discord (n.)

early 13c., descorde, "unfriendly feeling, ill will;" also "dissension, strife," from Old French descorde (12c.) "disagreement," from Latin discordia, from discors (genitive discordis) "disagreeing, disagreement," from dis- "apart" (see dis-) + cor (genitive cordis) "heart," from PIE root *kerd- "heart."

Musical sense "want of harmony between two notes sounded together; a combination of notes not in harmony with one another" is from late 14c.

c. 1300, discorden, "differ in will or opinion, disagree, quarrel," from Old French discorder (13c.) and directly from Latin discordare "be at variance, differ, quarrel," from discors (genitive discordis) "disagreeing, disagreement," from dis- "apart" (see dis-) + cor (genitive cordis) "heart," from PIE root *kerd- "heart."