mid-13c., "unblemished, refined, pure, free of impurities," also "of high quality, choice," from Old French fin "perfected, of highest quality" (12c.), a back-formation from finire or else from Latin finis "that which divides, a boundary, limit, border, end" (see finish (v.)); hence "acme, peak, height," as in finis boni "the highest good." The English word is from c. 1300 as "rich, valuable, costly;" also in a moral sense "true, genuine; faithful, constant." From late 14c. as "expertly fashioned, well or skillfully made," also, of cloth, "delicately wrought." Of weapons or edges, "sharp" from c. 1400. In reference to quality of gold and silver, late 15c.
In French, the main meaning remains "delicate, intricately skillful;" in English since c. 1300 fine has been also a general broad expression of admiration or approval, the equivalent of French beau (as in fine arts, "those which appeal to the mind and the imagination," 1767, translating French beaux-arts). Related: Finer; finest. Fine print is from 1861 as "type small and close-set;" by 1934 in the extended sense "qualifications and limitations of a deal."
"bring into a state of proper pitch," c. 1500, from tune (n.). Non-musical meaning "to adjust an organ or receiver, put into a state proper for some purpose" is recorded from 1887. Verbal phrase tune in in reference to radio (later also TV) is recorded from 1913; figurative sense of "become aware" is recorded from 1926. Tune out "eliminate radio reception" is recorded from 1908; figurative sense of "disregard, stop heeding" is from 1928. Related: Tuned; tuning.