Just Intonation in MilkyTracker

Almost all modern music is played and recorded in 12-tone equal tempered tuning (12TET), i.e. the standard mapping from notes "A" through "G" onto constant frequencies.
But it's impossible for such constant mapping to allow harmonically pure intervals, and indeed in 12TET all chord sound more or less dissonant. Especially major chords, where the major 3rd is about 14 cents too wide.
It is possible to tune a keyboard instrument to Just Intonation (only pure harmonic intervals), but only in one specific key, unless the player can change the key on the fly for each chord, of which I have yet to see an implementation.

However, composition done entirely in software does not (in theory) have this limitation. Every note could be specifically tuned to sit well in the harmony similar to e.g. a string quartet or a barbershop group. Software synths based on MIDI are still usually limited to 12TET or some other constant tuning. The easiest way I could find to make music with arbitrarily tuned notes is a tracker that supports fine tuning and pattern commands.

FastTracker2 has several commands to change the frequencies of notes. The most imporant ones for fine tuning notes are E1/E2 (Fine portamento up/down) and X1/X2 (Extra fine portamento up/down). The tuning is applied exactly at the start of the row, so notes can begin at the correct tuning and not just glide in.

E1/E2 changes tuning by (100/15) cents / param value / row
X1/X2 changes tuning by (25/15) cents / param value / row
For example C major triad: [C-4 ...] [E-4 E22] [G-4 X11]
E22 = -13 cents
X11 = +2 cents

Finally I made this demo tune in the FT2-compatible MilkyTracker with mostly major chords and possibly familiar melodies.

UPDATE: Links to XM modules.
This video: https://www.dropbox.com/s/jgw2h3wz6aa...
Eequal temperament: https://www.dropbox.com/s/z23zggu5s2x...
"Fixed JI": https://www.dropbox.com/s/7o5atofr403...

The video version's major 3rds aren't actually the closest possible to JI, so I updated the song... and I think it sounds worse than the slightly incorrect one. Judge for yourself.