Well, this turned out to be quite interesting. I first tried different turbo modes, but no difference. Then I tried booting without startup-sequence, and lo and behold - it worked, the music playing nicely! So I tried to figure out what in my startup-sequence that could cause it to play badly, but no success. Then something struck me - when I boot without startup-sequence, from boot menu, that is one of those cases when FastRAM is gone. So I set the MIST to boot by default directly into thelasttetris, which means with all 24MB of RAM available... and music was bad again. Curious I exited the game, checked with avail that all FastRAM was there (which it was), then ran "nofastmem" in the background and checked that FastRAM now was 0 before starting thelasttetris again, and lo and behold... music all good again! I exited the game, sent nofastmem a break, ran game again... bad music. I did this many times with and without FastRAM, and every time FastRAM is present, the music plays badly. So now I am extra interested in your next update!
Btw, when I say the music plays badly, it is not obvious, it just seems to skip "tones" here and there. I will try to find the module used, and see if it is a general problem with this song
EDIT: I found the mod, it has slightly different "lead" instrument than in the game, but otherwise identical and plays perfectly in HippoPlayer and Protracker on MIST http://aminet.net/package/mods/otis/sunnory