Next to the kazoo, the Jew's Harp (also known as "Jaw Harp" these days) is surely one of the most gnomish musical instruments, and is, apparently, one of the world's oldest musical instruments, so likely a gnome pawned this off on some hapless prehistoric human with the twin gnome-purposes of: 1) being annoying and 2) making you look ridiculous.
You can't even think of it without the annoying "boing-bidda-boing" sound coming immediately to mind. I can just see a group of gnomes perched on mushrooms, playing away on their mouth harps, being all smugly whimsical, like they're in on some gnome-joke and you're sure to be the butt of their gnomefoolery.