You can also modify the pitches of unaltered notes,
so that MIDI output and \transposition honor your tuning system.
The example below comes from Helmholtz and Ellis' book "on the Sensations of Tone". The notation indicates the precise pitches of just intonation based on perfect fifths and thirds. The sharp, flat and natural notes represent 'Pythagorean' tuning following the cycle of perfect fifths, which results in a very wide major third. The arrows represent the alteration that changes a Pythagorean major third to a perfect major third.
Notice the different shadings of pitch in the C-sharps, G-sharps and A-naturals, depending on their role in the harmony.