Rareness

noun

1. Thinness; tenuity; rarity: as, the rareness of air or vapor.
2. The state of being scarce, or of happening seldom; uncommonness; infrequeney.
3. Uncommon character or quality; especially, unusual excellence, fineness, or the like.
4. The state of being rare or underdone in cooking.
5. The state or quality of being rare.