1660s, "agreement, accord, harmony," from French concert (16c.), from Italian concerto "concert, harmony," from concertare "bring into agreement," in Latin "to contend, contest, dispute," from com "with" (see com-) + certare "to contend, strive," frequentative of certus, variant past participle of cernere "separate, distinguish, decide" (from PIE root *krei- "to sieve," thus "discriminate, distinguish").
In the Middle Ages, before the word entered English, the meaning shifted from "to strive against" to "to strive alongside." Sense of "public musical performance" is 1680s. But Klein considers this too much of a stretch and suggests Latin concentare "to sing together" (from con- + cantare "to sing") as the source of the Italian word in the musical sense.
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