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):

discordant
    adj 1: not in agreement or harmony; "views discordant with
           present-day ideas" [ant: accordant]
    2: lacking in harmony [syn: discordant, disharmonious,
       dissonant, inharmonic]

Moby Thesaurus II by Grady Ward, 1.0:

146 Moby Thesaurus words for "discordant":
   absonant, adversative, adverse, adversive, antagonistic, anti,
   antipathetic, antithetic, antonymous, assorted, at cross-purposes,
   at loggerheads, at odds, at variance, at war, atonal, balancing,
   cacophonic, cacophonous, clashing, colliding, compensating,
   conflicting, confronting, contradictory, contradistinct,
   contrapositive, contrarious, contrary, contrasted, contrasting,
   converse, counter, counterbalancing, counterpoised, countervailing,
   cracked, cranky, cross, dead against, departing, deviating,
   deviative, diaphonic, different, differentiated, differing,
   disaccordant, disagreeable, disagreeing, disconsonant, discrepant,
   discrete, discriminated, disharmonic, disharmonious, disjoined,
   disparate, disproportionate, dissentient, dissident, dissimilar,
   dissonant, distinct, distinguished, divergent, diverging, divers,
   diverse, diversified, eyeball to eyeball, flat, grating, harsh,
   heterogeneous, hostile, immelodious, immiscible, in disagreement,
   inaccordant, incompatible, incongruent, incongruous, inconsistent,
   inconsonant, inharmonic, inharmonious, inimical, inverse,
   irreconcilable, jangling, jarring, many, motley, multifarious,
   musicless, negative, nonmelodious, obverse, off, off-color,
   off-key, off-tone, opposed, opposing, opposite, oppositional,
   oppositive, oppugnant, out of accord, out of pitch, out of tone,
   out of tune, out of whack, perverse, poles apart, poles asunder,
   raucous, repugnant, reverse, separate, separated, several, sharp,
   shrill, sour, squared off, strident, tuneless, unconformable,
   uncongenial, unequal, unharmonious, unlike, unmelodious, unmusical,
   untunable, untuned, untuneful, variant, varied, variegated,
   various, varying, widely apart, worlds apart