For me a high TA causes my PH to slowly climb, then when the PH hits 8.0, I add muratic acid to lower PH & TA. Once my TA get's in the 60 -90 range the PH rise slows and stops, After that I can maintain PH & TA with little effort.
Some people lower TA by aereateing till the PH reaches 8.0, then add muratic acid to lower the PH to 7.2, and start the aereation process all over again. When you add muratic acid it lowers both PH & TA, then aereation raises PH without adding chemicals, This is a faster way to lower TA, but as stated above, I would just control PH and let the TA naturaly settle out.