My bike had a broken bearing race on one side of the BB, and it made a sound similar to yours. The cranks and BB seemed tight, so it puzzled me for a while until I finally had a chance to overhaul my BB. That's when I found the broken bearing race. YMMV. I finished my overhaul with all loose bearing so that problem won't happen again.

This, of course, may not apply in your case if your BB uses a sealed cartridge.