MIDI doesn't explicitly mandate 12-TET, but attempting to do anything more complicated than a mild re-tuning of a 12 note-per-octave scale usually results in a poor user experience. For instance, it's no longer plug-and-play because the instrument and the synthesizer need to agree on a what each note means, and there isn't a way to communicate that. (Well, technically there is: the Midi tuning standard, but it's rarely implemented.) There's also the problem of the number of notes: 128 often isn't enough.
A standard workaround if you want to do microtonal MIDI is the one note per channel trick: each simultaneously-sounding voice is on its own channel, which can be independently pitch-bent.
For instance, if you want to play a note 10 cents above middle C, you pick a MIDI channel you're not using right now, send a pitch bend command to raise it by 10 cents, then send a note-on for note 60.
This gives you 16-voice polyphony (because MIDI has 16 channels). The downsides are that this only works on multitimbral synths (i.e. it works with most "romplers" but very few analog synths), and you need a convenient way to set all the channels parameters the same.
The one note per channel trick can also enable individual note volume swells by using channel volume. One note per channel has been standardized recently in MIDI as MPE.
There's also MIDI 2.0 now, which has per-note pitch bend among other features. Time will tell if it actually gets widely adopted, and whether synths actually implement the full spec or if they leave out features that only a small minority of their users care about.
A standard workaround if you want to do microtonal MIDI is the one note per channel trick: each simultaneously-sounding voice is on its own channel, which can be independently pitch-bent.
For instance, if you want to play a note 10 cents above middle C, you pick a MIDI channel you're not using right now, send a pitch bend command to raise it by 10 cents, then send a note-on for note 60.
This gives you 16-voice polyphony (because MIDI has 16 channels). The downsides are that this only works on multitimbral synths (i.e. it works with most "romplers" but very few analog synths), and you need a convenient way to set all the channels parameters the same.
The one note per channel trick can also enable individual note volume swells by using channel volume. One note per channel has been standardized recently in MIDI as MPE.
There's also MIDI 2.0 now, which has per-note pitch bend among other features. Time will tell if it actually gets widely adopted, and whether synths actually implement the full spec or if they leave out features that only a small minority of their users care about.