The Collaborative International Dictionary of English v.0.48:

Abruptness \Ab*rupt"ness\, n.
   1. The state of being abrupt or broken; craggedness;
      ruggedness; steepness.
      [1913 Webster]

   2. Suddenness; unceremonious haste or vehemence; as,
      abruptness of style or manner.
      [1913 Webster]

WordNet (r) 3.0 (2006):

abruptness
    n 1: an abrupt discourteous manner [syn: abruptness,
         brusqueness, curtness, gruffness, shortness]
    2: the property possessed by a slope that is very steep [syn:
       abruptness, precipitousness, steepness] [ant:
       gentleness, gradualness]
    3: the quality of happening with headlong haste or without
       warning [syn: abruptness, precipitateness,
       precipitousness, precipitance, precipitancy,
       suddenness]