Synonyms for Foulness (same or very similar meaning)
WordNet sense 1 (a state characterized by foul or disgusting dirt and refuse):
filth, filthiness, nastinessWordNet sense 2 ((of weather) the badness of the weather):
raininessWordNet sense 3 (the attribute of having a strong offensive smell):
fetidness, rankness, malodorousness, stinkinessFrom the ODE community, based on WordNetadd/edit