Discordant means clashing, and not in harmony. Notes that fight, or facts that will not sit together.
Music has the original sense, where discordant notes sound harsh against one another, and discord is the noun. The figurative use is about disagreement, so a discordant note in a report is a detail that does not fit the rest, and discordant voices in a group are the ones dissenting. Both senses share the sense of things failing to agree. Its opposite is harmonious, and concord is the formal noun for agreement.
1adjectivediscordantClashing and not in harmony.
“There was one discordant voice at the meeting.”
Discord is hearts apart. Latin discors joins dis, apart, to cor, a heart, so discordant things have their hearts pulling in different directions. The sound came afterwards.
Proto-Indo-European
*dwóh₁
Proto-Indo-European
*ḱḗr — heart
Latin
discordāre
Old French
descordant
Middle French
descordant
Anglo-Norman
descordant
Middle English
discordaunt — (adjective) not in accord or harmony; dissonant; (noun) element not in accord or harmony
English, today
discordant
Built from
From Late Middle English discordaunt (“(adjective) not in accord or harmony; dissonant; (noun) element not in accord or harmony”), from Anglo-Norman descordant, discordant, Middle French descordant, discordant, and Old French descordant, discordant (“of people: quarrelsome; of things: in disagreement, at variance”) (modern French discordant), an use of the of descorder, discorder (“to fail to agree or harmonize, clash, disagree, discord”), from Latin discordāre, the of discordō (“to disagree, quarrel with”), from discors (“discordant, different, inharmonious”) + -ō. Discors is derived from dis- (“meaning ‘apart, in two’”) + cor (“heart; (figurative) mind; soul”) (ultimately from Proto-Indo-European ḱḗr (“heart”)). by surface analysis, discord + -ant.
Etymology from Wiktionary, CC BY-SA