early 13c., descorde, "unfriendly feeling, ill will;" also "dissention, 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" (see heart). Musical sense is late 14c.
discord (v.)
c. 1300, from Old French discorder (13c.), from Latin discordare (see discord (n.)).