If things don't go together well, you can call them dissonant. Dissonant voices are saying different things. Dissonant clothing choices clash. Dissonant chords lack harmony.
The word dissonant comes from the Old French dis- meaning "apart" and sonare meaning "to sound." When a noise is dissonant, it sounds like it's broken apart, or not meshing together well. Dissonant doesn't have to describe just music or sounds. It can also refer to something that clashes or doesn't fit well together. When two people's versions of a story are dissonant, that means they don't match. Either one of them is lying or they just don't see eye-to-eye.