I tried to turn down the music down to zero, but it keeps playing. Any ideas how to turn it off?

I think it's because it's emulated CD audio, which means the in-game slider has no effect on it. Thus, there's no way to lower/increase music volume in the game.

Oh well. That music sure gets annoying in the long run. Guess I can't listen to Justin Bieber while I'm torturing fairies! Thanks anyway...

next version of dosbox has better support for volume control with (emulated) CDROMS.

You can turn off the music by editing the config file that Dosbox uses.
Open up dosboxDK.conf in Program Files\GOG.com\Dungeon Keeper and scroll to the bottom. There should be a line that looks like "MIXER CDAUDIO 25:25". Try setting that to 0:0.
Let us know if it works so others can find this thread if they have the same problem!

I don't know about the OP, but I've checked, and there is no such line in any of the DOSBox config files in DK's directory.

Then add it at the end. That's how I lowered the music volume, and I'm just assuming that setting it so 0:0 will mute it.

I've tried adding it to the end of the dosboxDK.conf file, but it had no effect on the music volume.
Or should we try adding it to the end of the audio settings?

I have mine under the Autoexec section right before it executes Keeper.exe
Try setting it to 1:1, maybe it doesn't work with 0:0 (though, it should). The values are percentages.

More info about MIXER: http://www.dosbox.com/wiki/MIXER

It worked!
I put the line (with 1:1) between cls and keeper.exe and it did indeed lower the music volume to virtually nothing.

I was literally just going to make an account to update this post, then realized I already had one xD

THIS IS CURRENT AS OF 11/19/2013:

In the same file path, C:/GOG Games/Dungeon Keeper Gold/

Open dosboxDK_single.conf

Paste this in that block:
MIXER CDAUDIO 1:1

c:
[here]
cls
keeper.exe
exit

I'm having this same issue but I'm using a Macintosh computer and I can not find a line in the config file that looks anything like what the windows one is saying. I was looking for key words numbers or phrases but nothing is showing up. Any ideas on how to turn the music off on a mac computer cause boy is that sound annoying.

Maybe it is worth mentioning that your fix works, but the file in question to be edited is indeed dosboxDK_single.conf, not dosboxDX.conf.