The Collaborative International Dictionary of English v.0.48:

Dissonance \Dis"so*nance\, n. [L. dissonantia: cf. F.
   dissonance.]
   1. A mingling of discordant sounds; an inharmonious
      combination of sounds; discord.
      [1913 Webster]

            Filled the air with barbarous dissonance. --Milton.
      [1913 Webster]

   2. Want of agreement; incongruity. --Milton.
      [1913 Webster]

WordNet (r) 3.0 (2006):

dissonance
    n 1: a conflict of people's opinions or actions or characters
         [syn: disagreement, dissension, dissonance] [ant:
         accord, agreement]
    2: the auditory experience of sound that lacks musical quality;
       sound that is a disagreeable auditory experience; "modern
       music is just noise to me" [syn: noise, dissonance,
       racket]
    3: disagreeable sounds [ant: harmony]

Moby Thesaurus II by Grady Ward, 1.0:

82 Moby Thesaurus words for "dissonance":
   antagonism, argumentation, atonalism, atonality, cacophony,
   clashing, clinker, conflict, contention, contradiction,
   contrariety, contrast, controversy, departure, deviation,
   difference, disaccord, disaccordance, disagreement, disconformity,
   discongruity, discord, discordance, discordancy, discrepancy,
   discreteness, disharmony, disparity, dissension, dissent,
   dissidence, dissimilarity, dissonancy, dissonant chord,
   distinction, distinctness, disunion, disunity, divergence,
   divergency, diversity, faction, far cry, flatness, heterogeneity,
   inaccordance, incompatibility, incongruity, inconsistency,
   inconsonance, inequality, inharmoniousness, inharmony,
   irreconcilability, jarring, mixture, negation, nonconformity, odds,
   off note, opposition, oppugnancy, otherness, repugnance,
   separateness, sharpness, sour note, sourness, stridor, strife,
   tunelessness, unconformity, unharmoniousness, unlikeness,
   unmusicality, unorthodoxy, untunefulness, variance, variation,
   variegation, variety, wolf