i don't think it gets a lower volume. it's just muddier so it seems to not be as loud to your ears. brighter sounds louder to our ears naturally.
i don't even mess with the tone knob on my jazz. i leave it right in the middle or just slightly on the bright side of halfway. i do any tone shaping with my amp.
fender american standard jazz bass (blizzard pearl), Gallien-Krueger MB115-II, GK Club #1000, Fender Jazz Bass Club #1199