Have you determined whether or not your MIDI synth is tuned to A440? If you have a guitar or chromatic tuner it should be an easy test.

To me the first step would be to determine which is out of tune, the RT or the synth, then when I had that information, I would proceed to fix the faulty one.

I wouldn't use pith correction software except as a very last resort, as it won't solve the problem, just mask it, and may introduce other problems.

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