FC), and will add 3.3 ppm Cyanuric Acid (CYA) as well as increase your Total Dissolved Solids (TDS) by 7.4 ppm. Obviously, a larger pool scales these numbers down accordingly (proportionately). I assumed a TA of 100 with a CYA of 30 and a starting pH of 7.5 for the purposes of calculating the pH drop. To get back to the 7.5 pH, you would have to add either 4.7 ounces of Soda Ash (Sodium Carbonate) or 9.2 ounces of Borax.
The bottom line is that Tri-Chlor tablets are very acidic so you will always be fighting low pH if you use them. And just as bad, as was pointed out, you keep adding CYA to your pool. If you don't have much CYA then this can be OK for a while, but generally once you get to the CYA you want, you don't want to add any more. If you used liquid chlorine (or bleach) instead of Tri-Chlor, then the increase in pH from the initial liquid chlorine addition is exactly compensated by the acidic process of the chlorine getting used up so that you net out with no pH change (technically, there is a small rise from additional base in the liquid chlorine, but this is pretty small).
Richard
P.S.
The pH actually drops even further when the chlorine gets used up since that is also an acidic process. So when the 5.48 ppm of chlorine disinfects and kills bugs or oxidizes organics or gets broken down by sunlight, the pH from this process and the original Tri-Chlor results in a pH drop of 0.24 and requires 13.3 ounces of Soda Ash or 26.3 ounces of Borax to restore the pH. If you used liquid chlorine (or bleach) instead of Tri-Chlor tablets, then the increase in pH from adding liquid chlorine pretty much exactly compensates for the acidity from the chlorine getting used up so that you net out with virtually no change in pH. This means you will use less acid or base when using liquid chlorine as your primary source of chlorine.

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