I don't know about the Mac version, but I can confirm that the DOS version does not have any music, and barely has any sound. It is all just PC speaker, a few beeps and boops.

The Apple II version of MM1 does not have any music. MM2 does, same as the DOS version.

The DOS version of MM1 does have music, just not much of it. There's a 15 second loop on the title screen, and some quick ditties related to encounters. The Apple II version doesn't do anything except beep when something interesting happens.

You are right, I was forgetting about the title screen music. But these are still just PC speaker.

I don't remember the DOS version of MM2 having music... did I have it set up wrong in DOSBox? Or does it also only play in a few specific circumstances?

MM2 (all computer versions) have music for these situations:
Title screen
Encounter
Killed enemy
Won fight
Character down
Total party kill
Found treasure

In all cases, it's just a simple one channel square wave ditty. Even the Amiga version doesn't have any sort of polyphony or instrument samples, which is extra lazy considering that the C64 version of MM1 did (though barely).

MM1 DOS is the same, except it does not have a ditty for finding treasure.

It's also worth noting that, at least in MM2 DOS (haven't tried any other versions or any version of MM1), when the music plays, the entire game stops for it. This can be annoying when you are fighting 200+ foes; having to hear the music play 200+ times in a single battle gets old and slows things down. Therefore, you will probably want to disable sound in the game to remove these waits.

(It's also worth noting that console versions have constant music playing; it's decent for MM1 NES, but not so good for MM2 or MM3.)

OK, I remember these now. I was thinking more about constant background music (which the games do not have) rather than these little tunes. Thanks for the clarification!

I should have just let you answer the OP, since you clearly know more about it than I do!

The C64 and Amiga versions of MM2 do sound different than DOS -- though they are still not polyphonic. The Amiga version does have extra notes added in there though. The DOS version actually supports Tandy graphics, but not sound. It must have really sucked for Tandy owners that MM1 did not support TGA, though. I'd be pretty pissed to have to play it in 4 color CGA when C64 or EGA PC owners wouldn't have.

Also, MM1 plays the same jingle for opening treasures as the an encounter, I believe.