c. 1600, "increased," past-participle adjective from augment. The musical sense of "greater by a semitone than a perfect or major interval" (opposite of diminished) is attested by 1825.
Entries linking to augmented
augment v.
late 14c., "become more severe;" c. 1400, "to make larger; become larger," from Old French augmenter "increase, enhance" (14c.), from Late Latin augmentare "to increase," from Latin augmentum "an increase, growth," from augere "to increase, make big, enlarge, enrich" (from PIE root *aug- (1) "to increase"). Related: Augmented; augmenting. As a noun from early 15c.
augmentation n.
mid-15c., "act of making greater," from Old French augmentacion "increase," from Late Latin augmentationem (nominative augmentatio), noun of action from past-participle stem of augmentare "to increase" (see augment). The meaning "amount by which something is increased" is from 1520s. The musical sense is from 1590s, in fugues (compare augmented).