tenuity (http://definr.com/tenuity)

     n 1: relatively small dimension through an object as opposed to
          its length or width: "the tenuity of a hair"; "the
          thinness of a rope" [syn: thinness, slenderness]
          [ant: thickness]
     2: the quality of lacking intensity or substance; "a shrill yet
        sweet tenuity of voice"- Nathaniel Hawthorne [syn: feebleness]
     3: a rarified quality: "the tenuity of the upper atmosphere"
        [syn: rarity, low density]