(1) Clashing or discordant, especially in music. (2) Incompatible or disagreeing.
Example:
Critics of the health-care plan pointed its two seemingly dissonant goals: cost containment, which would try to control spending, and universal coverage, which could increase spending.
Dissonant includes the negative prefix dis-. What is dissonant sounds or feels unresolved, unharmonic, and clashing. Twentieth-century composers such as Arnold Schoenberg and his students Alban Berg and Anton Webern developed the use of dissonance in music as a style in itself. To many, such visual and jarring sounds are still unbearable; most listeners prefer music based on traditional tonality.