I have friends with carbon in their limbs, some of those limbs have a certain sound to them. Most of my limbs have bamboo in them, and a few have red elm. I have used rosewoods in risers, hard maple, sapele, black limba, dymondwood, resin impregnated wood and actionwood..I dont remember any of the being noisy or having a pitch difference.. I think limb design, string material and tuning has a lot to do with "limb noise"
I know almost nothing about "tone woods" I have a Fender Starcaster bass, it's Semi Hollow with an alder center block with maple body,maple fret board and maple neck. My Ibanez "Mikro" bass has a Mahogany body, maple neck with a rosewood fret board..But the one I like to play the most has a.....wait for it....plywood body yes plywood, rosewood fret board, neck is painted but I think its maple. Its a Danelectro "Longhorn" made in 2006, painted black body and back of neck.