וְכִפֶּ֕ר עַל־הַמִּטַּהֵ֖ר מִטֻּמְאָת֑וֹ I am having trouble truly understanding the difference of meaning using the different trope (zakef gadol, tipcha, etnachtah OR mercha tipcha etnachtah). I understand how to chant those signs, but I need more help in interpreting the difference in meaning. Vayikra 14:19
There are four things to keep in mind.
First, there are conjunctive and disjunctive trup symbols. Disjunctive divide up a phrase at the point they appear while conjunctive joins. Zakef gadol, tipcha and etnachtah are all disjunctive, usually. Mercha is conjunctive.
If a subphrase contains three words, it needs to be subdivided by a disjunctive trup.
However, as William Wickes writes, sometimes a phrase with only two words, ending in either etnachta (mid-pasuk) or silluq (end-pasuk) will have a foretone of tipcha, for what are essentially musical concerns. Such a tipcha doesn't divide.
Thus, if we consider what Sefaria has for Vayikra 14:19, matching the Leningrad Code: וְכִפֶּ֕ר עַל־הַמִּטַּהֵ֖ר מִטֻּמְאָת֑וֹ is divided as: וְכִפֶּ֕ר || עַל־הַמִּטַּהֵ֖ר מִטֻּמְאָת֑וֹ and atone || for the one being purified of his defilement
And the tipcha you see on al-hamitaher would be in a two-word phrase, and is simply musical.
That was pasuk 19. As you mention (in the comment), Koren and Tikkun Simanim has mercha in place of zakef. That would make it:
וְכִפֶּ֥ר עַל־הַמִּטַּהֵ֖ר מִטֻּמְאָת֑וֹ
Then, there would be no pause on the first word, and the first and second would join together. And, even according to Wickes, the tipcha would function in its usual role of disjunctive accent. Thus:
וְכִפֶּר עַל־הַמִּטַּהֵר || מִטֻּמְאָתוֹ and atone for the one being purified || of his defilement
Thus, in the former, the action is "atone", and the object is "the one being purified of his defilement". In the latter, the action is "atoning from defilement" while the object is "the one being purified". The meaning of these two actions may be different.
Please compare also the trup trees for Vayikra 14:19 and (although it isn't the verse in question) Vayikra 14:53. Though that doesn't treat the tipcha in a two word phrase as I described, it does give secondary treatment to tipcha over zakef.