Hermode tuning

MIDI contains note information (which key is being pressed), not tuning mode info. It has no idea what sound will be produced when you press that key. It could be a piano, organ, barbershop-tuned vocals, experimental synth, drums, an anvil... Anything.
 
You need an instrument that can be user-tuned, save that as part of a patch, then call it up before the song/passage starts.
 
Edit: It seems 2 techniques are used. One is synth specific Sysex messages, but that can only work if you know the specific sysex messages your synth accepts.
 
The other is by sending pitchbends on a note-by-note basis. Some Daws do this, apparently. But how an effect that works on a channel basis can be brought to bear on single notes beats me.