First, send yourself mail, to ensure this sound occurs upon mail receipt. Then, select a custom sound, and send yourself more mail, to see if the notification sound changes properly. If so, you could make a wave file of silence and use that as your notification.

Another possible cause is a virus or worm infection, or spyware/nuisanceware. This can be picked up at any time, particularly if you visit websites of unknown heritage. Many lyrics sites are spyware traps.