c. 1300, "something seen in the imagination or in the supernatural," from Anglo-French visioun, Old French vision "presence, sight; view, look, appearance; dream, supernatural sight" (12c.), from Latin visionem (nominative visio) "act of seeing, sight, thing seen," noun of action from past participle stem of videre "to see," from PIE root *weid- "to see." The meaning "sense of sight" is first recorded late 15c. Meaning "statesman-like foresight, political sagacity" is attested from 1926.
c. 1600, in music, "involving tones foreign to the normal tonality of the scale, not diatonic," from Latin chromaticus, from Greek khrōmatikos "relating to color, suited for color" (also used in reference to music), from khrōma (genitive khrōmatos) "color, complexion, character" (but chiefly used metaphorically of embellishments in music), originally "skin, surface" (see chroma).
Greek also used khrōma for certain modifications of the usual diatonic music scale. The reason the Greeks used this word in music is not now entirely clear. Perhaps the connection is the extended sense of khrōma, "ornaments, make-up, embellishments," via the notion of "characteristic" of a musical scale or speech.
In English, the musical sense of "progressing by half-tones, involving the sharps and flats of the staff" is by 1881. Meaning "of or pertaining to color" is from 1829.