late 14c., "non-essential," from Old French accidentel or directly from Medieval Latin accidentalis, from Latin accidentem "an accident, chance" (see accident). Meaning "outside the normal course of nature" is from early 15c.; that of "coming by chance, unintentional" is from 1570s. Accidential (1811) sometimes serves now in the sense "characterized by non-essential qualities" and goes with accidence.
late 14c., "non-essential quality," from accidental (adj.). The musical sense is from 1868; so called because they alter the note without essentially changing the key of the passage.