C3 C4 C5 are not fixed in Midi terms. What you call middle C therefore can’t relate to that reference, it has to relate to the Midi Number. The closest to 64 is 60 so start by comparing the location of midi note 60.
There’s no reason why a synth needs to be centered on middle C of course, but usually such keyboards will have transpose options and of course the voice architecture may allow oscillator transposition.
I’d imagine most are centred around 60-64, but some will default either side depending on their remit
All that to say is that a standard ‘tuning’ won’t exist and that quoting C(?) Isn’t a meaningful comparison given there are 3 or more ‘standards’ in use in terms of midi and there are 128 notes in Midi aot 88 on a concert piano
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