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]