Recently I came across this thread were somebody apparently has just changed a few parameters in a dll file and now HoMM3 can play it's music in stereo:
http://www.celestialheavens.com/forums//viewtopic.php?t=8031&start=0&postdays=0&postorder=asc&highlight=

The mp3 files that comes with HoMM 3 are just 128 kbs but they are in stereo and a sample rate of 44100. For some unknown reason however, in-game, they are played in mono at a sample rate of 22050. The difference is easy to hear, just try to play one of the mp3 files with your music player. Why the game was released this way I don't know. I don't think there were any technical reasons for it since HoMM 3 was released in 1999. If it was an error you would think it would have been discovered and fixed later in a patch. Maybe it was cheaper to buy the license for a worse mp3 codec back then?

Be warned however that this file could potentially be infected with some unknown trojan. It worked as it was supposed to and my outdated Antivirus program picked up nothing nor did I notice anything strange with my computer after I installed it. Bu the fix seems to be not very well known in the HoMM3 community, so the potential for some hidden payload is greater than with a well used fix. In the thread there actually was mentioned a couple of warnings from anti-virus programs. Whether that was just false positives or something else remains unknown but since the fix is over two years old there has at least been some time for someone to discover bad code. This mp3 fix has supposedly also been incorporated into the HD mod, so if you have a recent version of that you should also have this.

HoMM III was originally released in February 1999. The developers decide to reduce system requirements (and cover as much systems as possible) and thus include decoder that works even on 486DX2-66MHz CPU...

I guess on a 486 with 66MHz CPU, stereo decoding could slow down the game. But it must have been very slow anyway since i can remember that HoMM III was a bit sluggish (though playable) on our 133MHz Pentium machine.

@Sargon

There's a HD mod that includes a fix for the sound. It doesn't look like that they've updated changelogs in the last few builds, but it's stated under the 2.80 changelog on that site that the "music in the game is playing with 44 kHz Stereo quality instead of original 22 kHz quality".

I haven't tried the latest version 3.28f. I haven't played the game in quite a while. JFYI, when I was playing it last time, I recall that 2.98f may have caused my game to create a save every turn, so I went back to using 2.96f. It works great.

[url=https://sites.google.com/site/heroes3hd/eng/download ]https://sites.google.com/site/heroes3hd/eng/download [/url]