It's something we're regularly thinking about, but that isn't really simple to implement, notably because the MIDI protocol makes it hard to work with, and because there are few synths out there that understand the relevant MIDI messages. Anyway, MIDI isn't designed from the ground up to allow you to play outside the 12-tone equal temperament (12-TET), so a popular approach is to let your synth or virtual instrument handle this.
You might want to look at synths or virtual instruments that are explicitly designed for this (look for terms like microtuning), like the Samplemodeling virtual instruments.
In general, they allow you to define the exact frequency (or offset from a base frequency) of each of the 12 tones (C, C#, D, D#, E, F… B) that can be sent by your MIDI controller.