Microtuning with midi

In case it helps, Pianoteq supports scala files and has a lot of options under the "Advanced Tuning" window, many of which can be controlled by MIDI events and altered in real-time or near-real-time.  (Stage doesn't fully support this, but Standard and Pro both do.)

I think we'd need a little more information about your unique setup and needs before we could recommend something more specific than that for your needs.

For example, do you need to change every single note's pitch after the last note played (e.g. your system can't be expressed in a predetermined structure of some kind thus eliminating the usefulness of scala files)?

Does your setup send the tuning in Hz, cents, or decimal fractions of a semitone?

Is this microtonal system a regular octave fraction (of any division) or can it no be expressed in an octave scale division across the entire keyboard compass (like a novel system that divides octaves differently depending on the range)?

Are the pitches purely random (which could get prohibitively complicated if the floats require very high bit-depth decimal precision, particularly of poor-granularity units like Hz)?  Is there a method of expressing your general microtonal scale mathematically and then translating minor changes as temperaments in fractions of a cent (which is something scala can do quite effectively even if those adjustments fluctuate and are passed to PTQ in near-real-time)?

How precise and in what units are you communicating pitch information? (As the pitch bend wheel can easily be precise to half a percent +/- the base-line unit used by default, but again, if the floats are an expression of Hz instead of fractions of a cent or another more precise unit it would need to be converted to an integer within the range of +/- 200 based on the current default MIDI mapping--which can be adjusted but not necessarily to greater precision in certain situations...)

dv is right that MIDI 2 is definitely an option, but I suspect that there is a likely method using MIDI and creatively routing information or changing units.