The Collaborative International Dictionary of English v.0.48:

Impertinence \Im*per"ti*nence\, n. [Cf. F. impertinence. See
   Impertinent.]
   1. The condition or quality of being impertinent; absence of
      pertinence, or of adaptedness; irrelevance; unfitness.
      [1913 Webster]

   2. Conduct or language unbecoming the person, the society, or
      the circumstances; rudeness; incivility.
      [1913 Webster]

            We should avoid the vexation and impertinence of
            pedants who affect to talk in a language not to be
            understood.                           --Swift.
      [1913 Webster]

   3. That which is impertinent; a thing out of place, or of no
      value.
      [1913 Webster]

            There are many subtile impertinences learned in
            schools.                              --Watts.
      [1913 Webster]

WordNet (r) 3.0 (2006):

impertinence
    n 1: an impudent statement [syn: impudence, cheek,
         impertinence]
    2: the trait of being rude and impertinent; inclined to take
       liberties [syn: crust, gall, impertinence, impudence,
       insolence, cheekiness, freshness]
    3: inappropriate playfulness [syn: impertinence, perkiness,
       pertness, sauciness, archness]