LATIN DICTIONARYLexicon Latīnum
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“discordant” in Latin

The English word discordant itself goes back to Latin cor, through discordāre.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

discordant
PROPR. Of sounds, discors (e.g., symphonia, Hor.; but mostly IMPROP.): absonus: dissonus (the former with reference to the right note or key, or to a pleasant sound: the latter, to its disagreement with the other notes, instruments, voices, etc) :
IMPROPR. Disagreeing with, etc., discors (absolutely; secum ipse; in plur., inter se, with each other; also dative, filius patri, Velleius; in anything, aliqua re): absonus (with ab, or [ = alienus, “inconsistent with”] with dative, absoni a voce motus; absonus fidei divinae originis, both Liv.): dissonus (not pre-Augustan; nor in Verg., Hor., or Ov.; first in Livy; ab or absolutely; in anything, aliqua re): vix or non satis consonus (☞ Cic., Att., 4, 16): discrepans: dissentiens: dissidens: non congruens [SYN. in DISAGREE]. To be discordant [Vid: To DISCORD].
= At variance with itself, a se ipse dissidens secumque discordans (Cic.).

Quick answer

What is the Latin word for discordant?
The usual Latin words for “discordant” are discors, absonus, dissonus; also vix, discrepō, dissentiō. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.