The Collaborative International Dictionary of English v.0.48:

Dissonant \Dis"so*nant\, a. [L. dissonans, -antis, p. pr. of
   dissonare to disagree in sound, be discordant; dis- + sonare
   to sound: cf. F. dissonant. See Sonant.]
   1. Sounding harshly; discordant; unharmonious.
      [1913 Webster]

            With clamor of voices dissonant and loud.
                                                  --Longfellow.
      [1913 Webster]

   2. Disagreeing; incongruous; discrepant, -- with from or to.
      "Anything dissonant to truth." --South.
      [1913 Webster]

            What can be dissonant from reason and nature than
            that a man, naturally inclined to clemency, should
            show himself unkind and inhuman?      --Hakewill.
      [1913 Webster]

WordNet (r) 3.0 (2006):

dissonant
    adj 1: characterized by musical dissonance; harmonically
           unresolved [syn: unresolved, dissonant]
    2: lacking in harmony [syn: discordant, disharmonious,
       dissonant, inharmonic]
    3: not in accord; "desires at variance with his duty"; "widely
       discrepant statements" [syn: at variance(p), discrepant,
       dissonant]

Moby Thesaurus II by Grady Ward, 1.0:

115 Moby Thesaurus words for "dissonant":
   absonant, antagonistic, antipathetic, assorted, at cross-purposes,
   at loggerheads, at odds, at variance, at war, atonal, cacophonic,
   cacophonous, clashing, conflicting, contradictory, contrary,
   contrasted, contrasting, cracked, cranky, cross, departing,
   deviating, deviative, diaphonic, different, differentiated,
   differing, disaccordant, disagreeable, disagreeing, disconsonant,
   discordant, discrepant, discrete, discriminated, disharmonic,
   disharmonious, disjoined, disparate, disproportionate, dissident,
   dissimilar, distinct, distinguished, divergent, diverging, divers,
   diverse, diversified, flat, grating, harsh, heterogeneous, hoarse,
   hostile, immelodious, immiscible, in disagreement, inaccordant,
   incompatible, incongruent, incongruous, inconsistent, inconsonant,
   inharmonic, inharmonious, irreconcilable, jangling, jarring, many,
   motley, multifarious, musicless, negative, nonmelodious, off,
   off-key, off-tone, out of accord, out of pitch, out of tone,
   out of tune, out of whack, poles apart, poles asunder, raucous,
   repugnant, rude, rugged, separate, separated, several, sharp,
   shrill, sour, strident, tuneless, unconformable, uncongenial,
   unequal, unharmonious, unlike, unmelodious, unmusical, untunable,
   untuned, untuneful, variant, varied, variegated, various, varying,
   widely apart, worlds apart