If you'd want to, you can also open FFXIConfig through the Windows Start menu.
Start > All Programs > Playonline > Final Fantasy XI > Final Fantasy XI Config.
In the sound tab of FFXIConfig you can uncheck the box saying "Enable sound."
Doing this will disable
all in game sound from the moment you press the Play button in the PlayOnline Viewer. This will also help your game's overall performance a bit. I've had this done since over two years, due to the fact I also like to listen to music while playing, and with sound enabled loud, and even having all FFXI Music turned down as far as it goes through the in-game volume bars, you could still hear the game music a little bit if your volume is really loud.. and I like to listen to music really loud sometimes.
By the way, disabling FFXI sound will also help you get rid of the loud <call> noises which can't be muted by the in-game volume bars.
The only thing I haven't really got rid off yet is the PlayOnline Viewer music of the starting Login screen. ><