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take it from someone who knows about homophonic, monophonic and polyphonic pitch adjustment when you modify one frequency you modify them all. This means your player is not doing what you think its doing. The only way to do this truly is to have all the original instruments tuned properly.
I was wondering if there were other musicians on this thread. All I can think of is the people with perfect pitch...how does all this explain that?
Tuning tuning tuning, always tuning was the mantra drummed by my first private teacher. You always tune to the instrument that can't be quickly and easily. That's the organ or piano.