The Collaborative International Dictionary of English v.0.48:

Discordant \Dis*cord"ant\, a. [OE. discordant, descordaunt, OF.
   descordant, discordant, F. discordant, p. pr. of discorder,
   OF. also, descorder. See Discord, n.]
   1. Disagreeing; incongruous; being at variance; clashing;
      opposing; not harmonious.
      [1913 Webster]

            The discordant elements out of which the emperor had
            compounded his realm did not coalesce. --Motley.
      [1913 Webster]

   2. [See Discord, n.,

   2. ] (Mus.) Dissonant; not in harmony or musical concord;
      harsh; jarring; as, discordant notes or sounds.
      [1913 Webster]

            For still their music seemed to start
            Discordant echoes in each heart.      --Longfellow.
      [1913 Webster]

   3. (Geol.) Said of strata which lack conformity in direction
      of bedding, either as in unconformability, or as caused by
      a fault.

   Syn: Disagreeing; incongruous; contradictory; repugnant;
        opposite; contrary; inconsistent; dissonant; harsh;
        jarring; irreconcilable. -- Dis*cord"ant*ly, adv. --
        Dis*cord"ant*ness, n. [R.]
        [1913 Webster]

WordNet (r) 3.0 (2006):

discordantly
    adv 1: in a discordant manner; "the piece ended discordantly"
           [syn: discordantly, unharmoniously]