Discordant

Etymology

From Latin "discordare" (to disagree), from dis- (apart) and "cor," stem "cordis" (heart). The literal image is of hearts set apart — the same root gives us "concord" and "record." From that root sense of disunited hearts came both the musical clash and the broader sense of things that will not reconcile.

adjective · /dis-KOR-duhnt/
Clashing or jarringly out of harmony, in sound or in relation.
What it names
The specific unease of elements that ought to fit together but grate instead — notes, opinions, or tones that refuse to blend.
Example
A single discordant chord in the score signaled that the calm on screen was about to break.
Related idea
Cacophonous is simply loud and harsh; discordant is specifically the clash of things that were meant to harmonize.