Synonyms for Rarity (same or very similar meaning)
WordNet sense 1 (noteworthy scarcity):
infrequency, rarenessWordNet sense 2 (a rarified quality):
tenuityWordNet sense 3 (something unusual -- perhaps worthy of collecting):
curio, curiosity, oddity, oddment, peculiarityFrom the ODE community, based on WordNetadd/edit